LMFDB - Embedded newform 65.4.e.a.16.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,4,Mod(16,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("65.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	65.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:	$3.83512415037$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 45 x^{12} - 52 x^{11} + 1311 x^{10} - 1336 x^{9} + 20343 x^{8} - 11166 x^{7} + \cdots + 1157776 $ x^14 - 2x^13 + 45x^12 - 52x^11 + 1311x^10 - 1336x^9 + 20343x^8 - 11166x^7 + 216447x^6 - 107836x^5 + 1201133x^4 + 4392x^3 + 3890980x^2 - 1936800*x + 1157776
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.6
Root			$-1.78789 - 3.09671i$ of defining polynomial
Character	$\chi$	$=$	65.16
Dual form			65.4.e.a.61.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.78789 + 3.09671i) q^{2} +(4.37841 + 7.58363i) q^{3} +(-2.39307 + 4.14492i) q^{4} -5.00000 q^{5} +(-15.6562 + 27.1173i) q^{6} +(11.1225 - 19.2648i) q^{7} +11.4920 q^{8} +(-24.8410 + 43.0258i) q^{9} +O(q^{10})$	\(q+(1.78789 + 3.09671i) q^{2} +(4.37841 + 7.58363i) q^{3} +(-2.39307 + 4.14492i) q^{4} -5.00000 q^{5} +(-15.6562 + 27.1173i) q^{6} +(11.1225 - 19.2648i) q^{7} +11.4920 q^{8} +(-24.8410 + 43.0258i) q^{9} +(-8.93943 - 15.4835i) q^{10} +(-28.5093 - 49.3796i) q^{11} -41.9114 q^{12} +(31.1719 - 35.0045i) q^{13} +79.5433 q^{14} +(-21.8921 - 37.9182i) q^{15} +(39.6910 + 68.7468i) q^{16} +(-56.4039 + 97.6945i) q^{17} -177.651 q^{18} +(-28.4070 + 49.2023i) q^{19} +(11.9654 - 20.7246i) q^{20} +194.796 q^{21} +(101.943 - 176.570i) q^{22} +(-25.5700 - 44.2885i) q^{23} +(50.3168 + 87.1512i) q^{24} +25.0000 q^{25} +(164.130 + 33.9461i) q^{26} -198.622 q^{27} +(53.2341 + 92.2041i) q^{28} +(-62.1938 - 107.723i) q^{29} +(78.2810 - 135.587i) q^{30} +132.865 q^{31} +(-95.9578 + 166.204i) q^{32} +(249.651 - 432.408i) q^{33} -403.375 q^{34} +(-55.6127 + 96.3240i) q^{35} +(-118.892 - 205.928i) q^{36} +(71.0005 + 122.976i) q^{37} -203.154 q^{38} +(401.944 + 83.1318i) q^{39} -57.4601 q^{40} +(-126.432 - 218.987i) q^{41} +(348.273 + 603.227i) q^{42} +(67.0129 - 116.070i) q^{43} +272.899 q^{44} +(124.205 - 215.129i) q^{45} +(91.4325 - 158.366i) q^{46} +8.43814 q^{47} +(-347.567 + 602.004i) q^{48} +(-75.9218 - 131.500i) q^{49} +(44.6971 + 77.4177i) q^{50} -987.838 q^{51} +(70.4944 + 212.973i) q^{52} -337.313 q^{53} +(-355.113 - 615.073i) q^{54} +(142.547 + 246.898i) q^{55} +(127.820 - 221.391i) q^{56} -497.509 q^{57} +(222.391 - 385.192i) q^{58} +(-434.794 + 753.086i) q^{59} +209.557 q^{60} +(170.119 - 294.654i) q^{61} +(237.547 + 411.444i) q^{62} +(552.589 + 957.113i) q^{63} -51.1908 q^{64} +(-155.859 + 175.023i) q^{65} +1785.39 q^{66} +(-217.422 - 376.587i) q^{67} +(-269.957 - 467.580i) q^{68} +(223.912 - 387.827i) q^{69} -397.717 q^{70} +(23.9292 - 41.4466i) q^{71} +(-285.473 + 494.453i) q^{72} -171.520 q^{73} +(-253.882 + 439.736i) q^{74} +(109.460 + 189.591i) q^{75} +(-135.960 - 235.489i) q^{76} -1268.38 q^{77} +(461.196 + 1393.34i) q^{78} -332.117 q^{79} +(-198.455 - 343.734i) q^{80} +(-198.941 - 344.576i) q^{81} +(452.094 - 783.049i) q^{82} +1239.84 q^{83} +(-466.161 + 807.415i) q^{84} +(282.020 - 488.472i) q^{85} +479.246 q^{86} +(544.620 - 943.309i) q^{87} +(-327.630 - 567.471i) q^{88} +(-141.050 - 244.306i) q^{89} +888.256 q^{90} +(-327.645 - 989.859i) q^{91} +244.763 q^{92} +(581.737 + 1007.60i) q^{93} +(15.0864 + 26.1305i) q^{94} +(142.035 - 246.011i) q^{95} -1680.57 q^{96} +(9.26632 - 16.0497i) q^{97} +(271.479 - 470.215i) q^{98} +2832.80 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 4 q^{3} - 30 q^{4} - 70 q^{5} - 23 q^{6} - 7 q^{7} + 42 q^{8} - 87 q^{9}+O(q^{10}) $ 14 * q - 2 * q^2 + 4 * q^3 - 30 * q^4 - 70 * q^5 - 23 * q^6 - 7 * q^7 + 42 * q^8 - 87 * q^9	\( 14 q - 2 q^{2} + 4 q^{3} - 30 q^{4} - 70 q^{5} - 23 q^{6} - 7 q^{7} + 42 q^{8} - 87 q^{9} + 10 q^{10} - 87 q^{11} - 158 q^{12} + 123 q^{13} + 132 q^{14} - 20 q^{15} + 134 q^{16} + 114 q^{17} + 414 q^{18} - 245 q^{19} + 150 q^{20} - 76 q^{21} - 338 q^{22} + 74 q^{23} - 334 q^{24} + 350 q^{25} + 243 q^{26} - 884 q^{27} - 230 q^{28} + 88 q^{29} + 115 q^{30} + 1000 q^{31} - 80 q^{32} + 194 q^{33} + 854 q^{34} + 35 q^{35} - 425 q^{36} - 633 q^{37} - 596 q^{38} + 970 q^{39} - 210 q^{40} - 162 q^{41} + 1439 q^{42} + 280 q^{43} + 440 q^{44} + 435 q^{45} + 11 q^{46} + 950 q^{47} - 2281 q^{48} - 1694 q^{49} - 50 q^{50} - 860 q^{51} - 956 q^{52} - 1206 q^{53} - 51 q^{54} + 435 q^{55} + 1277 q^{56} + 916 q^{57} + 1213 q^{58} - 1410 q^{59} + 790 q^{60} - 412 q^{61} + 56 q^{62} - 1241 q^{63} - 2358 q^{64} - 615 q^{65} + 4346 q^{66} - 1398 q^{67} + 493 q^{68} - 1080 q^{69} - 660 q^{70} + 584 q^{71} - 1545 q^{72} + 5076 q^{73} - 3840 q^{74} + 100 q^{75} - 3292 q^{76} - 5506 q^{77} + 1179 q^{78} + 928 q^{79} - 670 q^{80} + 473 q^{81} + 1583 q^{82} + 932 q^{83} + 3081 q^{84} - 570 q^{85} + 9858 q^{86} + 282 q^{87} - 3389 q^{88} - 443 q^{89} - 2070 q^{90} + 487 q^{91} + 6182 q^{92} + 2116 q^{93} - 2017 q^{94} + 1225 q^{95} + 954 q^{96} + 1870 q^{97} - 1364 q^{98} + 11378 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 + 4 * q^3 - 30 * q^4 - 70 * q^5 - 23 * q^6 - 7 * q^7 + 42 * q^8 - 87 * q^9 + 10 * q^10 - 87 * q^11 - 158 * q^12 + 123 * q^13 + 132 * q^14 - 20 * q^15 + 134 * q^16 + 114 * q^17 + 414 * q^18 - 245 * q^19 + 150 * q^20 - 76 * q^21 - 338 * q^22 + 74 * q^23 - 334 * q^24 + 350 * q^25 + 243 * q^26 - 884 * q^27 - 230 * q^28 + 88 * q^29 + 115 * q^30 + 1000 * q^31 - 80 * q^32 + 194 * q^33 + 854 * q^34 + 35 * q^35 - 425 * q^36 - 633 * q^37 - 596 * q^38 + 970 * q^39 - 210 * q^40 - 162 * q^41 + 1439 * q^42 + 280 * q^43 + 440 * q^44 + 435 * q^45 + 11 * q^46 + 950 * q^47 - 2281 * q^48 - 1694 * q^49 - 50 * q^50 - 860 * q^51 - 956 * q^52 - 1206 * q^53 - 51 * q^54 + 435 * q^55 + 1277 * q^56 + 916 * q^57 + 1213 * q^58 - 1410 * q^59 + 790 * q^60 - 412 * q^61 + 56 * q^62 - 1241 * q^63 - 2358 * q^64 - 615 * q^65 + 4346 * q^66 - 1398 * q^67 + 493 * q^68 - 1080 * q^69 - 660 * q^70 + 584 * q^71 - 1545 * q^72 + 5076 * q^73 - 3840 * q^74 + 100 * q^75 - 3292 * q^76 - 5506 * q^77 + 1179 * q^78 + 928 * q^79 - 670 * q^80 + 473 * q^81 + 1583 * q^82 + 932 * q^83 + 3081 * q^84 - 570 * q^85 + 9858 * q^86 + 282 * q^87 - 3389 * q^88 - 443 * q^89 - 2070 * q^90 + 487 * q^91 + 6182 * q^92 + 2116 * q^93 - 2017 * q^94 + 1225 * q^95 + 954 * q^96 + 1870 * q^97 - 1364 * q^98 + 11378 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.78789	+	3.09671i	0.632113	+	1.09485i	0.987119	+	0.159988i	$0.0511455\pi$
$2$	1.78789	+	3.09671i	0.632113	+	1.09485i	−0.355006	+	0.934864i	$0.615521\pi$
$3$	4.37841	+	7.58363i	0.842626	+	1.45947i	0.887667	+	0.460485i	$0.152325\pi$
$3$	4.37841	+	7.58363i	0.842626	+	1.45947i	−0.0450418	+	0.998985i	$0.514342\pi$
$4$	−2.39307	+	4.14492i	−0.299134	+	0.518115i
$5$	−5.00000			−0.447214
$5$	−5.00000			−0.447214
$6$	−15.6562	+	27.1173i	−1.06527	+	1.84510i
$7$	11.1225	−	19.2648i	0.600561	−	1.04020i	−0.392176	−	0.919890i	$-0.628277\pi$
$7$	11.1225	−	19.2648i	0.600561	−	1.04020i	0.992736	−	0.120311i	$-0.0383892\pi$
$8$	11.4920			0.507880
$9$	−24.8410	+	43.0258i	−0.920036	+	1.59355i
$10$	−8.93943	−	15.4835i	−0.282690	−	0.489633i
$11$	−28.5093	−	49.3796i	−0.781444	−	1.35350i	−0.931101	−	0.364763i	$-0.881150\pi$
$11$	−28.5093	−	49.3796i	−0.781444	−	1.35350i	0.149657	−	0.988738i	$-0.452183\pi$
$12$	−41.9114			−1.00823
$13$	31.1719	−	35.0045i	0.665040	−	0.746808i
$13$	31.1719	−	35.0045i	0.665040	−	0.746808i
$14$	79.5433			1.51849
$15$	−21.8921	−	37.9182i	−0.376834	−	0.652695i
$16$	39.6910	+	68.7468i	0.620172	+	1.07417i
$17$	−56.4039	+	97.6945i	−0.804704	+	1.39379i	0.111787	+	0.993732i	$0.464342\pi$
$17$	−56.4039	+	97.6945i	−0.804704	+	1.39379i	−0.916491	+	0.400055i	$0.868991\pi$
$18$	−177.651			−2.32627
$19$	−28.4070	+	49.2023i	−0.343000	+	0.594094i	−0.984988	−	0.172621i	$-0.944776\pi$
$19$	−28.4070	+	49.2023i	−0.343000	+	0.594094i	0.641988	+	0.766715i	$0.278110\pi$
$20$	11.9654	−	20.7246i	0.133777	−	0.231708i
$21$	194.796			2.02419
$22$	101.943	−	176.570i	0.987922	−	1.71113i
$23$	−25.5700	−	44.2885i	−0.231814	−	0.401513i	0.726528	−	0.687137i	$-0.241133\pi$
$23$	−25.5700	−	44.2885i	−0.231814	−	0.401513i	−0.958342	+	0.285624i	$0.907799\pi$
$24$	50.3168	+	87.1512i	0.427953	+	0.741236i
$25$	25.0000			0.200000
$26$	164.130	+	33.9461i	1.23802	+	0.256053i
$27$	−198.622			−1.41573
$28$	53.2341	+	92.2041i	0.359296	+	0.622319i
$29$	−62.1938	−	107.723i	−0.398245	−	0.689780i	0.595265	−	0.803530i	$-0.297047\pi$
$29$	−62.1938	−	107.723i	−0.398245	−	0.689780i	−0.993509	+	0.113750i	$0.963714\pi$
$30$	78.2810	−	135.587i	0.476403	−	0.825154i
$31$	132.865			0.769782			0.384891	−	0.922962i	$-0.374239\pi$
$31$	132.865			0.769782			0.384891	+	0.922962i	$0.374239\pi$
$32$	−95.9578	+	166.204i	−0.530097	+	0.918155i
$33$	249.651	−	432.408i	1.31693	−	2.28099i
$34$	−403.375			−2.03465
$35$	−55.6127	+	96.3240i	−0.268579	+	0.465192i
$36$	−118.892	−	205.928i	−0.550428	−	0.953369i
$37$	71.0005	+	122.976i	0.315470	+	0.546411i	0.979537	−	0.201262i	$-0.0645043\pi$
$37$	71.0005	+	122.976i	0.315470	+	0.546411i	−0.664067	+	0.747673i	$0.731171\pi$
$38$	−203.154			−0.867260
$39$	401.944	+	83.1318i	1.65032	+	0.341327i
$40$	−57.4601			−0.227131
$41$	−126.432	−	218.987i	−0.481596	−	0.834148i	0.518181	−	0.855271i	$-0.326609\pi$
$41$	−126.432	−	218.987i	−0.481596	−	0.834148i	−0.999777	+	0.0211225i	$0.993276\pi$
$42$	348.273	+	603.227i	1.27952	+	2.21619i
$43$	67.0129	−	116.070i	0.237660	−	0.411639i	−0.722382	−	0.691494i	$-0.756953\pi$
$43$	67.0129	−	116.070i	0.237660	−	0.411639i	0.960042	+	0.279855i	$0.0902863\pi$
$44$	272.899			0.935026
$45$	124.205	−	215.129i	0.411452	−	0.712657i
$46$	91.4325	−	158.366i	0.293065	−	0.507603i
$47$	8.43814			0.0261879			0.0130939	−	0.999914i	$-0.495832\pi$
$47$	8.43814			0.0261879			0.0130939	+	0.999914i	$0.495832\pi$
$48$	−347.567	+	602.004i	−1.04515	+	1.81024i
$49$	−75.9218	−	131.500i	−0.221346	−	0.383383i
$50$	44.6971	+	77.4177i	0.126423	+	0.218970i
$51$	−987.838			−2.71226
$52$	70.4944	+	212.973i	0.187996	+	0.567963i
$53$	−337.313			−0.874216			−0.437108	−	0.899409i	$-0.643997\pi$
$53$	−337.313			−0.874216			−0.437108	+	0.899409i	$0.643997\pi$
$54$	−355.113	−	615.073i	−0.894902	−	1.55002i
$55$	142.547	+	246.898i	0.349472	+	0.605304i
$56$	127.820	−	221.391i	0.305013	−	0.528298i
$57$	−497.509			−1.15608
$58$	222.391	−	385.192i	0.503471	−	0.872038i
$59$	−434.794	+	753.086i	−0.959414	+	1.66175i	−0.235485	+	0.971878i	$0.575668\pi$
$59$	−434.794	+	753.086i	−0.959414	+	1.66175i	−0.723928	+	0.689875i	$0.757665\pi$
$60$	209.557			0.450895
$61$	170.119	−	294.654i	0.357073	−	0.618469i	−0.630397	−	0.776273i	$-0.717108\pi$
$61$	170.119	−	294.654i	0.357073	−	0.618469i	0.987471	+	0.157803i	$0.0504412\pi$
$62$	237.547	+	411.444i	0.486589	+	0.842797i
$63$	552.589	+	957.113i	1.10507	+	1.91405i
$64$	−51.1908			−0.0999821
$65$	−155.859	+	175.023i	−0.297415	+	0.333983i
$66$	1785.39			3.32979
$67$	−217.422	−	376.587i	−0.396453	−	0.686677i	0.596832	−	0.802366i	$-0.296426\pi$
$67$	−217.422	−	376.587i	−0.396453	−	0.686677i	−0.993286	+	0.115689i	$0.963092\pi$
$68$	−269.957	−	467.580i	−0.481428	−	0.833858i
$69$	223.912	−	387.827i	0.390664	−	0.676650i
$70$	−397.717			−0.679089
$71$	23.9292	−	41.4466i	0.0399982	−	0.0692790i	−0.845333	−	0.534239i	$-0.820598\pi$
$71$	23.9292	−	41.4466i	0.0399982	−	0.0692790i	0.885331	+	0.464960i	$0.153931\pi$
$72$	−285.473	+	494.453i	−0.467268	+	0.809332i
$73$	−171.520			−0.274998			−0.137499	−	0.990502i	$-0.543906\pi$
$73$	−171.520			−0.274998			−0.137499	+	0.990502i	$0.543906\pi$
$74$	−253.882	+	439.736i	−0.398826	+	0.690787i
$75$	109.460	+	189.591i	0.168525	+	0.291894i
$76$	−135.960	−	235.489i	−0.205206	−	0.355427i
$77$	−1268.38			−1.87722
$78$	461.196	+	1393.34i	0.669489	+	2.02262i
$79$	−332.117			−0.472988			−0.236494	−	0.971633i	$-0.575998\pi$
$79$	−332.117			−0.472988			−0.236494	+	0.971633i	$0.575998\pi$
$80$	−198.455	−	343.734i	−0.277349	−	0.480383i
$81$	−198.941	−	344.576i	−0.272896	−	0.472669i
$82$	452.094	−	783.049i	0.608846	−	1.05455i
$83$	1239.84			1.63965			0.819823	−	0.572617i	$-0.194072\pi$
$83$	1239.84			1.63965			0.819823	+	0.572617i	$0.194072\pi$
$84$	−466.161	+	807.415i	−0.605504	+	1.04876i
$85$	282.020	−	488.472i	0.359874	−	0.623321i
$86$	479.246			0.600912
$87$	544.620	−	943.309i	0.671142	−	1.16245i
$88$	−327.630	−	567.471i	−0.396880	−	0.687416i
$89$	−141.050	−	244.306i	−0.167992	−	0.290971i	0.769722	−	0.638380i	$-0.220395\pi$
$89$	−141.050	−	244.306i	−0.167992	−	0.290971i	−0.937714	+	0.347409i	$0.887062\pi$
$90$	888.256			1.04034
$91$	−327.645	−	989.859i	−0.377434	−	1.14028i
$92$	244.763			0.277373
$93$	581.737	+	1007.60i	0.648638	+	1.12347i
$94$	15.0864	+	26.1305i	0.0165537	+	0.0286718i
$95$	142.035	−	246.011i	0.153394	−	0.265687i
$96$	−1680.57			−1.78669
$97$	9.26632	−	16.0497i	0.00969951	−	0.0168000i	−0.861135	−	0.508376i	$-0.830246\pi$
$97$	9.26632	−	16.0497i	0.00969951	−	0.0168000i	0.870834	+	0.491576i	$0.163579\pi$
$98$	271.479	−	470.215i	0.279832	−	0.484683i
$99$	2832.80			2.87583
$100$	−59.8268	+	103.623i	−0.0598268	+	0.103623i
$101$	507.777	+	879.496i	0.500255	+	0.866467i	1.00000		0.000294400i	$9.37105e-5\pi$
$101$	507.777	+	879.496i	0.500255	+	0.866467i	−0.499745	+	0.866173i	$0.666573\pi$
$102$	−1766.14	−	3059.05i	−1.71445	−	2.96952i
$103$	−1408.75			−1.34766			−0.673829	−	0.738888i	$-0.735351\pi$
$103$	−1408.75			−1.34766			−0.673829	+	0.738888i	$0.735351\pi$
$104$	358.228	−	402.272i	0.337761	−	0.379289i
$105$	−973.981			−0.905246
$106$	−603.077	−	1044.56i	−0.552604	−	0.957137i
$107$	−176.543	−	305.781i	−0.159505	−	0.276271i	0.775185	−	0.631734i	$-0.217656\pi$
$107$	−176.543	−	305.781i	−0.159505	−	0.276271i	−0.934690	+	0.355463i	$0.884323\pi$
$108$	475.316	−	823.271i	0.423493	−	0.733512i
$109$	100.060			0.0879271			0.0439635	−	0.999033i	$-0.486001\pi$
$109$	100.060			0.0879271			0.0439635	+	0.999033i	$0.486001\pi$
$110$	−509.714	+	882.851i	−0.441812	+	0.765241i
$111$	−621.739	+	1076.88i	−0.531647	+	0.920840i
$112$	1765.86			1.48980
$113$	150.098	−	259.977i	0.124956	−	0.216430i	−0.796760	−	0.604296i	$-0.793454\pi$
$113$	150.098	−	259.977i	0.124956	−	0.216430i	0.921716	+	0.387866i	$0.126788\pi$
$114$	−889.490	−	1540.64i	−0.730775	−	1.26574i
$115$	127.850	+	221.443i	0.103670	+	0.179562i
$116$	595.336			0.476514
$117$	731.758	+	2210.74i	0.578214	+	1.74686i
$118$	−3109.45			−2.42583
$119$	1254.71	+	2173.22i	0.966547	+	1.67411i
$120$	−251.584	−	435.756i	−0.191386	−	0.331491i
$121$	−960.063	+	1662.88i	−0.721309	+	1.24934i
$122$	1216.61			0.902843
$123$	1107.15	−	1917.63i	0.811610	−	1.40575i
$124$	−317.955	+	550.714i	−0.230268	+	0.398836i
$125$	−125.000			−0.0894427
$126$	−1975.93	+	3422.42i	−1.39706	+	2.41979i
$127$	−267.809	−	463.858i	−0.187119	−	0.324100i	0.757169	−	0.653219i	$-0.226582\pi$
$127$	−267.809	−	463.858i	−0.187119	−	0.324100i	−0.944289	+	0.329118i	$0.893248\pi$
$128$	676.139	+	1171.11i	0.466897	+	0.808690i
$129$	1173.64			0.801034
$130$	−820.652	−	169.731i	−0.553661	−	0.114510i
$131$	2514.14			1.67680			0.838401	−	0.545054i	$-0.183491\pi$
$131$	2514.14			1.67680			0.838401	+	0.545054i	$0.183491\pi$
$132$	1194.87	+	2069.57i	0.787877	+	1.36464i
$133$	631.915	+	1094.51i	0.411985	+	0.713579i
$134$	777.453	−	1346.59i	0.501207	−	0.868115i
$135$	993.108			0.633134
$136$	−648.195	+	1122.71i	−0.408693	+	0.707877i
$137$	−779.278	+	1349.75i	−0.485972	+	0.841729i	−0.999870	−	0.0161228i	$-0.994868\pi$
$137$	−779.278	+	1349.75i	−0.485972	+	0.841729i	0.513898	+	0.857851i	$0.328201\pi$
$138$	1601.32			0.987776
$139$	−781.896	+	1354.28i	−0.477119	+	0.826395i	−0.999656	−	0.0262220i	$-0.991652\pi$
$139$	−781.896	+	1354.28i	−0.477119	+	0.826395i	0.522537	+	0.852617i	$0.324986\pi$
$140$	−266.170	−	461.021i	−0.160682	−	0.278310i
$141$	36.9456	+	63.9917i	0.0220666	+	0.0382204i
$142$	171.131			0.101134
$143$	−2617.20	−	541.299i	−1.53050	−	0.316543i
$144$	−3943.85			−2.28232
$145$	310.969	+	538.614i	0.178100	+	0.308479i
$146$	−306.657	−	531.146i	−0.173830	−	0.301082i
$147$	664.833	−	1151.52i	0.373024	−	0.646096i
$148$	−679.637			−0.377472
$149$	34.3439	−	59.4854i	0.0188830	−	0.0327063i	−0.856430	−	0.516264i	$-0.827322\pi$
$149$	34.3439	−	59.4854i	0.0188830	−	0.0327063i	0.875312	+	0.483558i	$0.160656\pi$
$150$	−391.405	+	677.933i	−0.213054	+	0.369020i
$151$	3529.25			1.90203			0.951013	−	0.309150i	$-0.100045\pi$
$151$	3529.25			1.90203			0.951013	+	0.309150i	$0.100045\pi$
$152$	−326.453	+	565.434i	−0.174203	+	0.301728i
$153$	−2802.26	−	4853.65i	−1.48071	−	2.56467i
$154$	−2267.73	−	3927.82i	−1.18661	−	2.05528i
$155$	−664.324			−0.344257
$156$	−1306.46	+	1467.09i	−0.670514	+	0.752955i
$157$	1255.50			0.638214			0.319107	−	0.947719i	$-0.396617\pi$
$157$	1255.50			0.638214			0.319107	+	0.947719i	$0.396617\pi$
$158$	−593.787	−	1028.47i	−0.298982	−	0.517852i
$159$	−1476.89	−	2558.05i	−0.736637	−	1.27589i
$160$	479.789	−	831.019i	0.237067	−	0.410612i
$161$	−1137.61			−0.556873
$162$	711.368	−	1232.12i	0.345002	−	0.597561i
$163$	25.0007	−	43.3025i	0.0120135	−	0.0208081i	−0.859956	−	0.510368i	$-0.829509\pi$
$163$	25.0007	−	43.3025i	0.0120135	−	0.0208081i	0.871970	+	0.489560i	$0.162843\pi$
$164$	1210.25			0.576247
$165$	−1248.26	+	2162.04i	−0.588949	+	1.02009i
$166$	2216.70	+	3839.44i	1.03644	+	1.79517i
$167$	116.646	+	202.037i	0.0540499	+	0.0936171i	0.891784	−	0.452461i	$-0.149454\pi$
$167$	116.646	+	202.037i	0.0540499	+	0.0936171i	−0.837735	+	0.546078i	$0.816120\pi$
$168$	2238.60			1.02805
$169$	−253.630	−	2182.31i	−0.115444	−	0.993314i
$170$	2016.88			0.909925
$171$	−1411.31	−	2444.46i	−0.631145	−	1.09317i
$172$	320.734	+	555.527i	0.142184	+	0.246270i
$173$	−376.241	+	651.668i	−0.165347	+	0.286390i	−0.936779	−	0.349923i	$-0.886208\pi$
$173$	−376.241	+	651.668i	−0.165347	+	0.286390i	0.771431	+	0.636313i	$0.219541\pi$
$174$	3894.87			1.69695
$175$	278.063	−	481.620i	0.120112	−	0.208040i
$176$	2263.13	−	3919.85i	0.969259	−	1.67881i
$177$	−7614.83			−3.23371
$178$	504.363	−	873.583i	0.212380	−	0.367853i
$179$	1929.80	+	3342.52i	0.805812	+	1.39571i	0.915741	+	0.401768i	$0.131604\pi$
$179$	1929.80	+	3342.52i	0.805812	+	1.39571i	−0.109929	+	0.993939i	$0.535062\pi$
$180$	594.462	+	1029.64i	0.246159	+	0.426360i
$181$	−2519.65			−1.03472			−0.517359	−	0.855768i	$-0.673085\pi$
$181$	−2519.65			−1.03472			−0.517359	+	0.855768i	$0.673085\pi$
$182$	2479.51	−	2784.37i	1.00986	−	1.13402i
$183$	2979.40			1.20352
$184$	−293.851	−	508.965i	−0.117734	−	0.203921i
$185$	−355.002	−	614.882i	−0.141083	−	0.244362i
$186$	−2080.16	+	3602.94i	−0.820025	+	1.42032i
$187$	6432.15			2.51532
$188$	−20.1931	+	34.9754i	−0.00783368	+	0.0135683i
$189$	−2209.18	+	3826.41i	−0.850233	+	1.47265i
$190$	1015.77			0.387850
$191$	−1971.47	+	3414.68i	−0.746860	+	1.29360i	0.202460	+	0.979290i	$0.435106\pi$
$191$	−1971.47	+	3414.68i	−0.746860	+	1.29360i	−0.949321	+	0.314310i	$0.898227\pi$
$192$	−224.135	−	388.212i	−0.0842475	−	0.145921i
$193$	−1647.00	−	2852.68i	−0.614266	−	1.06394i	−0.990513	−	0.137421i	$-0.956119\pi$
$193$	−1647.00	−	2852.68i	−0.614266	−	1.06394i	0.376247	−	0.926520i	$-0.377215\pi$
$194$	66.2685			0.0245247
$195$	−2009.72	−	415.659i	−0.738047	−	0.152646i
$196$	726.745			0.264849
$197$	−350.546	−	607.163i	−0.126778	−	0.219587i	0.795648	−	0.605759i	$-0.207130\pi$
$197$	−350.546	−	607.163i	−0.126778	−	0.219587i	−0.922427	+	0.386172i	$0.873797\pi$
$198$	5064.72	+	8772.35i	1.81785	+	3.14860i
$199$	−95.9215	+	166.141i	−0.0341693	+	0.0591830i	−0.882604	−	0.470117i	$-0.844212\pi$
$199$	−95.9215	+	166.141i	−0.0341693	+	0.0591830i	0.848435	+	0.529300i	$0.177545\pi$
$200$	287.300			0.101576
$201$	1903.93	−	3297.70i	0.668123	−	1.15722i
$202$	−1815.70	+	3144.88i	−0.632435	+	1.09541i
$203$	−2767.01			−0.956680
$204$	2363.97	−	4094.51i	0.811328	−	1.40526i
$205$	632.162	+	1094.94i	0.215376	+	0.373043i
$206$	−2518.69	−	4362.50i	−0.851872	−	1.47549i
$207$	2540.73			0.853107
$208$	3643.69	+	753.603i	1.21464	+	0.251216i
$209$	3239.45			1.07214
$210$	−1741.37	−	3016.14i	−0.572218	−	0.991110i
$211$	240.887	+	417.229i	0.0785940	+	0.136129i	0.902644	−	0.430389i	$-0.141624\pi$
$211$	240.887	+	417.229i	0.0785940	+	0.136129i	−0.824050	+	0.566518i	$0.808290\pi$
$212$	807.213	−	1398.13i	0.261508	−	0.452945i
$213$	419.088			0.134814
$214$	631.276	−	1093.40i	0.201650	−	0.349269i
$215$	−335.065	+	580.349i	−0.106285	+	0.184091i
$216$	−2282.56			−0.719022
$217$	1477.79	−	2559.62i	0.462301	−	0.800728i
$218$	178.897	+	309.858i	0.0555799	+	0.0962671i
$219$	−750.983	−	1300.74i	−0.231720	−	0.401351i
$220$	−1364.50			−0.418156
$221$	1661.53	+	5019.71i	0.505731	+	1.52788i
$222$	−4446.39			−1.34424
$223$	−93.0176	−	161.111i	−0.0279324	−	0.0483803i	0.851721	−	0.523995i	$-0.175559\pi$
$223$	−93.0176	−	161.111i	−0.0279324	−	0.0483803i	−0.879654	+	0.475615i	$0.842226\pi$
$224$	2134.59	+	3697.22i	0.636711	+	1.10282i
$225$	−621.024	+	1075.65i	−0.184007	+	0.318710i
$226$	1073.43			0.315945
$227$	1942.96	−	3365.30i	0.568100	−	0.983978i	−0.428654	−	0.903469i	$-0.641012\pi$
$227$	1942.96	−	3365.30i	0.568100	−	0.983978i	0.996754	−	0.0805090i	$-0.0256546\pi$
$228$	1190.58	−	2062.14i	0.345824	−	0.598984i
$229$	−1521.23			−0.438976			−0.219488	−	0.975615i	$-0.570439\pi$
$229$	−1521.23			−0.438976			−0.219488	+	0.975615i	$0.570439\pi$
$230$	−457.162	+	791.829i	−0.131063	+	0.227007i
$231$	−5553.51	−	9618.96i	−1.58179	−	2.73974i
$232$	−714.732	−	1237.95i	−0.202261	−	0.350326i
$233$	−5286.13			−1.48629			−0.743146	−	0.669129i	$-0.766667\pi$
$233$	−5286.13			−1.48629			−0.743146	+	0.669129i	$0.766667\pi$
$234$	−5537.72	+	6218.59i	−1.54706	+	1.73727i
$235$	−42.1907			−0.0117116
$236$	−2080.99	−	3604.38i	−0.573986	−	0.994174i
$237$	−1454.15	−	2518.65i	−0.398552	−	0.690313i
$238$	−4486.56	+	7770.94i	−1.22193	+	2.11645i
$239$	−6680.85			−1.80815			−0.904076	−	0.427371i	$-0.859440\pi$
$239$	−6680.85			−1.80815			−0.904076	+	0.427371i	$0.859440\pi$
$240$	1737.83	−	3010.02i	0.467403	−	0.809566i
$241$	3019.17	−	5229.35i	0.806978	−	1.39773i	−0.107969	−	0.994154i	$-0.534435\pi$
$241$	3019.17	−	5229.35i	0.806978	−	1.39773i	0.914948	−	0.403573i	$-0.132232\pi$
$242$	−6865.93			−1.82380
$243$	−939.301	+	1626.92i	−0.247968	+	0.429493i
$244$	814.213	+	1410.26i	0.213626	+	0.370010i
$245$	379.609	+	657.502i	0.0989890	+	0.171454i
$246$	7917.81			2.05212
$247$	836.804	+	2528.10i	0.215565	+	0.651251i
$248$	1526.89			0.390957
$249$	5428.55	+	9402.52i	1.38161	+	2.39301i
$250$	−223.486	−	387.089i	−0.0565379	−	0.0979265i
$251$	1461.66	−	2531.68i	0.367567	−	0.636645i	−0.621617	−	0.783321i	$-0.713524\pi$
$251$	1461.66	−	2531.68i	0.367567	−	0.636645i	0.989185	+	0.146676i	$0.0468574\pi$
$252$	−5289.54			−1.32226
$253$	−1457.97	+	2525.27i	−0.362299	+	0.627520i
$254$	957.622	−	1658.65i	0.236561	−	0.409736i
$255$	4939.19			1.21296
$256$	−2622.48	+	4542.27i	−0.640255	+	1.10895i
$257$	−1869.55	−	3238.15i	−0.453771	−	0.785954i	0.544846	−	0.838536i	$-0.316588\pi$
$257$	−1869.55	−	3238.15i	−0.453771	−	0.785954i	−0.998617	+	0.0525819i	$0.983255\pi$
$258$	2098.34	+	3634.42i	0.506344	+	0.877013i
$259$	3158.82			0.757837
$260$	−352.472	−	1064.87i	−0.0840746	−	0.254001i
$261$	6179.81			1.46560
$262$	4494.99	+	7785.55i	1.05993	+	1.83585i
$263$	841.740	+	1457.94i	0.197353	+	0.341826i	0.947669	−	0.319253i	$-0.103432\pi$
$263$	841.740	+	1457.94i	0.197353	+	0.341826i	−0.750316	+	0.661079i	$0.770099\pi$
$264$	2868.99	−	4969.24i	0.668842	−	1.15847i
$265$	1686.56			0.390961
$266$	−2259.58	+	3913.71i	−0.520842	+	0.902125i
$267$	1235.15	−	2139.35i	0.283109	−	0.490359i
$268$	2081.23			0.474371
$269$	2646.42	−	4583.74i	0.599834	−	1.03894i	−0.393011	−	0.919534i	$-0.628567\pi$
$269$	2646.42	−	4583.74i	0.599834	−	1.03894i	0.992845	−	0.119409i	$-0.0381000\pi$
$270$	1775.56	+	3075.37i	0.400213	+	0.693188i
$271$	3982.93	+	6898.64i	0.892789	+	1.54636i	0.836517	+	0.547941i	$0.184588\pi$
$271$	3982.93	+	6898.64i	0.892789	+	1.54636i	0.0562726	+	0.998415i	$0.482078\pi$
$272$	−8954.91			−1.99622
$273$	6072.16	−	6818.74i	1.34617	−	1.51168i
$274$	−5573.04			−1.22876
$275$	−712.733	−	1234.49i	−0.156289	−	0.270700i
$276$	1071.67	+	1856.19i	0.233722	+	0.404818i
$277$	−3210.85	+	5561.35i	−0.696466	+	1.20631i	0.273218	+	0.961952i	$0.411912\pi$
$277$	−3210.85	+	5561.35i	−0.696466	+	1.20631i	−0.969684	+	0.244362i	$0.921421\pi$
$278$	−5591.76			−1.20637
$279$	−3300.49	+	5716.62i	−0.708227	+	1.22668i
$280$	−639.102	+	1106.96i	−0.136406	+	0.236262i
$281$	−4999.67			−1.06141			−0.530703	−	0.847558i	$-0.678072\pi$
$281$	−4999.67			−1.06141			−0.530703	+	0.847558i	$0.678072\pi$
$282$	−132.109	+	228.820i	−0.0278971	+	0.0483192i
$283$	3530.57	+	6115.12i	0.741592	+	1.28447i	0.951770	+	0.306812i	$0.0992622\pi$
$283$	3530.57	+	6115.12i	0.741592	+	1.28447i	−0.210178	+	0.977663i	$0.567404\pi$
$284$	114.529	+	198.369i	0.0239297	+	0.0414474i
$285$	2487.55			0.517016
$286$	−3003.00	−	9072.48i	−0.620879	−	1.87576i
$287$	−5625.00			−1.15691
$288$	−4767.37	−	8257.33i	−0.975417	−	1.68947i
$289$	−3906.31	−	6765.92i	−0.795096	−	1.37715i
$290$	−1111.95	+	1925.96i	−0.225159	+	0.389987i
$291$	162.287			0.0326922
$292$	410.458	−	710.935i	0.0822612	−	0.142481i
$293$	2413.38	−	4180.10i	0.481199	−	0.833461i	−0.518569	−	0.855036i	$-0.673535\pi$
$293$	2413.38	−	4180.10i	0.481199	−	0.833461i	0.999767	+	0.0215755i	$0.00686822\pi$
$294$	4754.58			0.943173
$295$	2173.97	−	3765.43i	0.429063	−	0.743159i
$296$	815.939	+	1413.25i	0.160221	+	0.277511i
$297$	5662.57	+	9807.85i	1.10631	+	1.91619i
$298$	245.612			0.0477447
$299$	−2347.36	−	485.491i	−0.454018	−	0.0939019i
$300$	−1047.79			−0.201646
$301$	−1490.71	−	2581.98i	−0.285458	−	0.494429i
$302$	6309.89	+	10929.0i	1.20230	+	2.08244i
$303$	−4446.52	+	7701.59i	−0.843055	+	1.46021i
$304$	−4510.00			−0.850876
$305$	−850.594	+	1473.27i	−0.159688	+	0.276588i
$306$	10020.2	−	17355.5i	1.87196	−	3.24232i
$307$	6085.97			1.13142			0.565708	−	0.824606i	$-0.308603\pi$
$307$	6085.97			1.13142			0.565708	+	0.824606i	$0.308603\pi$
$308$	3035.33	−	5257.35i	0.561540	−	0.972615i
$309$	−6168.11	−	10683.5i	−1.13557	−	1.96687i
$310$	−1187.74	−	2057.22i	−0.217609	−	0.376910i
$311$	262.616			0.0478828			0.0239414	−	0.999713i	$-0.492378\pi$
$311$	262.616			0.0478828			0.0239414	+	0.999713i	$0.492378\pi$
$312$	4619.15	+	955.352i	0.838167	+	0.173353i
$313$	596.328			0.107688			0.0538442	−	0.998549i	$-0.482853\pi$
$313$	596.328			0.107688			0.0538442	+	0.998549i	$0.482853\pi$
$314$	2244.68	+	3887.91i	0.403423	+	0.698750i
$315$	−2762.95	−	4785.56i	−0.494204	−	0.855987i
$316$	794.780	−	1376.60i	0.141487	−	0.245063i
$317$	7299.30			1.29328			0.646640	−	0.762796i	$-0.276174\pi$
$317$	7299.30			1.29328			0.646640	+	0.762796i	$0.276174\pi$
$318$	5281.03	−	9147.02i	0.931276	−	1.61302i
$319$	−3546.20	+	6142.20i	−0.622412	+	1.07805i
$320$	255.954			0.0447134
$321$	1545.95	−	2677.67i	0.268806	−	0.465585i
$322$	−2033.92	−	3522.86i	−0.352006	−	0.609693i
$323$	−3204.53	−	5550.40i	−0.552027	−	0.956139i
$324$	1904.32			0.326530
$325$	779.297	−	875.113i	0.133008	−	0.149362i
$326$	178.794			0.0303757
$327$	438.106	+	758.821i	0.0740896	+	0.128327i
$328$	−1452.96	−	2516.61i	−0.244593	−	0.423648i
$329$	93.8535	−	162.559i	0.0157274	−	0.0272406i
$330$	−8926.95			−1.48913
$331$	−3131.90	+	5424.61i	−0.520075	+	0.900796i	0.479653	+	0.877458i	$0.340763\pi$
$331$	−3131.90	+	5424.61i	−0.520075	+	0.900796i	−0.999728	+	0.0233375i	$0.992571\pi$
$332$	−2967.04	+	5139.06i	−0.490474	+	0.849525i
$333$	−7054.88			−1.16098
$334$	−417.099	+	722.437i	−0.0683313	+	0.118353i
$335$	1087.11	+	1882.93i	0.177299	+	0.307091i
$336$	7731.65	+	13391.6i	1.25535	+	2.17432i
$337$	2696.53			0.435874			0.217937	−	0.975963i	$-0.430067\pi$
$337$	2696.53			0.435874			0.217937	+	0.975963i	$0.430067\pi$
$338$	6304.52	−	4687.14i	1.01456	−	0.754281i
$339$	2628.76			0.421164
$340$	1349.79	+	2337.90i	0.215301	+	0.372913i
$341$	−3787.89	−	6560.81i	−0.601541	−	1.04190i
$342$	5046.53	−	8740.85i	0.797910	−	1.38202i
$343$	4252.29			0.669394
$344$	770.114	−	1333.88i	0.120703	−	0.209063i
$345$	−1119.56	+	1939.13i	−0.174710	+	0.302607i
$346$	−2690.70			−0.418073
$347$	922.148	−	1597.21i	0.142661	−	0.247097i	−0.785837	−	0.618434i	$-0.787767\pi$
$347$	922.148	−	1597.21i	0.142661	−	0.247097i	0.928498	+	0.371337i	$0.121101\pi$
$348$	2606.63	+	4514.81i	0.401523	+	0.695458i
$349$	2983.24	+	5167.13i	0.457563	+	0.792522i	0.998832	−	0.0483278i	$-0.0153892\pi$
$349$	2983.24	+	5167.13i	0.457563	+	0.792522i	−0.541269	+	0.840850i	$0.682056\pi$
$350$	1988.58			0.303698
$351$	−6191.41	+	6952.65i	−0.941518	+	1.05728i
$352$	10942.8			1.65697
$353$	−3999.65	−	6927.60i	−0.603059	−	1.04453i	−0.992355	−	0.123416i	$-0.960615\pi$
$353$	−3999.65	−	6927.60i	−0.603059	−	1.04453i	0.389296	−	0.921113i	$-0.372718\pi$
$354$	−13614.5	−	23580.9i	−2.04407	−	3.54043i
$355$	−119.646	+	207.233i	−0.0178878	+	0.0309825i
$356$	1350.17			0.201008
$357$	−10987.3	+	19030.5i	−1.62887	+	2.82129i
$358$	−6900.54	+	11952.1i	−1.01873	+	1.76449i
$359$	4522.65			0.664892			0.332446	−	0.943122i	$-0.392126\pi$
$359$	4522.65			0.664892			0.332446	+	0.943122i	$0.392126\pi$
$360$	1427.36	−	2472.27i	0.208969	−	0.361944i
$361$	1815.59	+	3144.69i	0.264702	+	0.458477i
$362$	−4504.85	−	7802.62i	−0.654059	−	1.13286i
$363$	−16814.2			−2.43117
$364$	4886.96	+	1010.74i	0.703699	+	0.145542i
$365$	857.598			0.122983
$366$	5326.83	+	9226.34i	0.760759	+	1.31767i
$367$	−3328.36	−	5764.88i	−0.473403	−	0.819957i	0.526134	−	0.850402i	$-0.323641\pi$
$367$	−3328.36	−	5764.88i	−0.473403	−	0.819957i	−0.999536	+	0.0304443i	$0.990308\pi$
$368$	2029.80	−	3515.71i	0.287529	−	0.498014i
$369$	12562.8			1.77234
$370$	1269.41	−	2198.68i	0.178360	−	0.308929i
$371$	−3751.77	+	6498.26i	−0.525020	+	0.909361i
$372$	−5568.55			−0.776118
$373$	3398.60	−	5886.55i	0.471777	−	0.817142i	−0.527702	−	0.849430i	$-0.676946\pi$
$373$	3398.60	−	5886.55i	0.471777	−	0.817142i	0.999479	+	0.0322881i	$0.0102794\pi$
$374$	11500.0	+	19918.5i	1.58997	+	2.75391i
$375$	−547.301	−	947.954i	−0.0753667	−	0.130539i
$376$	96.9713			0.0133003
$377$	−5709.48	−	1180.86i	−0.779981	−	0.161319i
$378$	−15799.0			−2.14977
$379$	−3289.77	−	5698.04i	−0.445868	−	0.772266i	0.552244	−	0.833682i	$-0.313772\pi$
$379$	−3289.77	−	5698.04i	−0.445868	−	0.772266i	−0.998112	+	0.0614162i	$0.980438\pi$
$380$	679.799	+	1177.45i	0.0917709	+	0.158952i
$381$	2345.15	−	4061.92i	0.315343	−	0.546191i
$382$	−14099.0			−1.88840
$383$	5646.01	−	9779.17i	0.753257	−	1.30468i	−0.192979	−	0.981203i	$-0.561815\pi$
$383$	5646.01	−	9779.17i	0.753257	−	1.30468i	0.946236	−	0.323477i	$-0.104852\pi$
$384$	−5920.83	+	10255.2i	−0.786839	+	1.36285i
$385$	6341.92			0.839517
$386$	5889.28	−	10200.5i	0.776571	−	1.34506i
$387$	3329.33	+	5766.57i	0.437311	+	0.757445i
$388$	44.3499	+	76.8163i	0.00580290	+	0.0100509i
$389$	1140.52			0.148655			0.0743276	−	0.997234i	$-0.476319\pi$
$389$	1140.52			0.148655			0.0743276	+	0.997234i	$0.476319\pi$
$390$	−2305.98	−	6966.68i	−0.299405	−	0.904542i
$391$	5768.99			0.746165
$392$	−872.494	−	1511.20i	−0.112417	−	0.194713i
$393$	11007.9	+	19066.3i	1.41292	+	2.44724i
$394$	1253.47	−	2171.08i	0.160277	−	0.277607i
$395$	1660.59			0.211527
$396$	−6779.08	+	11741.7i	−0.860257	+	1.49001i
$397$	4850.40	−	8401.14i	0.613185	−	1.06207i	−0.377515	−	0.926004i	$-0.623221\pi$
$397$	4850.40	−	8401.14i	0.613185	−	1.06207i	0.990700	−	0.136065i	$-0.0434455\pi$
$398$	−685.986			−0.0863955
$399$	−5533.57	+	9584.42i	−0.694298	+	1.20256i
$400$	992.275	+	1718.67i	0.124034	+	0.214834i
$401$	2996.34	+	5189.81i	0.373142	+	0.646302i	0.990047	−	0.140736i	$-0.0449470\pi$
$401$	2996.34	+	5189.81i	0.373142	+	0.646302i	−0.616905	+	0.787038i	$0.711614\pi$
$402$	13616.0			1.68932
$403$	4141.64	−	4650.87i	0.511935	−	0.574879i
$404$	−4860.59			−0.598573
$405$	994.705	+	1722.88i	0.122043	+	0.211384i
$406$	−4947.10	−	8568.62i	−0.604730	−	1.04742i
$407$	4048.35	−	7011.95i	0.493045	−	0.853979i
$408$	−11352.3			−1.37750
$409$	−3431.38	+	5943.32i	−0.414842	+	0.718528i	−0.995412	−	0.0956825i	$-0.969497\pi$
$409$	−3431.38	+	5943.32i	−0.414842	+	0.718528i	0.580569	+	0.814211i	$0.302830\pi$
$410$	−2260.47	+	3915.24i	−0.272284	+	0.471610i
$411$	−13648.0			−1.63797
$412$	3371.25	−	5839.18i	0.403130	−	0.698242i
$413$	9672.03	+	16752.5i	1.15237	+	1.99597i
$414$	4542.54	+	7867.91i	0.539260	+	0.934026i
$415$	−6199.22			−0.733272
$416$	2826.70	+	8539.84i	0.333150	+	1.00649i
$417$	−13693.9			−1.60813
$418$	5791.77	+	10031.6i	0.677715	+	1.17384i
$419$	3904.41	+	6762.63i	0.455234	+	0.788488i	0.998702	−	0.0509422i	$-0.0162224\pi$
$419$	3904.41	+	6762.63i	0.455234	+	0.788488i	−0.543468	+	0.839430i	$0.682889\pi$
$420$	2330.81	−	4037.07i	0.270790	−	0.469022i
$421$	−2043.09			−0.236518			−0.118259	−	0.992983i	$-0.537731\pi$
$421$	−2043.09			−0.236518			−0.118259	+	0.992983i	$0.537731\pi$
$422$	−861.357	+	1491.91i	−0.0993607	+	0.172098i
$423$	−209.612	+	363.058i	−0.0240938	+	0.0417316i
$424$	−3876.40			−0.443997
$425$	−1410.10	+	2442.36i	−0.160941	+	0.278758i
$426$	749.281	+	1297.79i	0.0852178	+	0.147602i
$427$	−3784.31	−	6554.61i	−0.428889	−	0.742857i
$428$	1689.92			0.190853
$429$	−7354.15	−	22217.9i	−0.827650	−	2.50044i
$430$	−2396.23			−0.268736
$431$	−5251.86	−	9096.49i	−0.586945	−	1.01662i	−0.994630	−	0.103496i	$-0.966997\pi$
$431$	−5251.86	−	9096.49i	−0.586945	−	1.01662i	0.407685	−	0.913123i	$-0.366336\pi$
$432$	−7883.49	−	13654.6i	−0.877997	−	1.52073i
$433$	7004.46	−	12132.1i	0.777397	−	1.34649i	−0.156040	−	0.987751i	$-0.549873\pi$
$433$	7004.46	−	12132.1i	0.777397	−	1.34649i	0.933437	−	0.358740i	$-0.116794\pi$
$434$	10568.5			1.16890
$435$	−2723.10	+	4716.54i	−0.300144	+	0.519864i
$436$	−239.452	+	414.743i	−0.0263020	+	0.0455564i
$437$	2905.46			0.318048
$438$	2685.34	−	4651.15i	0.292947	−	0.507399i
$439$	−415.697	−	720.008i	−0.0451939	−	0.0782782i	0.842544	−	0.538628i	$-0.181057\pi$
$439$	−415.697	−	720.008i	−0.0451939	−	0.0782782i	−0.887737	+	0.460350i	$0.847724\pi$
$440$	1638.15	+	2837.36i	0.177490	+	0.307422i
$441$	7543.88			0.814586
$442$	−12574.0	+	14119.9i	−1.35313	+	1.51950i
$443$	11783.3			1.26375			0.631875	−	0.775070i	$-0.282286\pi$
$443$	11783.3			1.26375			0.631875	+	0.775070i	$0.282286\pi$
$444$	−2975.73	−	5154.12i	−0.318067	−	0.550909i
$445$	705.251	+	1221.53i	0.0751283	+	0.130126i
$446$	332.610	−	576.097i	0.0353128	−	0.0611636i
$447$	601.487			0.0636451
$448$	−569.372	+	986.181i	−0.0600453	+	0.104002i
$449$	−6853.36	+	11870.4i	−0.720335	+	1.24766i	0.240531	+	0.970641i	$0.422678\pi$
$449$	−6853.36	+	11870.4i	−0.720335	+	1.24766i	−0.960866	+	0.277015i	$0.910655\pi$
$450$	−4441.28			−0.465253
$451$	−7209.01	+	12486.4i	−0.752680	+	1.30368i
$452$	718.389	+	1244.29i	0.0747570	+	0.129483i
$453$	15452.5	+	26764.5i	1.60270	+	2.77595i
$454$	13895.1			1.43641
$455$	1638.22	+	4949.29i	0.168794	+	0.509948i
$456$	−5717.39			−0.587152
$457$	−6178.59	−	10701.6i	−0.632434	−	1.09541i	−0.987053	−	0.160396i	$-0.948723\pi$
$457$	−6178.59	−	10701.6i	−0.632434	−	1.09541i	0.354619	−	0.935011i	$-0.384611\pi$
$458$	−2719.78	−	4710.80i	−0.277483	−	0.480614i
$459$	11203.0	−	19404.2i	1.13924	−	1.97323i
$460$	−1223.82			−0.124045
$461$	1778.13	−	3079.81i	0.179644	−	0.311152i	−0.762115	−	0.647442i	$-0.775839\pi$
$461$	1778.13	−	3079.81i	0.179644	−	0.311152i	0.941759	+	0.336290i	$0.109172\pi$
$462$	19858.1	−	34395.2i	1.99974	−	3.46366i
$463$	−2285.46			−0.229404			−0.114702	−	0.993400i	$-0.536591\pi$
$463$	−2285.46			−0.229404			−0.114702	+	0.993400i	$0.536591\pi$
$464$	4937.06	−	8551.24i	0.493960	−	0.855564i
$465$	−2908.68	−	5037.99i	−0.290080	−	0.502433i
$466$	−9451.00	−	16369.6i	−0.939505	−	1.62727i
$467$	13988.9			1.38615			0.693074	−	0.720866i	$-0.256256\pi$
$467$	13988.9			1.38615			0.693074	+	0.720866i	$0.256256\pi$
$468$	−10914.5	−	2257.38i	−1.07804	−	0.222965i
$469$	−9673.16			−0.952377
$470$	−75.4321	−	130.652i	−0.00740303	−	0.0128224i
$471$	5497.08	+	9521.22i	0.537775	+	0.931454i
$472$	−4996.66	+	8654.48i	−0.487267	+	0.843972i
$473$	−7641.97			−0.742872
$474$	5199.69	−	9006.13i	0.503860	−	0.872711i
$475$	−710.174	+	1230.06i	−0.0686000	+	0.118819i
$476$	−12010.4			−1.15651
$477$	8379.17	−	14513.2i	0.804310	−	1.39311i
$478$	−11944.6	−	20688.7i	−1.14296	−	1.97966i
$479$	1529.06	+	2648.41i	0.145855	+	0.252629i	0.929692	−	0.368339i	$-0.120073\pi$
$479$	1529.06	+	2648.41i	0.145855	+	0.252629i	−0.783836	+	0.620967i	$0.786740\pi$
$480$	8402.86			0.799034
$481$	6517.95	+	1348.07i	0.617864	+	0.127789i
$482$	21591.7			2.04041
$483$	−4980.94	−	8627.24i	−0.469235	−	0.812739i
$484$	−4595.00	−	7958.77i	−0.431536	−	0.747443i
$485$	−46.3316	+	80.2487i	−0.00433775	+	0.00751321i
$486$	−6717.45			−0.626975
$487$	−2427.72	+	4204.94i	−0.225895	+	0.391261i	−0.956587	−	0.291445i	$-0.905864\pi$
$487$	−2427.72	+	4204.94i	−0.225895	+	0.391261i	0.730693	+	0.682706i	$0.239197\pi$
$488$	1955.01	−	3386.17i	0.181351	−	0.314108i
$489$	437.854			0.0404917
$490$	−1357.39	+	2351.08i	−0.125145	+	0.216757i
$491$	−5934.73	−	10279.3i	−0.545480	−	0.944799i	−0.998577	−	0.0533373i	$-0.983014\pi$
$491$	−5934.73	−	10279.3i	−0.545480	−	0.944799i	0.453097	−	0.891461i	$-0.350319\pi$
$492$	5298.96	+	9178.07i	0.485560	+	0.841015i
$493$	14031.9			1.28188
$494$	−6332.67	+	7111.29i	−0.576762	+	0.647676i
$495$	−14164.0			−1.28611
$496$	5273.54	+	9134.03i	0.477397	+	0.826875i
$497$	−532.307	−	921.983i	−0.0480427	−	0.0832125i
$498$	−19411.2	+	33621.3i	−1.74666	+	3.02531i
$499$	−3718.66			−0.333607			−0.166804	−	0.985990i	$-0.553345\pi$
$499$	−3718.66			−0.333607			−0.166804	+	0.985990i	$0.553345\pi$
$500$	299.134	−	518.115i	0.0267554	−	0.0463416i
$501$	−1021.45	+	1769.20i	−0.0910876	+	0.157768i
$502$	10453.2			0.929376
$503$	799.433	−	1384.66i	0.0708647	−	0.122741i	−0.828416	−	0.560114i	$-0.810757\pi$
$503$	799.433	−	1384.66i	0.0708647	−	0.122741i	0.899281	+	0.437372i	$0.144091\pi$
$504$	6350.37	+	10999.2i	0.561246	+	0.972106i
$505$	−2538.89	−	4397.48i	−0.223721	−	0.387496i
$506$	−10426.7			−0.916055
$507$	15439.3	−	11478.5i	1.35244	−	1.00548i
$508$	2563.54			0.223895
$509$	−1649.70	−	2857.36i	−0.143657	−	0.248822i	0.785214	−	0.619225i	$-0.212553\pi$
$509$	−1649.70	−	2857.36i	−0.143657	−	0.248822i	−0.928871	+	0.370403i	$0.879220\pi$
$510$	8830.71	+	15295.2i	0.766726	+	1.32801i
$511$	−1907.73	+	3304.29i	−0.165153	+	0.286053i
$512$	−7936.57			−0.685059
$513$	5642.24	−	9772.64i	0.485596	−	0.841077i
$514$	6685.07	−	11578.9i	0.573669	−	0.993624i
$515$	7043.77			0.602691
$516$	−2808.61	+	4864.65i	−0.239616	+	0.415028i
$517$	−240.566	−	416.672i	−0.0204643	−	0.0354453i
$518$	5647.61	+	9781.96i	0.479038	+	0.829719i
$519$	−6589.35			−0.557303
$520$	−1791.14	+	2011.36i	−0.151051	+	0.169623i
$521$	6137.75			0.516122			0.258061	−	0.966129i	$-0.416916\pi$
$521$	6137.75			0.516122			0.258061	+	0.966129i	$0.416916\pi$
$522$	11048.8	+	19137.1i	0.926423	+	1.60461i
$523$	3195.47	+	5534.72i	0.267167	+	0.462746i	0.968129	−	0.250452i	$-0.0805792\pi$
$523$	3195.47	+	5534.72i	0.267167	+	0.462746i	−0.700962	+	0.713198i	$0.747246\pi$
$524$	−6016.51	+	10420.9i	−0.501588	+	0.868777i
$525$	4869.90			0.404838
$526$	−3009.87	+	5213.25i	−0.249499	+	0.432145i
$527$	−7494.10	+	12980.2i	−0.619446	+	1.07291i
$528$	39635.6			3.26689
$529$	4775.85	−	8272.02i	0.392525	−	0.679873i
$530$	3015.38	+	5222.80i	0.247132	+	0.428045i
$531$	−21601.4	−	37414.8i	−1.76539	−	3.05774i
$532$	−6048.87			−0.492955
$533$	−11606.7	−	2400.54i	−0.943229	−	0.195082i
$534$	8833.24			0.715827
$535$	882.714	+	1528.90i	0.0713328	+	0.123552i
$536$	−2498.62	−	4327.74i	−0.201351	−	0.348750i
$537$	−16899.0	+	29269.9i	−1.35800	+	2.35212i
$538$	18926.0			1.51665
$539$	−4328.96	+	7497.97i	−0.345939	+	0.599185i
$540$	−2376.58	+	4116.36i	−0.189392	+	0.328037i
$541$	8246.42			0.655345			0.327672	−	0.944791i	$-0.393736\pi$
$541$	8246.42			0.655345			0.327672	+	0.944791i	$0.393736\pi$
$542$	−14242.1	+	24668.0i	−1.12869	+	1.95494i
$543$	−11032.1	−	19108.1i	−0.871880	−	1.51014i
$544$	−10824.8	−	18749.1i	−0.853142	−	1.47769i
$545$	−500.302			−0.0393222
$546$	31972.0	+	6612.58i	2.50600	+	0.518301i
$547$	1878.12			0.146805			0.0734026	−	0.997302i	$-0.476614\pi$
$547$	1878.12			0.146805			0.0734026	+	0.997302i	$0.476614\pi$
$548$	−3729.74	−	6460.09i	−0.290742	−	0.503579i
$549$	8451.83	+	14639.0i	0.657041	+	1.13803i
$550$	2548.57	−	4414.25i	0.197584	−	0.342226i
$551$	7066.94			0.546392
$552$	2573.20	−	4456.91i	0.198411	−	0.343657i
$553$	−3693.99	+	6398.17i	−0.284058	+	0.492003i
$554$	−22962.5			−1.76098
$555$	3108.69	−	5384.41i	0.237760	−	0.411812i
$556$	−3742.27	−	6481.80i	−0.285445	−	0.494405i
$557$	−2429.58	−	4208.15i	−0.184820	−	0.320117i	0.758696	−	0.651445i	$-0.225837\pi$
$557$	−2429.58	−	4208.15i	−0.184820	−	0.320117i	−0.943516	+	0.331328i	$0.892503\pi$
$558$	−23603.6			−1.79072
$559$	−1974.05	−	5963.87i	−0.149362	−	0.451243i
$560$	−8829.29			−0.666260
$561$	28162.6	+	48779.1i	2.11948	+	3.67104i
$562$	−8938.83	−	15482.5i	−0.670929	−	1.16208i
$563$	−4814.18	+	8338.41i	−0.360380	+	0.624196i	−0.988023	−	0.154305i	$-0.950686\pi$
$563$	−4814.18	+	8338.41i	−0.360380	+	0.624196i	0.627644	+	0.778501i	$0.284019\pi$
$564$	−353.654			−0.0264034
$565$	−750.489	+	1299.88i	−0.0558819	+	0.0967903i
$566$	−12624.5	+	21866.3i	−0.937540	+	1.62387i
$567$	−8850.92			−0.655562
$568$	274.995	−	476.305i	0.0203143	−	0.0351854i
$569$	−4580.24	−	7933.20i	−0.337458	−	0.584494i	0.646496	−	0.762917i	$-0.276234\pi$
$569$	−4580.24	−	7933.20i	−0.337458	−	0.584494i	−0.983954	+	0.178423i	$0.942900\pi$
$570$	4447.45	+	7703.21i	0.326813	+	0.566056i
$571$	−14088.2			−1.03252			−0.516262	−	0.856431i	$-0.672677\pi$
$571$	−14088.2			−1.03252			−0.516262	+	0.856431i	$0.672677\pi$
$572$	8506.78	−	9552.71i	0.621829	−	0.698284i
$573$	−34527.6			−2.51729
$574$	−10056.9	−	17419.0i	−0.731298	−	1.26665i
$575$	−639.250	−	1107.21i	−0.0463627	−	0.0803026i
$576$	1271.63	−	2202.53i	0.0919871	−	0.159326i
$577$	−10210.8			−0.736710			−0.368355	−	0.929685i	$-0.620079\pi$
$577$	−10210.8			−0.736710			−0.368355	+	0.929685i	$0.620079\pi$
$578$	13968.1	−	24193.4i	1.00518	−	1.74102i
$579$	14422.4	−	24980.4i	1.03519	−	1.79301i
$580$	−2976.68			−0.213103
$581$	13790.2	−	23885.4i	0.984707	−	1.70556i
$582$	290.151	+	502.556i	0.0206652	+	0.0357931i
$583$	9616.56	+	16656.4i	0.683151	+	1.18325i
$584$	−1971.11			−0.139666
$585$	−3658.79	−	11053.7i	−0.258585	−	0.781221i
$586$	17259.4			1.21669
$587$	−9556.30	−	16552.0i	−0.671943	−	1.16384i	−0.977352	−	0.211618i	$-0.932127\pi$
$587$	−9556.30	−	16552.0i	−0.671943	−	1.16384i	0.305409	−	0.952221i	$-0.401207\pi$
$588$	3181.99	+	5511.36i	0.223168	+	0.386539i
$589$	−3774.29	+	6537.25i	−0.264035	+	0.457322i
$590$	15547.3			1.08486
$591$	3069.67	−	5316.82i	0.213653	−	0.370059i
$592$	−5636.16	+	9762.11i	−0.391292	+	0.677737i
$593$	−24190.5			−1.67519			−0.837594	−	0.546293i	$-0.816038\pi$
$593$	−24190.5			−1.67519			−0.837594	+	0.546293i	$0.816038\pi$
$594$	−20248.0	+	35070.6i	−1.39863	+	2.42250i
$595$	−6273.55	−	10866.1i	−0.432253	−	0.748684i
$596$	164.375	+	284.706i	0.0112971	+	0.0195671i
$597$	−1679.93			−0.115168
$598$	−2693.39	−	8137.10i	−0.184182	−	0.556440i
$599$	25640.4			1.74898			0.874488	−	0.485048i	$-0.161198\pi$
$599$	25640.4			1.74898			0.874488	+	0.485048i	$0.161198\pi$
$600$	1257.92	+	2178.78i	0.0855906	+	0.148247i
$601$	−78.3648	−	135.732i	−0.00531875	−	0.00921235i	0.863354	−	0.504599i	$-0.168360\pi$
$601$	−78.3648	−	135.732i	−0.00531875	−	0.00921235i	−0.868673	+	0.495387i	$0.835026\pi$
$602$	5330.43	−	9232.58i	0.360884	−	0.625070i
$603$	21603.9			1.45901
$604$	−8445.74	+	14628.4i	−0.568961	+	0.985469i
$605$	4800.31	−	8314.39i	0.322579	−	0.558724i
$606$	−31799.5			−2.13162
$607$	−11398.0	+	19741.9i	−0.762158	+	1.32010i	0.179579	+	0.983744i	$0.442527\pi$
$607$	−11398.0	+	19741.9i	−0.762158	+	1.32010i	−0.941736	+	0.336352i	$0.890807\pi$
$608$	−5451.74	−	9442.69i	−0.363647	−	0.629855i
$609$	−12115.1	−	20984.0i	−0.806123	−	1.39625i
$610$	−6083.06			−0.403764
$611$	263.033	−	295.373i	0.0174160	−	0.0195573i
$612$	26824.0			1.77173
$613$	−1898.61	−	3288.50i	−0.125097	−	0.216674i	0.796674	−	0.604409i	$-0.206591\pi$
$613$	−1898.61	−	3288.50i	−0.125097	−	0.216674i	−0.921771	+	0.387735i	$0.873257\pi$
$614$	10881.0	+	18846.5i	0.715183	+	1.23873i
$615$	−5535.73	+	9588.17i	−0.362963	+	0.628670i
$616$	−14576.3			−0.953402
$617$	5184.35	−	8979.55i	0.338272	−	0.585904i	−0.645836	−	0.763476i	$-0.723491\pi$
$617$	5184.35	−	8979.55i	0.338272	−	0.585904i	0.984108	+	0.177572i	$0.0568242\pi$
$618$	22055.7	−	38201.7i	1.43562	−	2.48656i
$619$	12503.7			0.811900			0.405950	−	0.913895i	$-0.366941\pi$
$619$	12503.7			0.811900			0.405950	+	0.913895i	$0.366941\pi$
$620$	1589.78	−	2753.57i	0.102979	−	0.178365i
$621$	5078.75	+	8796.66i	0.328186	+	0.568435i
$622$	469.527	+	813.244i	0.0302674	+	0.0524246i
$623$	−6275.35			−0.403558
$624$	10238.5	+	30932.0i	0.656841	+	1.98441i
$625$	625.000			0.0400000
$626$	1066.17	+	1846.65i	0.0680712	+	0.117903i
$627$	14183.7	+	24566.8i	0.903414	+	1.56476i
$628$	−3004.49	+	5203.94i	−0.190911	+	0.330668i
$629$	−16018.8			−1.01544
$630$	9879.66	−	17112.1i	0.624786	−	1.08216i
$631$	−4641.83	+	8039.88i	−0.292850	+	0.507231i	−0.974482	−	0.224464i	$-0.927937\pi$
$631$	−4641.83	+	8039.88i	−0.292850	+	0.507231i	0.681632	+	0.731695i	$0.261270\pi$
$632$	−3816.70			−0.240222
$633$	−2109.40	+	3653.60i	−0.132451	+	0.229411i
$634$	13050.3	+	22603.8i	0.817499	+	1.41595i
$635$	1339.04	+	2319.29i	0.0836824	+	0.144942i
$636$	14137.2			0.881413
$637$	−6969.73	−	1441.51i	−0.433517	−	0.0896618i
$638$	−25360.8			−1.57374
$639$	1188.85	+	2059.15i	0.0735996	+	0.127478i
$640$	−3380.70	−	5855.54i	−0.208803	−	0.361657i
$641$	−7467.16	+	12933.5i	−0.460117	+	0.796947i	−0.998966	−	0.0454557i	$-0.985526\pi$
$641$	−7467.16	+	12933.5i	−0.460117	+	0.796947i	0.538849	+	0.842402i	$0.318859\pi$
$642$	11056.0			0.679663
$643$	−541.859	+	938.528i	−0.0332330	+	0.0575613i	−0.882164	−	0.470943i	$-0.843914\pi$
$643$	−541.859	+	938.528i	−0.0332330	+	0.0575613i	0.848931	+	0.528504i	$0.177247\pi$
$644$	2722.39	−	4715.32i	0.166579	−	0.288524i
$645$	−5868.20			−0.358233
$646$	11458.7	−	19847.0i	0.697887	−	1.20878i
$647$	−3594.14	−	6225.23i	−0.218393	−	0.378267i	0.735924	−	0.677064i	$-0.236748\pi$
$647$	−3594.14	−	6225.23i	−0.218393	−	0.378267i	−0.954317	+	0.298797i	$0.903415\pi$
$648$	−2286.23	−	3959.87i	−0.138598	−	0.240059i
$649$	49582.8			2.99891
$650$	4103.26	+	848.653i	0.247605	+	0.0512107i
$651$	25881.6			1.55819
$652$	119.657	+	207.252i	0.00718732	+	0.0124488i
$653$	8854.00	+	15335.6i	0.530603	+	0.919032i	0.999362	+	0.0357058i	$0.0113679\pi$
$653$	8854.00	+	15335.6i	0.530603	+	0.919032i	−0.468759	+	0.883326i	$0.655299\pi$
$654$	−1566.57	+	2713.37i	−0.0936660	+	0.162234i
$655$	−12570.7			−0.749889
$656$	10036.5	−	17383.7i	0.597344	−	1.03463i
$657$	4260.71	−	7379.77i	0.253008	−	0.438222i
$658$	671.198			0.0397660
$659$	−3818.93	+	6614.57i	−0.225742	+	0.390997i	−0.956542	−	0.291595i	$-0.905814\pi$
$659$	−3818.93	+	6614.57i	−0.225742	+	0.390997i	0.730800	+	0.682592i	$0.239147\pi$
$660$	−5974.33	−	10347.8i	−0.352349	−	0.610287i
$661$	−3602.36	−	6239.47i	−0.211975	−	0.367151i	0.740358	−	0.672213i	$-0.234656\pi$
$661$	−3602.36	−	6239.47i	−0.211975	−	0.367151i	−0.952333	+	0.305062i	$0.901323\pi$
$662$	−22397.9			−1.31498
$663$	−30792.8	+	34578.8i	−1.80376	+	2.02553i
$664$	14248.3			0.832744
$665$	−3159.57	−	5472.54i	−0.184245	−	0.319122i
$666$	−12613.3	−	21846.9i	−0.733868	−	1.27110i
$667$	−3180.59	+	5508.94i	−0.184637	+	0.319801i
$668$	−1116.57			−0.0646726
$669$	814.539	−	1410.82i	0.0470731	−	0.0815329i
$670$	−3887.26	+	6732.94i	−0.224146	+	0.388233i
$671$	−19399.9			−1.11613
$672$	−18692.2	+	32375.9i	−1.07302	+	1.85852i
$673$	841.833	+	1458.10i	0.0482173	+	0.0835149i	0.889127	−	0.457661i	$-0.151313\pi$
$673$	841.833	+	1458.10i	0.0482173	+	0.0835149i	−0.840909	+	0.541176i	$0.817979\pi$
$674$	4821.10	+	8350.38i	0.275522	+	0.477218i
$675$	−4965.54			−0.283146
$676$	9652.46	+	4171.15i	0.549184	+	0.237321i
$677$	31345.0			1.77945			0.889723	−	0.456500i	$-0.150897\pi$
$677$	31345.0			1.77945			0.889723	+	0.456500i	$0.150897\pi$
$678$	4699.92	+	8140.50i	0.266223	+	0.461112i
$679$	−206.130	−	357.028i	−0.0116503	−	0.0201789i
$680$	3240.97	−	5613.53i	0.182773	−	0.316572i
$681$	34028.3			1.91478
$682$	13544.6	−	23460.0i	0.760484	−	1.31720i
$683$	−4305.25	+	7456.91i	−0.241194	+	0.417761i	−0.961055	−	0.276358i	$-0.910872\pi$
$683$	−4305.25	+	7456.91i	−0.241194	+	0.417761i	0.719860	+	0.694119i	$0.244206\pi$
$684$	13509.5			0.755187
$685$	3896.39	−	6748.74i	0.217333	−	0.376432i
$686$	7602.61	+	13168.1i	0.423133	+	0.732887i
$687$	−6660.56	−	11536.4i	−0.369893	−	0.640673i
$688$	10639.2			0.589560
$689$	−10514.7	+	11807.5i	−0.581389	+	0.652872i
$690$	−8006.58			−0.441747
$691$	1588.23	+	2750.89i	0.0874370	+	0.151445i	0.906427	−	0.422362i	$-0.138799\pi$
$691$	1588.23	+	2750.89i	0.0874370	+	0.151445i	−0.818990	+	0.573808i	$0.805466\pi$
$692$	−1800.74	−	3118.98i	−0.0989219	−	0.171338i
$693$	31507.9	−	54573.3i	1.72711	−	2.99144i
$694$	6594.78			0.360713
$695$	3909.48	−	6771.42i	0.213374	−	0.369575i
$696$	6258.78	−	10840.5i	0.340860	−	0.590386i
$697$	28525.1			1.55017
$698$	−10667.4	+	18476.5i	−0.578463	+	1.00193i
$699$	−23144.9	−	40088.1i	−1.25239	−	2.16920i
$700$	1330.85	+	2305.10i	0.0718592	+	0.124464i
$701$	−5959.22			−0.321079			−0.160540	−	0.987029i	$-0.551323\pi$
$701$	−5959.22			−0.321079			−0.160540	+	0.987029i	$0.551323\pi$
$702$	−32599.9	−	6742.44i	−1.75271	−	0.362503i
$703$	−8067.63			−0.432826
$704$	1459.42	+	2527.78i	0.0781304	+	0.135326i
$705$	−184.728	−	319.959i	−0.00986846	−	0.0170927i
$706$	14301.8	−	24771.5i	0.762403	−	1.32052i
$707$	22591.1			1.20173
$708$	18222.8	−	31562.9i	0.967311	−	1.67543i
$709$	−358.955	+	621.728i	−0.0190139	+	0.0329330i	−0.875376	−	0.483443i	$-0.839386\pi$
$709$	−358.955	+	621.728i	−0.0190139	+	0.0329330i	0.856362	+	0.516376i	$0.172719\pi$
$710$	−855.654			−0.0452283
$711$	8250.11	−	14289.6i	0.435166	−	0.753730i
$712$	−1620.95	−	2807.57i	−0.0853198	−	0.147778i
$713$	−3397.35	−	5884.39i	−0.178446	−	0.309077i
$714$	−78575.9			−4.11853
$715$	13086.0	+	2706.50i	0.684459	+	0.141563i
$716$	−18472.6			−0.964183
$717$	−29251.5	−	50665.1i	−1.52360	−	2.63895i
$718$	8085.98	+	14005.3i	0.420287	+	0.727958i
$719$	−6959.11	+	12053.5i	−0.360961	+	0.625203i	−0.988119	−	0.153689i	$-0.950885\pi$
$719$	−6959.11	+	12053.5i	−0.360961	+	0.625203i	0.627158	+	0.778892i	$0.284218\pi$
$720$	19719.2			1.02068
$721$	−15668.9	+	27139.4i	−0.809350	+	1.40184i
$722$	−6492.13	+	11244.7i	−0.334643	+	0.579619i
$723$	52876.6			2.71992
$724$	6029.70	−	10443.7i	0.309519	−	0.536103i
$725$	−1554.84	−	2693.07i	−0.0796489	−	0.137956i
$726$	−30061.9	−	52068.7i	−1.53678	−	2.66178i
$727$	−29891.7			−1.52492			−0.762462	−	0.647033i	$-0.776010\pi$
$727$	−29891.7			−1.52492			−0.762462	+	0.647033i	$0.776010\pi$
$728$	−3765.30	−	11375.5i	−0.191691	−	0.579125i
$729$	−27193.4			−1.38157
$730$	1533.29	+	2655.73i	0.0777390	+	0.134648i
$731$	7559.59	+	13093.6i	0.382492	+	0.662495i
$732$	−7129.92	+	12349.4i	−0.360013	+	0.623560i
$733$	−19352.2			−0.975159			−0.487579	−	0.873079i	$-0.662120\pi$
$733$	−19352.2			−0.975159			−0.487579	+	0.873079i	$0.662120\pi$
$734$	11901.4	−	20613.9i	0.598488	−	1.03661i
$735$	−3324.17	+	5757.62i	−0.166821	+	0.288943i
$736$	9814.57			0.491535
$737$	−12397.1	+	21472.5i	−0.619612	+	1.07320i
$738$	22460.9	+	38903.4i	1.12032	+	1.94045i
$739$	−1444.91	−	2502.66i	−0.0719242	−	0.124576i	0.827820	−	0.560993i	$-0.189581\pi$
$739$	−1444.91	−	2502.66i	−0.0719242	−	0.124576i	−0.899745	+	0.436417i	$0.856247\pi$
$740$	3398.18			0.168810
$741$	−15508.3	+	17415.1i	−0.768841	+	0.863372i
$742$	−26831.0			−1.32749
$743$	68.6310	+	118.872i	0.00338873	+	0.00586945i	0.867715	−	0.497062i	$-0.165588\pi$
$743$	68.6310	+	118.872i	0.00338873	+	0.00586945i	−0.864326	+	0.502932i	$0.832255\pi$
$744$	6685.33	+	11579.3i	0.329430	+	0.570590i
$745$	−171.720	+	297.427i	−0.00844472	+	0.0146267i
$746$	24305.2			1.19287
$747$	−30798.9	+	53345.3i	−1.50853	+	2.61286i
$748$	−15392.6	+	26660.8i	−0.752419	+	1.30323i
$749$	−7854.41			−0.383170
$750$	1957.02	−	3389.67i	0.0952806	−	0.165031i
$751$	9116.92	+	15791.0i	0.442984	+	0.767271i	0.997909	−	0.0646292i	$-0.0205865\pi$
$751$	9116.92	+	15791.0i	0.442984	+	0.767271i	−0.554925	+	0.831900i	$0.687253\pi$
$752$	334.918	+	580.095i	0.0162410	+	0.0281302i
$753$	25599.1			1.23889
$754$	−6551.12	−	19791.8i	−0.316416	−	0.955936i
$755$	−17646.2			−0.850612
$756$	−10573.4	−	18313.7i	−0.508667	−	0.881037i
$757$	−15282.1	−	26469.4i	−0.733737	−	1.27087i	−0.955275	−	0.295718i	$-0.904441\pi$
$757$	−15282.1	−	26469.4i	−0.733737	−	1.27087i	0.221538	−	0.975152i	$-0.428892\pi$
$758$	11763.5	−	20374.9i	0.563678	−	0.976319i
$759$	−25534.3			−1.22113
$760$	1632.27	−	2827.17i	0.0779059	−	0.134937i
$761$	16006.5	−	27724.1i	0.762464	−	1.32063i	−0.179113	−	0.983828i	$-0.557323\pi$
$761$	16006.5	−	27724.1i	0.762464	−	1.32063i	0.941577	−	0.336798i	$-0.109344\pi$
$762$	16771.5			0.797331
$763$	1112.93	−	1927.64i	0.0528055	−	0.0914619i
$764$	−9435.72	−	16343.1i	−0.446823	−	0.773919i
$765$	14011.3	+	24268.2i	0.662195	+	1.14695i
$766$	40377.7			1.90457
$767$	12808.0	+	38694.8i	0.602962	+	1.82163i
$768$	−45929.2			−2.15798
$769$	16954.1	+	29365.4i	0.795034	+	1.37704i	0.922817	+	0.385238i	$0.125881\pi$
$769$	16954.1	+	29365.4i	0.795034	+	1.37704i	−0.127783	+	0.991802i	$0.540786\pi$
$770$	11338.6	+	19639.1i	0.530670	+	0.919147i
$771$	16371.3	−	28355.9i	0.764718	−	1.32453i
$772$	15765.5			0.734991
$773$	−6128.44	+	10614.8i	−0.285155	+	0.493903i	−0.972647	−	0.232289i	$-0.925378\pi$
$773$	−6128.44	+	10614.8i	−0.285155	+	0.493903i	0.687492	+	0.726192i	$0.258712\pi$
$774$	−11904.9	+	20619.9i	−0.552860	+	0.957582i
$775$	3321.62			0.153956
$776$	106.489	−	184.444i	0.00492619	−	0.00853241i
$777$	13830.6	+	23955.3i	0.638573	+	1.10604i
$778$	2039.13	+	3531.87i	0.0939669	+	0.162755i
$779$	14366.2			0.660750
$780$	6532.28	−	7335.44i	0.299863	−	0.336732i
$781$	−2728.82			−0.125026
$782$	10314.3	+	17864.9i	0.471661	+	0.816940i
$783$	12353.0	+	21396.1i	0.563807	+	0.976543i
$784$	6026.82	−	10438.8i	0.274545	−	0.475526i
$785$	−6277.48			−0.285418
$786$	−39361.8	+	68176.6i	−1.78625	+	3.09387i
$787$	−5158.11	+	8934.11i	−0.233630	+	0.404659i	−0.958874	−	0.283833i	$-0.908394\pi$
$787$	−5158.11	+	8934.11i	−0.233630	+	0.404659i	0.725244	+	0.688492i	$0.241727\pi$
$788$	3355.52			0.151695
$789$	−7370.97	+	12766.9i	−0.332590	+	0.576063i
$790$	2968.94	+	5142.35i	0.133709	+	0.231591i
$791$	−3338.94	−	5783.21i	−0.150087	−	0.259958i
$792$	32554.5			1.46058
$793$	−5011.31	−	15139.9i	−0.224410	−	0.677972i
$794$	34687.8			1.55041
$795$	7384.47	+	12790.3i	0.329434	+	0.570597i
$796$	−459.094	−	795.174i	−0.0204424	−	0.0354073i
$797$	13961.1	−	24181.3i	0.620486	−	1.07471i	−0.368910	−	0.929465i	$-0.620269\pi$
$797$	13961.1	−	24181.3i	0.620486	−	1.07471i	0.989395	−	0.145248i	$-0.0463979\pi$
$798$	−39573.5			−1.75550
$799$	−475.944	+	824.360i	−0.0210735	+	0.0365003i
$800$	−2398.95	+	4155.10i	−0.106019	+	0.183631i
$801$	14015.3			0.618235
$802$	−10714.2	+	18557.6i	−0.471736	+	0.817071i
$803$	4889.90	+	8469.56i	0.214895	+	0.372210i
$804$	9112.48	+	15783.3i	0.399717	+	0.692330i
$805$	5688.07			0.249041
$806$	21807.2	+	4510.25i	0.953008	+	0.197105i
$807$	46348.5			2.02174
$808$	5835.39	+	10107.2i	0.254070	+	0.440061i
$809$	−11434.1	−	19804.5i	−0.496912	−	0.860677i	0.503081	−	0.864239i	$-0.332200\pi$
$809$	−11434.1	−	19804.5i	−0.496912	−	0.860677i	−0.999994	+	0.00356185i	$0.998866\pi$
$810$	−3556.84	+	6160.62i	−0.154290	+	0.267237i
$811$	−5369.61			−0.232494			−0.116247	−	0.993220i	$-0.537086\pi$
$811$	−5369.61			−0.232494			−0.116247	+	0.993220i	$0.537086\pi$
$812$	6621.65	−	11469.0i	0.286175	−	0.495670i
$813$	−34877.8	+	60410.2i	−1.50457	+	2.60600i
$814$	28952.0			1.24664
$815$	−125.004	+	216.513i	−0.00537262	+	0.00930565i
$816$	−39208.3	−	67910.7i	−1.68206	−	2.91342i
$817$	3807.27	+	6594.38i	0.163035	+	0.282385i
$818$	−24539.6			−1.04891
$819$	50728.5	+	10491.9i	2.16434	+	0.447638i
$820$	−6051.24			−0.257705
$821$	−17684.3	−	30630.1i	−0.751749	−	1.30207i	−0.946974	−	0.321310i	$-0.895877\pi$
$821$	−17684.3	−	30630.1i	−0.751749	−	1.30207i	0.195225	−	0.980759i	$-0.437456\pi$
$822$	−24401.1	−	42263.9i	−1.03538	−	1.79334i
$823$	61.3032	−	106.180i	0.00259647	−	0.00449722i	−0.864724	−	0.502247i	$-0.832507\pi$
$823$	61.3032	−	106.180i	0.00259647	−	0.00449722i	0.867321	+	0.497750i	$0.165840\pi$
$824$	−16189.4			−0.684449
$825$	6241.28	−	10810.2i	0.263386	−	0.456198i
$826$	−34585.0	+	59903.0i	−1.45686	+	2.52335i
$827$	−16787.5			−0.705874			−0.352937	−	0.935647i	$-0.614817\pi$
$827$	−16787.5			−0.705874			−0.352937	+	0.935647i	$0.614817\pi$
$828$	−6080.16	+	10531.1i	−0.255193	+	0.442008i
$829$	−9420.27	−	16316.4i	−0.394668	−	0.683584i	0.598391	−	0.801204i	$-0.295807\pi$
$829$	−9420.27	−	16316.4i	−0.394668	−	0.683584i	−0.993059	+	0.117620i	$0.962474\pi$
$830$	−11083.5	−	19197.2i	−0.463511	−	0.802824i
$831$	−56233.6			−2.34744
$832$	−1595.71	+	1791.91i	−0.0664921	+	0.0746674i
$833$	17129.1			0.712472
$834$	−24483.0	−	42405.9i	−1.01652	−	1.76067i
$835$	−583.229	−	1010.18i	−0.0241718	−	0.0418669i
$836$	−7752.24	+	13427.3i	−0.320714	+	0.555493i
$837$	−26389.8			−1.08980
$838$	−13961.3	+	24181.6i	−0.575518	+	0.996827i
$839$	23021.3	−	39874.1i	0.947300	−	1.64077i	0.196222	−	0.980560i	$-0.437133\pi$
$839$	23021.3	−	39874.1i	0.947300	−	1.64077i	0.751079	−	0.660213i	$-0.229534\pi$
$840$	−11193.0			−0.459756
$841$	4458.37	−	7722.13i	0.182803	−	0.316623i
$842$	−3652.81	−	6326.85i	−0.149506	−	0.258952i
$843$	−21890.6	−	37915.6i	−0.894368	−	1.54909i
$844$	−2305.84			−0.0940406
$845$	1268.15	+	10911.6i	0.0516281	+	0.444224i
$846$	−1499.05			−0.0609199
$847$	21356.7	+	36990.8i	0.866380	+	1.50061i
$848$	−13388.3	−	23189.2i	−0.542164	−	0.939056i
$849$	−30916.6	+	53549.0i	−1.24977	+	2.16466i
$850$	−10084.4			−0.406931
$851$	3630.96	−	6289.02i	0.146261	−	0.253331i
$852$	−1002.91	+	1737.09i	−0.0403275	+	0.0698493i
$853$	16832.9			0.675672			0.337836	−	0.941205i	$-0.390305\pi$
$853$	16832.9			0.675672			0.337836	+	0.941205i	$0.390305\pi$
$854$	13531.8	−	23437.8i	0.542212	−	0.939139i
$855$	7056.56	+	12222.3i	0.282257	+	0.488883i
$856$	−2028.83	−	3514.04i	−0.0810094	−	0.140312i
$857$	27166.1			1.08282			0.541410	−	0.840759i	$-0.317891\pi$
$857$	27166.1			1.08282			0.541410	+	0.840759i	$0.317891\pi$
$858$	55653.9	−	62496.7i	2.21445	−	2.48672i
$859$	−20292.7			−0.806028			−0.403014	−	0.915194i	$-0.632037\pi$
$859$	−20292.7			−0.806028			−0.403014	+	0.915194i	$0.632037\pi$
$860$	−1603.67	−	2777.63i	−0.0635868	−	0.110136i
$861$	−24628.6	−	42657.9i	−0.974842	−	1.68848i
$862$	18779.5	−	32527.0i	0.742031	−	1.28524i
$863$	41928.1			1.65382			0.826911	−	0.562333i	$-0.190096\pi$
$863$	41928.1			1.65382			0.826911	+	0.562333i	$0.190096\pi$
$864$	19059.3	−	33011.7i	0.750475	−	1.29986i
$865$	1881.20	−	3258.34i	0.0739455	−	0.128077i
$866$	50092.7			1.96561
$867$	34206.8	−	59248.0i	1.33994	−	2.32084i
$868$	7072.94	+	12250.7i	0.276580	+	0.479050i
$869$	9468.43	+	16399.8i	0.369614	+	0.640190i
$870$	−19474.4			−0.758899
$871$	−19959.7	−	4128.14i	−0.776473	−	0.160593i
$872$	1149.90			0.0446564
$873$	460.369	+	797.382i	0.0178478	+	0.0309133i
$874$	5194.64	+	8997.37i	0.201043	+	0.348216i
$875$	−1390.32	+	2408.10i	−0.0537158	+	0.0930385i
$876$	7188.62			0.277261
$877$	−7367.15	+	12760.3i	−0.283661	+	0.491316i	−0.972284	−	0.233804i	$-0.924882\pi$
$877$	−7367.15	+	12760.3i	−0.283661	+	0.491316i	0.688622	+	0.725120i	$0.258216\pi$
$878$	1486.44	−	2574.59i	0.0571354	−	0.0989613i
$879$	42267.1			1.62188
$880$	−11315.6	+	19599.2i	−0.433466	+	0.750785i
$881$	6596.07	+	11424.7i	0.252244	+	0.436900i	0.964143	−	0.265382i	$-0.0854981\pi$
$881$	6596.07	+	11424.7i	0.252244	+	0.436900i	−0.711899	+	0.702282i	$0.752165\pi$
$882$	13487.6	+	23361.2i	0.514910	+	0.891851i
$883$	18768.0			0.715283			0.357641	−	0.933859i	$-0.383581\pi$
$883$	18768.0			0.715283			0.357641	+	0.933859i	$0.383581\pi$
$884$	−24782.5	−	5125.61i	−0.942901	−	0.195015i
$885$	38074.2			1.44616
$886$	21067.2	+	36489.4i	0.798833	+	1.38362i
$887$	15510.0	+	26864.1i	0.587119	+	1.01692i	0.994608	+	0.103710i	$0.0330713\pi$
$887$	15510.0	+	26864.1i	0.587119	+	1.01692i	−0.407488	+	0.913210i	$0.633595\pi$
$888$	−7145.03	+	12375.6i	−0.270013	+	0.467676i
$889$	−11914.8			−0.449506
$890$	−2521.82	+	4367.91i	−0.0949792	+	0.164509i
$891$	−11343.3	+	19647.3i	−0.426505	+	0.738729i
$892$	890.391			0.0334221
$893$	−239.702	+	415.176i	−0.00898244	+	0.0155580i
$894$	1075.39	+	1862.63i	0.0402309	+	0.0696820i
$895$	−9649.02	−	16712.6i	−0.360370	−	0.624179i
$896$	30081.5			1.12160
$897$	−6595.93	−	19927.2i	−0.245520	−	0.741750i
$898$	−49012.1			−1.82133
$899$	−8263.36	−	14312.6i	−0.306561	−	0.530980i
$900$	−2972.31	−	5148.19i	−0.110086	−	0.190674i
$901$	19025.8	−	32953.6i	0.703485	−	1.21847i
$902$	−51555.5			−1.90312
$903$	13053.9	−	22610.0i	0.481069	−	0.833236i
$904$	1724.93	−	2987.66i	0.0634626	−	0.109920i
$905$	12598.2			0.462740
$906$	−55254.6	+	95703.7i	−2.02617	+	3.50943i
$907$	−8412.86	−	14571.5i	−0.307987	−	0.533450i	0.669935	−	0.742420i	$-0.266322\pi$
$907$	−8412.86	−	14571.5i	−0.307987	−	0.533450i	−0.977922	+	0.208970i	$0.932989\pi$
$908$	9299.27	+	16106.8i	0.339876	+	0.588682i
$909$	−50454.7			−1.84101
$910$	−12397.6	+	13921.9i	−0.451621	+	0.507149i
$911$	−45071.8			−1.63918			−0.819591	−	0.572949i	$-0.805799\pi$
$911$	−45071.8			−1.63918			−0.819591	+	0.572949i	$0.805799\pi$
$912$	−19746.6	−	34202.2i	−0.716970	−	1.24183i
$913$	−35347.1	−	61223.0i	−1.28129	−	2.21926i
$914$	22093.2	−	38266.6i	0.799539	−	1.38484i
$915$	−14897.0			−0.538229
$916$	3640.41	−	6305.37i	0.131313	−	0.227440i
$917$	27963.6	−	48434.3i	1.00702	−	1.74421i
$918$	80119.0			2.88052
$919$	−8020.55	+	13892.0i	−0.287893	+	0.498645i	−0.973307	−	0.229509i	$-0.926288\pi$
$919$	−8020.55	+	13892.0i	−0.287893	+	0.498645i	0.685414	+	0.728154i	$0.259621\pi$
$920$	1469.25	+	2544.82i	0.0526521	+	0.0911960i
$921$	26646.9	+	46153.8i	0.953360	+	1.65127i
$922$	12716.4			0.454221
$923$	−704.900	−	2129.60i	−0.0251377	−	0.0759443i
$924$	53159.8			1.89267
$925$	1775.01	+	3074.41i	0.0630941	+	0.109282i
$926$	−4086.14	−	7077.40i	−0.145010	−	0.251164i
$927$	34994.8	−	60612.8i	1.23989	−	2.14756i
$928$	23871.9			0.844433
$929$	−23747.7	+	41132.2i	−0.838682	+	1.45264i	0.0523143	+	0.998631i	$0.483340\pi$
$929$	−23747.7	+	41132.2i	−0.838682	+	1.45264i	−0.890997	+	0.454010i	$0.849993\pi$
$930$	10400.8	−	18014.7i	0.366726	−	0.635188i
$931$	8626.82			0.303687
$932$	12650.1	−	21910.6i	0.444601	−	0.770071i
$933$	1149.84	+	1991.58i	0.0403473	+	0.0698836i
$934$	25010.6	+	43319.7i	0.876202	+	1.51763i
$935$	−32160.8			−1.12489
$936$	8409.38	+	25405.9i	0.293664	+	0.887197i
$937$	−46028.1			−1.60477			−0.802387	−	0.596804i	$-0.796437\pi$
$937$	−46028.1			−1.60477			−0.802387	+	0.596804i	$0.796437\pi$
$938$	−17294.5	−	29955.0i	−0.602010	−	1.04271i
$939$	2610.97	+	4522.33i	0.0907409	+	0.157168i
$940$	100.965	−	174.877i	0.00350333	−	0.00606794i
$941$	13733.5			0.475771			0.237885	−	0.971293i	$-0.423546\pi$
$941$	13733.5			0.475771			0.237885	+	0.971293i	$0.423546\pi$
$942$	−19656.3	+	34045.7i	−0.679869	+	1.17757i
$943$	−6465.75	+	11199.0i	−0.223281	+	0.386734i
$944$	−69029.7			−2.38000
$945$	11045.9	−	19132.0i	0.380236	−	0.658587i
$946$	−13663.0	−	23665.0i	−0.469579	−	0.813335i
$947$	−21500.1	−	37239.3i	−0.737760	−	1.27784i	−0.953502	−	0.301388i	$-0.902550\pi$
$947$	−21500.1	−	37239.3i	−0.737760	−	1.27784i	0.215741	−	0.976451i	$-0.430783\pi$
$948$	13919.5			0.476882
$949$	−5346.58	+	6003.95i	−0.182885	+	0.205371i
$950$	−5078.84			−0.173452
$951$	31959.3	+	55355.2i	1.08975	+	1.88750i
$952$	14419.1	+	24974.7i	0.490890	+	0.850246i
$953$	−22834.1	+	39549.8i	−0.776148	+	1.34433i	0.157999	+	0.987439i	$0.449496\pi$
$953$	−22834.1	+	39549.8i	−0.776148	+	1.34433i	−0.934147	+	0.356888i	$0.883838\pi$
$954$	59924.0			2.03366
$955$	9857.33	−	17073.4i	0.334006	−	0.578516i
$956$	15987.8	−	27691.6i	0.540880	−	0.936831i
$957$	−62106.9			−2.09784
$958$	−5467.58	+	9470.13i	−0.184394	+	0.319380i
$959$	17335.1	+	30025.3i	0.583712	+	1.01102i
$960$	1120.67	+	1941.06i	0.0376766	+	0.0652578i
$961$	−12137.9			−0.407436
$962$	7478.77	+	22594.4i	0.250650	+	0.757247i
$963$	17542.0			0.587001
$964$	14450.2	+	25028.4i	0.482789	+	0.836215i
$965$	8234.98	+	14263.4i	0.274708	+	0.475808i
$966$	17810.7	−	30849.0i	0.593219	−	1.02749i
$967$	44508.1			1.48013			0.740064	−	0.672536i	$-0.234795\pi$
$967$	44508.1			1.48013			0.740064	+	0.672536i	$0.234795\pi$
$968$	−11033.1	+	19109.8i	−0.366339	+	0.634517i
$969$	28061.5	−	48603.9i	0.930304	−	1.61133i
$970$	−331.342			−0.0109678
$971$	−4130.88	+	7154.89i	−0.136525	+	0.236469i	−0.926179	−	0.377084i	$-0.876927\pi$
$971$	−4130.88	+	7154.89i	−0.136525	+	0.236469i	0.789654	+	0.613553i	$0.210260\pi$
$972$	−4495.63	−	7786.66i	−0.148351	−	0.256952i
$973$	17393.3	+	30126.2i	0.573078	+	0.992600i
$974$	−17362.0			−0.571164
$975$	10048.6	+	2078.29i	0.330065	+	0.0682653i
$976$	27008.7			0.885788
$977$	780.758	+	1352.31i	0.0255667	+	0.0442828i	0.878526	−	0.477695i	$-0.158528\pi$
$977$	780.758	+	1352.31i	0.0255667	+	0.0442828i	−0.852959	+	0.521978i	$0.825194\pi$
$978$	782.833	+	1355.91i	0.0255953	+	0.0443324i
$979$	−8042.49	+	13930.0i	−0.262553	+	0.454755i
$980$	−3633.72			−0.118444
$981$	−2485.60	+	4305.18i	−0.0808960	+	0.140116i
$982$	21221.2	−	36756.3i	0.689610	−	1.19444i
$983$	1621.36			0.0526076			0.0263038	−	0.999654i	$-0.491626\pi$
$983$	1621.36			0.0526076			0.0263038	+	0.999654i	$0.491626\pi$
$984$	12723.3	−	22037.5i	0.412201	−	0.713953i
$985$	1752.73	+	3035.81i	0.0566970	+	0.0982021i
$986$	25087.4	+	43452.7i	0.810290	+	1.40346i
$987$	1643.72			0.0530092
$988$	−12481.3	−	2581.43i	−0.401906	−	0.0831238i
$989$	−6854.08			−0.220371
$990$	−25323.6	−	43861.7i	−0.812966	−	1.40810i
$991$	−9124.80	−	15804.6i	−0.292491	−	0.506610i	0.681907	−	0.731439i	$-0.261151\pi$
$991$	−9124.80	−	15804.6i	−0.292491	−	0.506610i	−0.974398	+	0.224829i	$0.927818\pi$
$992$	−12749.4	+	22082.6i	−0.408059	+	0.706779i
$993$	−54851.0			−1.75291
$994$	1903.41	−	3296.80i	0.0607369	−	0.105199i
$995$	479.607	−	830.704i	0.0152810	−	0.0264674i
$996$	−51963.6			−1.65314
$997$	−30216.7	+	52336.8i	−0.959851	+	1.66251i	−0.236997	+	0.971510i	$0.576163\pi$
$997$	−30216.7	+	52336.8i	−0.959851	+	1.66251i	−0.722854	+	0.691001i	$0.757170\pi$
$998$	−6648.53	−	11515.6i	−0.210877	−	0.365250i
$999$	−14102.2	−	24425.8i	−0.446621	−	0.773571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.4.e.a.16.6	✓	14
13.3	even	3		845.4.a.k.1.2		7
13.9	even	3	inner	65.4.e.a.61.6	yes	14
13.10	even	6		845.4.a.h.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.4.e.a.16.6	✓	14	1.1	even	1	trivial
65.4.e.a.61.6	yes	14	13.9	even	3	inner
845.4.a.h.1.6		7	13.10	even	6
845.4.a.k.1.2		7	13.3	even	3

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	65.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.78789 + 3.09671i) q^{2} +(4.37841 + 7.58363i) q^{3} +(-2.39307 + 4.14492i) q^{4} -5.00000 q^{5} +(-15.6562 + 27.1173i) q^{6} +(11.1225 - 19.2648i) q^{7} +11.4920 q^{8} +(-24.8410 + 43.0258i) q^{9} +O(q^{10})\)	\(q+(1.78789 + 3.09671i) q^{2} +(4.37841 + 7.58363i) q^{3} +(-2.39307 + 4.14492i) q^{4} -5.00000 q^{5} +(-15.6562 + 27.1173i) q^{6} +(11.1225 - 19.2648i) q^{7} +11.4920 q^{8} +(-24.8410 + 43.0258i) q^{9} +(-8.93943 - 15.4835i) q^{10} +(-28.5093 - 49.3796i) q^{11} -41.9114 q^{12} +(31.1719 - 35.0045i) q^{13} +79.5433 q^{14} +(-21.8921 - 37.9182i) q^{15} +(39.6910 + 68.7468i) q^{16} +(-56.4039 + 97.6945i) q^{17} -177.651 q^{18} +(-28.4070 + 49.2023i) q^{19} +(11.9654 - 20.7246i) q^{20} +194.796 q^{21} +(101.943 - 176.570i) q^{22} +(-25.5700 - 44.2885i) q^{23} +(50.3168 + 87.1512i) q^{24} +25.0000 q^{25} +(164.130 + 33.9461i) q^{26} -198.622 q^{27} +(53.2341 + 92.2041i) q^{28} +(-62.1938 - 107.723i) q^{29} +(78.2810 - 135.587i) q^{30} +132.865 q^{31} +(-95.9578 + 166.204i) q^{32} +(249.651 - 432.408i) q^{33} -403.375 q^{34} +(-55.6127 + 96.3240i) q^{35} +(-118.892 - 205.928i) q^{36} +(71.0005 + 122.976i) q^{37} -203.154 q^{38} +(401.944 + 83.1318i) q^{39} -57.4601 q^{40} +(-126.432 - 218.987i) q^{41} +(348.273 + 603.227i) q^{42} +(67.0129 - 116.070i) q^{43} +272.899 q^{44} +(124.205 - 215.129i) q^{45} +(91.4325 - 158.366i) q^{46} +8.43814 q^{47} +(-347.567 + 602.004i) q^{48} +(-75.9218 - 131.500i) q^{49} +(44.6971 + 77.4177i) q^{50} -987.838 q^{51} +(70.4944 + 212.973i) q^{52} -337.313 q^{53} +(-355.113 - 615.073i) q^{54} +(142.547 + 246.898i) q^{55} +(127.820 - 221.391i) q^{56} -497.509 q^{57} +(222.391 - 385.192i) q^{58} +(-434.794 + 753.086i) q^{59} +209.557 q^{60} +(170.119 - 294.654i) q^{61} +(237.547 + 411.444i) q^{62} +(552.589 + 957.113i) q^{63} -51.1908 q^{64} +(-155.859 + 175.023i) q^{65} +1785.39 q^{66} +(-217.422 - 376.587i) q^{67} +(-269.957 - 467.580i) q^{68} +(223.912 - 387.827i) q^{69} -397.717 q^{70} +(23.9292 - 41.4466i) q^{71} +(-285.473 + 494.453i) q^{72} -171.520 q^{73} +(-253.882 + 439.736i) q^{74} +(109.460 + 189.591i) q^{75} +(-135.960 - 235.489i) q^{76} -1268.38 q^{77} +(461.196 + 1393.34i) q^{78} -332.117 q^{79} +(-198.455 - 343.734i) q^{80} +(-198.941 - 344.576i) q^{81} +(452.094 - 783.049i) q^{82} +1239.84 q^{83} +(-466.161 + 807.415i) q^{84} +(282.020 - 488.472i) q^{85} +479.246 q^{86} +(544.620 - 943.309i) q^{87} +(-327.630 - 567.471i) q^{88} +(-141.050 - 244.306i) q^{89} +888.256 q^{90} +(-327.645 - 989.859i) q^{91} +244.763 q^{92} +(581.737 + 1007.60i) q^{93} +(15.0864 + 26.1305i) q^{94} +(142.035 - 246.011i) q^{95} -1680.57 q^{96} +(9.26632 - 16.0497i) q^{97} +(271.479 - 470.215i) q^{98} +2832.80 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 4 q^{3} - 30 q^{4} - 70 q^{5} - 23 q^{6} - 7 q^{7} + 42 q^{8} - 87 q^{9}+O(q^{10}) \) 14 * q - 2 * q^2 + 4 * q^3 - 30 * q^4 - 70 * q^5 - 23 * q^6 - 7 * q^7 + 42 * q^8 - 87 * q^9	\( 14 q - 2 q^{2} + 4 q^{3} - 30 q^{4} - 70 q^{5} - 23 q^{6} - 7 q^{7} + 42 q^{8} - 87 q^{9} + 10 q^{10} - 87 q^{11} - 158 q^{12} + 123 q^{13} + 132 q^{14} - 20 q^{15} + 134 q^{16} + 114 q^{17} + 414 q^{18} - 245 q^{19} + 150 q^{20} - 76 q^{21} - 338 q^{22} + 74 q^{23} - 334 q^{24} + 350 q^{25} + 243 q^{26} - 884 q^{27} - 230 q^{28} + 88 q^{29} + 115 q^{30} + 1000 q^{31} - 80 q^{32} + 194 q^{33} + 854 q^{34} + 35 q^{35} - 425 q^{36} - 633 q^{37} - 596 q^{38} + 970 q^{39} - 210 q^{40} - 162 q^{41} + 1439 q^{42} + 280 q^{43} + 440 q^{44} + 435 q^{45} + 11 q^{46} + 950 q^{47} - 2281 q^{48} - 1694 q^{49} - 50 q^{50} - 860 q^{51} - 956 q^{52} - 1206 q^{53} - 51 q^{54} + 435 q^{55} + 1277 q^{56} + 916 q^{57} + 1213 q^{58} - 1410 q^{59} + 790 q^{60} - 412 q^{61} + 56 q^{62} - 1241 q^{63} - 2358 q^{64} - 615 q^{65} + 4346 q^{66} - 1398 q^{67} + 493 q^{68} - 1080 q^{69} - 660 q^{70} + 584 q^{71} - 1545 q^{72} + 5076 q^{73} - 3840 q^{74} + 100 q^{75} - 3292 q^{76} - 5506 q^{77} + 1179 q^{78} + 928 q^{79} - 670 q^{80} + 473 q^{81} + 1583 q^{82} + 932 q^{83} + 3081 q^{84} - 570 q^{85} + 9858 q^{86} + 282 q^{87} - 3389 q^{88} - 443 q^{89} - 2070 q^{90} + 487 q^{91} + 6182 q^{92} + 2116 q^{93} - 2017 q^{94} + 1225 q^{95} + 954 q^{96} + 1870 q^{97} - 1364 q^{98} + 11378 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 + 4 * q^3 - 30 * q^4 - 70 * q^5 - 23 * q^6 - 7 * q^7 + 42 * q^8 - 87 * q^9 + 10 * q^10 - 87 * q^11 - 158 * q^12 + 123 * q^13 + 132 * q^14 - 20 * q^15 + 134 * q^16 + 114 * q^17 + 414 * q^18 - 245 * q^19 + 150 * q^20 - 76 * q^21 - 338 * q^22 + 74 * q^23 - 334 * q^24 + 350 * q^25 + 243 * q^26 - 884 * q^27 - 230 * q^28 + 88 * q^29 + 115 * q^30 + 1000 * q^31 - 80 * q^32 + 194 * q^33 + 854 * q^34 + 35 * q^35 - 425 * q^36 - 633 * q^37 - 596 * q^38 + 970 * q^39 - 210 * q^40 - 162 * q^41 + 1439 * q^42 + 280 * q^43 + 440 * q^44 + 435 * q^45 + 11 * q^46 + 950 * q^47 - 2281 * q^48 - 1694 * q^49 - 50 * q^50 - 860 * q^51 - 956 * q^52 - 1206 * q^53 - 51 * q^54 + 435 * q^55 + 1277 * q^56 + 916 * q^57 + 1213 * q^58 - 1410 * q^59 + 790 * q^60 - 412 * q^61 + 56 * q^62 - 1241 * q^63 - 2358 * q^64 - 615 * q^65 + 4346 * q^66 - 1398 * q^67 + 493 * q^68 - 1080 * q^69 - 660 * q^70 + 584 * q^71 - 1545 * q^72 + 5076 * q^73 - 3840 * q^74 + 100 * q^75 - 3292 * q^76 - 5506 * q^77 + 1179 * q^78 + 928 * q^79 - 670 * q^80 + 473 * q^81 + 1583 * q^82 + 932 * q^83 + 3081 * q^84 - 570 * q^85 + 9858 * q^86 + 282 * q^87 - 3389 * q^88 - 443 * q^89 - 2070 * q^90 + 487 * q^91 + 6182 * q^92 + 2116 * q^93 - 2017 * q^94 + 1225 * q^95 + 954 * q^96 + 1870 * q^97 - 1364 * q^98 + 11378 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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