LMFDB - Embedded newform 18.4.c.b.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,4,Mod(7,18)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("18.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	18.c (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:	$1.06203438010$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-35})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 8x^{2} - 9x + 81 $ x^4 - x^3 - 8x^2 - 9x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			13.1
Root			$2.81174 - 1.04601i$ of defining polynomial
Character	$\chi$	$=$	18.13
Dual form			18.4.c.b.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.73205i) q^{2} +(-1.81174 + 4.87007i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(9.93521 - 17.2083i) q^{5} +(-10.2470 + 1.73205i) q^{6} +(2.93521 + 5.08394i) q^{7} -8.00000 q^{8} +(-20.4352 - 17.6466i) q^{9} +39.7409 q^{10} +(-9.37043 - 16.2301i) q^{11} +(-13.2470 - 16.0162i) q^{12} +(-22.9352 + 39.7250i) q^{13} +(-5.87043 + 10.1679i) q^{14} +(65.8056 + 79.5621i) q^{15} +(-8.00000 - 13.8564i) q^{16} +16.8704 q^{17} +(10.1296 - 53.0414i) q^{18} -10.3521 q^{19} +(39.7409 + 68.8332i) q^{20} +(-30.0770 + 5.08394i) q^{21} +(18.7409 - 32.4601i) q^{22} +(-24.9352 + 43.1891i) q^{23} +(14.4939 - 38.9606i) q^{24} +(-134.917 - 233.683i) q^{25} -91.7409 q^{26} +(122.963 - 67.5500i) q^{27} -23.4817 q^{28} +(-5.45351 - 9.44575i) q^{29} +(-72.0000 + 193.541i) q^{30} +(-75.8056 + 131.299i) q^{31} +(16.0000 - 27.7128i) q^{32} +(96.0183 - 16.2301i) q^{33} +(16.8704 + 29.2204i) q^{34} +116.648 q^{35} +(102.000 - 35.4965i) q^{36} +346.186 q^{37} +(-10.3521 - 17.9304i) q^{38} +(-151.911 - 183.667i) q^{39} +(-79.4817 + 137.666i) q^{40} +(-132.370 + 229.272i) q^{41} +(-38.8826 - 47.0109i) q^{42} +(205.945 + 356.707i) q^{43} +74.9634 q^{44} +(-506.696 + 176.333i) q^{45} -99.7409 q^{46} +(-236.028 - 408.813i) q^{47} +(81.9756 - 13.8564i) q^{48} +(154.269 - 267.202i) q^{49} +(269.834 - 467.366i) q^{50} +(-30.5648 + 82.1602i) q^{51} +(-91.7409 - 158.900i) q^{52} +290.186 q^{53} +(239.963 + 145.429i) q^{54} -372.389 q^{55} +(-23.4817 - 40.6715i) q^{56} +(18.7553 - 50.4156i) q^{57} +(10.9070 - 18.8915i) q^{58} +(-26.6296 + 46.1238i) q^{59} +(-407.223 + 68.8332i) q^{60} +(146.972 + 254.563i) q^{61} -303.223 q^{62} +(29.7325 - 155.688i) q^{63} +64.0000 q^{64} +(455.732 + 789.352i) q^{65} +(124.130 + 150.079i) q^{66} +(199.277 - 345.159i) q^{67} +(-33.7409 + 58.4409i) q^{68} +(-165.158 - 199.684i) q^{69} +(116.648 + 202.040i) q^{70} -647.854 q^{71} +(163.482 + 141.173i) q^{72} -478.279 q^{73} +(346.186 + 599.612i) q^{74} +(1382.49 - 233.683i) q^{75} +(20.7043 - 35.8608i) q^{76} +(55.0084 - 95.2773i) q^{77} +(166.210 - 446.785i) q^{78} +(-187.158 - 324.167i) q^{79} -317.927 q^{80} +(106.196 + 721.224i) q^{81} -529.482 q^{82} +(-466.639 - 808.243i) q^{83} +(42.5427 - 114.358i) q^{84} +(167.611 - 290.311i) q^{85} +(-411.890 + 713.415i) q^{86} +(55.8818 - 9.44575i) q^{87} +(74.9634 + 129.840i) q^{88} +368.817 q^{89} +(-812.113 - 701.290i) q^{90} -269.279 q^{91} +(-99.7409 - 172.756i) q^{92} +(-502.097 - 607.059i) q^{93} +(472.056 - 817.626i) q^{94} +(-102.851 + 178.143i) q^{95} +(105.976 + 128.130i) q^{96} +(-137.075 - 237.420i) q^{97} +617.076 q^{98} +(-94.9184 + 497.021i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 3 q^{3} - 8 q^{4} + 9 q^{5} - 19 q^{7} - 32 q^{8} - 51 q^{9} + 36 q^{10} + 24 q^{11} - 12 q^{12} - 61 q^{13} + 38 q^{14} + 171 q^{15} - 32 q^{16} + 6 q^{17} + 102 q^{18} + 266 q^{19} + 36 q^{20}+ \cdots + 1557 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 3 * q^3 - 8 * q^4 + 9 * q^5 - 19 * q^7 - 32 * q^8 - 51 * q^9 + 36 * q^10 + 24 * q^11 - 12 * q^12 - 61 * q^13 + 38 * q^14 + 171 * q^15 - 32 * q^16 + 6 * q^17 + 102 * q^18 + 266 * q^19 + 36 * q^20 - 315 * q^21 - 48 * q^22 - 69 * q^23 - 24 * q^24 - 263 * q^25 - 244 * q^26 + 152 * q^28 - 237 * q^29 - 288 * q^30 - 211 * q^31 + 64 * q^32 + 630 * q^33 + 6 * q^34 + 774 * q^35 + 408 * q^36 + 524 * q^37 + 266 * q^38 - 249 * q^39 - 72 * q^40 - 468 * q^41 - 258 * q^42 + 86 * q^43 - 192 * q^44 - 459 * q^45 - 276 * q^46 - 483 * q^47 + 33 * q^49 + 526 * q^50 - 153 * q^51 - 244 * q^52 + 300 * q^53 + 468 * q^54 - 1674 * q^55 + 152 * q^56 + 987 * q^57 + 474 * q^58 - 168 * q^59 - 1260 * q^60 + 1049 * q^61 - 844 * q^62 - 957 * q^63 + 256 * q^64 + 747 * q^65 + 558 * q^66 + 1166 * q^67 - 12 * q^68 - 261 * q^69 + 774 * q^70 - 624 * q^71 + 408 * q^72 - 622 * q^73 + 524 * q^74 + 2835 * q^75 - 532 * q^76 + 1173 * q^77 + 132 * q^78 - 349 * q^79 - 288 * q^80 - 1143 * q^81 - 1872 * q^82 - 1221 * q^83 + 744 * q^84 + 486 * q^85 - 172 * q^86 - 2205 * q^87 - 192 * q^88 - 984 * q^89 - 1404 * q^90 + 214 * q^91 - 276 * q^92 - 789 * q^93 + 966 * q^94 - 1764 * q^95 + 96 * q^96 + 128 * q^97 + 132 * q^98 + 1557 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$3$	−1.81174	+	4.87007i	−0.348669	+	0.937246i
$3$	−1.81174	+	4.87007i	−0.348669	+	0.937246i
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	9.93521	−	17.2083i	0.888632	−	1.53916i	0.0471396	−	0.998888i	$-0.484989\pi$
$5$	9.93521	−	17.2083i	0.888632	−	1.53916i	0.841493	−	0.540268i	$-0.181677\pi$
$6$	−10.2470	+	1.73205i	−0.697217	+	0.117851i
$7$	2.93521	+	5.08394i	0.158487	+	0.274507i	0.934323	−	0.356427i	$-0.116005\pi$
$7$	2.93521	+	5.08394i	0.158487	+	0.274507i	−0.775837	+	0.630934i	$0.782672\pi$
$8$	−8.00000			−0.353553
$9$	−20.4352	−	17.6466i	−0.756860	−	0.653577i
$10$	39.7409			1.25672
$11$	−9.37043	−	16.2301i	−0.256845	−	0.444868i	0.708550	−	0.705660i	$-0.249349\pi$
$11$	−9.37043	−	16.2301i	−0.256845	−	0.444868i	−0.965395	+	0.260792i	$0.916016\pi$
$12$	−13.2470	−	16.0162i	−0.318672	−	0.385290i
$13$	−22.9352	+	39.7250i	−0.489314	+	0.847517i	−0.999924	−	0.0122953i	$-0.996086\pi$
$13$	−22.9352	+	39.7250i	−0.489314	+	0.847517i	0.510610	+	0.859812i	$0.329420\pi$
$14$	−5.87043	+	10.1679i	−0.112067	+	0.194106i
$15$	65.8056	+	79.5621i	1.13273	+	1.36952i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	16.8704			0.240687			0.120344	−	0.992732i	$-0.461600\pi$
$17$	16.8704			0.240687			0.120344	+	0.992732i	$0.461600\pi$
$18$	10.1296	−	53.0414i	0.132642	−	0.694555i
$19$	−10.3521			−0.124997			−0.0624985	−	0.998045i	$-0.519907\pi$
$19$	−10.3521			−0.124997			−0.0624985	+	0.998045i	$0.519907\pi$
$20$	39.7409	+	68.8332i	0.444316	+	0.769578i
$21$	−30.0770	+	5.08394i	−0.312540	+	0.0528289i
$22$	18.7409	−	32.4601i	0.181617	−	0.314569i
$23$	−24.9352	+	43.1891i	−0.226059	+	0.391545i	−0.956637	−	0.291284i	$-0.905917\pi$
$23$	−24.9352	+	43.1891i	−0.226059	+	0.391545i	0.730578	+	0.682829i	$0.239251\pi$
$24$	14.4939	−	38.9606i	0.123273	−	0.331366i
$25$	−134.917	−	233.683i	−1.07934	−	1.86946i
$26$	−91.7409			−0.691995
$27$	122.963	−	67.5500i	0.876456	−	0.481481i
$28$	−23.4817			−0.158487
$29$	−5.45351	−	9.44575i	−0.0349204	−	0.0604839i	0.848037	−	0.529937i	$-0.177784\pi$
$29$	−5.45351	−	9.44575i	−0.0349204	−	0.0604839i	−0.882957	+	0.469453i	$0.844451\pi$
$30$	−72.0000	+	193.541i	−0.438178	+	1.17785i
$31$	−75.8056	+	131.299i	−0.439197	+	0.760711i	−0.997628	−	0.0688401i	$-0.978070\pi$
$31$	−75.8056	+	131.299i	−0.439197	+	0.760711i	0.558431	+	0.829551i	$0.311404\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$	96.0183	−	16.2301i	0.506504	−	0.0856148i
$34$	16.8704	+	29.2204i	0.0850957	+	0.147390i
$35$	116.648			0.563345
$36$	102.000	−	35.4965i	0.472222	−	0.164336i
$37$	346.186			1.53818			0.769089	−	0.639141i	$-0.220710\pi$
$37$	346.186			1.53818			0.769089	+	0.639141i	$0.220710\pi$
$38$	−10.3521	−	17.9304i	−0.0441931	−	0.0765447i
$39$	−151.911	−	183.667i	−0.623723	−	0.754111i
$40$	−79.4817	+	137.666i	−0.314179	+	0.544174i
$41$	−132.370	+	229.272i	−0.504214	+	0.873325i	0.495774	+	0.868452i	$0.334885\pi$
$41$	−132.370	+	229.272i	−0.504214	+	0.873325i	−0.999988	+	0.00487314i	$0.998449\pi$
$42$	−38.8826	−	47.0109i	−0.142850	−	0.172713i
$43$	205.945	+	356.707i	0.730380	+	1.26506i	0.956721	+	0.291007i	$0.0939903\pi$
$43$	205.945	+	356.707i	0.730380	+	1.26506i	−0.226341	+	0.974048i	$0.572676\pi$
$44$	74.9634			0.256845
$45$	−506.696	+	176.333i	−1.67853	+	0.584136i
$46$	−99.7409			−0.319695
$47$	−236.028	−	408.813i	−0.732516	−	1.26875i	−0.955805	−	0.294003i	$-0.905013\pi$
$47$	−236.028	−	408.813i	−0.732516	−	1.26875i	0.223289	−	0.974752i	$-0.428321\pi$
$48$	81.9756	−	13.8564i	0.246503	−	0.0416667i
$49$	154.269	−	267.202i	0.449764	−	0.779014i
$50$	269.834	−	467.366i	0.763205	−	1.32191i
$51$	−30.5648	+	82.1602i	−0.0839201	+	0.225583i
$52$	−91.7409	−	158.900i	−0.244657	−	0.423758i
$53$	290.186			0.752078			0.376039	−	0.926604i	$-0.377286\pi$
$53$	290.186			0.752078			0.376039	+	0.926604i	$0.377286\pi$
$54$	239.963	+	145.429i	0.604720	+	0.366488i
$55$	−372.389			−0.912962
$56$	−23.4817	−	40.6715i	−0.0560335	−	0.0970528i
$57$	18.7553	−	50.4156i	0.0435826	−	0.117153i
$58$	10.9070	−	18.8915i	0.0246924	−	0.0427686i
$59$	−26.6296	+	46.1238i	−0.0587606	+	0.101776i	−0.893909	−	0.448248i	$-0.852048\pi$
$59$	−26.6296	+	46.1238i	−0.0587606	+	0.101776i	0.835149	+	0.550024i	$0.185382\pi$
$60$	−407.223	+	68.8332i	−0.876203	+	0.148105i
$61$	146.972	+	254.563i	0.308489	+	0.534318i	0.978032	−	0.208455i	$-0.0668435\pi$
$61$	146.972	+	254.563i	0.308489	+	0.534318i	−0.669543	+	0.742773i	$0.733510\pi$
$62$	−303.223			−0.621118
$63$	29.7325	−	155.688i	0.0594593	−	0.311346i
$64$	64.0000			0.125000
$65$	455.732	+	789.352i	0.869641	+	1.50626i
$66$	124.130	+	150.079i	0.231504	+	0.279900i
$67$	199.277	−	345.159i	0.363367	−	0.629371i	−0.625145	−	0.780508i	$-0.714960\pi$
$67$	199.277	−	345.159i	0.363367	−	0.629371i	0.988513	+	0.151138i	$0.0482936\pi$
$68$	−33.7409	+	58.4409i	−0.0601718	+	0.104221i
$69$	−165.158	−	199.684i	−0.288154	−	0.348392i
$70$	116.648	+	202.040i	0.199173	+	0.344977i
$71$	−647.854			−1.08290			−0.541451	−	0.840732i	$-0.682125\pi$
$71$	−647.854			−1.08290			−0.541451	+	0.840732i	$0.682125\pi$
$72$	163.482	+	141.173i	0.267590	+	0.231074i
$73$	−478.279			−0.766826			−0.383413	−	0.923577i	$-0.625251\pi$
$73$	−478.279			−0.766826			−0.383413	+	0.923577i	$0.625251\pi$
$74$	346.186	+	599.612i	0.543828	+	0.941938i
$75$	1382.49	−	233.683i	2.12848	−	0.359778i
$76$	20.7043	−	35.8608i	0.0312492	−	0.0541253i
$77$	55.0084	−	95.2773i	0.0814128	−	0.141011i
$78$	166.210	−	446.785i	0.241277	−	0.648569i
$79$	−187.158	−	324.167i	−0.266543	−	0.461666i	0.701424	−	0.712744i	$-0.252548\pi$
$79$	−187.158	−	324.167i	−0.266543	−	0.461666i	−0.967967	+	0.251079i	$0.919215\pi$
$80$	−317.927			−0.444316
$81$	106.196	+	721.224i	0.145673	+	0.989333i
$82$	−529.482			−0.713067
$83$	−466.639	−	808.243i	−0.617112	−	1.06887i	−0.990010	−	0.140998i	$-0.954969\pi$
$83$	−466.639	−	808.243i	−0.617112	−	1.06887i	0.372897	−	0.927873i	$-0.378364\pi$
$84$	42.5427	−	114.358i	0.0552594	−	0.148541i
$85$	167.611	−	290.311i	0.213882	−	0.370455i
$86$	−411.890	+	713.415i	−0.516457	+	0.894529i
$87$	55.8818	−	9.44575i	0.0688639	−	0.0116401i
$88$	74.9634	+	129.840i	0.0908083	+	0.157285i
$89$	368.817			0.439264			0.219632	−	0.975583i	$-0.429514\pi$
$89$	368.817			0.439264			0.219632	+	0.975583i	$0.429514\pi$
$90$	−812.113	−	701.290i	−0.951158	−	0.821361i
$91$	−269.279			−0.310199
$92$	−99.7409	−	172.756i	−0.113029	−	0.195773i
$93$	−502.097	−	607.059i	−0.559839	−	0.676872i
$94$	472.056	−	817.626i	0.517967	−	0.897145i
$95$	−102.851	+	178.143i	−0.111076	+	0.192390i
$96$	105.976	+	128.130i	0.112668	+	0.136220i
$97$	−137.075	−	237.420i	−0.143483	−	0.248519i	0.785323	−	0.619086i	$-0.212497\pi$
$97$	−137.075	−	237.420i	−0.143483	−	0.248519i	−0.928806	+	0.370567i	$0.879163\pi$
$98$	617.076			0.636062
$99$	−94.9184	+	497.021i	−0.0963602	+	0.504570i
$100$	1079.34			1.07934
$101$	4.78584	+	8.28931i	0.00471494	+	0.00816651i	0.868373	−	0.495911i	$-0.165166\pi$
$101$	4.78584	+	8.28931i	0.00471494	+	0.00816651i	−0.863658	+	0.504078i	$0.831833\pi$
$102$	−172.870	+	29.2204i	−0.167811	+	0.0283652i
$103$	−985.752	+	1707.37i	−0.943001	+	1.63332i	−0.183295	+	0.983058i	$0.558676\pi$
$103$	−985.752	+	1707.37i	−0.943001	+	1.63332i	−0.759706	+	0.650267i	$0.774657\pi$
$104$	183.482	−	317.800i	0.172999	−	0.299642i
$105$	−211.335	+	568.084i	−0.196421	+	0.527993i
$106$	290.186	+	502.617i	0.265900	+	0.460552i
$107$	1441.13			1.30205			0.651025	−	0.759057i	$-0.274339\pi$
$107$	1441.13			1.30205			0.651025	+	0.759057i	$0.274339\pi$
$108$	−11.9268	+	561.058i	−0.0106265	+	0.499887i
$109$	−90.3323			−0.0793786			−0.0396893	−	0.999212i	$-0.512637\pi$
$109$	−90.3323			−0.0793786			−0.0396893	+	0.999212i	$0.512637\pi$
$110$	−372.389	−	644.996i	−0.322781	−	0.559072i
$111$	−627.198	+	1685.95i	−0.536315	+	1.44165i
$112$	46.9634	−	81.3430i	0.0396217	−	0.0686267i
$113$	825.364	−	1429.57i	0.687112	−	1.19011i	−0.285656	−	0.958332i	$-0.592211\pi$
$113$	825.364	−	1429.57i	0.687112	−	1.19011i	0.972768	−	0.231781i	$-0.0744552\pi$
$114$	106.078	−	17.9304i	0.0871499	−	0.0147310i
$115$	495.473	+	858.185i	0.401766	+	0.695880i
$116$	43.6281			0.0349204
$117$	1169.70	−	407.060i	0.924260	−	0.321647i
$118$	−106.518			−0.0831000
$119$	49.5183	+	85.7682i	0.0381457	+	0.0660702i
$120$	−526.445	−	636.497i	−0.400480	−	0.484200i
$121$	489.890	−	848.515i	0.368062	−	0.637502i
$122$	−293.944	+	509.125i	−0.218134	+	0.377820i
$123$	−876.752	−	1060.03i	−0.642716	−	0.777074i
$124$	−303.223	−	525.197i	−0.219598	−	0.380355i
$125$	−2877.91			−2.05926
$126$	299.392	−	104.190i	0.211682	−	0.0736663i
$127$	1997.45			1.39563			0.697814	−	0.716279i	$-0.254156\pi$
$127$	1997.45			1.39563			0.697814	+	0.716279i	$0.254156\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$	−2110.31	+	356.707i	−1.44033	+	0.243460i
$130$	−911.465	+	1578.70i	−0.614929	+	1.06509i
$131$	61.8224	−	107.080i	0.0412324	−	0.0714167i	−0.844673	−	0.535283i	$-0.820205\pi$
$131$	61.8224	−	107.080i	0.0412324	−	0.0714167i	0.885905	+	0.463866i	$0.153538\pi$
$132$	−135.814	+	365.077i	−0.0895537	+	0.240726i
$133$	−30.3857	−	52.6296i	−0.0198103	−	0.0343125i
$134$	797.110			0.513879
$135$	59.2477	−	2787.11i	0.0377721	−	1.77686i
$136$	−134.963			−0.0850957
$137$	−56.7028	−	98.2121i	−0.0353609	−	0.0612469i	0.847803	−	0.530311i	$-0.177925\pi$
$137$	−56.7028	−	98.2121i	−0.0353609	−	0.0612469i	−0.883164	+	0.469064i	$0.844591\pi$
$138$	180.704	−	485.745i	0.111468	−	0.299633i
$139$	196.799	−	340.865i	0.120088	−	0.207999i	−0.799714	−	0.600381i	$-0.795016\pi$
$139$	196.799	−	340.865i	0.120088	−	0.207999i	0.919802	+	0.392382i	$0.128349\pi$
$140$	−233.296	+	404.080i	−0.140836	+	0.243936i
$141$	2418.57	−	408.813i	1.44454	−	0.244172i
$142$	−647.854	−	1122.12i	−0.382864	−	0.663140i
$143$	859.651			0.502711
$144$	−81.0366	+	424.331i	−0.0468962	+	0.245562i
$145$	−216.727			−0.124126
$146$	−478.279	−	828.403i	−0.271114	−	0.469583i
$147$	1021.80	+	1235.40i	0.573309	+	0.693158i
$148$	−692.372	+	1199.22i	−0.384545	+	0.666051i
$149$	−753.606	+	1305.28i	−0.414348	+	0.717671i	−0.995360	−	0.0962237i	$-0.969324\pi$
$149$	−753.606	+	1305.28i	−0.414348	+	0.717671i	0.581012	+	0.813895i	$0.302657\pi$
$150$	1787.24	+	2160.85i	0.972849	+	1.17622i
$151$	−1580.70	−	2737.85i	−0.851890	−	1.47552i	−0.879500	−	0.475899i	$-0.842123\pi$
$151$	−1580.70	−	2737.85i	−0.851890	−	1.47552i	0.0276097	−	0.999619i	$-0.491210\pi$
$152$	82.8170			0.0441931
$153$	−344.751	−	297.705i	−0.182166	−	0.157308i
$154$	220.034			0.115135
$155$	1506.29	+	2608.97i	0.780569	+	1.35198i
$156$	940.064	−	158.900i	0.482470	−	0.0815524i
$157$	−687.806	+	1191.31i	−0.349636	+	0.605587i	−0.986185	−	0.165649i	$-0.947028\pi$
$157$	−687.806	+	1191.31i	−0.349636	+	0.605587i	0.636549	+	0.771237i	$0.280361\pi$
$158$	374.316	−	648.334i	0.188474	−	0.326447i
$159$	−525.741	+	1413.23i	−0.262226	+	0.704882i
$160$	−317.927	−	550.665i	−0.157090	−	0.272087i
$161$	−292.761			−0.143309
$162$	−1143.00	+	905.160i	−0.554337	+	0.438988i
$163$	542.073			0.260481			0.130241	−	0.991482i	$-0.458425\pi$
$163$	542.073			0.260481			0.130241	+	0.991482i	$0.458425\pi$
$164$	−529.482	−	917.089i	−0.252107	−	0.436662i
$165$	674.671	−	1813.56i	0.318321	−	0.855669i
$166$	933.279	−	1616.49i	0.436364	−	0.755805i
$167$	−1564.81	+	2710.33i	−0.725081	+	1.25588i	0.233860	+	0.972270i	$0.424864\pi$
$167$	−1564.81	+	2710.33i	−0.725081	+	1.25588i	−0.958941	+	0.283607i	$0.908469\pi$
$168$	240.616	−	40.6715i	0.110500	−	0.0186778i
$169$	46.4520	+	80.4572i	0.0211434	+	0.0366214i
$170$	670.445			0.302475
$171$	211.548	+	182.680i	0.0946051	+	0.0816952i
$172$	−1647.56			−0.730380
$173$	1259.14	+	2180.89i	0.553355	+	0.958440i	0.998029	+	0.0627472i	$0.0199862\pi$
$173$	1259.14	+	2180.89i	0.553355	+	0.958440i	−0.444674	+	0.895692i	$0.646680\pi$
$174$	72.2424	+	87.3444i	0.0314752	+	0.0380550i
$175$	792.020	−	1371.82i	0.342120	−	0.592570i
$176$	−149.927	+	259.681i	−0.0642111	+	0.111217i
$177$	−176.380	−	213.252i	−0.0749015	−	0.0905594i
$178$	368.817	+	638.810i	0.155303	+	0.268993i
$179$	−2331.26			−0.973443			−0.486721	−	0.873557i	$-0.661807\pi$
$179$	−2331.26			−0.973443			−0.486721	+	0.873557i	$0.661807\pi$
$180$	402.558	−	2107.91i	0.166694	−	0.872858i
$181$	734.969			0.301822			0.150911	−	0.988547i	$-0.451779\pi$
$181$	734.969			0.301822			0.150911	+	0.988547i	$0.451779\pi$
$182$	−269.279	−	466.405i	−0.109672	−	0.189957i
$183$	−1506.01	+	254.563i	−0.608348	+	0.102830i
$184$	199.482	−	345.512i	0.0799238	−	0.138432i
$185$	3439.43	−	5957.27i	1.36688	−	2.36750i
$186$	549.360	−	1476.72i	0.216565	−	0.582140i
$187$	−158.083	−	273.808i	−0.0618191	−	0.107074i
$188$	1888.23			0.732516
$189$	704.344	+	426.865i	0.271077	+	0.164285i
$190$	−411.402			−0.157086
$191$	−1808.88	−	3133.07i	−0.685266	−	1.18692i	−0.973353	−	0.229312i	$-0.926352\pi$
$191$	−1808.88	−	3133.07i	−0.685266	−	1.18692i	0.288087	−	0.957604i	$-0.406981\pi$
$192$	−115.951	+	311.685i	−0.0435836	+	0.117156i
$193$	−2170.56	+	3759.52i	−0.809536	+	1.40216i	0.103649	+	0.994614i	$0.466948\pi$
$193$	−2170.56	+	3759.52i	−0.809536	+	1.40216i	−0.913186	+	0.407544i	$0.866385\pi$
$194$	274.149	−	474.841i	0.101458	−	0.175730i
$195$	−4669.87	+	789.352i	−1.71495	+	0.289880i
$196$	617.076	+	1068.81i	0.224882	+	0.389507i
$197$	−3286.20			−1.18849			−0.594243	−	0.804285i	$-0.702548\pi$
$197$	−3286.20			−1.18849			−0.594243	+	0.804285i	$0.702548\pi$
$198$	−955.783	+	332.617i	−0.343053	+	0.119384i
$199$	332.265			0.118360			0.0591800	−	0.998247i	$-0.481151\pi$
$199$	332.265			0.118360			0.0591800	+	0.998247i	$0.481151\pi$
$200$	1079.34	+	1869.46i	0.381603	+	0.660955i
$201$	1319.91	+	1595.83i	0.463180	+	0.560007i
$202$	−9.57168	+	16.5786i	−0.00333396	+	0.00577460i
$203$	32.0144	−	55.4506i	0.0110688	−	0.0191718i
$204$	−223.482	−	270.200i	−0.0767002	−	0.0927342i
$205$	2630.26	+	4555.74i	0.896122	+	1.55213i
$206$	−3943.01			−1.33360
$207$	1271.70	−	442.556i	0.427000	−	0.148598i
$208$	733.927			0.244657
$209$	97.0039	+	168.016i	0.0321048	+	0.0556071i
$210$	−1195.28	+	202.040i	−0.392774	+	0.0663909i
$211$	2871.24	−	4973.13i	0.936797	−	1.62258i	0.165398	−	0.986227i	$-0.447109\pi$
$211$	2871.24	−	4973.13i	0.936797	−	1.62258i	0.771398	−	0.636353i	$-0.219558\pi$
$212$	−580.372	+	1005.23i	−0.188019	+	0.325659i
$213$	1173.74	−	3155.09i	0.377575	−	1.01495i
$214$	1441.13	+	2496.11i	0.460344	+	0.797339i
$215$	8184.43			2.59616
$216$	−983.707	+	540.400i	−0.309874	+	0.170229i
$217$	−890.023			−0.278427
$218$	−90.3323	−	156.460i	−0.0280646	−	0.0486093i
$219$	866.516	−	2329.25i	0.267369	−	0.718705i
$220$	744.777	−	1289.99i	0.228240	−	0.395324i
$221$	−386.927	+	670.177i	−0.117772	+	0.203986i
$222$	−3547.35	+	599.612i	−1.07244	+	0.181276i
$223$	1231.31	+	2132.69i	0.369751	+	0.640427i	0.989526	−	0.144352i	$-0.0461097\pi$
$223$	1231.31	+	2132.69i	0.369751	+	0.640427i	−0.619776	+	0.784779i	$0.712776\pi$
$224$	187.854			0.0560335
$225$	−1366.65	+	7156.18i	−0.404934	+	2.12035i
$226$	3301.45			0.971723
$227$	−1399.67	−	2424.30i	−0.409248	−	0.708838i	0.585558	−	0.810631i	$-0.300876\pi$
$227$	−1399.67	−	2424.30i	−0.409248	−	0.708838i	−0.994806	+	0.101792i	$0.967542\pi$
$228$	137.134	+	165.802i	0.0398330	+	0.0481600i
$229$	−706.423	+	1223.56i	−0.203850	+	0.353079i	−0.949766	−	0.312961i	$-0.898679\pi$
$229$	−706.423	+	1223.56i	−0.203850	+	0.353079i	0.745915	+	0.666041i	$0.232012\pi$
$230$	−990.947	+	1716.37i	−0.284092	+	0.492061i
$231$	364.347	+	440.512i	0.103776	+	0.125470i
$232$	43.6281	+	75.5660i	0.0123462	+	0.0213843i
$233$	2033.81			0.571843			0.285922	−	0.958253i	$-0.407700\pi$
$233$	2033.81			0.571843			0.285922	+	0.958253i	$0.407700\pi$
$234$	1874.74	+	1618.91i	0.523743	+	0.452272i
$235$	−9379.96			−2.60375
$236$	−106.518	−	184.495i	−0.0293803	−	0.0508882i
$237$	1917.80	−	324.167i	0.525630	−	0.0888477i
$238$	−99.0366	+	171.536i	−0.0269731	+	0.0467187i
$239$	260.806	−	451.729i	0.0705863	−	0.122259i	−0.828572	−	0.559882i	$-0.810846\pi$
$239$	260.806	−	451.729i	0.0705863	−	0.122259i	0.899158	+	0.437623i	$0.144180\pi$
$240$	576.000	−	1548.33i	0.154919	−	0.416434i
$241$	−2957.82	−	5123.10i	−0.790582	−	1.36933i	−0.925607	−	0.378486i	$-0.876445\pi$
$241$	−2957.82	−	5123.10i	−0.790582	−	1.36933i	0.135025	−	0.990842i	$-0.456888\pi$
$242$	1959.56			0.520518
$243$	−3704.81	−	789.486i	−0.978040	−	0.208418i
$244$	−1175.77			−0.308489
$245$	−3065.39	−	5309.41i	−0.799350	−	1.38451i
$246$	959.282	−	2578.61i	0.248624	−	0.668319i
$247$	237.428	−	411.238i	0.0611628	−	0.105937i
$248$	606.445	−	1050.39i	0.155279	−	0.268952i
$249$	4781.63	−	808.243i	1.21696	−	0.205704i
$250$	−2877.91	−	4984.69i	−0.728060	−	1.26104i
$251$	710.127			0.178577			0.0892884	−	0.996006i	$-0.471541\pi$
$251$	710.127			0.178577			0.0892884	+	0.996006i	$0.471541\pi$
$252$	479.854	+	414.372i	0.119952	+	0.103583i
$253$	934.614			0.232248
$254$	1997.45	+	3459.68i	0.493429	+	0.854645i
$255$	1110.17	+	1342.25i	0.272633	+	0.329627i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−3150.50	+	5456.83i	−0.764681	+	1.32447i	0.175734	+	0.984438i	$0.443770\pi$
$257$	−3150.50	+	5456.83i	−0.764681	+	1.32447i	−0.940415	+	0.340028i	$0.889563\pi$
$258$	−2728.14	−	3298.46i	−0.658321	−	0.795941i
$259$	1016.13	+	1759.99i	0.243781	+	0.422241i
$260$	−3645.86			−0.869641
$261$	−55.2417	+	289.262i	−0.0131011	+	0.0686010i
$262$	247.290			0.0583115
$263$	2460.91	+	4262.42i	0.576981	+	0.999361i	0.995823	+	0.0913017i	$0.0291028\pi$
$263$	2460.91	+	4262.42i	0.576981	+	0.999361i	−0.418842	+	0.908059i	$0.637564\pi$
$264$	−768.146	+	129.840i	−0.179076	+	0.0302694i
$265$	2883.06	−	4993.61i	0.668320	−	1.15757i
$266$	60.7714	−	105.259i	0.0140080	−	0.0242626i
$267$	−668.200	+	1796.17i	−0.153158	+	0.411699i
$268$	797.110	+	1380.63i	0.181684	+	0.314685i
$269$	−5454.50			−1.23631			−0.618154	−	0.786057i	$-0.712119\pi$
$269$	−5454.50			−1.23631			−0.618154	+	0.786057i	$0.712119\pi$
$270$	4886.67	−	2684.49i	1.10146	−	0.605086i
$271$	2797.10			0.626981			0.313491	−	0.949591i	$-0.398502\pi$
$271$	2797.10			0.626981			0.313491	+	0.949591i	$0.398502\pi$
$272$	−134.963	−	233.763i	−0.0300859	−	0.0521103i
$273$	487.863	−	1311.41i	0.108157	−	0.290733i
$274$	113.406	−	196.424i	0.0250039	−	0.0433081i
$275$	−2528.46	+	4379.42i	−0.554443	+	0.960323i
$276$	1022.04	−	172.756i	0.222897	−	0.0376765i
$277$	1072.59	+	1857.77i	0.232655	+	0.402970i	0.958589	−	0.284794i	$-0.0919254\pi$
$277$	1072.59	+	1857.77i	0.232655	+	0.402970i	−0.725934	+	0.687765i	$0.758592\pi$
$278$	787.195			0.169830
$279$	3866.09	−	1345.42i	0.829594	−	0.288702i
$280$	−933.183			−0.199173
$281$	2754.88	+	4771.60i	0.584849	+	1.01299i	0.994894	+	0.100923i	$0.0321797\pi$
$281$	2754.88	+	4771.60i	0.584849	+	1.01299i	−0.410045	+	0.912065i	$0.634487\pi$
$282$	3126.65	+	3780.27i	0.660247	+	0.798269i
$283$	−2003.92	+	3470.89i	−0.420921	+	0.729056i	−0.996030	−	0.0890206i	$-0.971626\pi$
$283$	−2003.92	+	3470.89i	−0.420921	+	0.729056i	0.575109	+	0.818077i	$0.304960\pi$
$284$	1295.71	−	2244.23i	0.270726	−	0.468911i
$285$	−681.229	−	823.637i	−0.141588	−	0.171186i
$286$	859.651	+	1488.96i	0.177735	+	0.307846i
$287$	−1554.14			−0.319645
$288$	−816.000	+	283.972i	−0.166956	+	0.0581014i
$289$	−4628.39			−0.942070
$290$	−216.727	−	375.382i	−0.0438850	−	0.0760111i
$291$	1404.60	−	237.420i	0.282952	−	0.0478276i
$292$	956.558	−	1656.81i	0.191707	−	0.332046i
$293$	2904.62	−	5030.95i	0.579146	−	1.00311i	−0.416432	−	0.909167i	$-0.636720\pi$
$293$	2904.62	−	5030.95i	0.579146	−	1.00311i	0.995578	−	0.0939429i	$-0.0299471\pi$
$294$	−1117.98	+	3005.21i	−0.221775	+	0.596147i
$295$	529.141	+	916.499i	0.104433	+	0.180884i
$296$	−2769.49			−0.543828
$297$	−2248.56	−	1362.73i	−0.439309	−	0.266241i
$298$	−3014.42			−0.585976
$299$	−1143.79	−	1981.10i	−0.221227	−	0.383177i
$300$	−1955.47	+	5256.44i	−0.376331	+	1.01160i
$301$	−1208.99	+	2094.02i	−0.231511	+	0.400989i
$302$	3161.40	−	5475.70i	0.602377	−	1.04335i
$303$	−49.0402	+	8.28931i	−0.00929798	+	0.00157165i
$304$	82.8170	+	143.443i	0.0156246	+	0.0270626i
$305$	5840.78			1.09653
$306$	170.890	−	894.831i	0.0319253	−	0.167170i
$307$	8688.30			1.61520			0.807602	−	0.589728i	$-0.200765\pi$
$307$	8688.30			1.61520			0.807602	+	0.589728i	$0.200765\pi$
$308$	220.034	+	381.109i	0.0407064	+	0.0705056i
$309$	−6529.11	−	7894.00i	−1.20203	−	1.45331i
$310$	−3012.58	+	5217.94i	−0.551945	+	0.955998i
$311$	−716.005	+	1240.16i	−0.130550	+	0.226119i	−0.923889	−	0.382662i	$-0.875008\pi$
$311$	−716.005	+	1240.16i	−0.130550	+	0.226119i	0.793339	+	0.608780i	$0.208341\pi$
$312$	1215.29	+	1469.34i	0.220519	+	0.266618i
$313$	−3307.26	−	5728.34i	−0.597244	−	1.03446i	−0.993226	−	0.116199i	$-0.962929\pi$
$313$	−3307.26	−	5728.34i	−0.597244	−	1.03446i	0.395982	−	0.918258i	$-0.370404\pi$
$314$	−2751.22			−0.494460
$315$	−2383.72	−	2058.44i	−0.426373	−	0.368190i
$316$	1497.26			0.266543
$317$	−712.045	−	1233.30i	−0.126159	−	0.218514i	0.796026	−	0.605262i	$-0.206932\pi$
$317$	−712.045	−	1233.30i	−0.126159	−	0.218514i	−0.922185	+	0.386748i	$0.873598\pi$
$318$	−2973.52	+	502.617i	−0.524361	+	0.0886332i
$319$	−102.203	+	177.021i	−0.0179382	+	0.0310699i
$320$	635.854	−	1101.33i	0.111079	−	0.192395i
$321$	−2610.95	+	7018.41i	−0.453984	+	1.22034i
$322$	−292.761	−	507.076i	−0.0506674	−	0.0877586i
$323$	−174.645			−0.0300851
$324$	−2710.78	−	1074.57i	−0.464812	−	0.184255i
$325$	12377.4			2.11254
$326$	542.073	+	938.898i	0.0920940	+	0.159512i
$327$	163.658	−	439.925i	0.0276769	−	0.0743973i
$328$	1058.96	−	1834.18i	0.178267	−	0.308767i
$329$	1385.59	−	2399.91i	0.232188	−	0.402161i
$330$	3815.85	−	644.996i	0.636532	−	0.107594i
$331$	−1768.83	−	3063.70i	−0.293726	−	0.508749i	0.680961	−	0.732319i	$-0.261562\pi$
$331$	−1768.83	−	3063.70i	−0.293726	−	0.508749i	−0.974688	+	0.223570i	$0.928229\pi$
$332$	3733.12			0.617112
$333$	−7074.38	−	6109.00i	−1.16419	−	1.00532i
$334$	−6259.23			−1.02542
$335$	−3959.73	−	6858.45i	−0.645800	−	1.11856i
$336$	311.061	+	376.087i	0.0505053	+	0.0610632i
$337$	880.140	−	1524.45i	0.142268	−	0.246415i	−0.786082	−	0.618122i	$-0.787894\pi$
$337$	880.140	−	1524.45i	0.142268	−	0.246415i	0.928350	+	0.371706i	$0.121227\pi$
$338$	−92.9040	+	160.914i	−0.0149506	+	0.0258952i
$339$	5466.78	+	6609.59i	0.875854	+	1.05895i
$340$	670.445	+	1161.25i	0.106941	+	0.185228i
$341$	2841.32			0.451221
$342$	−104.863	+	549.092i	−0.0165799	+	0.0868172i
$343$	3824.81			0.602099
$344$	−1647.56	−	2853.66i	−0.258228	−	0.447265i
$345$	−5077.09	+	858.185i	−0.792294	+	0.133922i
$346$	−2518.28	+	4361.78i	−0.391281	+	0.677719i
$347$	802.720	−	1390.35i	0.124185	−	0.215095i	−0.797229	−	0.603677i	$-0.793702\pi$
$347$	802.720	−	1390.35i	0.124185	−	0.215095i	0.921414	+	0.388582i	$0.127035\pi$
$348$	−79.0426	+	212.472i	−0.0121757	+	0.0327290i
$349$	3320.94	+	5752.04i	0.509358	+	0.882235i	0.999941	+	0.0108400i	$0.00345056\pi$
$349$	3320.94	+	5752.04i	0.509358	+	0.882235i	−0.490583	+	0.871395i	$0.663216\pi$
$350$	3168.08			0.483831
$351$	−136.772	+	6433.99i	−0.0207987	+	0.978407i
$352$	−599.707			−0.0908083
$353$	1528.13	+	2646.81i	0.230409	+	0.399080i	0.957929	−	0.287007i	$-0.0926603\pi$
$353$	1528.13	+	2646.81i	0.230409	+	0.399080i	−0.727520	+	0.686087i	$0.759327\pi$
$354$	192.983	−	518.752i	0.0289744	−	0.0778852i
$355$	−6436.56	+	11148.5i	−0.962302	+	1.66676i
$356$	−737.634	+	1277.62i	−0.109816	+	0.190207i
$357$	−507.412	+	85.7682i	−0.0752243	+	0.0127152i
$358$	−2331.26	−	4037.85i	−0.344164	−	0.596110i
$359$	−2489.46			−0.365985			−0.182993	−	0.983114i	$-0.558578\pi$
$359$	−2489.46			−0.365985			−0.182993	+	0.983114i	$0.558578\pi$
$360$	4053.57	−	1410.66i	0.593449	−	0.206523i
$361$	−6751.83			−0.984376
$362$	734.969	+	1273.00i	0.106710	+	0.184828i
$363$	3244.78	+	3923.09i	0.469164	+	0.567242i
$364$	538.558	−	932.810i	0.0775497	−	0.134320i
$365$	−4751.80	+	8230.36i	−0.681427	+	1.18027i
$366$	−1946.93	−	2353.93i	−0.278053	−	0.336180i
$367$	−1177.52	−	2039.53i	−0.167483	−	0.290089i	0.770051	−	0.637982i	$-0.220231\pi$
$367$	−1177.52	−	2039.53i	−0.167483	−	0.290089i	−0.937534	+	0.347893i	$0.886897\pi$
$368$	797.927			0.113029
$369$	6750.89	−	2349.34i	0.952405	−	0.331441i
$370$	13757.7			1.93305
$371$	851.758	+	1475.29i	0.119194	+	0.206450i
$372$	3107.11	−	525.197i	0.433054	−	0.0731994i
$373$	1378.51	−	2387.65i	0.191358	−	0.331443i	−0.754342	−	0.656481i	$-0.772044\pi$
$373$	1378.51	−	2387.65i	0.191358	−	0.331443i	0.945701	+	0.325039i	$0.105377\pi$
$374$	316.166	−	547.616i	0.0437127	−	0.0757127i
$375$	5214.02	−	14015.6i	0.718002	−	1.93004i
$376$	1888.23	+	3270.50i	0.258984	+	0.448573i
$377$	500.310			0.0683481
$378$	−35.0078	+	1646.82i	−0.00476350	+	0.224083i
$379$	246.459			0.0334030			0.0167015	−	0.999861i	$-0.494683\pi$
$379$	246.459			0.0334030			0.0167015	+	0.999861i	$0.494683\pi$
$380$	−411.402	−	712.570i	−0.0555382	−	0.0961949i
$381$	−3618.85	+	9727.72i	−0.486613	+	1.30805i
$382$	3617.76	−	6266.14i	0.484557	−	0.839276i
$383$	−325.287	+	563.414i	−0.0433979	+	0.0751674i	−0.886908	−	0.461945i	$-0.847152\pi$
$383$	−325.287	+	563.414i	−0.0433979	+	0.0751674i	0.843511	+	0.537113i	$0.180485\pi$
$384$	−655.805	+	110.851i	−0.0871521	+	0.0147314i
$385$	−1093.04	−	1893.20i	−0.144692	−	0.250614i
$386$	−8682.25			−1.14486
$387$	2086.14	−	10923.6i	0.274016	−	1.43483i
$388$	1096.60			0.143483
$389$	5123.08	+	8873.44i	0.667739	+	1.15656i	0.978535	+	0.206082i	$0.0660713\pi$
$389$	5123.08	+	8873.44i	0.667739	+	1.15656i	−0.310795	+	0.950477i	$0.600595\pi$
$390$	−6037.07	−	7299.10i	−0.783843	−	0.947703i
$391$	−420.668	+	728.618i	−0.0544094	+	0.0942399i
$392$	−1234.15	+	2137.61i	−0.159016	+	0.275423i
$393$	409.479	+	495.080i	0.0525585	+	0.0635457i
$394$	−3286.20	−	5691.86i	−0.420194	−	0.727797i
$395$	−7437.81			−0.947435
$396$	−1531.89	−	1322.85i	−0.194395	−	0.167868i
$397$	−9453.68			−1.19513			−0.597565	−	0.801820i	$-0.703865\pi$
$397$	−9453.68			−1.19513			−0.597565	+	0.801820i	$0.703865\pi$
$398$	332.265	+	575.500i	0.0418466	+	0.0724804i
$399$	311.361	−	52.6296i	0.0390665	−	0.00660345i
$400$	−2158.67	+	3738.93i	−0.269834	+	0.467366i
$401$	−135.361	+	234.453i	−0.0168569	+	0.0291970i	−0.874331	−	0.485330i	$-0.838699\pi$
$401$	−135.361	+	234.453i	−0.0168569	+	0.0291970i	0.857474	+	0.514527i	$0.172033\pi$
$402$	−1444.15	+	3881.98i	−0.179174	+	0.481631i
$403$	−3477.24	−	6022.75i	−0.429810	−	0.744453i
$404$	−38.2867			−0.00471494
$405$	13466.1	+	5338.06i	1.65219	+	0.654939i
$406$	128.058			0.0156537
$407$	−3243.91	−	5618.62i	−0.395073	−	0.684286i
$408$	244.518	−	657.282i	0.0296702	−	0.0797556i
$409$	5793.08	−	10033.9i	0.700366	−	1.21307i	−0.267972	−	0.963427i	$-0.586354\pi$
$409$	5793.08	−	10033.9i	0.700366	−	1.21307i	0.968338	−	0.249642i	$-0.0803130\pi$
$410$	−5260.51	+	9111.48i	−0.633654	+	1.09752i
$411$	581.030	−	98.2121i	0.0697326	−	0.0117870i
$412$	−3943.01	−	6829.49i	−0.471500	−	0.816662i
$413$	−312.654			−0.0372511
$414$	2038.23	+	1760.09i	0.241965	+	0.208946i
$415$	−18544.7			−2.19354
$416$	733.927	+	1271.20i	0.0864993	+	0.149821i
$417$	1303.49	+	1575.98i	0.153075	+	0.185075i
$418$	−194.008	+	336.031i	−0.0227015	+	0.0393202i
$419$	8066.87	−	13972.2i	0.940554	−	1.62909i	0.176137	−	0.984366i	$-0.443640\pi$
$419$	8066.87	−	13972.2i	0.940554	−	1.62909i	0.764417	−	0.644722i	$-0.223027\pi$
$420$	−1545.23	−	1868.25i	−0.179522	−	0.217051i
$421$	−2495.96	−	4323.14i	−0.288945	−	0.500467i	0.684613	−	0.728907i	$-0.259971\pi$
$421$	−2495.96	−	4323.14i	−0.288945	−	0.500467i	−0.973558	+	0.228439i	$0.926638\pi$
$422$	11484.9			1.32483
$423$	−2390.87	+	12519.3i	−0.274818	+	1.43903i
$424$	−2321.49			−0.265900
$425$	−2276.11	−	3942.33i	−0.259782	−	0.449956i
$426$	6638.52	−	1122.12i	0.755018	−	0.127621i
$427$	−862.787	+	1494.39i	−0.0977827	+	0.169365i
$428$	−2882.26	+	4992.22i	−0.325512	+	0.563804i
$429$	−1557.46	+	4186.56i	−0.175280	+	0.471163i
$430$	8184.43	+	14175.9i	0.917880	+	1.58982i
$431$	8184.74			0.914722			0.457361	−	0.889281i	$-0.348795\pi$
$431$	8184.74			0.914722			0.457361	+	0.889281i	$0.348795\pi$
$432$	−1919.71	−	1163.43i	−0.213801	−	0.129573i
$433$	8663.17			0.961490			0.480745	−	0.876860i	$-0.340366\pi$
$433$	8663.17			0.961490			0.480745	+	0.876860i	$0.340366\pi$
$434$	−890.023	−	1541.56i	−0.0984389	−	0.170501i
$435$	392.653	−	1055.48i	0.0432787	−	0.116336i
$436$	180.665	−	312.920i	0.0198447	−	0.0343719i
$437$	258.133	−	447.099i	0.0282567	−	0.0489420i
$438$	4900.90	−	828.403i	0.534644	−	0.0903713i
$439$	7932.15	+	13738.9i	0.862371	+	1.49367i	0.869634	+	0.493697i	$0.164355\pi$
$439$	7932.15	+	13738.9i	0.862371	+	1.49367i	−0.00726314	+	0.999974i	$0.502312\pi$
$440$	2979.11			0.322781
$441$	−7867.72	+	2738.00i	−0.849554	+	0.295649i
$442$	−1547.71			−0.166554
$443$	199.820	+	346.099i	0.0214306	+	0.0371189i	0.876542	−	0.481326i	$-0.159845\pi$
$443$	199.820	+	346.099i	0.0214306	+	0.0371189i	−0.855111	+	0.518445i	$0.826511\pi$
$444$	−4585.91	−	5544.58i	−0.490175	−	0.592644i
$445$	3664.28	−	6346.71i	0.390345	−	0.676097i
$446$	−2462.61	+	4265.37i	−0.261453	+	0.452850i
$447$	−4991.49	−	6034.95i	−0.528164	−	0.638575i
$448$	187.854	+	325.372i	0.0198108	+	0.0343134i
$449$	5924.51			0.622706			0.311353	−	0.950294i	$-0.399218\pi$
$449$	5924.51			0.622706			0.311353	+	0.950294i	$0.399218\pi$
$450$	−13761.5	+	4789.08i	−1.44161	+	0.501687i
$451$	4961.47			0.518019
$452$	3301.45	+	5718.29i	0.343556	+	0.595057i
$453$	16197.3	−	2737.85i	1.67995	−	0.283963i
$454$	2799.34	−	4848.60i	0.289382	−	0.501224i
$455$	−2675.34	+	4633.83i	−0.275653	+	0.477445i
$456$	−150.043	+	403.325i	−0.0154088	+	0.0414198i
$457$	3945.57	+	6833.93i	0.403864	+	0.699513i	0.994189	−	0.107653i	$-0.0343335\pi$
$457$	3945.57	+	6833.93i	0.403864	+	0.699513i	−0.590324	+	0.807166i	$0.701000\pi$
$458$	−2825.69			−0.288288
$459$	2074.45	−	1139.60i	0.210952	−	0.115886i
$460$	−3963.79			−0.401766
$461$	1631.09	+	2825.13i	0.164789	+	0.285422i	0.936580	−	0.350453i	$-0.113972\pi$
$461$	1631.09	+	2825.13i	0.164789	+	0.285422i	−0.771792	+	0.635876i	$0.780639\pi$
$462$	−398.643	+	1071.58i	−0.0401441	+	0.107910i
$463$	−1845.20	+	3195.98i	−0.185213	+	0.320799i	−0.943648	−	0.330950i	$-0.892631\pi$
$463$	−1845.20	+	3195.98i	−0.185213	+	0.320799i	0.758435	+	0.651749i	$0.225964\pi$
$464$	−87.2561	+	151.132i	−0.00873010	+	0.0151210i
$465$	−15434.9	+	2608.97i	−1.53930	+	0.260190i
$466$	2033.81	+	3522.67i	0.202177	+	0.350181i
$467$	−10193.2			−1.01003			−0.505017	−	0.863110i	$-0.668514\pi$
$467$	−10193.2			−1.01003			−0.505017	+	0.863110i	$0.668514\pi$
$468$	−929.296	+	4866.06i	−0.0917878	+	0.480628i
$469$	2339.69			0.230355
$470$	−9379.96	−	16246.6i	−0.920565	−	1.59446i
$471$	−4555.66	−	5508.01i	−0.445677	−	0.538845i
$472$	213.037	−	368.990i	0.0207750	−	0.0359834i
$473$	3859.59	−	6685.00i	0.375188	−	0.649845i
$474$	2479.27	+	2997.55i	0.240246	+	0.290469i
$475$	1396.68	+	2419.12i	0.134914	+	0.233677i
$476$	−396.146			−0.0381457
$477$	−5930.01	−	5120.79i	−0.569217	−	0.491541i
$478$	1043.22			0.0998240
$479$	−420.034	−	727.521i	−0.0400665	−	0.0693972i	0.845297	−	0.534297i	$-0.179424\pi$
$479$	−420.034	−	727.521i	−0.0400665	−	0.0693972i	−0.885363	+	0.464900i	$0.846090\pi$
$480$	3257.78	−	550.665i	0.309785	−	0.0523632i
$481$	−7939.85	+	13752.2i	−0.752653	+	1.30363i
$482$	5915.65	−	10246.2i	0.559026	−	0.968261i
$483$	530.406	−	1425.77i	0.0499675	−	0.134316i
$484$	1959.56	+	3394.06i	0.184031	+	0.318751i
$485$	−5447.46			−0.510014
$486$	−2337.38	−	7206.41i	−0.218160	−	0.672612i
$487$	−3367.28			−0.313319			−0.156659	−	0.987653i	$-0.550072\pi$
$487$	−3367.28			−0.313319			−0.156659	+	0.987653i	$0.550072\pi$
$488$	−1175.77	−	2036.50i	−0.109067	−	0.188910i
$489$	−982.094	+	2639.94i	−0.0908218	+	0.244135i
$490$	6130.78	−	10618.8i	0.565226	−	0.979000i
$491$	9434.55	−	16341.1i	0.867160	−	1.50196i	0.00227283	−	0.999997i	$-0.499277\pi$
$491$	9434.55	−	16341.1i	0.867160	−	1.50196i	0.864887	−	0.501967i	$-0.167390\pi$
$492$	5425.57	−	917.089i	0.497162	−	0.0840357i
$493$	−92.0030	−	159.354i	−0.00840488	−	0.0145577i
$494$	949.713			0.0864972
$495$	7609.84	+	6571.39i	0.690984	+	0.596691i
$496$	2425.78			0.219598
$497$	−1901.59	−	3293.65i	−0.171626	−	0.297264i
$498$	6181.55	+	7473.79i	0.556229	+	0.672507i
$499$	7283.00	−	12614.5i	0.653371	−	1.13167i	−0.328929	−	0.944355i	$-0.606688\pi$
$499$	7283.00	−	12614.5i	0.653371	−	1.13167i	0.982300	−	0.187317i	$-0.0599791\pi$
$500$	5755.82	−	9969.37i	0.514816	−	0.891688i
$501$	−10364.5	−	12531.1i	−0.924252	−	1.11746i
$502$	710.127	+	1229.98i	0.0631365	+	0.109356i
$503$	−17361.6			−1.53900			−0.769499	−	0.638648i	$-0.779494\pi$
$503$	−17361.6			−1.53900			−0.769499	+	0.638648i	$0.779494\pi$
$504$	−237.860	+	1245.50i	−0.0210220	+	0.110078i
$505$	190.193			0.0167594
$506$	934.614	+	1618.80i	0.0821120	+	0.142222i
$507$	−475.991	+	80.4572i	−0.0416953	+	0.00704779i
$508$	−3994.90	+	6919.36i	−0.348907	+	0.604325i
$509$	−6966.63	+	12066.6i	−0.606661	+	1.05077i	0.385126	+	0.922864i	$0.374158\pi$
$509$	−6966.63	+	12066.6i	−0.606661	+	1.05077i	−0.991787	+	0.127903i	$0.959175\pi$
$510$	−1214.67	+	3265.12i	−0.105464	+	0.283494i
$511$	−1403.85	−	2431.54i	−0.121532	−	0.210499i
$512$	−512.000			−0.0441942
$513$	−1272.93	+	699.286i	−0.109554	+	0.0601837i
$514$	−12602.0			−1.08142
$515$	19587.3	+	33926.2i	1.67596	+	2.90285i
$516$	2984.95	−	8023.74i	0.254661	−	0.684546i
$517$	−4423.37	+	7661.50i	−0.376285	+	0.651745i
$518$	−2032.26	+	3519.98i	−0.172379	+	0.298569i
$519$	−12902.3	+	2180.89i	−1.09123	+	0.184452i
$520$	−3645.86	−	6314.81i	−0.307464	−	0.532544i
$521$	5024.22			0.422486			0.211243	−	0.977434i	$-0.432249\pi$
$521$	5024.22			0.422486			0.211243	+	0.977434i	$0.432249\pi$
$522$	−556.258	+	193.580i	−0.0466413	+	0.0162314i
$523$	16008.7			1.33845			0.669226	−	0.743059i	$-0.266626\pi$
$523$	16008.7			1.33845			0.669226	+	0.743059i	$0.266626\pi$
$524$	247.290	+	428.318i	0.0206162	+	0.0357083i
$525$	5245.92	+	6342.57i	0.436097	+	0.527262i
$526$	−4921.82	+	8524.83i	−0.407987	+	0.706655i
$527$	−1278.87	+	2215.07i	−0.105709	+	0.183093i
$528$	−993.037	−	1200.63i	−0.0818492	−	0.0989595i
$529$	4839.97	+	8383.07i	0.397795	+	0.689001i
$530$	11532.2			0.945148
$531$	1358.11	−	472.628i	0.110992	−	0.0386258i
$532$	243.086			0.0198103
$533$	−6071.89	−	10516.8i	−0.493438	−	0.854660i
$534$	−3779.25	+	638.810i	−0.306262	+	0.0517678i
$535$	14317.9	−	24799.4i	1.15704	−	2.00406i
$536$	−1594.22	+	2761.27i	−0.128470	+	0.222516i
$537$	4223.62	−	11353.4i	0.339409	−	0.912355i
$538$	−5454.50	−	9447.48i	−0.437101	−	0.757081i
$539$	−5782.27			−0.462078
$540$	9536.35	+	5779.47i	0.759961	+	0.460572i
$541$	−10094.1			−0.802179			−0.401089	−	0.916039i	$-0.631368\pi$
$541$	−10094.1			−0.802179			−0.401089	+	0.916039i	$0.631368\pi$
$542$	2797.10	+	4844.73i	0.221671	+	0.383946i
$543$	−1331.57	+	3579.35i	−0.105236	+	0.282882i
$544$	269.927	−	467.527i	0.0212739	−	0.0368475i
$545$	−897.471	+	1554.47i	−0.0705384	+	0.122176i
$546$	2759.29	−	466.405i	0.216276	−	0.0365573i
$547$	3030.27	+	5248.58i	0.236865	+	0.410262i	0.959813	−	0.280640i	$-0.0905468\pi$
$547$	3030.27	+	5248.58i	0.236865	+	0.410262i	−0.722948	+	0.690902i	$0.757213\pi$
$548$	453.622			0.0353609
$549$	1488.76	−	7795.59i	0.115736	−	0.606025i
$550$	−10113.8			−0.784100
$551$	56.4554	+	97.7837i	0.00436494	+	0.00756030i
$552$	1321.26	+	1597.47i	0.101878	+	0.123175i
$553$	1098.70	−	1903.00i	0.0844870	−	0.146336i
$554$	−2145.17	+	3715.55i	−0.164512	+	0.284943i
$555$	22781.0	+	27543.3i	1.74234	+	2.10657i
$556$	787.195	+	1363.46i	0.0600441	+	0.103999i
$557$	13688.4			1.04128			0.520642	−	0.853775i	$-0.325693\pi$
$557$	13688.4			1.04128			0.520642	+	0.853775i	$0.325693\pi$
$558$	6196.42	+	5350.84i	0.470099	+	0.405949i
$559$	−18893.6			−1.42954
$560$	−933.183	−	1616.32i	−0.0704182	−	0.121968i
$561$	1619.87	−	273.808i	0.121909	−	0.0206064i
$562$	−5509.77	+	9543.20i	−0.413551	+	0.716291i
$563$	−11173.3	+	19352.8i	−0.836411	+	1.44871i	0.0564662	+	0.998405i	$0.482017\pi$
$563$	−11173.3	+	19352.8i	−0.836411	+	1.44871i	−0.892877	+	0.450301i	$0.851317\pi$
$564$	−3420.97	+	9195.80i	−0.255406	+	0.686548i
$565$	−16400.3	−	28406.2i	−1.22118	−	2.11515i
$566$	−8015.67			−0.595272
$567$	−3354.95	+	2656.84i	−0.248491	+	0.196784i
$568$	5182.83			0.382864
$569$	−4058.97	−	7030.34i	−0.299052	−	0.517974i	0.676867	−	0.736105i	$-0.263337\pi$
$569$	−4058.97	−	7030.34i	−0.299052	−	0.517974i	−0.975919	+	0.218131i	$0.930004\pi$
$570$	745.353	−	2003.56i	0.0547709	−	0.147228i
$571$	−3491.49	+	6047.43i	−0.255892	+	0.443217i	−0.965137	−	0.261744i	$-0.915702\pi$
$571$	−3491.49	+	6047.43i	−0.255892	+	0.443217i	0.709246	+	0.704961i	$0.249036\pi$
$572$	−1719.30	+	2977.92i	−0.125678	+	0.217680i
$573$	18535.5	−	3133.07i	1.35136	−	0.228422i
$574$	−1554.14	−	2691.85i	−0.113012	−	0.195742i
$575$	13456.7			0.975973
$576$	−1307.85	−	1129.38i	−0.0946075	−	0.0816972i
$577$	13972.4			1.00811			0.504055	−	0.863671i	$-0.331841\pi$
$577$	13972.4			1.00811			0.504055	+	0.863671i	$0.331841\pi$
$578$	−4628.39	−	8016.60i	−0.333072	−	0.576898i
$579$	−14376.7	−	17382.1i	−1.03191	−	1.24762i
$580$	433.454	−	750.765i	0.0310314	−	0.0537479i
$581$	2739.37	−	4744.73i	0.195608	−	0.338803i
$582$	1815.82	+	2195.41i	0.129327	+	0.156362i
$583$	−2719.17	−	4709.73i	−0.193167	−	0.334575i
$584$	3826.23			0.271114
$585$	4616.38	−	24172.7i	0.326263	−	1.70841i
$586$	11618.5			0.819036
$587$	754.756	+	1307.28i	0.0530701	+	0.0919200i	0.891340	−	0.453335i	$-0.149766\pi$
$587$	754.756	+	1307.28i	0.0530701	+	0.0919200i	−0.838270	+	0.545255i	$0.816433\pi$
$588$	−6323.15	+	1068.81i	−0.443473	+	0.0749607i
$589$	784.750	−	1359.23i	0.0548982	−	0.0950865i
$590$	−1058.28	+	1833.00i	−0.0738454	+	0.127904i
$591$	5953.73	−	16004.0i	0.414389	−	1.11390i
$592$	−2769.49	−	4796.89i	−0.192272	−	0.333026i
$593$	−21495.3			−1.48854			−0.744270	−	0.667879i	$-0.767202\pi$
$593$	−21495.3			−1.48854			−0.744270	+	0.667879i	$0.767202\pi$
$594$	111.759	−	5257.35i	0.00771977	−	0.363151i
$595$	1967.90			0.135590
$596$	−3014.42	−	5221.13i	−0.207174	−	0.358836i
$597$	−601.977	+	1618.16i	−0.0412685	+	0.110932i
$598$	2287.58	−	3962.20i	0.156431	−	0.270947i
$599$	−5052.44	+	8751.08i	−0.344636	+	0.596927i	−0.985288	−	0.170905i	$-0.945331\pi$
$599$	−5052.44	+	8751.08i	−0.344636	+	0.596927i	0.640652	+	0.767832i	$0.278664\pi$
$600$	−11059.9	+	1869.46i	−0.752531	+	0.127201i
$601$	5504.09	+	9533.37i	0.373572	+	0.647045i	0.990112	−	0.140278i	$-0.0447997\pi$
$601$	5504.09	+	9533.37i	0.373572	+	0.647045i	−0.616540	+	0.787323i	$0.711466\pi$
$602$	−4835.94			−0.327406
$603$	−10163.1	+	3536.82i	−0.686361	+	0.238857i
$604$	12645.6			0.851890
$605$	−9734.33	−	16860.3i	−0.654143	−	1.13301i
$606$	−63.3978	−	76.6509i	−0.00424977	−	0.00513817i
$607$	−7340.08	+	12713.4i	−0.490815	+	0.850116i	−0.999944	−	0.0105740i	$-0.996634\pi$
$607$	−7340.08	+	12713.4i	−0.490815	+	0.850116i	0.509129	+	0.860690i	$0.329967\pi$
$608$	−165.634	+	286.887i	−0.0110483	+	0.0191362i
$609$	212.047	+	256.374i	0.0141093	+	0.0170588i
$610$	5840.78	+	10116.5i	0.387683	+	0.671486i
$611$	21653.4			1.43372
$612$	1720.78	−	598.841i	0.113658	−	0.0395534i
$613$	235.863			0.0155407			0.00777033	−	0.999970i	$-0.497527\pi$
$613$	235.863			0.0155407			0.00777033	+	0.999970i	$0.497527\pi$
$614$	8688.30	+	15048.6i	0.571061	+	0.989106i
$615$	−26952.1	+	4555.74i	−1.76718	+	0.298707i
$616$	−440.067	+	762.219i	−0.0287838	+	0.0498550i
$617$	−9156.53	+	15859.6i	−0.597452	+	1.03482i	0.395744	+	0.918361i	$0.370487\pi$
$617$	−9156.53	+	15859.6i	−0.597452	+	1.03482i	−0.993196	+	0.116457i	$0.962846\pi$
$618$	7143.70	−	19202.7i	0.464987	−	1.24992i
$619$	−3424.73	−	5931.81i	−0.222377	−	0.385169i	0.733152	−	0.680065i	$-0.238048\pi$
$619$	−3424.73	−	5931.81i	−0.222377	−	0.385169i	−0.955529	+	0.294896i	$0.904715\pi$
$620$	−12050.3			−0.780569
$621$	−148.699	+	6995.05i	−0.00960883	+	0.452015i
$622$	−2864.02			−0.184625
$623$	1082.56	+	1875.04i	0.0696175	+	0.120581i
$624$	−1329.68	+	3574.28i	−0.0853044	+	0.229304i
$625$	−11728.0	+	20313.6i	−0.750594	+	1.30007i
$626$	6614.52	−	11456.7i	0.422315	−	0.731472i
$627$	−993.994	+	168.016i	−0.0633115	+	0.0107016i
$628$	−2751.22	−	4765.26i	−0.174818	−	0.302794i
$629$	5840.30			0.370220
$630$	1181.59	−	6187.17i	0.0747235	−	0.391274i
$631$	22464.3			1.41726			0.708629	−	0.705581i	$-0.249314\pi$
$631$	22464.3			1.41726			0.708629	+	0.705581i	$0.249314\pi$
$632$	1497.26	+	2593.33i	0.0942372	+	0.163224i
$633$	19017.6	+	22993.1i	1.19412	+	1.44375i
$634$	1424.09	−	2466.60i	0.0892079	−	0.154513i
$635$	19845.1	−	34372.7i	1.24020	−	2.14809i
$636$	−3844.08	−	4647.67i	−0.239666	−	0.289768i
$637$	7076.39	+	12256.7i	0.440152	+	0.762365i
$638$	−408.814			−0.0253685
$639$	13239.0	+	11432.4i	0.819605	+	0.707761i
$640$	2543.41			0.157090
$641$	−9444.39	−	16358.2i	−0.581952	−	1.00797i	−0.995248	−	0.0973730i	$-0.968956\pi$
$641$	−9444.39	−	16358.2i	−0.581952	−	1.00797i	0.413296	−	0.910597i	$-0.364377\pi$
$642$	−14767.2	+	2496.11i	−0.907810	+	0.153448i
$643$	−3396.98	+	5883.74i	−0.208342	+	0.360858i	−0.951192	−	0.308599i	$-0.900140\pi$
$643$	−3396.98	+	5883.74i	−0.208342	+	0.360858i	0.742851	+	0.669457i	$0.233473\pi$
$644$	585.521	−	1014.15i	0.0358273	−	0.0620547i
$645$	−14828.0	+	39858.8i	−0.905200	+	2.43324i
$646$	−174.645	−	302.494i	−0.0106367	−	0.0184233i
$647$	5277.92			0.320706			0.160353	−	0.987060i	$-0.448737\pi$
$647$	5277.92			0.320706			0.160353	+	0.987060i	$0.448737\pi$
$648$	−849.567	−	5769.79i	−0.0515033	−	0.349782i
$649$	998.122			0.0603694
$650$	12377.4	+	21438.3i	0.746894	+	1.29366i
$651$	1612.49	−	4334.48i	0.0970789	−	0.260955i
$652$	−1084.15	+	1877.80i	−0.0651203	+	0.112792i
$653$	8282.09	−	14345.0i	0.496330	−	0.859668i	−0.503661	−	0.863901i	$-0.668014\pi$
$653$	8282.09	−	14345.0i	0.496330	−	0.859668i	0.999991	+	0.00423291i	$0.00134738\pi$
$654$	925.631	−	156.460i	0.0553441	−	0.00935486i
$655$	−1228.44	−	2127.72i	−0.0732810	−	0.126926i
$656$	4235.85			0.252107
$657$	9773.73	+	8439.99i	0.580380	+	0.501180i
$658$	5542.34			0.328363
$659$	1650.51	+	2858.77i	0.0975641	+	0.168986i	0.910676	−	0.413122i	$-0.135562\pi$
$659$	1650.51	+	2858.77i	0.0975641	+	0.168986i	−0.813112	+	0.582108i	$0.802228\pi$
$660$	4933.02	+	5964.25i	0.290935	+	0.351755i
$661$	−6495.17	+	11250.0i	−0.382198	+	0.661986i	−0.991376	−	0.131047i	$-0.958166\pi$
$661$	−6495.17	+	11250.0i	−0.382198	+	0.661986i	0.609178	+	0.793033i	$0.291499\pi$
$662$	3537.65	−	6127.39i	0.207696	−	0.359740i
$663$	−2562.80	−	3098.55i	−0.150122	−	0.181505i
$664$	3733.12	+	6465.95i	0.218182	+	0.377903i
$665$	−1207.55			−0.0704164
$666$	3506.72	−	18362.2i	0.204028	−	1.06835i
$667$	543.938			0.0315762
$668$	−6259.23	−	10841.3i	−0.362541	−	0.627939i
$669$	−12617.1	+	2132.69i	−0.729158	+	0.123250i
$670$	7919.46	−	13716.9i	0.456650	−	0.790940i
$671$	2754.38	−	4770.72i	0.158467	−	0.274473i
$672$	−340.342	+	914.861i	−0.0195371	+	0.0525171i
$673$	−9257.15	−	16033.9i	−0.530219	−	0.918365i	−0.999378	−	0.0352522i	$-0.988777\pi$
$673$	−9257.15	−	16033.9i	−0.530219	−	0.918365i	0.469160	−	0.883113i	$-0.344557\pi$
$674$	3520.56			0.201197
$675$	−32375.1	−	19620.8i	−1.84610	−	1.11882i
$676$	−371.616			−0.0211434
$677$	3050.00	+	5282.75i	0.173148	+	0.299900i	0.939519	−	0.342498i	$-0.111273\pi$
$677$	3050.00	+	5282.75i	0.173148	+	0.299900i	−0.766371	+	0.642398i	$0.777940\pi$
$678$	−5981.37	+	16078.3i	−0.338810	+	0.910744i
$679$	804.687	−	1393.76i	0.0454802	−	0.0787740i
$680$	−1340.89	+	2322.49i	−0.0756188	+	0.130976i
$681$	14342.3	−	2424.30i	0.807048	−	0.136416i
$682$	2841.32	+	4921.32i	0.159531	+	0.276315i
$683$	−22630.0			−1.26781			−0.633905	−	0.773411i	$-0.718549\pi$
$683$	−22630.0			−1.26781			−0.633905	+	0.773411i	$0.718549\pi$
$684$	−1055.92	+	367.464i	−0.0590263	+	0.0205414i
$685$	−2253.42			−0.125691
$686$	3824.81	+	6624.76i	0.212874	+	0.368709i
$687$	−4678.97	−	5657.10i	−0.259846	−	0.314166i
$688$	3295.12	−	5707.32i	0.182595	−	0.316264i
$689$	−6655.48	+	11527.6i	−0.368002	+	0.637398i
$690$	−6563.51	−	7935.59i	−0.362128	−	0.437830i
$691$	−11493.4	−	19907.2i	−0.632750	−	1.09595i	−0.986987	−	0.160799i	$-0.948593\pi$
$691$	−11493.4	−	19907.2i	−0.632750	−	1.09595i	0.354237	−	0.935156i	$-0.384741\pi$
$692$	−10073.1			−0.553355
$693$	−2805.43	+	976.302i	−0.153780	+	0.0535161i
$694$	3210.88			0.175624
$695$	−3910.48	−	6773.14i	−0.213428	−	0.369669i
$696$	−447.055	+	75.5660i	−0.0243471	+	0.00411541i
$697$	−2233.15	+	3867.92i	−0.121358	+	0.210198i
$698$	−6641.89	+	11504.1i	−0.360171	+	0.623834i
$699$	−3684.73	+	9904.81i	−0.199384	+	0.535958i
$700$	3168.08	+	5487.27i	0.171060	+	0.296285i
$701$	27015.5			1.45558			0.727790	−	0.685800i	$-0.240548\pi$
$701$	27015.5			1.45558			0.727790	+	0.685800i	$0.240548\pi$
$702$	−11280.8	+	6197.09i	−0.606503	+	0.333183i
$703$	−3583.76			−0.192268
$704$	−599.707	−	1038.72i	−0.0321056	−	0.0556085i
$705$	16994.0	−	45681.1i	0.907847	−	2.44035i
$706$	−3056.27	+	5293.61i	−0.162924	+	0.282192i
$707$	−28.0949	+	48.6618i	−0.00149451	+	0.00258857i
$708$	1091.49	−	184.495i	0.0579387	−	0.00979343i
$709$	9588.67	+	16608.1i	0.507912	+	0.879730i	0.999958	+	0.00916077i	$0.00291601\pi$
$709$	9588.67	+	16608.1i	0.507912	+	0.879730i	−0.492046	+	0.870569i	$0.663751\pi$
$710$	−25746.3			−1.36090
$711$	−1895.83	+	9927.11i	−0.0999988	+	0.523623i
$712$	−2950.54			−0.155303
$713$	−3780.46	−	6547.95i	−0.198568	−	0.343931i
$714$	−655.966	−	793.094i	−0.0343822	−	0.0415698i
$715$	8540.81	−	14793.1i	0.446725	−	0.773750i
$716$	4662.51	−	8075.71i	0.243361	−	0.421513i
$717$	1727.44	+	2088.56i	0.0899755	+	0.108785i
$718$	−2489.46	−	4311.87i	−0.129395	−	0.224119i
$719$	25931.8			1.34505			0.672526	−	0.740073i	$-0.265209\pi$
$719$	25931.8			1.34505			0.672526	+	0.740073i	$0.265209\pi$
$720$	6496.90	+	5610.32i	0.336285	+	0.290395i
$721$	−11573.6			−0.597812
$722$	−6751.83	−	11694.5i	−0.348029	−	0.602805i
$723$	30308.7	−	5123.10i	1.55905	−	0.263527i
$724$	−1469.94	+	2546.01i	−0.0754556	+	0.130693i
$725$	−1471.54	+	2548.78i	−0.0753816	+	0.130565i
$726$	−3550.21	+	9543.20i	−0.181489	+	0.487853i
$727$	−2915.25	−	5049.36i	−0.148722	−	0.257594i	0.782034	−	0.623236i	$-0.214183\pi$
$727$	−2915.25	−	5049.36i	−0.148722	−	0.257594i	−0.930755	+	0.365643i	$0.880849\pi$
$728$	2154.23			0.109672
$729$	10557.0	−	16612.4i	0.536351	−	0.843995i
$730$	−19007.2			−0.963683
$731$	3474.38	+	6017.81i	0.175793	+	0.304482i
$732$	2130.19	−	5726.11i	0.107560	−	0.289130i
$733$	11577.3	−	20052.4i	0.583379	−	1.01044i	−0.411696	−	0.911321i	$-0.635064\pi$
$733$	11577.3	−	20052.4i	0.583379	−	1.01044i	0.995075	−	0.0991211i	$-0.0316031\pi$
$734$	2355.05	−	4079.06i	0.118428	−	0.205124i
$735$	31410.9	−	5309.41i	1.57634	−	0.266450i
$736$	797.927	+	1382.05i	0.0399619	+	0.0692161i
$737$	−7469.26			−0.373316
$738$	10820.1	+	9343.55i	0.539692	+	0.466044i
$739$	−27085.8			−1.34827			−0.674133	−	0.738610i	$-0.735483\pi$
$739$	−27085.8			−1.34827			−0.674133	+	0.738610i	$0.735483\pi$
$740$	13757.7	+	23829.1i	0.683438	+	1.18375i
$741$	1572.60	+	1901.35i	0.0779635	+	0.0942615i
$742$	−1703.52	+	2950.58i	−0.0842830	+	0.145983i
$743$	−16093.8	+	27875.3i	−0.794650	+	1.37637i	0.128412	+	0.991721i	$0.459012\pi$
$743$	−16093.8	+	27875.3i	−0.794650	+	1.37637i	−0.923061	+	0.384653i	$0.874321\pi$
$744$	4016.77	+	4856.47i	0.197933	+	0.239310i
$745$	14974.5	+	25936.5i	0.736406	+	1.27549i
$746$	5514.05			0.270622
$747$	−4726.86	+	24751.2i	−0.231522	+	1.21232i
$748$	1264.66			0.0618191
$749$	4230.02	+	7326.61i	0.206357	+	0.357421i
$750$	29489.8	−	4984.69i	1.43575	−	0.242687i
$751$	1366.46	−	2366.78i	0.0663954	−	0.115000i	−0.830917	−	0.556397i	$-0.812183\pi$
$751$	1366.46	−	2366.78i	0.0663954	−	0.115000i	0.897312	+	0.441397i	$0.145517\pi$
$752$	−3776.45	+	6541.01i	−0.183129	+	0.317189i
$753$	−1286.56	+	3458.37i	−0.0622642	+	0.167370i
$754$	500.310	+	866.562i	0.0241647	+	0.0418545i
$755$	−62818.3			−3.02807
$756$	−2887.39	+	1586.19i	−0.138907	+	0.0763084i
$757$	−6315.62			−0.303230			−0.151615	−	0.988440i	$-0.548447\pi$
$757$	−6315.62			−0.303230			−0.151615	+	0.988440i	$0.548447\pi$
$758$	246.459	+	426.879i	0.0118097	+	0.0204551i
$759$	−1693.28	+	4551.64i	−0.0809776	+	0.217673i
$760$	822.805	−	1425.14i	0.0392714	−	0.0680201i
$761$	−15740.7	+	27263.6i	−0.749801	+	1.29869i	0.198116	+	0.980179i	$0.436518\pi$
$761$	−15740.7	+	27263.6i	−0.749801	+	1.29869i	−0.947918	+	0.318516i	$0.896816\pi$
$762$	−20467.8	+	3459.68i	−0.973056	+	0.164476i
$763$	−265.145	−	459.244i	−0.0125804	−	0.0217900i
$764$	14471.0			0.685266
$765$	−8548.18	+	2974.81i	−0.404000	+	0.140594i
$766$	−1301.15			−0.0613739
$767$	−1221.51	−	2115.72i	−0.0575048	−	0.0996012i
$768$	−847.805	−	1025.04i	−0.0398340	−	0.0481612i
$769$	13648.3	−	23639.6i	0.640014	−	1.10854i	−0.345415	−	0.938450i	$-0.612262\pi$
$769$	13648.3	−	23639.6i	0.640014	−	1.10854i	0.985429	−	0.170087i	$-0.0544048\pi$
$770$	2186.08	−	3786.40i	0.102313	−	0.177211i
$771$	−20867.3	−	25229.5i	−0.974730	−	1.17849i
$772$	−8682.25	−	15038.1i	−0.404768	−	0.701079i
$773$	24025.2			1.11789			0.558943	−	0.829206i	$-0.311207\pi$
$773$	24025.2			1.11789			0.558943	+	0.829206i	$0.311207\pi$
$774$	21006.4	−	7310.33i	0.975529	−	0.339489i
$775$	40909.9			1.89616
$776$	1096.60	+	1899.36i	0.0507288	+	0.0878649i
$777$	−10412.2	+	1759.99i	−0.480742	+	0.0812603i
$778$	−10246.2	+	17746.9i	−0.472163	+	0.817810i
$779$	1370.32	−	2373.46i	0.0630252	−	0.109163i
$780$	6605.34	−	17755.6i	0.303217	−	0.815067i
$781$	6070.66	+	10514.7i	0.278138	+	0.481748i
$782$	−1682.67			−0.0769465
$783$	−1308.64	−	793.098i	−0.0597281	−	0.0361980i
$784$	−4936.61			−0.224882
$785$	13667.0	+	23671.9i	0.621396	+	1.07629i
$786$	−448.024	+	1204.32i	−0.0203314	+	0.0546522i
$787$	5279.44	−	9144.26i	0.239125	−	0.414177i	−0.721338	−	0.692583i	$-0.756473\pi$
$787$	5279.44	−	9144.26i	0.239125	−	0.414177i	0.960464	+	0.278406i	$0.0898059\pi$
$788$	6572.40	−	11383.7i	0.297122	−	0.514630i
$789$	−25216.8	+	4262.42i	−1.13782	+	0.192327i
$790$	−7437.81	−	12882.7i	−0.334969	−	0.580183i
$791$	9690.47			0.435592
$792$	759.347	−	3976.17i	0.0340685	−	0.178393i
$793$	−13483.3			−0.603792
$794$	−9453.68	−	16374.3i	−0.422542	−	0.731865i
$795$	19095.9	+	23087.8i	0.851900	+	1.02999i
$796$	−664.530	+	1151.00i	−0.0295900	+	0.0512514i
$797$	13444.6	−	23286.7i	0.597529	−	1.03495i	−0.395656	−	0.918399i	$-0.629483\pi$
$797$	13444.6	−	23286.7i	0.597529	−	1.03495i	0.993185	−	0.116552i	$-0.0371841\pi$
$798$	402.518	+	486.663i	0.0178559	+	0.0215886i
$799$	−3981.90	−	6896.85i	−0.176307	−	0.305373i
$800$	−8634.68			−0.381603
$801$	−7536.85	−	6508.36i	−0.332462	−	0.287093i
$802$	−541.446			−0.0238393
$803$	4481.68	+	7762.49i	0.196955	+	0.341136i
$804$	−8167.94	+	1380.63i	−0.358285	+	0.0605612i
$805$	−2908.64	+	5037.91i	−0.127349	+	0.220575i
$806$	6954.47	−	12045.5i	0.303922	−	0.526408i
$807$	9882.13	−	26563.8i	0.431062	−	1.15872i
$808$	−38.2867	−	66.3145i	−0.00166698	−	0.00288730i
$809$	−18643.8			−0.810236			−0.405118	−	0.914264i	$-0.632770\pi$
$809$	−18643.8			−0.810236			−0.405118	+	0.914264i	$0.632770\pi$
$810$	4220.31	+	28662.0i	0.183070	+	1.24331i
$811$	−23870.8			−1.03356			−0.516781	−	0.856118i	$-0.672870\pi$
$811$	−23870.8			−1.03356			−0.516781	+	0.856118i	$0.672870\pi$
$812$	128.058	+	221.802i	0.00553441	+	0.00958588i
$813$	−5067.62	+	13622.1i	−0.218609	+	0.587636i
$814$	6487.82	−	11237.2i	0.279359	−	0.483863i
$815$	5385.61	−	9328.15i	0.231472	−	0.400921i
$816$	1382.96	−	233.763i	0.0593302	−	0.0100286i
$817$	−2131.97	−	3692.68i	−0.0912952	−	0.158128i
$818$	23172.3			0.990467
$819$	5502.77	+	4751.85i	0.234777	+	0.202739i
$820$	−21042.1			−0.896122
$821$	−7266.51	−	12586.0i	−0.308895	−	0.535022i	0.669226	−	0.743059i	$-0.266626\pi$
$821$	−7266.51	−	12586.0i	−0.308895	−	0.535022i	−0.978121	+	0.208037i	$0.933293\pi$
$822$	751.139	+	908.162i	0.0318722	+	0.0385350i
$823$	−4434.21	+	7680.28i	−0.187809	+	0.325295i	−0.944520	−	0.328455i	$-0.893472\pi$
$823$	−4434.21	+	7680.28i	−0.187809	+	0.325295i	0.756710	+	0.653750i	$0.226805\pi$
$824$	7886.02	−	13659.0i	0.333401	−	0.577468i
$825$	−16747.2	−	20248.1i	−0.706742	−	0.854484i
$826$	−312.654	−	541.532i	−0.0131702	−	0.0228115i
$827$	25059.3			1.05369			0.526843	−	0.849963i	$-0.323376\pi$
$827$	25059.3			1.05369			0.526843	+	0.849963i	$0.323376\pi$
$828$	−1010.33	+	5290.40i	−0.0424052	+	0.222046i
$829$	−22556.3			−0.945009			−0.472505	−	0.881328i	$-0.656650\pi$
$829$	−22556.3			−0.945009			−0.472505	+	0.881328i	$0.656650\pi$
$830$	−18544.7	−	32120.3i	−0.775535	−	1.34327i
$831$	−10990.7	+	1857.77i	−0.458802	+	0.0775517i
$832$	−1467.85	+	2542.40i	−0.0611643	+	0.105940i
$833$	2602.58	−	4507.81i	0.108252	−	0.187499i
$834$	−1426.19	+	3833.70i	−0.0592146	+	0.159173i
$835$	31093.4	+	53855.4i	1.28866	+	2.23203i
$836$	−776.031			−0.0321048
$837$	−452.060	+	21265.7i	−0.0186684	+	0.878195i
$838$	32267.5			1.33014
$839$	−10604.8	−	18368.0i	−0.436374	−	0.755822i	0.561033	−	0.827794i	$-0.310404\pi$
$839$	−10604.8	−	18368.0i	−0.436374	−	0.755822i	−0.997407	+	0.0719718i	$0.977071\pi$
$840$	1690.68	−	4544.67i	0.0694454	−	0.186674i
$841$	12135.0	−	21018.5i	0.497561	−	0.861801i
$842$	4991.93	−	8646.27i	0.204315	−	0.353884i
$843$	−28229.2	+	4771.60i	−1.15334	+	0.194950i
$844$	11484.9	+	19892.5i	0.468398	+	0.811290i
$845$	1846.04			0.0751548
$846$	−24074.9	+	8378.17i	−0.978382	+	0.340482i
$847$	5751.73			0.233331
$848$	−2321.49	−	4020.93i	−0.0940097	−	0.162830i
$849$	−13272.9	−	16047.6i	−0.536543	−	0.648706i
$850$	4552.21	−	7884.66i	0.183694	−	0.318167i
$851$	−8632.22	+	14951.4i	−0.347719	+	0.602267i
$852$	8582.09	+	10376.1i	0.345091	+	0.417231i
$853$	−14058.1	−	24349.4i	−0.564292	−	0.977382i	−0.997115	−	0.0759030i	$-0.975816\pi$
$853$	−14058.1	−	24349.4i	−0.564292	−	0.977382i	0.432824	−	0.901479i	$-0.357517\pi$
$854$	−3451.15			−0.138286
$855$	5245.38	−	1825.42i	0.209811	−	0.0730152i
$856$	−11529.0			−0.460344
$857$	4738.82	+	8207.87i	0.188886	+	0.327159i	0.944879	−	0.327420i	$-0.106179\pi$
$857$	4738.82	+	8207.87i	0.188886	+	0.327159i	−0.755993	+	0.654579i	$0.772846\pi$
$858$	−8808.80	+	1488.96i	−0.350498	+	0.0592450i
$859$	−14772.9	+	25587.4i	−0.586780	+	1.01633i	0.407871	+	0.913040i	$0.366271\pi$
$859$	−14772.9	+	25587.4i	−0.586780	+	1.01633i	−0.994651	+	0.103293i	$0.967062\pi$
$860$	−16368.9	+	28351.7i	−0.649039	+	1.12417i
$861$	2815.70	−	7568.78i	0.111450	−	0.299586i
$862$	8184.74	+	14176.4i	0.323403	+	0.560150i
$863$	9932.53			0.391781			0.195891	−	0.980626i	$-0.437240\pi$
$863$	9932.53			0.391781			0.195891	+	0.980626i	$0.437240\pi$
$864$	95.4145	−	4488.46i	0.00375702	−	0.176737i
$865$	50039.2			1.96692
$866$	8663.17	+	15005.0i	0.339938	+	0.588790i
$867$	8385.43	−	22540.6i	0.328471	−	0.882951i
$868$	1780.05	−	3083.13i	0.0696068	−	0.120562i
$869$	−3507.50	+	6075.16i	−0.136920	+	0.237153i
$870$	2220.79	−	375.382i	0.0865424	−	0.0146283i
$871$	9140.94	+	15832.6i	0.355602	+	0.615920i
$872$	722.659			0.0280646
$873$	−1388.51	+	7270.64i	−0.0538303	+	0.281871i
$874$	1032.53			0.0399609
$875$	−8447.28	−	14631.1i	−0.326366	−	0.565282i
$876$	6335.74	+	7660.21i	0.244366	+	0.295450i
$877$	13512.7	−	23404.7i	0.520288	−	0.901165i	−0.479434	−	0.877578i	$-0.659158\pi$
$877$	13512.7	−	23404.7i	0.520288	−	0.901165i	0.999722	−	0.0235871i	$-0.00750870\pi$
$878$	−15864.3	+	27477.8i	−0.609788	+	1.05618i
$879$	19238.7	+	23260.5i	0.738230	+	0.892555i
$880$	2979.11	+	5159.97i	0.114120	+	0.197662i
$881$	−12798.1			−0.489422			−0.244711	−	0.969596i	$-0.578693\pi$
$881$	−12798.1			−0.489422			−0.244711	+	0.969596i	$0.578693\pi$
$882$	−12610.1	−	10889.3i	−0.481410	−	0.415716i
$883$	27016.7			1.02965			0.514826	−	0.857294i	$-0.327856\pi$
$883$	27016.7			1.02965			0.514826	+	0.857294i	$0.327856\pi$
$884$	−1547.71	−	2680.71i	−0.0588858	−	0.101993i
$885$	−5422.08	+	916.499i	−0.205945	+	0.0348110i
$886$	−399.641	+	692.198i	−0.0151537	+	0.0262470i
$887$	10075.1	−	17450.5i	0.381384	−	0.660576i	−0.609876	−	0.792497i	$-0.708781\pi$
$887$	10075.1	−	17450.5i	0.381384	−	0.660576i	0.991260	+	0.131920i	$0.0421143\pi$
$888$	5017.59	−	13487.6i	0.189616	−	0.509701i
$889$	5862.94	+	10154.9i	0.221188	+	0.383110i
$890$	14657.1			0.552031
$891$	10710.4	−	8481.74i	0.402707	−	0.318910i
$892$	−9850.46			−0.369751
$893$	2443.39	+	4232.08i	0.0915622	+	0.158590i
$894$	5461.34	−	14680.5i	0.204312	−	0.549204i
$895$	−23161.5	+	40116.9i	−0.865033	+	1.49828i
$896$	−375.707	+	650.744i	−0.0140084	+	0.0242632i
$897$	11720.3	−	1981.10i	0.436266	−	0.0737425i
$898$	5924.51	+	10261.6i	0.220160	+	0.381328i
$899$	1653.63			0.0613477
$900$	−22056.4	−	19046.6i	−0.816905	−	0.705429i
$901$	4895.56			0.181015
$902$	4961.47	+	8593.52i	0.183147	+	0.317220i
$903$	−8007.69	−	9681.67i	−0.295104	−	0.356795i
$904$	−6602.91	+	11436.6i	−0.242931	+	0.420769i
$905$	7302.08	−	12647.6i	0.268209	−	0.464552i
$906$	20939.4	+	25316.8i	0.767844	+	0.928359i
$907$	−4639.96	−	8036.64i	−0.169865	−	0.294214i	0.768508	−	0.639841i	$-0.221000\pi$
$907$	−4639.96	−	8036.64i	−0.169865	−	0.294214i	−0.938372	+	0.345627i	$0.887666\pi$
$908$	11197.4			0.409248
$909$	48.4785	−	253.848i	0.00176890	−	0.00926248i
$910$	−10701.4			−0.389832
$911$	−8200.30	−	14203.3i	−0.298231	−	0.516551i	0.677501	−	0.735522i	$-0.263063\pi$
$911$	−8200.30	−	14203.3i	−0.298231	−	0.516551i	−0.975731	+	0.218972i	$0.929730\pi$
$912$	−848.622	+	143.443i	−0.0308122	+	0.00520821i
$913$	−8745.22	+	15147.2i	−0.317004	+	0.549067i
$914$	−7891.14	+	13667.9i	−0.285575	+	0.494631i
$915$	−10582.0	+	28445.0i	−0.382327	+	1.02772i
$916$	−2825.69	−	4894.24i	−0.101925	−	0.176540i
$917$	725.848			0.0261392
$918$	4048.28	+	2453.45i	0.145548	+	0.0882090i
$919$	−11704.6			−0.420128			−0.210064	−	0.977688i	$-0.567367\pi$
$919$	−11704.6			−0.420128			−0.210064	+	0.977688i	$0.567367\pi$
$920$	−3963.79	−	6865.48i	−0.142046	−	0.246031i
$921$	−15740.9	+	42312.7i	−0.563172	+	1.51384i
$922$	−3262.18	+	5650.27i	−0.116523	+	0.201824i
$923$	14858.7	−	25736.0i	0.529880	−	0.917778i
$924$	−2254.67	+	381.109i	−0.0802741	+	0.0135688i
$925$	−46706.3	−	80897.8i	−1.66021	−	2.87557i
$926$	−7380.81			−0.261931
$927$	50273.4	−	17495.4i	1.78122	−	0.619874i
$928$	−349.025			−0.0123462
$929$	−8162.22	−	14137.4i	−0.288260	−	0.499281i	0.685134	−	0.728417i	$-0.259743\pi$
$929$	−8162.22	−	14137.4i	−0.288260	−	0.499281i	−0.973395	+	0.229136i	$0.926410\pi$
$930$	−19953.8	−	24125.0i	−0.703558	−	0.850635i
$931$	−1597.01	+	2766.11i	−0.0562191	+	0.0973744i
$932$	−4067.62	+	7045.33i	−0.142961	+	0.247615i
$933$	−4742.44	−	5733.84i	−0.166410	−	0.201198i
$934$	−10193.2	−	17655.2i	−0.357101	−	0.618516i
$935$	−6282.36			−0.219738
$936$	−9357.57	+	3256.48i	−0.326775	+	0.113719i
$937$	−7397.79			−0.257925			−0.128962	−	0.991649i	$-0.541165\pi$
$937$	−7397.79			−0.257925			−0.128962	+	0.991649i	$0.541165\pi$
$938$	2339.69	+	4052.46i	0.0814430	+	0.141063i
$939$	33889.3	−	5728.34i	1.17778	−	0.199081i
$940$	18759.9	−	32493.1i	0.650937	−	1.12746i
$941$	−3713.44	+	6431.87i	−0.128645	+	0.222819i	−0.923152	−	0.384436i	$-0.874396\pi$
$941$	−3713.44	+	6431.87i	−0.128645	+	0.222819i	0.794507	+	0.607255i	$0.207729\pi$
$942$	4984.49	−	13398.7i	0.172403	−	0.463431i
$943$	−6601.37	−	11433.9i	−0.227964	−	0.394845i
$944$	852.146			0.0293803
$945$	14343.4	−	7879.56i	0.493748	−	0.271240i
$946$	15438.3			0.530596
$947$	11526.0	+	19963.6i	0.395505	+	0.685035i	0.993166	−	0.116714i	$-0.0372362\pi$
$947$	11526.0	+	19963.6i	0.395505	+	0.685035i	−0.597660	+	0.801749i	$0.703903\pi$
$948$	−2712.65	+	7291.78i	−0.0929353	+	0.249816i
$949$	10969.4	−	18999.6i	0.375219	−	0.649898i
$950$	−2793.36	+	4838.23i	−0.0953983	+	0.165235i
$951$	7296.29	−	1233.30i	0.248789	−	0.0420530i
$952$	−396.146	−	686.146i	−0.0134865	−	0.0233594i
$953$	−23445.7			−0.796936			−0.398468	−	0.917182i	$-0.630458\pi$
$953$	−23445.7			−0.796936			−0.398468	+	0.917182i	$0.630458\pi$
$954$	2939.46	−	15391.9i	0.0997574	−	0.522359i
$955$	−71886.4			−2.43580
$956$	1043.22	+	1806.91i	0.0352931	+	0.0611295i
$957$	−676.942	−	818.454i	−0.0228656	−	0.0276456i
$958$	840.068	−	1455.04i	0.0283313	−	0.0490712i
$959$	332.869	−	576.547i	0.0112085	−	0.0194136i
$960$	4211.56	+	5091.98i	0.141591	+	0.171190i
$961$	3402.51	+	5893.32i	0.114213	+	0.197822i
$962$	−31759.4			−1.06441
$963$	−29449.8	−	25431.0i	−0.985469	−	0.850990i
$964$	23662.6			0.790582
$965$	43130.0	+	74703.4i	1.43876	+	2.49201i
$966$	2999.90	−	507.076i	0.0999175	−	0.0168891i
$967$	8370.95	−	14498.9i	0.278378	−	0.482165i	−0.692604	−	0.721318i	$-0.743536\pi$
$967$	8370.95	−	14498.9i	0.278378	−	0.482165i	0.970982	+	0.239153i	$0.0768698\pi$
$968$	−3919.12	+	6788.12i	−0.130129	+	0.225391i
$969$	316.411	−	850.533i	0.0104898	−	0.0281972i
$970$	−5447.46	−	9435.29i	−0.180317	−	0.312318i
$971$	−43037.7			−1.42240			−0.711198	−	0.702992i	$-0.751847\pi$
$971$	−43037.7			−1.42240			−0.711198	+	0.702992i	$0.751847\pi$
$972$	10144.5	−	11254.9i	0.334758	−	0.371399i
$973$	2310.59			0.0761295
$974$	−3367.28	−	5832.31i	−0.110775	−	0.191868i
$975$	−22424.6	+	60278.8i	−0.736576	+	1.97997i
$976$	2351.55	−	4073.00i	0.0771222	−	0.133580i
$977$	8949.91	−	15501.7i	0.293074	−	0.507619i	−0.681461	−	0.731854i	$-0.738655\pi$
$977$	8949.91	−	15501.7i	0.293074	−	0.507619i	0.974535	+	0.224236i	$0.0719885\pi$
$978$	−5554.60	+	938.898i	−0.181612	+	0.0306980i
$979$	−3455.97	−	5985.92i	−0.112823	−	0.195415i
$980$	24523.1			0.799350
$981$	1845.96	+	1594.06i	0.0600785	+	0.0518801i
$982$	37738.2			1.22635
$983$	23150.1	+	40097.2i	0.751144	+	1.30102i	0.947269	+	0.320441i	$0.103831\pi$
$983$	23150.1	+	40097.2i	0.751144	+	1.30102i	−0.196124	+	0.980579i	$0.562836\pi$
$984$	7014.02	+	8480.28i	0.227234	+	0.274737i
$985$	−32649.1	+	56549.9i	−1.05613	+	1.82927i
$986$	184.006	−	318.708i	0.00594315	−	0.0102938i
$987$	9177.40	+	11095.9i	0.295967	+	0.357838i
$988$	949.713	+	1644.95i	0.0305814	+	0.0529685i
$989$	−20541.1			−0.660435
$990$	−3772.14	+	19752.0i	−0.121097	+	0.634102i
$991$	4621.74			0.148148			0.0740739	−	0.997253i	$-0.476400\pi$
$991$	4621.74			0.148148			0.0740739	+	0.997253i	$0.476400\pi$
$992$	2425.78	+	4201.57i	0.0776397	+	0.134476i
$993$	18125.1	−	3063.70i	0.579236	−	0.0979088i
$994$	3803.18	−	6587.30i	0.121358	−	0.210198i
$995$	3301.13	−	5717.72i	0.105179	−	0.182175i
$996$	−6763.43	+	18180.5i	−0.215168	+	0.578386i
$997$	−9972.43	−	17272.8i	−0.316780	−	0.548680i	0.663034	−	0.748589i	$-0.269268\pi$
$997$	−9972.43	−	17272.8i	−0.316780	−	0.548680i	−0.979814	+	0.199910i	$0.935935\pi$
$998$	29132.0			0.924006
$999$	42568.2	−	23384.9i	1.34815	−	0.740605i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.4.c.b.13.1	yes	4
3.2	odd	2		54.4.c.b.37.1		4
4.3	odd	2		144.4.i.b.49.2		4
9.2	odd	6		54.4.c.b.19.1		4
9.4	even	3		162.4.a.f.1.1		2
9.5	odd	6		162.4.a.g.1.2		2
9.7	even	3	inner	18.4.c.b.7.1	✓	4
12.11	even	2		432.4.i.b.145.1		4
36.7	odd	6		144.4.i.b.97.2		4
36.11	even	6		432.4.i.b.289.1		4
36.23	even	6		1296.4.a.r.1.2		2
36.31	odd	6		1296.4.a.l.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.4.c.b.7.1	✓	4	9.7	even	3	inner
18.4.c.b.13.1	yes	4	1.1	even	1	trivial
54.4.c.b.19.1		4	9.2	odd	6
54.4.c.b.37.1		4	3.2	odd	2
144.4.i.b.49.2		4	4.3	odd	2
144.4.i.b.97.2		4	36.7	odd	6
162.4.a.f.1.1		2	9.4	even	3
162.4.a.g.1.2		2	9.5	odd	6
432.4.i.b.145.1		4	12.11	even	2
432.4.i.b.289.1		4	36.11	even	6
1296.4.a.l.1.1		2	36.31	odd	6
1296.4.a.r.1.2		2	36.23	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:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	18.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-1.81174 + 4.87007i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(9.93521 - 17.2083i) q^{5} +(-10.2470 + 1.73205i) q^{6} +(2.93521 + 5.08394i) q^{7} -8.00000 q^{8} +(-20.4352 - 17.6466i) q^{9} +39.7409 q^{10} +(-9.37043 - 16.2301i) q^{11} +(-13.2470 - 16.0162i) q^{12} +(-22.9352 + 39.7250i) q^{13} +(-5.87043 + 10.1679i) q^{14} +(65.8056 + 79.5621i) q^{15} +(-8.00000 - 13.8564i) q^{16} +16.8704 q^{17} +(10.1296 - 53.0414i) q^{18} -10.3521 q^{19} +(39.7409 + 68.8332i) q^{20} +(-30.0770 + 5.08394i) q^{21} +(18.7409 - 32.4601i) q^{22} +(-24.9352 + 43.1891i) q^{23} +(14.4939 - 38.9606i) q^{24} +(-134.917 - 233.683i) q^{25} -91.7409 q^{26} +(122.963 - 67.5500i) q^{27} -23.4817 q^{28} +(-5.45351 - 9.44575i) q^{29} +(-72.0000 + 193.541i) q^{30} +(-75.8056 + 131.299i) q^{31} +(16.0000 - 27.7128i) q^{32} +(96.0183 - 16.2301i) q^{33} +(16.8704 + 29.2204i) q^{34} +116.648 q^{35} +(102.000 - 35.4965i) q^{36} +346.186 q^{37} +(-10.3521 - 17.9304i) q^{38} +(-151.911 - 183.667i) q^{39} +(-79.4817 + 137.666i) q^{40} +(-132.370 + 229.272i) q^{41} +(-38.8826 - 47.0109i) q^{42} +(205.945 + 356.707i) q^{43} +74.9634 q^{44} +(-506.696 + 176.333i) q^{45} -99.7409 q^{46} +(-236.028 - 408.813i) q^{47} +(81.9756 - 13.8564i) q^{48} +(154.269 - 267.202i) q^{49} +(269.834 - 467.366i) q^{50} +(-30.5648 + 82.1602i) q^{51} +(-91.7409 - 158.900i) q^{52} +290.186 q^{53} +(239.963 + 145.429i) q^{54} -372.389 q^{55} +(-23.4817 - 40.6715i) q^{56} +(18.7553 - 50.4156i) q^{57} +(10.9070 - 18.8915i) q^{58} +(-26.6296 + 46.1238i) q^{59} +(-407.223 + 68.8332i) q^{60} +(146.972 + 254.563i) q^{61} -303.223 q^{62} +(29.7325 - 155.688i) q^{63} +64.0000 q^{64} +(455.732 + 789.352i) q^{65} +(124.130 + 150.079i) q^{66} +(199.277 - 345.159i) q^{67} +(-33.7409 + 58.4409i) q^{68} +(-165.158 - 199.684i) q^{69} +(116.648 + 202.040i) q^{70} -647.854 q^{71} +(163.482 + 141.173i) q^{72} -478.279 q^{73} +(346.186 + 599.612i) q^{74} +(1382.49 - 233.683i) q^{75} +(20.7043 - 35.8608i) q^{76} +(55.0084 - 95.2773i) q^{77} +(166.210 - 446.785i) q^{78} +(-187.158 - 324.167i) q^{79} -317.927 q^{80} +(106.196 + 721.224i) q^{81} -529.482 q^{82} +(-466.639 - 808.243i) q^{83} +(42.5427 - 114.358i) q^{84} +(167.611 - 290.311i) q^{85} +(-411.890 + 713.415i) q^{86} +(55.8818 - 9.44575i) q^{87} +(74.9634 + 129.840i) q^{88} +368.817 q^{89} +(-812.113 - 701.290i) q^{90} -269.279 q^{91} +(-99.7409 - 172.756i) q^{92} +(-502.097 - 607.059i) q^{93} +(472.056 - 817.626i) q^{94} +(-102.851 + 178.143i) q^{95} +(105.976 + 128.130i) q^{96} +(-137.075 - 237.420i) q^{97} +617.076 q^{98} +(-94.9184 + 497.021i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 3 q^{3} - 8 q^{4} + 9 q^{5} - 19 q^{7} - 32 q^{8} - 51 q^{9} + 36 q^{10} + 24 q^{11} - 12 q^{12} - 61 q^{13} + 38 q^{14} + 171 q^{15} - 32 q^{16} + 6 q^{17} + 102 q^{18} + 266 q^{19} + 36 q^{20}+ \cdots + 1557 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 3 * q^3 - 8 * q^4 + 9 * q^5 - 19 * q^7 - 32 * q^8 - 51 * q^9 + 36 * q^10 + 24 * q^11 - 12 * q^12 - 61 * q^13 + 38 * q^14 + 171 * q^15 - 32 * q^16 + 6 * q^17 + 102 * q^18 + 266 * q^19 + 36 * q^20 - 315 * q^21 - 48 * q^22 - 69 * q^23 - 24 * q^24 - 263 * q^25 - 244 * q^26 + 152 * q^28 - 237 * q^29 - 288 * q^30 - 211 * q^31 + 64 * q^32 + 630 * q^33 + 6 * q^34 + 774 * q^35 + 408 * q^36 + 524 * q^37 + 266 * q^38 - 249 * q^39 - 72 * q^40 - 468 * q^41 - 258 * q^42 + 86 * q^43 - 192 * q^44 - 459 * q^45 - 276 * q^46 - 483 * q^47 + 33 * q^49 + 526 * q^50 - 153 * q^51 - 244 * q^52 + 300 * q^53 + 468 * q^54 - 1674 * q^55 + 152 * q^56 + 987 * q^57 + 474 * q^58 - 168 * q^59 - 1260 * q^60 + 1049 * q^61 - 844 * q^62 - 957 * q^63 + 256 * q^64 + 747 * q^65 + 558 * q^66 + 1166 * q^67 - 12 * q^68 - 261 * q^69 + 774 * q^70 - 624 * q^71 + 408 * q^72 - 622 * q^73 + 524 * q^74 + 2835 * q^75 - 532 * q^76 + 1173 * q^77 + 132 * q^78 - 349 * q^79 - 288 * q^80 - 1143 * q^81 - 1872 * q^82 - 1221 * q^83 + 744 * q^84 + 486 * q^85 - 172 * q^86 - 2205 * q^87 - 192 * q^88 - 984 * q^89 - 1404 * q^90 + 214 * q^91 - 276 * q^92 - 789 * q^93 + 966 * q^94 - 1764 * q^95 + 96 * q^96 + 128 * q^97 + 132 * q^98 + 1557 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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