LMFDB - Embedded newform 105.4.i.d.46.2

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			46.2
Root			$-1.33997 - 2.32090i$ of defining polynomial
Character	$\chi$	$=$	105.46
Dual form			105.4.i.d.16.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.83997 - 3.18692i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.77099 + 4.79950i) q^{4} +(-2.50000 - 4.33013i) q^{5} +11.0398 q^{6} +(5.08172 - 17.8094i) q^{7} -9.04535 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.83997 - 3.18692i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.77099 + 4.79950i) q^{4} +(-2.50000 - 4.33013i) q^{5} +11.0398 q^{6} +(5.08172 - 17.8094i) q^{7} -9.04535 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-9.19986 + 15.9346i) q^{10} +(-32.5290 + 56.3418i) q^{11} +(-8.31298 - 14.3985i) q^{12} -6.87328 q^{13} +(-66.1076 + 16.5738i) q^{14} +15.0000 q^{15} +(38.8111 + 67.2229i) q^{16} +(-34.0063 + 58.9006i) q^{17} +(-16.5597 + 28.6823i) q^{18} +(-11.7761 - 20.3968i) q^{19} +27.7099 q^{20} +(38.6477 + 39.9169i) q^{21} +239.409 q^{22} +(2.74967 + 4.76257i) q^{23} +(13.5680 - 23.5005i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(12.6467 + 21.9046i) q^{26} +27.0000 q^{27} +(71.3950 + 73.7396i) q^{28} -138.643 q^{29} +(-27.5996 - 47.8039i) q^{30} +(-125.954 + 218.158i) q^{31} +(106.641 - 184.708i) q^{32} +(-97.5869 - 169.025i) q^{33} +250.282 q^{34} +(-89.8214 + 22.5191i) q^{35} +49.8779 q^{36} +(-63.7644 - 110.443i) q^{37} +(-43.3354 + 75.0591i) q^{38} +(10.3099 - 17.8573i) q^{39} +(22.6134 + 39.1675i) q^{40} -126.581 q^{41} +(56.1014 - 196.613i) q^{42} +91.5924 q^{43} +(-180.275 - 312.245i) q^{44} +(-22.5000 + 38.9711i) q^{45} +(10.1186 - 17.5260i) q^{46} +(-284.233 - 492.306i) q^{47} -232.867 q^{48} +(-291.352 - 181.005i) q^{49} +91.9986 q^{50} +(-102.019 - 176.702i) q^{51} +(19.0458 - 32.9883i) q^{52} +(295.199 - 511.300i) q^{53} +(-49.6792 - 86.0470i) q^{54} +325.290 q^{55} +(-45.9660 + 161.093i) q^{56} +70.6566 q^{57} +(255.099 + 441.844i) q^{58} +(-254.890 + 441.483i) q^{59} +(-41.5649 + 71.9925i) q^{60} +(-130.771 - 226.502i) q^{61} +927.006 q^{62} +(-161.679 + 40.5344i) q^{63} -163.890 q^{64} +(17.1832 + 29.7622i) q^{65} +(-359.114 + 622.004i) q^{66} +(461.391 - 799.152i) q^{67} +(-188.462 - 326.426i) q^{68} -16.4980 q^{69} +(237.036 + 244.820i) q^{70} +519.662 q^{71} +(40.7041 + 70.5015i) q^{72} +(-533.244 + 923.606i) q^{73} +(-234.649 + 406.424i) q^{74} +(-37.5000 - 64.9519i) q^{75} +130.526 q^{76} +(838.113 + 865.636i) q^{77} -75.8799 q^{78} +(56.4067 + 97.6992i) q^{79} +(194.056 - 336.114i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(232.906 + 403.405i) q^{82} -593.552 q^{83} +(-298.674 + 74.8803i) q^{84} +340.063 q^{85} +(-168.527 - 291.898i) q^{86} +(207.964 - 360.205i) q^{87} +(294.236 - 509.631i) q^{88} +(121.163 + 209.860i) q^{89} +165.597 q^{90} +(-34.9281 + 122.409i) q^{91} -30.4773 q^{92} +(-377.862 - 654.475i) q^{93} +(-1045.96 + 1811.66i) q^{94} +(-58.8805 + 101.984i) q^{95} +(319.924 + 554.125i) q^{96} -1536.88 q^{97} +(-40.7705 + 1261.56i) q^{98} +585.521 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 $

$2$	−1.83997	−	3.18692i	−0.650528	−	1.12675i	−0.982995	−	0.183633i	$-0.941214\pi$
$2$	−1.83997	−	3.18692i	−0.650528	−	1.12675i	0.332467	−	0.943115i	$-0.392119\pi$
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$4$	−2.77099	+	4.79950i	−0.346374	+	0.599938i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$6$	11.0398			0.751165
$7$	5.08172	−	17.8094i	0.274387	−	0.961619i
$7$	5.08172	−	17.8094i	0.274387	−	0.961619i
$8$	−9.04535			−0.399752
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	−9.19986	+	15.9346i	−0.290925	+	0.503897i
$11$	−32.5290	+	56.3418i	−0.891622	+	1.54434i	−0.0536927	+	0.998558i	$0.517099\pi$
$11$	−32.5290	+	56.3418i	−0.891622	+	1.54434i	−0.837930	+	0.545778i	$0.816234\pi$
$12$	−8.31298	−	14.3985i	−0.199979	−	0.346374i
$13$	−6.87328			−0.146639			−0.0733195	−	0.997309i	$-0.523359\pi$
$13$	−6.87328			−0.146639			−0.0733195	+	0.997309i	$0.523359\pi$
$14$	−66.1076	+	16.5738i	−1.26200	+	0.316395i
$15$	15.0000			0.258199
$16$	38.8111	+	67.2229i	0.606424	+	1.05036i
$17$	−34.0063	+	58.9006i	−0.485161	+	0.840323i	−0.999855	−	0.0170509i	$-0.994572\pi$
$17$	−34.0063	+	58.9006i	−0.485161	+	0.840323i	0.514694	+	0.857374i	$0.327906\pi$
$18$	−16.5597	+	28.6823i	−0.216843	+	0.375583i
$19$	−11.7761	−	20.3968i	−0.142191	−	0.246282i	0.786131	−	0.618060i	$-0.212081\pi$
$19$	−11.7761	−	20.3968i	−0.142191	−	0.246282i	−0.928321	+	0.371779i	$0.878748\pi$
$20$	27.7099			0.309806
$21$	38.6477	+	39.9169i	0.401601	+	0.414789i
$22$	239.409			2.32010
$23$	2.74967	+	4.76257i	0.0249281	+	0.0431767i	0.878220	−	0.478256i	$-0.158731\pi$
$23$	2.74967	+	4.76257i	0.0249281	+	0.0431767i	−0.853292	+	0.521433i	$0.825398\pi$
$24$	13.5680	−	23.5005i	0.115398	−	0.199876i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	12.6467	+	21.9046i	0.0953928	+	0.165225i
$27$	27.0000			0.192450
$28$	71.3950	+	73.7396i	0.481871	+	0.497695i
$29$	−138.643			−0.887770			−0.443885	−	0.896084i	$-0.646400\pi$
$29$	−138.643			−0.887770			−0.443885	+	0.896084i	$0.646400\pi$
$30$	−27.5996	−	47.8039i	−0.167966	−	0.290925i
$31$	−125.954	+	218.158i	−0.729741	+	1.26395i	0.227251	+	0.973836i	$0.427026\pi$
$31$	−125.954	+	218.158i	−0.729741	+	1.26395i	−0.956992	+	0.290113i	$0.906307\pi$
$32$	106.641	−	184.708i	0.589116	−	1.02038i
$33$	−97.5869	−	169.025i	−0.514778	−	0.891622i
$34$	250.282			1.26244
$35$	−89.8214	+	22.5191i	−0.433788	+	0.108755i
$36$	49.8779			0.230916
$37$	−63.7644	−	110.443i	−0.283319	−	0.490723i	0.688881	−	0.724874i	$-0.258102\pi$
$37$	−63.7644	−	110.443i	−0.283319	−	0.490723i	−0.972200	+	0.234152i	$0.924769\pi$
$38$	−43.3354	+	75.0591i	−0.184998	+	0.320426i
$39$	10.3099	−	17.8573i	0.0423310	−	0.0733195i
$40$	22.6134	+	39.1675i	0.0893872	+	0.154823i
$41$	−126.581			−0.482163			−0.241082	−	0.970505i	$-0.577502\pi$
$41$	−126.581			−0.482163			−0.241082	+	0.970505i	$0.577502\pi$
$42$	56.1014	−	196.613i	0.206110	−	0.722335i
$43$	91.5924			0.324830			0.162415	−	0.986723i	$-0.448072\pi$
$43$	91.5924			0.324830			0.162415	+	0.986723i	$0.448072\pi$
$44$	−180.275	−	312.245i	−0.617670	−	1.06984i
$45$	−22.5000	+	38.9711i	−0.0745356	+	0.129099i
$46$	10.1186	−	17.5260i	0.0324328	−	0.0561753i
$47$	−284.233	−	492.306i	−0.882119	−	1.52788i	−0.848980	−	0.528425i	$-0.822783\pi$
$47$	−284.233	−	492.306i	−0.882119	−	1.52788i	−0.0331392	−	0.999451i	$-0.510550\pi$
$48$	−232.867			−0.700238
$49$	−291.352	−	181.005i	−0.849423	−	0.527712i
$50$	91.9986			0.260211
$51$	−102.019	−	176.702i	−0.280108	−	0.485161i
$52$	19.0458	−	32.9883i	0.0507919	−	0.0879742i
$53$	295.199	−	511.300i	0.765071	−	1.32514i	−0.175138	−	0.984544i	$-0.556037\pi$
$53$	295.199	−	511.300i	0.765071	−	1.32514i	0.940209	−	0.340598i	$-0.110629\pi$
$54$	−49.6792	−	86.0470i	−0.125194	−	0.216843i
$55$	325.290			0.797491
$56$	−45.9660	+	161.093i	−0.109687	+	0.384409i
$57$	70.6566			0.164188
$58$	255.099	+	441.844i	0.577520	+	1.00029i
$59$	−254.890	+	441.483i	−0.562438	+	0.974172i	0.434844	+	0.900506i	$0.356803\pi$
$59$	−254.890	+	441.483i	−0.562438	+	0.974172i	−0.997283	+	0.0736665i	$0.976530\pi$
$60$	−41.5649	+	71.9925i	−0.0894334	+	0.154903i
$61$	−130.771	−	226.502i	−0.274483	−	0.475419i	0.695521	−	0.718506i	$-0.255174\pi$
$61$	−130.771	−	226.502i	−0.274483	−	0.475419i	−0.970005	+	0.243086i	$0.921840\pi$
$62$	927.006			1.89887
$63$	−161.679	+	40.5344i	−0.323327	+	0.0810611i
$64$	−163.890			−0.320099
$65$	17.1832	+	29.7622i	0.0327895	+	0.0567930i
$66$	−359.114	+	622.004i	−0.669756	+	1.16005i
$67$	461.391	−	799.152i	0.841311	−	1.45719i	−0.0474760	−	0.998872i	$-0.515118\pi$
$67$	461.391	−	799.152i	0.841311	−	1.45719i	0.888787	−	0.458321i	$-0.151549\pi$
$68$	−188.462	−	326.426i	−0.336094	−	0.582132i
$69$	−16.4980			−0.0287845
$70$	237.036	+	244.820i	0.404731	+	0.418022i
$71$	519.662			0.868627			0.434314	−	0.900762i	$-0.356991\pi$
$71$	519.662			0.868627			0.434314	+	0.900762i	$0.356991\pi$
$72$	40.7041	+	70.5015i	0.0666253	+	0.115398i
$73$	−533.244	+	923.606i	−0.854952	+	1.48082i	0.0217370	+	0.999764i	$0.493080\pi$
$73$	−533.244	+	923.606i	−0.854952	+	1.48082i	−0.876689	+	0.481057i	$0.840253\pi$
$74$	−234.649	+	406.424i	−0.368614	+	0.638458i
$75$	−37.5000	−	64.9519i	−0.0577350	−	0.100000i
$76$	130.526			0.197005
$77$	838.113	+	865.636i	1.24041	+	1.28115i
$78$	−75.8799			−0.110150
$79$	56.4067	+	97.6992i	0.0803322	+	0.139139i	0.903393	−	0.428814i	$-0.141069\pi$
$79$	56.4067	+	97.6992i	0.0803322	+	0.139139i	−0.823060	+	0.567954i	$0.807735\pi$
$80$	194.056	−	336.114i	0.271201	−	0.469734i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	232.906	+	403.405i	0.313661	+	0.543277i
$83$	−593.552			−0.784949			−0.392474	−	0.919763i	$-0.628381\pi$
$83$	−593.552			−0.784949			−0.392474	+	0.919763i	$0.628381\pi$
$84$	−298.674	+	74.8803i	−0.387952	+	0.0972632i
$85$	340.063			0.433941
$86$	−168.527	−	291.898i	−0.211311	−	0.366002i
$87$	207.964	−	360.205i	0.256277	−	0.443885i
$88$	294.236	−	509.631i	0.356428	−	0.617351i
$89$	121.163	+	209.860i	0.144306	+	0.249945i	0.929114	−	0.369794i	$-0.120572\pi$
$89$	121.163	+	209.860i	0.144306	+	0.249945i	−0.784808	+	0.619739i	$0.787238\pi$
$90$	165.597			0.193950
$91$	−34.9281	+	122.409i	−0.0402359	+	0.141011i
$92$	−30.4773			−0.0345378
$93$	−377.862	−	654.475i	−0.421316	−	0.729741i
$94$	−1045.96	+	1811.66i	−1.14769	+	1.98785i
$95$	−58.8805	+	101.984i	−0.0635896	+	0.110140i
$96$	319.924	+	554.125i	0.340126	+	0.589116i
$97$	−1536.88			−1.60873			−0.804366	−	0.594134i	$-0.797495\pi$
$97$	−1536.88			−1.60873			−0.804366	+	0.594134i	$0.797495\pi$
$98$	−40.7705	+	1261.56i	−0.0420249	+	1.30038i
$99$	585.521			0.594415
$100$	−69.2748	−	119.988i	−0.0692748	−	0.119988i
$101$	857.920	−	1485.96i	0.845210	−	1.46395i	−0.0402290	−	0.999190i	$-0.512809\pi$
$101$	857.920	−	1485.96i	0.845210	−	1.46395i	0.885439	−	0.464756i	$-0.153858\pi$
$102$	−375.424	+	650.253i	−0.364436	+	0.631222i
$103$	143.826	+	249.114i	0.137588	+	0.238310i	0.926583	−	0.376090i	$-0.122732\pi$
$103$	143.826	+	249.114i	0.137588	+	0.238310i	−0.788995	+	0.614400i	$0.789398\pi$
$104$	62.1713			0.0586192
$105$	76.2259	−	267.142i	0.0708465	−	0.248289i
$106$	−2172.63			−1.99080
$107$	525.298	+	909.842i	0.474602	+	0.822035i	0.999577	−	0.0290827i	$-0.00925862\pi$
$107$	525.298	+	909.842i	0.474602	+	0.822035i	−0.524975	+	0.851118i	$0.675925\pi$
$108$	−74.8168	+	129.587i	−0.0666597	+	0.115458i
$109$	92.4004	−	160.042i	0.0811959	−	0.140635i	−0.822568	−	0.568667i	$-0.807459\pi$
$109$	92.4004	−	160.042i	0.0811959	−	0.140635i	0.903764	+	0.428031i	$0.140793\pi$
$110$	−598.524	−	1036.67i	−0.518791	−	0.898572i
$111$	382.586			0.327148
$112$	1394.43	−	349.597i	1.17644	−	0.294944i
$113$	−2100.22			−1.74842			−0.874212	−	0.485545i	$-0.838621\pi$
$113$	−2100.22			−1.74842			−0.874212	+	0.485545i	$0.838621\pi$
$114$	−130.006	−	225.177i	−0.106809	−	0.184998i
$115$	13.7483	−	23.8128i	0.0111482	−	0.0193092i
$116$	384.178	−	665.417i	0.307501	−	0.532607i
$117$	30.9298	+	53.5720i	0.0244398	+	0.0423310i
$118$	1875.96			1.46353
$119$	876.176	+	904.949i	0.674949	+	0.697114i
$120$	−135.680			−0.103215
$121$	−1450.77	−	2512.80i	−1.08998	−	1.88790i
$122$	−481.229	+	833.514i	−0.357118	+	0.618547i
$123$	189.872	−	328.868i	0.139189	−	0.241082i
$124$	−698.035	−	1209.03i	−0.505527	−	0.875599i
$125$	125.000			0.0894427
$126$	426.664	+	440.675i	0.301669	+	0.311575i
$127$	760.110			0.531094			0.265547	−	0.964098i	$-0.414448\pi$
$127$	760.110			0.531094			0.265547	+	0.964098i	$0.414448\pi$
$128$	−551.577	−	955.360i	−0.380883	−	0.659708i
$129$	−137.389	+	237.964i	−0.0937704	+	0.162415i
$130$	63.2333	−	109.523i	0.0426609	−	0.0738909i
$131$	5.05499	+	8.75549i	0.00337142	+	0.00583947i	0.867706	−	0.497077i	$-0.165594\pi$
$131$	5.05499	+	8.75549i	0.00337142	+	0.00583947i	−0.864335	+	0.502917i	$0.832260\pi$
$132$	1081.65			0.713224
$133$	−423.099	+	106.075i	−0.275844	+	0.0691568i
$134$	−3395.78			−2.18919
$135$	−67.5000	−	116.913i	−0.0430331	−	0.0745356i
$136$	307.599	−	532.777i	0.193944	−	0.335921i
$137$	−1395.86	+	2417.70i	−0.870485	+	1.50772i	−0.00898882	+	0.999960i	$0.502861\pi$
$137$	−1395.86	+	2417.70i	−0.870485	+	1.50772i	−0.861496	+	0.507764i	$0.830472\pi$
$138$	30.3559	+	52.5779i	0.0187251	+	0.0324328i
$139$	517.250			0.315630			0.157815	−	0.987469i	$-0.449555\pi$
$139$	517.250			0.315630			0.157815	+	0.987469i	$0.449555\pi$
$140$	140.814	−	493.498i	0.0850070	−	0.297916i
$141$	1705.40			1.01858
$142$	−956.163	−	1656.12i	−0.565067	−	0.978724i
$143$	223.581	−	387.253i	0.130747	−	0.226460i
$144$	349.300	−	605.006i	0.202141	−	0.350119i
$145$	346.607	+	600.341i	0.198511	+	0.343832i
$146$	3924.62			2.22468
$147$	907.294	−	485.447i	0.509063	−	0.272374i
$148$	706.762			0.392537
$149$	985.657	+	1707.21i	0.541934	+	0.938658i	0.998793	+	0.0491184i	$0.0156412\pi$
$149$	985.657	+	1707.21i	0.541934	+	0.938658i	−0.456859	+	0.889539i	$0.651025\pi$
$150$	−137.998	+	239.019i	−0.0751165	+	0.130106i
$151$	80.8806	−	140.089i	0.0435892	−	0.0754987i	−0.843408	−	0.537274i	$-0.819454\pi$
$151$	80.8806	−	140.089i	0.0435892	−	0.0754987i	0.886997	+	0.461775i	$0.152787\pi$
$152$	106.519	+	184.496i	0.0568410	+	0.0984515i
$153$	612.113			0.323441
$154$	1216.61	−	4263.75i	0.636607	−	2.23106i
$155$	1259.54			0.652700
$156$	57.1375	+	98.9650i	0.0293247	+	0.0507919i
$157$	53.7440	−	93.0873i	0.0273200	−	0.0473196i	−0.852042	−	0.523473i	$-0.824636\pi$
$157$	53.7440	−	93.0873i	0.0273200	−	0.0473196i	0.879362	+	0.476154i	$0.157969\pi$
$158$	207.573	−	359.528i	0.104517	−	0.181028i
$159$	885.598	+	1533.90i	0.441714	+	0.765071i
$160$	−1066.41			−0.526921
$161$	98.7917	−	24.7680i	0.0483595	−	0.0121242i
$162$	298.075			0.144562
$163$	1004.14	+	1739.21i	0.482515	+	0.835741i	0.999799	−	0.0200735i	$-0.00639003\pi$
$163$	1004.14	+	1739.21i	0.482515	+	0.835741i	−0.517283	+	0.855814i	$0.673057\pi$
$164$	350.756	−	607.528i	0.167009	−	0.289268i
$165$	−487.934	+	845.127i	−0.230216	+	0.398746i
$166$	1092.12	+	1891.60i	0.510632	+	0.884440i
$167$	−566.505			−0.262500			−0.131250	−	0.991349i	$-0.541899\pi$
$167$	−566.505			−0.262500			−0.131250	+	0.991349i	$0.541899\pi$
$168$	−349.582	−	361.062i	−0.160541	−	0.165813i
$169$	−2149.76			−0.978497
$170$	−625.706	−	1083.75i	−0.282291	−	0.488942i
$171$	−105.985	+	183.571i	−0.0473969	+	0.0820938i
$172$	−253.802	+	439.598i	−0.112513	+	0.194878i
$173$	373.967	+	647.729i	0.164348	+	0.284659i	0.936423	−	0.350872i	$-0.114115\pi$
$173$	373.967	+	647.729i	0.164348	+	0.284659i	−0.772076	+	0.635531i	$0.780781\pi$
$174$	−1530.59			−0.666862
$175$	322.064	+	332.641i	0.139119	+	0.143687i
$176$	−5049.94			−2.16281
$177$	−764.670	−	1324.45i	−0.324724	−	0.562438i
$178$	445.872	−	772.272i	0.187750	−	0.325192i
$179$	2023.57	−	3504.93i	0.844965	−	1.46352i	−0.0406860	−	0.999172i	$-0.512954\pi$
$179$	2023.57	−	3504.93i	0.844965	−	1.46352i	0.885651	−	0.464351i	$-0.153712\pi$
$180$	−124.695	−	215.978i	−0.0516344	−	0.0894334i
$181$	−2930.28			−1.20335			−0.601673	−	0.798742i	$-0.705499\pi$
$181$	−2930.28			−1.20335			−0.601673	+	0.798742i	$0.705499\pi$
$182$	454.376	−	113.916i	0.185058	−	0.0463959i
$183$	784.625			0.316946
$184$	−24.8717	−	43.0791i	−0.00996504	−	0.0172600i
$185$	−318.822	+	552.216i	−0.126704	+	0.219458i
$186$	−1390.51	+	2408.43i	−0.548156	+	0.949435i
$187$	−2212.38	−	3831.95i	−0.865160	−	1.49850i
$188$	3150.43			1.22217
$189$	137.207	−	480.855i	0.0528059	−	0.185064i
$190$	433.354			0.165467
$191$	−1508.61	−	2613.00i	−0.571516	−	0.989894i	−0.996411	−	0.0846516i	$-0.973022\pi$
$191$	−1508.61	−	2613.00i	−0.571516	−	0.989894i	0.424895	−	0.905243i	$-0.360311\pi$
$192$	245.836	−	425.800i	0.0924045	−	0.160049i
$193$	−393.459	+	681.491i	−0.146745	+	0.254170i	−0.930023	−	0.367502i	$-0.880213\pi$
$193$	−393.459	+	681.491i	−0.146745	+	0.254170i	0.783278	+	0.621672i	$0.213546\pi$
$194$	2827.82	+	4897.94i	1.04653	+	1.81264i
$195$	−103.099			−0.0378620
$196$	1676.07	−	896.781i	0.610813	−	0.326815i
$197$	−2009.92			−0.726910			−0.363455	−	0.931612i	$-0.618403\pi$
$197$	−2009.92			−0.726910			−0.363455	+	0.931612i	$0.618403\pi$
$198$	−1077.34	−	1866.01i	−0.386684	−	0.669756i
$199$	−1360.62	+	2356.66i	−0.484681	+	0.839492i	−0.999845	−	0.0175996i	$-0.994398\pi$
$199$	−1360.62	+	2356.66i	−0.484681	+	0.839492i	0.515164	+	0.857091i	$0.327731\pi$
$200$	113.067	−	195.838i	0.0399752	−	0.0692391i
$201$	1384.17	+	2397.46i	0.485731	+	0.841311i
$202$	−6314.19			−2.19933
$203$	−704.545	+	2469.15i	−0.243593	+	0.853697i
$204$	1130.77			0.388088
$205$	316.454	+	548.114i	0.107815	+	0.186741i
$206$	529.271	−	916.725i	0.179010	−	0.310055i
$207$	24.7470	−	42.8631i	0.00830936	−	0.0143922i
$208$	−266.760	−	462.042i	−0.0889254	−	0.154023i
$209$	1532.26			0.507122
$210$	−991.614	+	248.607i	−0.325847	+	0.0816929i
$211$	640.229			0.208887			0.104444	−	0.994531i	$-0.466694\pi$
$211$	640.229			0.208887			0.104444	+	0.994531i	$0.466694\pi$
$212$	1635.99	+	2833.62i	0.530002	+	0.917990i
$213$	−779.493	+	1350.12i	−0.250751	+	0.434314i
$214$	1933.07	−	3348.17i	0.617484	−	1.06951i
$215$	−228.981	−	396.607i	−0.0726343	−	0.125806i
$216$	−244.225			−0.0769323
$217$	3245.22	+	3351.79i	1.01521	+	1.04854i
$218$	−680.057			−0.211281
$219$	−1599.73	−	2770.82i	−0.493607	−	0.854952i
$220$	−901.375	+	1561.23i	−0.276230	+	0.478445i
$221$	233.735	−	404.841i	0.0711435	−	0.123224i
$222$	−703.948	−	1219.27i	−0.212819	−	0.368614i
$223$	−1970.27			−0.591655			−0.295828	−	0.955241i	$-0.595595\pi$
$223$	−1970.27			−0.591655			−0.295828	+	0.955241i	$0.595595\pi$
$224$	−2747.63	−	2837.86i	−0.819570	−	0.846484i
$225$	225.000			0.0666667
$226$	3864.34	+	6693.24i	1.13740	+	1.97003i
$227$	2298.03	−	3980.31i	0.671920	−	1.16380i	−0.305439	−	0.952212i	$-0.598803\pi$
$227$	2298.03	−	3980.31i	0.671920	−	1.16380i	0.977359	−	0.211588i	$-0.0678636\pi$
$228$	−195.789	+	339.116i	−0.0568704	+	0.0985024i
$229$	2312.71	+	4005.73i	0.667371	+	1.15592i	0.978637	+	0.205598i	$0.0659138\pi$
$229$	2312.71	+	4005.73i	0.667371	+	1.15592i	−0.311266	+	0.950323i	$0.600753\pi$
$230$	−101.186			−0.0290088
$231$	−3506.16	+	879.027i	−0.998650	+	0.250371i
$232$	1254.07			0.354888
$233$	948.296	+	1642.50i	0.266631	+	0.461818i	0.967990	−	0.250990i	$-0.0807563\pi$
$233$	948.296	+	1642.50i	0.266631	+	0.461818i	−0.701359	+	0.712808i	$0.747423\pi$
$234$	113.820	−	197.142i	0.0317976	−	0.0550750i
$235$	−1421.16	+	2461.53i	−0.394496	+	0.683287i
$236$	−1412.60	−	2446.69i	−0.389628	−	0.674856i
$237$	−338.440			−0.0927596
$238$	1271.87	−	4457.39i	0.346398	−	1.21399i
$239$	7217.92			1.95351			0.976754	−	0.214362i	$-0.0687673\pi$
$239$	7217.92			1.95351			0.976754	+	0.214362i	$0.0687673\pi$
$240$	582.167	+	1008.34i	0.156578	+	0.271201i
$241$	−480.020	+	831.419i	−0.128302	+	0.222226i	−0.923019	−	0.384755i	$-0.874286\pi$
$241$	−480.020	+	831.419i	−0.128302	+	0.222226i	0.794717	+	0.606980i	$0.207619\pi$
$242$	−5338.73	+	9246.96i	−1.41813	+	2.45627i
$243$	−121.500	−	210.444i	−0.0320750	−	0.0555556i
$244$	1449.46			0.380296
$245$	−55.3955	+	1714.11i	−0.0144453	+	0.446980i
$246$	−1397.44			−0.362184
$247$	80.9405	+	140.193i	0.0208507	+	0.0361145i
$248$	1139.30	−	1973.32i	0.291715	−	0.505266i
$249$	890.328	−	1542.09i	0.226595	−	0.392474i
$250$	−229.996	−	398.366i	−0.0581850	−	0.100779i
$251$	2907.61			0.731183			0.365592	−	0.930775i	$-0.380867\pi$
$251$	2907.61			0.731183			0.365592	+	0.930775i	$0.380867\pi$
$252$	253.466	−	888.297i	0.0633604	−	0.222053i
$253$	−357.775			−0.0889057
$254$	−1398.58	−	2422.41i	−0.345491	−	0.598409i
$255$	−510.094	+	883.509i	−0.125268	+	0.216970i
$256$	−2685.34	+	4651.14i	−0.655599	+	1.13553i
$257$	−1839.05	−	3185.32i	−0.446368	−	0.773132i	0.551778	−	0.833991i	$-0.313949\pi$
$257$	−1839.05	−	3185.32i	−0.446368	−	0.773132i	−0.998146	+	0.0608588i	$0.980616\pi$
$258$	1011.16			0.244001
$259$	−2290.96	+	574.366i	−0.549627	+	0.137797i
$260$	−190.458			−0.0454297
$261$	623.893	+	1080.61i	0.147962	+	0.256277i
$262$	18.6021	−	32.2197i	0.00438641	−	0.00759749i
$263$	2934.87	−	5083.35i	0.688107	−	1.19184i	−0.284343	−	0.958723i	$-0.591775\pi$
$263$	2934.87	−	5083.35i	0.688107	−	1.19184i	0.972450	−	0.233113i	$-0.0748913\pi$
$264$	882.707	+	1528.89i	0.205784	+	0.356428i
$265$	−2951.99			−0.684300
$266$	1116.54	+	1153.21i	0.257367	+	0.265819i
$267$	−726.976			−0.166630
$268$	2557.02	+	4428.89i	0.582817	+	1.00947i
$269$	−230.381	+	399.031i	−0.0522177	+	0.0904438i	−0.890953	−	0.454096i	$-0.849962\pi$
$269$	−230.381	+	399.031i	−0.0522177	+	0.0904438i	0.838735	+	0.544540i	$0.183296\pi$
$270$	−248.396	+	430.235i	−0.0559886	+	0.0969750i
$271$	2657.50	+	4602.93i	0.595689	+	1.03176i	0.993449	+	0.114275i	$0.0364544\pi$
$271$	2657.50	+	4602.93i	0.595689	+	1.03176i	−0.397760	+	0.917490i	$0.630212\pi$
$272$	−5279.29			−1.17685
$273$	−265.637	−	274.360i	−0.0588903	−	0.0608243i
$274$	10273.4			2.26510
$275$	−813.224	−	1408.54i	−0.178324	−	0.308867i
$276$	45.7159	−	79.1822i	0.00997019	−	0.0172689i
$277$	1190.29	−	2061.65i	0.258187	−	0.447193i	−0.707569	−	0.706644i	$-0.750208\pi$
$277$	1190.29	−	2061.65i	0.258187	−	0.447193i	0.965756	+	0.259451i	$0.0835415\pi$
$278$	−951.725	−	1648.44i	−0.205326	−	0.355635i
$279$	2267.17			0.486494
$280$	812.467	−	203.693i	0.173408	−	0.0434750i
$281$	1769.23			0.375599			0.187800	−	0.982207i	$-0.439864\pi$
$281$	1769.23			0.375599			0.187800	+	0.982207i	$0.439864\pi$
$282$	−3137.88	−	5434.97i	−0.662618	−	1.14769i
$283$	−728.463	+	1261.74i	−0.153013	+	0.265026i	−0.932334	−	0.361599i	$-0.882231\pi$
$283$	−728.463	+	1261.74i	−0.153013	+	0.265026i	0.779321	+	0.626625i	$0.215564\pi$
$284$	−1439.98	+	2494.12i	−0.300870	+	0.521122i
$285$	−176.642	−	305.952i	−0.0367135	−	0.0635896i
$286$	−1645.53			−0.340217
$287$	−643.252	+	2254.34i	−0.132299	+	0.463658i
$288$	−1919.55			−0.392744
$289$	143.647	+	248.803i	0.0292381	+	0.0506418i
$290$	1275.49	−	2209.22i	0.258275	−	0.447345i
$291$	2305.33	−	3992.94i	0.464401	−	0.804366i
$292$	−2955.23	−	5118.61i	−0.592267	−	1.02584i
$293$	−2743.56			−0.547032			−0.273516	−	0.961868i	$-0.588187\pi$
$293$	−2743.56			−0.547032			−0.273516	+	0.961868i	$0.588187\pi$
$294$	−3216.48	−	1998.27i	−0.638057	−	0.396399i
$295$	2548.90			0.503060
$296$	576.771	+	998.997i	0.113257	+	0.196167i
$297$	−878.282	+	1521.23i	−0.171593	+	0.297207i
$298$	3627.16	−	6282.43i	0.705087	−	1.22125i
$299$	−18.8993	−	32.7345i	−0.00365543	−	0.00633138i
$300$	415.649			0.0799917
$301$	465.447	−	1631.21i	0.0891293	−	0.312363i
$302$	−595.272			−0.113424
$303$	2573.76	+	4457.88i	0.487982	+	0.845210i
$304$	914.088	−	1583.25i	0.172456	−	0.298702i
$305$	−653.854	+	1132.51i	−0.122753	+	0.212614i
$306$	−1126.27	−	1950.76i	−0.210407	−	0.364436i
$307$	3367.27			0.625995			0.312997	−	0.949754i	$-0.398667\pi$
$307$	3367.27			0.625995			0.312997	+	0.949754i	$0.398667\pi$
$308$	−6477.02	+	1623.85i	−1.19826	+	0.300414i
$309$	−862.955			−0.158873
$310$	−2317.52	−	4014.05i	−0.424600	−	0.735429i
$311$	3100.15	−	5369.61i	0.565251	−	0.979044i	−0.431775	−	0.901981i	$-0.642113\pi$
$311$	3100.15	−	5369.61i	0.565251	−	0.979044i	0.997026	−	0.0770626i	$-0.0245541\pi$
$312$	−93.2569	+	161.526i	−0.0169219	+	0.0293096i
$313$	−5169.97	−	8954.65i	−0.933622	−	1.61708i	−0.777072	−	0.629412i	$-0.783296\pi$
$313$	−5169.97	−	8954.65i	−0.933622	−	1.61708i	−0.156550	−	0.987670i	$-0.550037\pi$
$314$	−395.550			−0.0710897
$315$	579.715	+	598.753i	0.103693	+	0.107098i
$316$	−625.210			−0.111300
$317$	−1488.66	−	2578.43i	−0.263758	−	0.456842i	0.703480	−	0.710715i	$-0.251629\pi$
$317$	−1488.66	−	2578.43i	−0.263758	−	0.456842i	−0.967237	+	0.253873i	$0.918295\pi$
$318$	3258.95	−	5644.67i	0.574695	−	0.995401i
$319$	4509.91	−	7811.39i	0.791556	−	1.37102i
$320$	409.726	+	709.667i	0.0715762	+	0.123974i
$321$	−3151.79			−0.548023
$322$	−260.708	−	269.269i	−0.0451201	−	0.0466018i
$323$	1601.85			0.275941
$324$	−224.450	−	388.760i	−0.0384860	−	0.0666597i
$325$	85.9161	−	148.811i	0.0146639	−	0.0253986i
$326$	3695.16	−	6400.21i	0.627779	−	1.08735i
$327$	277.201	+	480.127i	0.0468785	+	0.0811959i
$328$	1144.97			0.192746
$329$	−10212.1	+	2560.26i	−1.71128	+	0.429033i
$330$	3591.14			0.599048
$331$	3378.51	+	5851.75i	0.561027	+	0.971727i	0.997407	+	0.0719644i	$0.0229268\pi$
$331$	3378.51	+	5851.75i	0.561027	+	0.971727i	−0.436381	+	0.899762i	$0.643740\pi$
$332$	1644.73	−	2848.75i	0.271886	−	0.470920i
$333$	−573.879	+	993.988i	−0.0944396	+	0.163574i
$334$	1042.35	+	1805.41i	0.170764	+	0.295771i
$335$	−4613.91			−0.752491
$336$	−1183.36	+	4147.23i	−0.192136	+	0.673363i
$337$	10292.1			1.66364			0.831818	−	0.555048i	$-0.187300\pi$
$337$	10292.1			1.66364			0.831818	+	0.555048i	$0.187300\pi$
$338$	3955.49	+	6851.12i	0.636540	+	1.10252i
$339$	3150.33	−	5456.53i	0.504726	−	0.874212i
$340$	−942.312	+	1632.13i	−0.150306	+	0.260338i
$341$	−8194.29	−	14192.9i	−1.30131	−	2.25393i
$342$	780.037			0.123332
$343$	−4704.17	+	4269.00i	−0.740529	+	0.672024i
$344$	−828.485			−0.129852
$345$	41.2450	+	71.4385i	0.00643640	+	0.0111482i
$346$	1376.18	−	2383.61i	0.213826	−	0.370357i
$347$	−4520.22	+	7829.25i	−0.699303	+	1.21123i	0.269406	+	0.963027i	$0.413173\pi$
$347$	−4520.22	+	7829.25i	−0.699303	+	1.21123i	−0.968708	+	0.248201i	$0.920161\pi$
$348$	1152.54	+	1996.25i	0.177536	+	0.307501i
$349$	−7449.27			−1.14255			−0.571275	−	0.820759i	$-0.693551\pi$
$349$	−7449.27			−1.14255			−0.571275	+	0.820759i	$0.693551\pi$
$350$	467.511	−	1638.44i	0.0713987	−	0.250224i
$351$	−185.579			−0.0282207
$352$	6937.87	+	12016.7i	1.05054	+	1.81959i
$353$	−848.018	+	1468.81i	−0.127862	+	0.221464i	−0.922848	−	0.385164i	$-0.874145\pi$
$353$	−848.018	+	1468.81i	−0.127862	+	0.221464i	0.794986	+	0.606628i	$0.207478\pi$
$354$	−2813.94	+	4873.89i	−0.422484	+	0.731764i
$355$	−1299.16	−	2250.20i	−0.194231	−	0.336418i
$356$	−1342.96			−0.199935
$357$	−3665.39	+	918.948i	−0.543398	+	0.136235i
$358$	−14893.3			−2.19870
$359$	−2393.00	−	4144.81i	−0.351805	−	0.609344i	0.634761	−	0.772709i	$-0.281099\pi$
$359$	−2393.00	−	4144.81i	−0.351805	−	0.609344i	−0.986566	+	0.163365i	$0.947765\pi$
$360$	203.520	−	352.508i	0.0297957	−	0.0516077i
$361$	3152.15	−	5459.68i	0.459564	−	0.795988i
$362$	5391.63	+	9338.57i	0.782811	+	1.35587i
$363$	8704.59			1.25860
$364$	−490.718	−	506.833i	−0.0706610	−	0.0729815i
$365$	5332.44			0.764693
$366$	−1443.69	−	2500.54i	−0.206182	−	0.357118i
$367$	−956.276	+	1656.32i	−0.136014	+	0.235583i	−0.925984	−	0.377562i	$-0.876763\pi$
$367$	−956.276	+	1656.32i	−0.136014	+	0.235583i	0.789970	+	0.613145i	$0.210096\pi$
$368$	−213.436	+	369.681i	−0.0302340	+	0.0523668i
$369$	569.616	+	986.605i	0.0803606	+	0.139189i
$370$	2346.49			0.329698
$371$	−7605.85	−	7855.62i	−1.06436	−	1.09931i
$372$	4188.21			0.583732
$373$	6402.04	+	11088.7i	0.888700	+	1.53927i	0.841413	+	0.540392i	$0.181724\pi$
$373$	6402.04	+	11088.7i	0.888700	+	1.53927i	0.0472865	+	0.998881i	$0.484943\pi$
$374$	−8141.42	+	14101.4i	−1.12562	+	1.94964i
$375$	−187.500	+	324.760i	−0.0258199	+	0.0447214i
$376$	2570.99	+	4453.08i	0.352629	+	0.610771i
$377$	952.932			0.130182
$378$	−1784.90	+	447.492i	−0.242872	+	0.0608903i
$379$	−5817.74			−0.788489			−0.394244	−	0.919006i	$-0.628994\pi$
$379$	−5817.74			−0.788489			−0.394244	+	0.919006i	$0.628994\pi$
$380$	−326.315	−	565.194i	−0.0440516	−	0.0762996i
$381$	−1140.17	+	1974.82i	−0.153314	+	0.265547i
$382$	−5551.62	+	9615.68i	−0.743574	+	1.28791i
$383$	5650.48	+	9786.92i	0.753854	+	1.30571i	0.945942	+	0.324335i	$0.105141\pi$
$383$	5650.48	+	9786.92i	0.753854	+	1.30571i	−0.192088	+	0.981378i	$0.561526\pi$
$384$	3309.46			0.439806
$385$	1653.03	−	5793.22i	0.218822	−	0.766883i
$386$	2895.81			0.381847
$387$	−412.166	−	713.892i	−0.0541384	−	0.0937704i
$388$	4258.70	−	7376.28i	0.557223	−	0.965139i
$389$	−635.322	+	1100.41i	−0.0828075	+	0.143427i	−0.904455	−	0.426569i	$-0.859722\pi$
$389$	−635.322	+	1100.41i	−0.0828075	+	0.143427i	0.821647	+	0.569996i	$0.193055\pi$
$390$	189.700	+	328.570i	0.0246303	+	0.0426609i
$391$	−374.024			−0.0483765
$392$	2635.38	+	1637.26i	0.339559	+	0.210954i
$393$	−30.3299			−0.00389298
$394$	3698.21	+	6405.48i	0.472875	+	0.819044i
$395$	282.033	−	488.496i	0.0359257	−	0.0622251i
$396$	−1622.47	+	2810.21i	−0.205890	+	0.356612i
$397$	−5657.04	−	9798.28i	−0.715161	−	1.23869i	−0.962898	−	0.269867i	$-0.913020\pi$
$397$	−5657.04	−	9798.28i	−0.715161	−	1.23869i	0.247737	−	0.968827i	$-0.420313\pi$
$398$	10014.0			1.26119
$399$	359.057	−	1258.35i	0.0450510	−	0.157886i
$400$	−1940.56			−0.242570
$401$	3398.03	+	5885.57i	0.423166	+	0.732945i	0.996247	−	0.0865533i	$-0.0275853\pi$
$401$	3398.03	+	5885.57i	0.423166	+	0.732945i	−0.573081	+	0.819499i	$0.694252\pi$
$402$	5093.67	−	8822.50i	0.631964	−	1.09459i
$403$	865.717	−	1499.47i	0.107008	−	0.185344i
$404$	4754.58	+	8235.17i	0.585518	+	1.01415i
$405$	405.000			0.0496904
$406$	9165.34	−	2297.84i	1.12037	−	0.280886i
$407$	8296.75			1.01045
$408$	922.796	+	1598.33i	0.111974	+	0.193944i
$409$	−4012.23	+	6949.39i	−0.485067	+	0.840160i	−0.999853	−	0.0171587i	$-0.994538\pi$
$409$	−4012.23	+	6949.39i	−0.485067	+	0.840160i	0.514786	+	0.857319i	$0.327871\pi$
$410$	1164.53	−	2017.03i	0.140273	−	0.242961i
$411$	−4187.58	−	7253.10i	−0.502575	−	0.870485i
$412$	−1594.16			−0.190628
$413$	6567.28	+	6782.94i	0.782457	+	0.808152i
$414$	−182.135			−0.0216219
$415$	1483.88	+	2570.15i	0.175520	+	0.304009i
$416$	−732.977	+	1269.55i	−0.0863874	+	0.149627i
$417$	−775.874	+	1343.85i	−0.0911145	+	0.157815i
$418$	−2819.31	−	4883.19i	−0.329897	−	0.571398i
$419$	2524.40			0.294332			0.147166	−	0.989112i	$-0.452985\pi$
$419$	2524.40			0.294332			0.147166	+	0.989112i	$0.452985\pi$
$420$	1070.92	+	1106.09i	0.124419	+	0.128504i
$421$	−7844.12			−0.908074			−0.454037	−	0.890983i	$-0.650017\pi$
$421$	−7844.12			−0.908074			−0.454037	+	0.890983i	$0.650017\pi$
$422$	−1178.00	−	2040.36i	−0.135887	−	0.235363i
$423$	−2558.09	+	4430.75i	−0.294040	+	0.509292i
$424$	−2670.18	+	4624.89i	−0.305839	+	0.529728i
$425$	−850.157	−	1472.51i	−0.0970322	−	0.168065i
$426$	5736.98			0.652483
$427$	−4698.41	+	1177.94i	−0.532487	+	0.133500i
$428$	−5822.38			−0.657560
$429$	670.742	+	1161.76i	0.0754866	+	0.130747i
$430$	−842.637	+	1459.49i	−0.0945013	+	0.163681i
$431$	−3411.88	+	5909.55i	−0.381310	+	0.660448i	−0.991250	−	0.132000i	$-0.957860\pi$
$431$	−3411.88	+	5909.55i	−0.381310	+	0.660448i	0.609940	+	0.792448i	$0.291193\pi$
$432$	1047.90	+	1815.02i	0.116706	+	0.202141i
$433$	−9283.82			−1.03037			−0.515187	−	0.857078i	$-0.672277\pi$
$433$	−9283.82			−1.03037			−0.515187	+	0.857078i	$0.672277\pi$
$434$	4710.79	−	16509.5i	0.521026	−	1.82599i
$435$	−2079.64			−0.229221
$436$	512.082	+	886.952i	0.0562483	+	0.0974250i
$437$	64.7608	−	112.169i	0.00708908	−	0.0122786i
$438$	−5886.93	+	10196.5i	−0.642211	+	1.11234i
$439$	−334.674	−	579.672i	−0.0363852	−	0.0630210i	0.847259	−	0.531179i	$-0.178251\pi$
$439$	−334.674	−	579.672i	−0.0363852	−	0.0630210i	−0.883645	+	0.468158i	$0.844918\pi$
$440$	−2942.36			−0.318799
$441$	−99.7119	+	3085.39i	−0.0107669	+	0.333159i
$442$	−1720.26			−0.185123
$443$	−4874.38	−	8442.68i	−0.522774	−	0.905472i	−0.999649	−	0.0265002i	$-0.991564\pi$
$443$	−4874.38	−	8442.68i	−0.522774	−	0.905472i	0.476875	−	0.878971i	$-0.341770\pi$
$444$	−1060.14	+	1836.22i	−0.113316	+	0.196269i
$445$	605.813	−	1049.30i	0.0645355	−	0.111779i
$446$	3625.24	+	6279.11i	0.384888	+	0.666646i
$447$	−5913.94			−0.625772
$448$	−832.846	+	2918.80i	−0.0878310	+	0.307813i
$449$	5113.54			0.537467			0.268734	−	0.963215i	$-0.413395\pi$
$449$	5113.54			0.537467			0.268734	+	0.963215i	$0.413395\pi$
$450$	−413.994	−	717.058i	−0.0433686	−	0.0751165i
$451$	4117.56	−	7131.82i	0.429908	−	0.744622i
$452$	5819.69	−	10080.0i	0.605609	−	1.04895i
$453$	242.642	+	420.268i	0.0251662	+	0.0435892i
$454$	−16913.3			−1.74841
$455$	617.368	−	154.780i	0.0636103	−	0.0159477i
$456$	−639.114			−0.0656343
$457$	1739.10	+	3012.20i	0.178012	+	0.308326i	0.941200	−	0.337851i	$-0.109700\pi$
$457$	1739.10	+	3012.20i	0.178012	+	0.308326i	−0.763187	+	0.646177i	$0.776367\pi$
$458$	8510.63	−	14740.8i	0.868287	−	1.50392i
$459$	−918.169	+	1590.32i	−0.0933692	+	0.161720i
$460$	76.1931	+	131.970i	0.00772288	+	0.0133764i
$461$	−996.935			−0.100720			−0.0503600	−	0.998731i	$-0.516037\pi$
$461$	−996.935			−0.100720			−0.0503600	+	0.998731i	$0.516037\pi$
$462$	9252.62	+	9556.47i	0.931755	+	0.962354i
$463$	−12681.1			−1.27287			−0.636436	−	0.771330i	$-0.719592\pi$
$463$	−12681.1			−1.27287			−0.636436	+	0.771330i	$0.719592\pi$
$464$	−5380.89	−	9319.97i	−0.538365	−	0.932476i
$465$	−1889.31	+	3272.38i	−0.188418	+	0.326350i
$466$	3489.68	−	6044.30i	0.346902	−	0.600851i
$467$	33.5108	+	58.0425i	0.00332055	+	0.00575136i	0.867681	−	0.497122i	$-0.165610\pi$
$467$	33.5108	+	58.0425i	0.00332055	+	0.00575136i	−0.864360	+	0.502873i	$0.832276\pi$
$468$	−342.825			−0.0338613
$469$	−11887.8	−	12278.2i	−1.17042	−	1.20886i
$470$	10459.6			1.02652
$471$	161.232	+	279.262i	0.0157732	+	0.0273200i
$472$	2305.57	−	3993.37i	0.224836	−	0.389427i
$473$	−2979.40	+	5160.48i	−0.289626	+	0.501647i
$474$	622.720	+	1078.58i	0.0603428	+	0.104517i
$475$	588.805			0.0568763
$476$	−6771.18	+	1697.60i	−0.652010	+	0.163465i
$477$	−5313.59			−0.510047
$478$	−13280.8	−	23003.0i	−1.27081	−	2.20111i
$479$	−7832.74	+	13566.7i	−0.747155	+	1.29411i	0.202027	+	0.979380i	$0.435247\pi$
$479$	−7832.74	+	13566.7i	−0.747155	+	1.29411i	−0.949181	+	0.314730i	$0.898086\pi$
$480$	1599.62	−	2770.62i	0.152109	−	0.263461i
$481$	438.271	+	759.107i	0.0415456	+	0.0719590i
$482$	3532.89			0.333857
$483$	−83.8384	+	293.820i	−0.00789809	+	0.0276797i
$484$	16080.2			1.51017
$485$	3842.21	+	6654.91i	0.359723	+	0.623059i
$486$	−447.113	+	774.423i	−0.0417314	+	0.0722809i
$487$	5862.43	−	10154.0i	0.545486	−	0.944810i	−0.453090	−	0.891465i	$-0.649678\pi$
$487$	5862.43	−	10154.0i	0.545486	−	0.944810i	0.998576	−	0.0533453i	$-0.0169884\pi$
$488$	1182.87	+	2048.79i	0.109725	+	0.190050i
$489$	−6024.81			−0.557160
$490$	5564.65	−	2977.36i	0.513031	−	0.274497i
$491$	10584.2			0.972823			0.486412	−	0.873730i	$-0.338306\pi$
$491$	10584.2			0.972823			0.486412	+	0.873730i	$0.338306\pi$
$492$	1052.27	+	1822.58i	0.0964226	+	0.167009i
$493$	4714.73	−	8166.15i	0.430711	−	0.746014i
$494$	297.857	−	515.903i	0.0271279	−	0.0469870i
$495$	−1463.80	−	2535.38i	−0.132915	−	0.230216i
$496$	−19553.7			−1.77013
$497$	2640.78	−	9254.89i	0.238340	−	0.835289i
$498$	−6552.71			−0.589626
$499$	−5221.55	−	9044.00i	−0.468435	−	0.811352i	0.530915	−	0.847425i	$-0.321848\pi$
$499$	−5221.55	−	9044.00i	−0.468435	−	0.811352i	−0.999349	+	0.0360729i	$0.988515\pi$
$500$	−346.374	+	599.938i	−0.0309806	+	0.0536601i
$501$	849.758	−	1471.82i	0.0757772	−	0.131250i
$502$	−5349.93	−	9266.35i	−0.475655	−	0.823859i
$503$	−13824.2			−1.22543			−0.612713	−	0.790305i	$-0.709922\pi$
$503$	−13824.2			−1.22543			−0.612713	+	0.790305i	$0.709922\pi$
$504$	1462.44	−	366.647i	0.129250	−	0.0324043i
$505$	−8579.20			−0.755979
$506$	658.297	+	1140.20i	0.0578357	+	0.100174i
$507$	3224.64	−	5585.24i	0.282468	−	0.489249i
$508$	−2106.26	+	3648.15i	−0.183957	+	0.318623i
$509$	2750.71	+	4764.38i	0.239535	+	0.414887i	0.960581	−	0.278001i	$-0.0896717\pi$
$509$	2750.71	+	4764.38i	0.239535	+	0.414887i	−0.721046	+	0.692887i	$0.756338\pi$
$510$	3754.24			0.325961
$511$	13739.1	+	14190.3i	1.18940	+	1.22846i
$512$	10938.5			0.944178
$513$	−317.955	−	550.714i	−0.0273646	−	0.0473969i
$514$	−6767.59	+	11721.8i	−0.580750	+	1.00589i
$515$	719.130	−	1245.57i	0.0615313	−	0.106575i
$516$	−761.405	−	1318.79i	−0.0649593	−	0.112513i
$517$	36983.2			3.14607
$518$	6045.77	+	6244.31i	0.512810	+	0.529651i
$519$	−2243.80			−0.189772
$520$	−155.428	−	269.210i	−0.0131076	−	0.0227031i
$521$	−4102.73	+	7106.13i	−0.344998	+	0.597553i	−0.985353	−	0.170525i	$-0.945454\pi$
$521$	−4102.73	+	7106.13i	−0.344998	+	0.597553i	0.640356	+	0.768079i	$0.278787\pi$
$522$	2295.89	−	3976.60i	0.192507	−	0.333431i
$523$	9320.29	+	16143.2i	0.779250	+	1.34970i	0.932375	+	0.361494i	$0.117733\pi$
$523$	9320.29	+	16143.2i	0.779250	+	1.34970i	−0.153125	+	0.988207i	$0.548934\pi$
$524$	−56.0293			−0.00467109
$525$	−1347.32	+	337.786i	−0.112004	+	0.0280804i
$526$	−21600.3			−1.79053
$527$	−8566.44	−	14837.5i	−0.708084	−	1.22644i
$528$	7574.91	−	13120.1i	0.624348	−	1.08140i
$529$	6068.38	−	10510.7i	0.498757	−	0.863873i
$530$	5431.59	+	9407.78i	0.445157	+	0.771034i
$531$	4588.02			0.374959
$532$	663.297	−	2324.59i	0.0540556	−	0.189444i
$533$	870.030			0.0707039
$534$	1337.61	+	2316.82i	0.108397	+	0.187750i
$535$	2626.49	−	4549.21i	0.212249	−	0.367625i
$536$	−4173.44	+	7228.61i	−0.336316	+	0.582516i
$537$	6070.71	+	10514.8i	0.487841	+	0.844965i
$538$	1695.58			0.135876
$539$	19675.5	−	10527.4i	1.57233	−	0.841274i
$540$	748.168			0.0596223
$541$	−2401.26	−	4159.10i	−0.190829	−	0.330525i	0.754697	−	0.656074i	$-0.227784\pi$
$541$	−2401.26	−	4159.10i	−0.190829	−	0.330525i	−0.945525	+	0.325549i	$0.894451\pi$
$542$	9779.46	−	16938.5i	0.775025	−	1.34238i
$543$	4395.42	−	7613.08i	0.347376	−	0.601673i
$544$	7252.95	+	12562.5i	0.571632	+	0.990096i
$545$	−924.004			−0.0726238
$546$	−385.601	+	1351.38i	−0.0302238	+	0.105922i
$547$	1125.69			0.0879913			0.0439956	−	0.999032i	$-0.485991\pi$
$547$	1125.69			0.0879913			0.0439956	+	0.999032i	$0.485991\pi$
$548$	−7735.84	−	13398.9i	−0.603027	−	1.04447i
$549$	−1176.94	+	2038.52i	−0.0914945	+	0.158473i
$550$	−2992.62	+	5183.37i	−0.232010	+	0.401854i
$551$	1632.67	+	2827.87i	0.126233	+	0.218641i
$552$	149.230			0.0115066
$553$	2026.61	−	508.090i	0.155841	−	0.0390709i
$554$	−8760.43			−0.671832
$555$	−956.465	−	1656.65i	−0.0731526	−	0.126704i
$556$	−1433.30	+	2482.54i	−0.109326	+	0.189358i
$557$	−4482.81	+	7764.45i	−0.341010	+	0.590647i	−0.984621	−	0.174707i	$-0.944102\pi$
$557$	−4482.81	+	7764.45i	−0.341010	+	0.590647i	0.643611	+	0.765353i	$0.277436\pi$
$558$	−4171.53	−	7225.30i	−0.316478	−	0.548156i
$559$	−629.540			−0.0476328
$560$	−4999.87	−	5164.06i	−0.377291	−	0.389681i
$561$	13274.3			0.999001
$562$	−3255.33	−	5638.40i	−0.244338	−	0.423206i
$563$	−6032.82	+	10449.2i	−0.451604	+	0.782201i	−0.998486	−	0.0550087i	$-0.982481\pi$
$563$	−6032.82	+	10449.2i	−0.451604	+	0.782201i	0.546882	+	0.837210i	$0.315815\pi$
$564$	−4725.64	+	8185.05i	−0.352811	+	0.611087i
$565$	5250.55	+	9094.21i	0.390959	+	0.677162i
$566$	5361.41			0.398157
$567$	1043.49	+	1077.76i	0.0772881	+	0.0798262i
$568$	−4700.53			−0.347235
$569$	−5902.60	−	10223.6i	−0.434886	−	0.753244i	0.562401	−	0.826865i	$-0.309878\pi$
$569$	−5902.60	−	10223.6i	−0.434886	−	0.753244i	−0.997286	+	0.0736208i	$0.976545\pi$
$570$	−650.031	+	1125.89i	−0.0477663	+	0.0827337i
$571$	−514.397	+	890.962i	−0.0377003	+	0.0652988i	−0.884260	−	0.466995i	$-0.845337\pi$
$571$	−514.397	+	890.962i	−0.0377003	+	0.0652988i	0.846560	+	0.532294i	$0.178670\pi$
$572$	1239.08	+	2146.15i	0.0905745	+	0.156880i
$573$	9051.69			0.659930
$574$	8367.99	−	2097.93i	0.608490	−	0.152554i
$575$	−137.483			−0.00997123
$576$	737.507	+	1277.40i	0.0533498	+	0.0924045i
$577$	−5312.66	+	9201.79i	−0.383308	+	0.663909i	−0.991533	−	0.129856i	$-0.958549\pi$
$577$	−5312.66	+	9201.79i	−0.383308	+	0.663909i	0.608225	+	0.793765i	$0.291882\pi$
$578$	528.612	−	915.582i	0.0380404	−	0.0658879i
$579$	−1180.38	−	2044.47i	−0.0847233	−	0.146745i
$580$	−3841.78			−0.275037
$581$	−3016.27	+	10570.8i	−0.215380	+	0.754822i
$582$	−16966.9			−1.20842
$583$	19205.1	+	33264.1i	1.36431	+	2.36305i
$584$	4823.38	−	8354.34i	0.341769	−	0.591961i
$585$	154.649	−	267.860i	0.0109298	−	0.0189310i
$586$	5048.07	+	8743.51i	0.355860	+	0.616367i
$587$	−4881.61			−0.343246			−0.171623	−	0.985163i	$-0.554901\pi$
$587$	−4881.61			−0.343246			−0.171623	+	0.985163i	$0.554901\pi$
$588$	−184.201	+	5699.73i	−0.0129189	+	0.399750i
$589$	5932.98			0.415050
$590$	−4689.91	−	8123.16i	−0.327255	−	0.566822i
$591$	3014.89	−	5221.94i	0.209841	−	0.363455i
$592$	4949.54	−	8572.85i	0.343623	−	0.595172i
$593$	−6931.35	−	12005.4i	−0.479994	−	0.831373i	0.519743	−	0.854323i	$-0.326028\pi$
$593$	−6931.35	−	12005.4i	−0.479994	−	0.831373i	−0.999737	+	0.0229493i	$0.992694\pi$
$594$	6464.05			0.446504
$595$	1728.10	−	6056.33i	0.119068	−	0.417286i
$596$	−10925.0			−0.750848
$597$	−4081.85	−	7069.97i	−0.279831	−	0.484681i
$598$	−69.5482	+	120.461i	−0.00475592	+	0.00823749i
$599$	−12524.5	+	21693.1i	−0.854320	+	1.47973i	0.0229544	+	0.999737i	$0.492693\pi$
$599$	−12524.5	+	21693.1i	−0.854320	+	1.47973i	−0.877274	+	0.479989i	$0.840641\pi$
$600$	339.201	+	587.513i	0.0230797	+	0.0399752i
$601$	20281.5			1.37654			0.688268	−	0.725457i	$-0.258371\pi$
$601$	20281.5			1.37654			0.688268	+	0.725457i	$0.258371\pi$
$602$	−6054.95	+	1518.03i	−0.409936	+	0.102775i
$603$	−8305.03			−0.560874
$604$	448.239	+	776.373i	0.0301963	+	0.0523016i
$605$	−7253.83	+	12564.0i	−0.487454	+	0.844296i
$606$	9471.29	−	16404.8i	0.634892	−	1.09967i
$607$	681.260	+	1179.98i	0.0455544	+	0.0789025i	0.887904	−	0.460030i	$-0.152161\pi$
$607$	681.260	+	1179.98i	0.0455544	+	0.0789025i	−0.842349	+	0.538932i	$0.818828\pi$
$608$	−5023.28			−0.335067
$609$	−5358.23	−	5534.19i	−0.356529	−	0.368238i
$610$	4812.29			0.319416
$611$	1953.61	+	3383.76i	0.129353	+	0.224046i
$612$	−1696.16	+	2937.84i	−0.112031	+	0.194044i
$613$	6988.02	−	12103.6i	0.460430	−	0.797488i	−0.538552	−	0.842592i	$-0.681029\pi$
$613$	6988.02	−	12103.6i	0.460430	−	0.797488i	0.998982	+	0.0451040i	$0.0143619\pi$
$614$	−6195.68	−	10731.2i	−0.407227	−	0.705338i
$615$	−1898.72			−0.124494
$616$	−7581.02	−	7829.98i	−0.495857	−	0.512141i
$617$	−3529.04			−0.230265			−0.115133	−	0.993350i	$-0.536729\pi$
$617$	−3529.04			−0.230265			−0.115133	+	0.993350i	$0.536729\pi$
$618$	1587.81	+	2750.17i	0.103352	+	0.179010i
$619$	−4348.23	+	7531.36i	−0.282343	+	0.489032i	−0.971961	−	0.235141i	$-0.924445\pi$
$619$	−4348.23	+	7531.36i	−0.282343	+	0.489032i	0.689618	+	0.724173i	$0.257778\pi$
$620$	−3490.17	+	6045.16i	−0.226079	+	0.391580i
$621$	74.2411	+	128.589i	0.00479741	+	0.00830936i
$622$	−22816.7			−1.47085
$623$	4353.20	−	1091.39i	0.279948	−	0.0701855i
$624$	1600.56			0.102682
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	−19025.2	+	32952.6i	−1.21470	+	2.10391i
$627$	−2298.39	+	3980.92i	−0.146393	+	0.253561i
$628$	297.848	+	515.889i	0.0189259	+	0.0327806i
$629$	8673.55			0.549821
$630$	841.521	−	2949.20i	0.0532174	−	0.186506i
$631$	−24940.4			−1.57347			−0.786737	−	0.617289i	$-0.788231\pi$
$631$	−24940.4			−1.57347			−0.786737	+	0.617289i	$0.788231\pi$
$632$	−510.218	−	883.724i	−0.0321129	−	0.0556213i
$633$	−960.344	+	1663.36i	−0.0603006	+	0.104444i
$634$	−5478.17	+	9488.47i	−0.343164	+	0.594377i
$635$	−1900.28	−	3291.37i	−0.118756	−	0.205692i
$636$	−9815.95			−0.611993
$637$	2002.55	+	1244.10i	0.124559	+	0.0773832i
$638$	−33192.4			−2.05972
$639$	−2338.48	−	4050.36i	−0.144771	−	0.250751i
$640$	−2757.89	+	4776.80i	−0.170336	+	0.295031i
$641$	−10589.4	+	18341.3i	−0.652503	+	1.13017i	0.330011	+	0.943977i	$0.392948\pi$
$641$	−10589.4	+	18341.3i	−0.652503	+	1.13017i	−0.982514	+	0.186191i	$0.940386\pi$
$642$	5799.20	+	10044.5i	0.356505	+	0.617484i
$643$	27000.8			1.65600			0.828001	−	0.560727i	$-0.189478\pi$
$643$	27000.8			1.65600			0.828001	+	0.560727i	$0.189478\pi$
$644$	−154.877	+	542.783i	−0.00947672	+	0.0332122i
$645$	1373.89			0.0838708
$646$	−2947.35	−	5104.96i	−0.179508	−	0.310916i
$647$	−7642.44	+	13237.1i	−0.464382	+	0.804334i	−0.999173	−	0.0406506i	$-0.987057\pi$
$647$	−7642.44	+	13237.1i	−0.464382	+	0.804334i	0.534791	+	0.844984i	$0.320390\pi$
$648$	366.337	−	634.514i	0.0222084	−	0.0384661i
$649$	−16582.6	−	28721.9i	−1.00297	−	1.73719i
$650$	−632.333			−0.0381571
$651$	−13576.0	+	3403.64i	−0.817337	+	0.204914i
$652$	−11129.8			−0.668523
$653$	−138.967	−	240.698i	−0.00832802	−	0.0144246i	0.861831	−	0.507195i	$-0.169318\pi$
$653$	−138.967	−	240.698i	−0.00832802	−	0.0144246i	−0.870159	+	0.492770i	$0.835984\pi$
$654$	1020.09	−	1766.84i	0.0609916	−	0.105640i
$655$	25.2749	−	43.7775i	0.00150775	−	0.00261149i
$656$	−4912.77	−	8509.17i	−0.292395	−	0.506444i
$657$	9598.40			0.569968
$658$	26949.3	+	27834.3i	1.59665	+	1.64908i
$659$	31344.1			1.85280			0.926398	−	0.376545i	$-0.122888\pi$
$659$	31344.1			1.85280			0.926398	+	0.376545i	$0.122888\pi$
$660$	−2704.12	−	4683.68i	−0.159482	−	0.276230i
$661$	16157.6	−	27985.8i	0.950768	−	1.64678i	0.207000	−	0.978341i	$-0.433630\pi$
$661$	16157.6	−	27985.8i	0.950768	−	1.64678i	0.743768	−	0.668438i	$-0.233037\pi$
$662$	12432.7	−	21534.1i	0.729927	−	1.26427i
$663$	701.204	+	1214.52i	0.0410747	+	0.0711435i
$664$	5368.88			0.313785
$665$	1517.06	+	1566.88i	0.0884650	+	0.0913701i
$666$	4223.69			0.245743
$667$	−381.222	−	660.296i	−0.0221304	−	0.0383310i
$668$	1569.78	−	2718.94i	0.0909232	−	0.157484i
$669$	2955.41	−	5118.91i	0.170796	−	0.295828i
$670$	8489.46	+	14704.2i	0.489517	+	0.847868i
$671$	17015.4			0.978942
$672$	11494.4	−	2881.76i	0.659832	−	0.165426i
$673$	19454.9			1.11431			0.557156	−	0.830408i	$-0.311892\pi$
$673$	19454.9			1.11431			0.557156	+	0.830408i	$0.311892\pi$
$674$	−18937.1	−	32800.1i	−1.08224	−	1.87450i
$675$	−337.500	+	584.567i	−0.0192450	+	0.0333333i
$676$	5956.96	−	10317.8i	0.338926	−	0.587037i
$677$	−2611.65	−	4523.51i	−0.148263	−	0.256799i	0.782323	−	0.622873i	$-0.214035\pi$
$677$	−2611.65	−	4523.51i	−0.148263	−	0.256799i	−0.930585	+	0.366075i	$0.880701\pi$
$678$	−23186.1			−1.31336
$679$	−7810.02	+	27371.1i	−0.441416	+	1.54699i
$680$	−3075.99			−0.173469
$681$	6894.10	+	11940.9i	0.387933	+	0.671920i
$682$	−30154.5	+	52229.2i	−1.69307	+	2.93249i
$683$	9508.03	−	16468.4i	0.532672	−	0.922614i	−0.466601	−	0.884468i	$-0.654521\pi$
$683$	9508.03	−	16468.4i	0.532672	−	0.922614i	0.999272	−	0.0381462i	$-0.0121452\pi$
$684$	−587.367	−	1017.35i	−0.0328341	−	0.0568704i
$685$	13958.6			0.778585
$686$	22260.5	+	7137.01i	1.23894	+	0.397219i
$687$	−13876.2			−0.770614
$688$	3554.80	+	6157.10i	0.196985	+	0.341188i
$689$	−2028.99	+	3514.31i	−0.112189	+	0.194317i
$690$	151.779	−	262.890i	0.00837412	−	0.0145044i
$691$	−2024.13	−	3505.90i	−0.111435	−	0.193011i	0.804914	−	0.593391i	$-0.202211\pi$
$691$	−2024.13	−	3505.90i	−0.111435	−	0.193011i	−0.916349	+	0.400380i	$0.868878\pi$
$692$	−4145.04			−0.227703
$693$	2975.46	−	10427.8i	0.163100	−	0.571601i
$694$	33268.3			1.81967
$695$	−1293.12	−	2239.76i	−0.0705770	−	0.122243i
$696$	−1881.11	+	3258.18i	−0.102447	+	0.177444i
$697$	4304.56	−	7455.72i	0.233927	−	0.405173i
$698$	13706.4	+	23740.3i	0.743261	+	1.28737i
$699$	−5689.78			−0.307879
$700$	−2488.95	+	624.002i	−0.134390	+	0.0336930i
$701$	12385.2			0.667306			0.333653	−	0.942696i	$-0.391719\pi$
$701$	12385.2			0.667306			0.333653	+	0.942696i	$0.391719\pi$
$702$	341.460	+	591.425i	0.0183583	+	0.0317976i
$703$	−1501.79	+	2601.18i	−0.0805706	+	0.139552i
$704$	5331.19	−	9233.88i	0.285407	−	0.494340i
$705$	−4263.49	−	7384.58i	−0.227762	−	0.394496i
$706$	6241.32			0.332713
$707$	−22104.4	−	22830.3i	−1.17584	−	1.21446i
$708$	8475.59			0.449904
$709$	2630.05	+	4555.37i	0.139314	+	0.241298i	0.927237	−	0.374475i	$-0.122177\pi$
$709$	2630.05	+	4555.37i	0.139314	+	0.241298i	−0.787923	+	0.615773i	$0.788844\pi$
$710$	−4780.82	+	8280.62i	−0.252705	+	0.437699i
$711$	507.660	−	879.293i	0.0267774	−	0.0463798i
$712$	−1095.96	−	1898.26i	−0.0576865	−	0.0999159i
$713$	−1385.33			−0.0727642
$714$	9672.84	+	9990.49i	0.506998	+	0.523648i
$715$	−2235.81			−0.116943
$716$	11214.6	+	19424.3i	0.585348	+	1.01385i
$717$	−10826.9	+	18752.7i	−0.563929	+	0.976754i
$718$	−8806.12	+	15252.7i	−0.457718	+	0.792791i
$719$	−676.337	−	1171.45i	−0.0350808	−	0.0607618i	0.847952	−	0.530073i	$-0.177836\pi$
$719$	−676.337	−	1171.45i	−0.0350808	−	0.0607618i	−0.883033	+	0.469311i	$0.844502\pi$
$720$	−3493.00			−0.180801
$721$	5167.46	−	1295.53i	0.266916	−	0.0669183i
$722$	−23199.4			−1.19584
$723$	−1440.06	−	2494.26i	−0.0740753	−	0.128302i
$724$	8119.78	−	14063.9i	0.416808	−	0.721933i
$725$	1733.04	−	3001.71i	0.0887770	−	0.153766i
$726$	−16016.2	−	27740.9i	−0.818756	−	1.41813i
$727$	−2491.53			−0.127106			−0.0635528	−	0.997978i	$-0.520243\pi$
$727$	−2491.53			−0.127106			−0.0635528	+	0.997978i	$0.520243\pi$
$728$	315.937	−	1107.24i	0.0160844	−	0.0563693i
$729$	729.000			0.0370370
$730$	−9811.54	−	16994.1i	−0.497454	−	0.861616i
$731$	−3114.71	+	5394.84i	−0.157595	+	0.272962i
$732$	−2174.19	+	3765.81i	−0.109782	+	0.190148i
$733$	−13868.1	−	24020.2i	−0.698811	−	1.21038i	−0.968879	−	0.247535i	$-0.920380\pi$
$733$	−13868.1	−	24020.2i	−0.698811	−	1.21038i	0.270068	−	0.962841i	$-0.412954\pi$
$734$	7038.08			0.353924
$735$	−4370.28	−	2715.08i	−0.219320	−	0.136255i
$736$	1172.91			0.0587421
$737$	30017.1	+	51991.1i	1.50026	+	2.59853i
$738$	2096.16	−	3630.65i	0.104554	−	0.181092i
$739$	−19681.8	+	34089.9i	−0.979713	+	1.69691i	−0.316299	+	0.948659i	$0.602440\pi$
$739$	−19681.8	+	34089.9i	−0.979713	+	1.69691i	−0.663414	+	0.748253i	$0.730893\pi$
$740$	−1766.91	−	3060.37i	−0.0877740	−	0.152029i
$741$	−485.643			−0.0240763
$742$	−11040.7	+	38693.4i	−0.546251	+	1.91439i
$743$	−14854.4			−0.733451			−0.366725	−	0.930329i	$-0.619521\pi$
$743$	−14854.4			−0.733451			−0.366725	+	0.930329i	$0.619521\pi$
$744$	3417.89	+	5919.96i	0.168422	+	0.291715i
$745$	4928.29	−	8536.04i	0.242360	−	0.419780i
$746$	23559.1	−	40805.6i	1.15625	−	2.00268i
$747$	2670.98	+	4626.28i	0.130825	+	0.226595i
$748$	24521.9			1.19868
$749$	18873.2	−	4731.69i	0.920710	−	0.230831i
$750$	1379.98			0.0671863
$751$	−19784.3	−	34267.4i	−0.961302	−	1.66502i	−0.719237	−	0.694765i	$-0.755508\pi$
$751$	−19784.3	−	34267.4i	−0.961302	−	1.66502i	−0.242065	−	0.970260i	$-0.577825\pi$
$752$	22062.8	−	38213.9i	1.06988	−	1.85308i
$753$	−4361.42	+	7554.20i	−0.211074	+	0.365592i
$754$	−1753.37	−	3036.92i	−0.0846869	−	0.146682i
$755$	−808.806			−0.0389874
$756$	1927.66	+	1990.97i	0.0927361	+	0.0957815i
$757$	−8043.85			−0.386207			−0.193103	−	0.981178i	$-0.561855\pi$
$757$	−8043.85			−0.386207			−0.193103	+	0.981178i	$0.561855\pi$
$758$	10704.5	+	18540.7i	0.512934	+	0.888428i
$759$	536.663	−	929.528i	0.0256649	−	0.0444529i
$760$	532.595	−	922.482i	0.0254201	−	0.0440288i
$761$	−16112.9	−	27908.4i	−0.767532	−	1.32940i	−0.938897	−	0.344197i	$-0.888151\pi$
$761$	−16112.9	−	27908.4i	−0.767532	−	1.32940i	0.171365	−	0.985208i	$-0.445182\pi$
$762$	8391.49			0.398939
$763$	−2380.71	−	2458.89i	−0.112959	−	0.116668i
$764$	16721.4			0.791833
$765$	−1530.28	−	2650.53i	−0.0723235	−	0.125268i
$766$	20793.4	−	36015.3i	0.980806	−	1.69881i
$767$	1751.93	−	3034.44i	0.0824754	−	0.142852i
$768$	−8056.01	−	13953.4i	−0.378511	−	0.655599i
$769$	11196.5			0.525041			0.262521	−	0.964926i	$-0.415446\pi$
$769$	11196.5			0.525041			0.262521	+	0.964926i	$0.415446\pi$
$770$	−21504.1	+	5391.28i	−1.00643	+	0.252322i
$771$	11034.3			0.515421
$772$	−2180.54	−	3776.81i	−0.101657	−	0.176076i
$773$	10198.4	−	17664.1i	0.474528	−	0.821907i	−0.525046	−	0.851074i	$-0.675952\pi$
$773$	10198.4	−	17664.1i	0.474528	−	0.821907i	0.999575	+	0.0291664i	$0.00928527\pi$
$774$	−1516.75	+	2627.08i	−0.0704371	+	0.122001i
$775$	−3148.85	−	5453.96i	−0.145948	−	0.252790i
$776$	13901.7			0.643094
$777$	1944.20	−	6813.64i	0.0897654	−	0.314592i
$778$	4675.90			0.215474
$779$	1490.64	+	2581.86i	0.0685591	+	0.118748i
$780$	285.687	−	494.825i	0.0131144	−	0.0227148i
$781$	−16904.1	+	29278.7i	−0.774488	+	1.34145i
$782$	688.194	+	1191.99i	0.0314703	+	0.0545081i
$783$	−3743.36			−0.170851
$784$	859.985	−	26610.5i	0.0391757	−	1.21222i
$785$	−537.440			−0.0244357
$786$	55.8062	+	96.6592i	0.00253250	+	0.00438641i
$787$	−11037.5	+	19117.5i	−0.499928	+	0.865901i	−1.00000		8.30685e-5i	$-0.999974\pi$
$787$	−11037.5	+	19117.5i	−0.499928	+	0.865901i	0.500072	+	0.865984i	$0.333307\pi$
$788$	5569.49	−	9646.64i	0.251783	−	0.436100i
$789$	8804.62	+	15250.1i	0.397279	+	0.688107i
$790$	−2075.73			−0.0934826
$791$	−10672.7	+	37403.7i	−0.479745	+	1.68132i
$792$	−5296.24			−0.237619
$793$	898.825	+	1556.81i	0.0402500	+	0.0697150i
$794$	−20817.6	+	36057.1i	−0.930465	+	1.61161i
$795$	4427.99	−	7669.51i	0.197540	−	0.342150i
$796$	−7540.51	−	13060.6i	−0.335762	−	0.581557i
$797$	9131.50			0.405840			0.202920	−	0.979195i	$-0.434957\pi$
$797$	9131.50			0.405840			0.202920	+	0.979195i	$0.434957\pi$
$798$	−4670.94	+	1171.05i	−0.207205	+	0.0519482i
$799$	38662.8			1.71188
$800$	2666.04	+	4617.71i	0.117823	+	0.204076i
$801$	1090.46	−	1888.74i	0.0481019	−	0.0833150i
$802$	12504.6	−	21658.6i	0.550563	−	0.953604i
$803$	−34691.8	−	60087.9i	−1.52459	−	2.64067i
$804$	−15342.1			−0.672979
$805$	−354.228	−	365.861i	−0.0155092	−	0.0160185i
$806$	−6371.58			−0.278448
$807$	−691.143	−	1197.09i	−0.0301479	−	0.0522177i
$808$	−7760.19	+	13441.0i	−0.337874	+	0.585215i
$809$	9548.26	−	16538.1i	0.414956	−	0.718724i	−0.580468	−	0.814283i	$-0.697130\pi$
$809$	9548.26	−	16538.1i	0.414956	−	0.718724i	0.995424	+	0.0955587i	$0.0304638\pi$
$810$	−745.189	−	1290.70i	−0.0323250	−	0.0559886i
$811$	−9090.20			−0.393588			−0.196794	−	0.980445i	$-0.563053\pi$
$811$	−9090.20			−0.393588			−0.196794	+	0.980445i	$0.563053\pi$
$812$	−9898.41	−	10223.5i	−0.427791	−	0.441839i
$813$	−15945.0			−0.687843
$814$	−15265.8	−	26441.1i	−0.657329	−	1.13853i
$815$	5020.68	−	8696.07i	0.215787	−	0.373755i
$816$	7918.93	−	13716.0i	0.339728	−	0.588426i
$817$	−1078.60	−	1868.19i	−0.0461878	−	0.0799997i
$818$	29529.6			1.26220
$819$	1111.26	−	278.604i	0.0474123	−	0.0118867i
$820$	−3507.56			−0.149377
$821$	−10587.9	−	18338.8i	−0.450085	−	0.779571i	0.548305	−	0.836278i	$-0.315273\pi$
$821$	−10587.9	−	18338.8i	−0.450085	−	0.779571i	−0.998391	+	0.0567074i	$0.981940\pi$
$822$	−15410.1	+	26691.0i	−0.653878	+	1.13255i
$823$	−7456.89	+	12915.7i	−0.315833	+	0.547040i	−0.979614	−	0.200888i	$-0.935617\pi$
$823$	−7456.89	+	12915.7i	−0.315833	+	0.547040i	0.663781	+	0.747927i	$0.268951\pi$
$824$	−1300.96	−	2253.32i	−0.0550012	−	0.0952648i
$825$	4879.34			0.205911
$826$	9533.13	−	33409.8i	0.401574	−	1.40736i
$827$	−36795.0			−1.54714			−0.773571	−	0.633710i	$-0.781531\pi$
$827$	−36795.0			−1.54714			−0.773571	+	0.633710i	$0.781531\pi$
$828$	137.148	+	237.547i	0.00575629	+	0.00997019i
$829$	−6029.62	+	10443.6i	−0.252614	+	0.437541i	−0.964245	−	0.265013i	$-0.914624\pi$
$829$	−6029.62	+	10443.6i	−0.252614	+	0.437541i	0.711631	+	0.702554i	$0.247957\pi$
$830$	5460.59	−	9458.02i	0.228361	−	0.395533i
$831$	3570.88	+	6184.95i	0.149064	+	0.258187i
$832$	1126.47			0.0469389
$833$	20569.1	−	11005.5i	0.855556	−	0.457765i
$834$	5710.35			0.237090
$835$	1416.26	+	2453.04i	0.0586968	+	0.101666i
$836$	−4245.87	+	7354.07i	−0.175654	+	0.304241i
$837$	−3400.75	+	5890.28i	−0.140439	+	0.243247i
$838$	−4644.82	−	8045.07i	−0.191471	−	0.331638i
$839$	−30556.5			−1.25736			−0.628681	−	0.777663i	$-0.716405\pi$
$839$	−30556.5			−1.25736			−0.628681	+	0.777663i	$0.716405\pi$
$840$	−689.490	+	2416.39i	−0.0283210	+	0.0992540i
$841$	−5167.15			−0.211864
$842$	14433.0	+	24998.6i	0.590728	+	1.02317i
$843$	−2653.84	+	4596.59i	−0.108426	+	0.187800i
$844$	−1774.07	+	3072.78i	−0.0723531	+	0.125319i
$845$	5374.39	+	9308.73i	0.218799	+	0.378970i
$846$	18827.3			0.765125
$847$	−52123.9	+	13068.0i	−2.11452	+	0.530130i
$848$	45828.1			1.85583
$849$	−2185.39	−	3785.21i	−0.0883420	−	0.153013i
$850$	−3128.53	+	5418.77i	−0.126244	+	0.218662i
$851$	350.662	−	607.364i	0.0141252	−	0.0244655i
$852$	−4319.94	−	7482.35i	−0.173707	−	0.300870i
$853$	−42918.6			−1.72275			−0.861375	−	0.507969i	$-0.830396\pi$
$853$	−42918.6			−1.72275			−0.861375	+	0.507969i	$0.830396\pi$
$854$	12398.9	+	12806.1i	0.496818	+	0.513134i
$855$	1059.85			0.0423931
$856$	−4751.50	−	8229.84i	−0.189723	−	0.328610i
$857$	3089.36	−	5350.92i	0.123139	−	0.213284i	−0.797865	−	0.602837i	$-0.794037\pi$
$857$	3089.36	−	5350.92i	0.123139	−	0.213284i	0.921004	+	0.389553i	$0.127370\pi$
$858$	2468.29	−	4275.21i	0.0982123	−	0.170109i
$859$	−2545.27	−	4408.53i	−0.101098	−	0.175107i	0.811039	−	0.584992i	$-0.198902\pi$
$859$	−2545.27	−	4408.53i	−0.101098	−	0.175107i	−0.912137	+	0.409885i	$0.865569\pi$
$860$	2538.02			0.100635
$861$	−4892.08	−	5052.73i	−0.193637	−	0.199996i
$862$	25111.0			0.992211
$863$	−5734.20	−	9931.92i	−0.226181	−	0.391757i	0.730492	−	0.682921i	$-0.239291\pi$
$863$	−5734.20	−	9931.92i	−0.226181	−	0.391757i	−0.956673	+	0.291164i	$0.905957\pi$
$864$	2879.32	−	4987.12i	0.113375	−	0.196372i
$865$	1869.83	−	3238.65i	0.0734985	−	0.127303i
$866$	17082.0	+	29586.8i	0.670287	+	1.16097i
$867$	−861.880			−0.0337612
$868$	−25079.4	+	6287.64i	−0.980703	+	0.245871i
$869$	−7339.40			−0.286504
$870$	3826.48	+	6627.67i	0.149115	+	0.258275i
$871$	−3171.27	+	5492.80i	−0.123369	+	0.213681i
$872$	−835.794	+	1447.64i	−0.0324582	+	0.0562193i
$873$	6915.98	+	11978.8i	0.268122	+	0.464401i
$874$	−476.632			−0.0184466
$875$	635.215	−	2226.18i	0.0245419	−	0.0860098i
$876$	17731.4			0.683891
$877$	2773.13	+	4803.21i	0.106775	+	0.184940i	0.914462	−	0.404671i	$-0.132614\pi$
$877$	2773.13	+	4803.21i	0.106775	+	0.184940i	−0.807687	+	0.589612i	$0.799281\pi$
$878$	−1231.58	+	2133.16i	−0.0473392	+	0.0819939i
$879$	4115.33	−	7127.97i	0.157914	−	0.273516i
$880$	12624.9	+	21866.9i	0.483618	+	0.837651i
$881$	1259.32			0.0481586			0.0240793	−	0.999710i	$-0.492335\pi$
$881$	1259.32			0.0481586			0.0240793	+	0.999710i	$0.492335\pi$
$882$	10016.4	−	5359.26i	0.382391	−	0.204598i
$883$	−155.096			−0.00591100			−0.00295550	−	0.999996i	$-0.500941\pi$
$883$	−155.096			−0.00591100			−0.00295550	+	0.999996i	$0.500941\pi$
$884$	1295.36	+	2243.62i	0.0492845	+	0.0853633i
$885$	−3823.35	+	6622.24i	−0.145221	+	0.251530i
$886$	−17937.5	+	31068.6i	−0.680159	+	1.17807i
$887$	10447.4	+	18095.5i	0.395479	+	0.684990i	0.993162	−	0.116742i	$-0.0372451\pi$
$887$	10447.4	+	18095.5i	0.395479	+	0.684990i	−0.597683	+	0.801733i	$0.703912\pi$
$888$	−3460.63			−0.130778
$889$	3862.67	−	13537.1i	0.145725	−	0.510710i
$890$	−4458.72			−0.167929
$891$	−2634.84	−	4563.69i	−0.0990692	−	0.171593i
$892$	5459.61	−	9456.32i	0.204934	−	0.354956i
$893$	−6694.31	+	11594.9i	−0.250858	+	0.434499i
$894$	10881.5	+	18847.3i	0.407082	+	0.705087i
$895$	−20235.7			−0.755760
$896$	−19817.4	+	4968.41i	−0.738898	+	0.185249i
$897$	113.396			0.00422092
$898$	−9408.77	−	16296.5i	−0.349638	−	0.605590i
$899$	17462.6	−	30246.1i	0.647843	−	1.12210i
$900$	−623.473	+	1079.89i	−0.0230916	+	0.0399958i
$901$	20077.3	+	34774.8i	0.742365	+	1.28581i
$902$	−30304.8			−1.11867
$903$	3539.83	+	3656.08i	0.130452	+	0.134736i
$904$	18997.2			0.698936
$905$	7325.69	+	12688.5i	0.269077	+	0.466054i
$906$	892.908	−	1546.56i	0.0327427	−	0.0567120i
$907$	19876.3	−	34426.7i	0.727653	−	1.26033i	−0.230220	−	0.973139i	$-0.573945\pi$
$907$	19876.3	−	34426.7i	0.727653	−	1.26033i	0.957873	−	0.287193i	$-0.0927220\pi$
$908$	12735.7	+	22058.8i	0.465472	+	0.806221i
$909$	−15442.6			−0.563473
$910$	−1629.21	−	1682.72i	−0.0593493	−	0.0612983i
$911$	494.980			0.0180015			0.00900077	−	0.999959i	$-0.497135\pi$
$911$	494.980			0.0180015			0.00900077	+	0.999959i	$0.497135\pi$
$912$	2742.26	+	4749.74i	0.0995674	+	0.172456i
$913$	19307.6	−	33441.8i	0.699878	−	1.21222i
$914$	6399.78	−	11084.7i	0.231604	−	0.401149i
$915$	−1961.56	−	3397.53i	−0.0708713	−	0.122753i
$916$	−25634.0			−0.924640
$917$	181.618	−	45.5335i	0.00654043	−	0.00163975i
$918$	6757.62			0.242957
$919$	16893.8	+	29260.9i	0.606393	+	1.05030i	0.991830	+	0.127569i	$0.0407173\pi$
$919$	16893.8	+	29260.9i	0.606393	+	1.05030i	−0.385437	+	0.922734i	$0.625949\pi$
$920$	−124.359	+	215.395i	−0.00445650	+	0.00771889i
$921$	−5050.91	+	8748.43i	−0.180709	+	0.312997i
$922$	1834.33	+	3177.16i	0.0655212	+	0.113486i
$923$	−3571.78			−0.127375
$924$	5496.65	−	19263.6i	0.195700	−	0.685850i
$925$	3188.22			0.113328
$926$	23332.8	+	40413.6i	0.828039	+	1.43421i
$927$	1294.43	−	2242.02i	0.0458627	−	0.0794366i
$928$	−14785.1	+	25608.5i	−0.523000	+	0.905862i
$929$	19884.7	+	34441.3i	0.702256	+	1.21634i	0.967673	+	0.252210i	$0.0811573\pi$
$929$	19884.7	+	34441.3i	0.702256	+	1.21634i	−0.265416	+	0.964134i	$0.585509\pi$
$930$	13905.1			0.490286
$931$	−260.937	+	8074.19i	−0.00918569	+	0.284233i
$932$	−10510.9			−0.369416
$933$	9300.44	+	16108.8i	0.326348	+	0.565251i
$934$	123.318	−	213.593i	0.00432022	−	0.00748284i
$935$	−11061.9	+	19159.7i	−0.386912	+	0.670150i
$936$	−279.771	−	484.577i	−0.00976987	−	0.0169219i
$937$	16823.9			0.586568			0.293284	−	0.956025i	$-0.405252\pi$
$937$	16823.9			0.586568			0.293284	+	0.956025i	$0.405252\pi$
$938$	−17256.4	+	60477.0i	−0.600685	+	2.10516i
$939$	31019.8			1.07805
$940$	−7876.07	−	13641.8i	−0.273286	−	0.473346i
$941$	307.746	−	533.031i	0.0106612	−	0.0184658i	−0.860646	−	0.509204i	$-0.829940\pi$
$941$	307.746	−	533.031i	0.0106612	−	0.0184658i	0.871307	+	0.490739i	$0.163273\pi$
$942$	593.324	−	1027.67i	0.0205218	−	0.0355448i
$943$	−348.057	−	602.852i	−0.0120194	−	0.0208182i
$944$	−39570.3			−1.36430
$945$	−2425.18	+	608.015i	−0.0834826	+	0.0209299i
$946$	21928.1			0.753640
$947$	−21017.8	−	36403.9i	−0.721211	−	1.24917i	−0.960515	−	0.278230i	$-0.910252\pi$
$947$	−21017.8	−	36403.9i	−0.721211	−	1.24917i	0.239303	−	0.970945i	$-0.423081\pi$
$948$	937.815	−	1624.34i	0.0321295	−	0.0556500i
$949$	3665.14	−	6348.21i	0.125369	−	0.217146i
$950$	−1083.38	−	1876.48i	−0.0369996	−	0.0640852i
$951$	8931.93			0.304561
$952$	−7925.32	−	8185.58i	−0.269812	−	0.278673i
$953$	−16830.2			−0.572070			−0.286035	−	0.958219i	$-0.592337\pi$
$953$	−16830.2			−0.572070			−0.286035	+	0.958219i	$0.592337\pi$
$954$	9776.86	+	16934.0i	0.331800	+	0.574695i
$955$	−7543.07	+	13065.0i	−0.255590	+	0.442694i
$956$	−20000.8	+	34642.4i	−0.676645	+	1.17198i
$957$	13529.7	+	23434.2i	0.457005	+	0.791556i
$958$	57648.1			1.94418
$959$	35964.5	+	37145.6i	1.21101	+	1.25078i
$960$	−2458.36			−0.0826491
$961$	−16833.3	−	29156.0i	−0.565045	−	0.978686i
$962$	1612.81	−	2793.47i	0.0540531	−	0.0936228i
$963$	4727.68	−	8188.58i	0.158201	−	0.274012i
$964$	−2660.27	−	4607.71i	−0.0888811	−	0.153947i
$965$	3934.59			0.131253
$966$	1090.64	−	273.435i	0.0363260	−	0.00910726i
$967$	−3695.45			−0.122893			−0.0614466	−	0.998110i	$-0.519571\pi$
$967$	−3695.45			−0.122893			−0.0614466	+	0.998110i	$0.519571\pi$
$968$	13122.7	+	22729.2i	0.435722	+	0.754693i
$969$	−2402.77	+	4161.72i	−0.0796574	+	0.137971i
$970$	14139.1	−	24489.7i	0.468020	−	0.810635i
$971$	−11182.2	−	19368.1i	−0.369571	−	0.640115i	0.619928	−	0.784659i	$-0.287162\pi$
$971$	−11182.2	−	19368.1i	−0.369571	−	0.640115i	−0.989498	+	0.144544i	$0.953829\pi$
$972$	1346.70			0.0444398
$973$	2628.52	−	9211.93i	0.0866048	−	0.303516i
$974$	−43146.8			−1.41942
$975$	257.748	+	446.433i	0.00846620	+	0.0146639i
$976$	10150.7	−	17581.6i	0.332907	−	0.576611i
$977$	17216.9	−	29820.6i	0.563786	−	0.976505i	−0.433376	−	0.901213i	$-0.642678\pi$
$977$	17216.9	−	29820.6i	0.563786	−	0.976505i	0.997162	−	0.0752921i	$-0.0239889\pi$
$978$	11085.5	+	19200.6i	0.362449	+	0.627779i
$979$	−15765.2			−0.514665
$980$	−8073.35	−	5015.64i	−0.263157	−	0.163489i
$981$	−1663.21			−0.0541306
$982$	−19474.6	−	33730.9i	−0.632849	−	1.09613i
$983$	−3696.27	+	6402.13i	−0.119932	+	0.207728i	−0.919740	−	0.392527i	$-0.871601\pi$
$983$	−3696.27	+	6402.13i	−0.119932	+	0.207728i	0.799809	+	0.600255i	$0.204934\pi$
$984$	−1717.46	+	2974.73i	−0.0556409	+	0.0963729i
$985$	5024.81	+	8703.23i	0.162542	+	0.281531i
$986$	−34699.9			−1.12076
$987$	8666.35	−	30372.2i	0.279486	−	0.979490i
$988$	−897.142			−0.0288886
$989$	251.849	+	436.215i	0.00809739	+	0.0140251i
$990$	−5386.71	+	9330.06i	−0.172930	+	0.299524i
$991$	−20793.5	+	36015.4i	−0.666526	+	1.15446i	0.312344	+	0.949969i	$0.398886\pi$
$991$	−20793.5	+	36015.4i	−0.666526	+	1.15446i	−0.978869	+	0.204487i	$0.934447\pi$
$992$	26863.8	+	46529.5i	0.859805	+	1.48923i
$993$	−20271.1			−0.647818
$994$	−34353.6	+	8612.77i	−1.09621	+	0.274829i
$995$	13606.2			0.433512
$996$	4934.18	+	8546.26i	0.156973	+	0.271886i
$997$	5336.16	−	9242.51i	0.169507	−	0.293594i	−0.768740	−	0.639561i	$-0.779116\pi$
$997$	5336.16	−	9242.51i	0.169507	−	0.293594i	0.938246	+	0.345968i	$0.112449\pi$
$998$	−19215.0	+	33281.4i	−0.609460	+	1.05562i
$999$	−1721.64	−	2981.96i	−0.0545247	−	0.0944396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.i.d.46.2	yes	10
3.2	odd	2		315.4.j.h.46.4		10
7.2	even	3	inner	105.4.i.d.16.2	✓	10
7.3	odd	6		735.4.a.z.1.4		5
7.4	even	3		735.4.a.ba.1.4		5
21.2	odd	6		315.4.j.h.226.4		10
21.11	odd	6		2205.4.a.br.1.2		5
21.17	even	6		2205.4.a.bs.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.i.d.16.2	✓	10	7.2	even	3	inner
105.4.i.d.46.2	yes	10	1.1	even	1	trivial
315.4.j.h.46.4		10	3.2	odd	2
315.4.j.h.226.4		10	21.2	odd	6
735.4.a.z.1.4		5	7.3	odd	6
735.4.a.ba.1.4		5	7.4	even	3
2205.4.a.br.1.2		5	21.11	odd	6
2205.4.a.bs.1.2		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)

\(f(q)\)	\(=\)	\(q+(-1.83997 - 3.18692i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.77099 + 4.79950i) q^{4} +(-2.50000 - 4.33013i) q^{5} +11.0398 q^{6} +(5.08172 - 17.8094i) q^{7} -9.04535 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.83997 - 3.18692i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.77099 + 4.79950i) q^{4} +(-2.50000 - 4.33013i) q^{5} +11.0398 q^{6} +(5.08172 - 17.8094i) q^{7} -9.04535 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-9.19986 + 15.9346i) q^{10} +(-32.5290 + 56.3418i) q^{11} +(-8.31298 - 14.3985i) q^{12} -6.87328 q^{13} +(-66.1076 + 16.5738i) q^{14} +15.0000 q^{15} +(38.8111 + 67.2229i) q^{16} +(-34.0063 + 58.9006i) q^{17} +(-16.5597 + 28.6823i) q^{18} +(-11.7761 - 20.3968i) q^{19} +27.7099 q^{20} +(38.6477 + 39.9169i) q^{21} +239.409 q^{22} +(2.74967 + 4.76257i) q^{23} +(13.5680 - 23.5005i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(12.6467 + 21.9046i) q^{26} +27.0000 q^{27} +(71.3950 + 73.7396i) q^{28} -138.643 q^{29} +(-27.5996 - 47.8039i) q^{30} +(-125.954 + 218.158i) q^{31} +(106.641 - 184.708i) q^{32} +(-97.5869 - 169.025i) q^{33} +250.282 q^{34} +(-89.8214 + 22.5191i) q^{35} +49.8779 q^{36} +(-63.7644 - 110.443i) q^{37} +(-43.3354 + 75.0591i) q^{38} +(10.3099 - 17.8573i) q^{39} +(22.6134 + 39.1675i) q^{40} -126.581 q^{41} +(56.1014 - 196.613i) q^{42} +91.5924 q^{43} +(-180.275 - 312.245i) q^{44} +(-22.5000 + 38.9711i) q^{45} +(10.1186 - 17.5260i) q^{46} +(-284.233 - 492.306i) q^{47} -232.867 q^{48} +(-291.352 - 181.005i) q^{49} +91.9986 q^{50} +(-102.019 - 176.702i) q^{51} +(19.0458 - 32.9883i) q^{52} +(295.199 - 511.300i) q^{53} +(-49.6792 - 86.0470i) q^{54} +325.290 q^{55} +(-45.9660 + 161.093i) q^{56} +70.6566 q^{57} +(255.099 + 441.844i) q^{58} +(-254.890 + 441.483i) q^{59} +(-41.5649 + 71.9925i) q^{60} +(-130.771 - 226.502i) q^{61} +927.006 q^{62} +(-161.679 + 40.5344i) q^{63} -163.890 q^{64} +(17.1832 + 29.7622i) q^{65} +(-359.114 + 622.004i) q^{66} +(461.391 - 799.152i) q^{67} +(-188.462 - 326.426i) q^{68} -16.4980 q^{69} +(237.036 + 244.820i) q^{70} +519.662 q^{71} +(40.7041 + 70.5015i) q^{72} +(-533.244 + 923.606i) q^{73} +(-234.649 + 406.424i) q^{74} +(-37.5000 - 64.9519i) q^{75} +130.526 q^{76} +(838.113 + 865.636i) q^{77} -75.8799 q^{78} +(56.4067 + 97.6992i) q^{79} +(194.056 - 336.114i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(232.906 + 403.405i) q^{82} -593.552 q^{83} +(-298.674 + 74.8803i) q^{84} +340.063 q^{85} +(-168.527 - 291.898i) q^{86} +(207.964 - 360.205i) q^{87} +(294.236 - 509.631i) q^{88} +(121.163 + 209.860i) q^{89} +165.597 q^{90} +(-34.9281 + 122.409i) q^{91} -30.4773 q^{92} +(-377.862 - 654.475i) q^{93} +(-1045.96 + 1811.66i) q^{94} +(-58.8805 + 101.984i) q^{95} +(319.924 + 554.125i) q^{96} -1536.88 q^{97} +(-40.7705 + 1261.56i) q^{98} +585.521 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more