LMFDB - Embedded newform 165.4.c.b.34.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,4,Mod(34,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("165.34");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	165.c (of order $2$, degree $1$, 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:	$9.73531515095$
Analytic rank:	$0$
Dimension:	$14$
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} + 66x^{12} + 1705x^{10} + 22060x^{8} + 151880x^{6} + 537860x^{4} + 825344x^{2} + 262144 $ x^14 + 66x^12 + 1705x^10 + 22060x^8 + 151880x^6 + 537860x^4 + 825344x^2 + 262144
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.12
Root			$4.57884i$ of defining polynomial
Character	$\chi$	$=$	165.34
Dual form			165.4.c.b.34.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.57884i q^{2} -3.00000i q^{3} -4.80807 q^{4} +(-0.925309 + 11.1420i) q^{5} +10.7365 q^{6} -7.85216i q^{7} +11.4234i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+3.57884i q^{2} -3.00000i q^{3} -4.80807 q^{4} +(-0.925309 + 11.1420i) q^{5} +10.7365 q^{6} -7.85216i q^{7} +11.4234i q^{8} -9.00000 q^{9} +(-39.8753 - 3.31153i) q^{10} +11.0000 q^{11} +14.4242i q^{12} +74.4243i q^{13} +28.1016 q^{14} +(33.4260 + 2.77593i) q^{15} -79.3470 q^{16} -45.2599i q^{17} -32.2095i q^{18} -126.908 q^{19} +(4.44895 - 53.5714i) q^{20} -23.5565 q^{21} +39.3672i q^{22} +191.703i q^{23} +34.2702 q^{24} +(-123.288 - 20.6196i) q^{25} -266.352 q^{26} +27.0000i q^{27} +37.7537i q^{28} +38.0790 q^{29} +(-9.93459 + 119.626i) q^{30} -10.1038 q^{31} -192.583i q^{32} -33.0000i q^{33} +161.978 q^{34} +(87.4886 + 7.26568i) q^{35} +43.2726 q^{36} -277.510i q^{37} -454.184i q^{38} +223.273 q^{39} +(-127.279 - 10.5702i) q^{40} +42.1151 q^{41} -84.3048i q^{42} +294.515i q^{43} -52.8887 q^{44} +(8.32778 - 100.278i) q^{45} -686.074 q^{46} +136.845i q^{47} +238.041i q^{48} +281.344 q^{49} +(73.7940 - 441.226i) q^{50} -135.780 q^{51} -357.837i q^{52} -404.781i q^{53} -96.6286 q^{54} +(-10.1784 + 122.562i) q^{55} +89.6984 q^{56} +380.725i q^{57} +136.278i q^{58} +729.685 q^{59} +(-160.714 - 13.3468i) q^{60} +388.529 q^{61} -36.1598i q^{62} +70.6694i q^{63} +54.4458 q^{64} +(-829.234 - 68.8655i) q^{65} +118.102 q^{66} +1000.11i q^{67} +217.612i q^{68} +575.109 q^{69} +(-26.0027 + 313.107i) q^{70} +300.729 q^{71} -102.811i q^{72} +791.763i q^{73} +993.163 q^{74} +(-61.8587 + 369.863i) q^{75} +610.183 q^{76} -86.3738i q^{77} +799.057i q^{78} +129.787 q^{79} +(73.4205 - 884.083i) q^{80} +81.0000 q^{81} +150.723i q^{82} +757.192i q^{83} +113.261 q^{84} +(504.285 + 41.8794i) q^{85} -1054.02 q^{86} -114.237i q^{87} +125.657i q^{88} +545.691 q^{89} +(358.878 + 29.8038i) q^{90} +584.391 q^{91} -921.721i q^{92} +30.3114i q^{93} -489.745 q^{94} +(117.429 - 1414.01i) q^{95} -577.748 q^{96} -1426.70i q^{97} +1006.88i q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 26 q^{4} - 14 q^{5} - 30 q^{6} - 126 q^{9}+O(q^{10}) $ 14 * q - 26 * q^4 - 14 * q^5 - 30 * q^6 - 126 * q^9	$ 14 q - 26 q^{4} - 14 q^{5} - 30 q^{6} - 126 q^{9} - 48 q^{10} + 154 q^{11} - 84 q^{14} - 86 q^{16} - 116 q^{19} + 442 q^{20} - 204 q^{21} + 450 q^{24} + 162 q^{25} - 400 q^{26} - 128 q^{29} + 246 q^{30} - 696 q^{31} - 412 q^{34} + 672 q^{35} + 234 q^{36} + 480 q^{39} + 1612 q^{40} - 664 q^{41} - 286 q^{44} + 126 q^{45} - 656 q^{46} + 834 q^{49} + 1908 q^{50} - 972 q^{51} + 270 q^{54} - 154 q^{55} - 3236 q^{56} + 664 q^{59} + 108 q^{60} + 44 q^{61} - 1122 q^{64} - 2328 q^{65} - 330 q^{66} + 1944 q^{69} + 1220 q^{70} - 1032 q^{71} - 3256 q^{74} + 84 q^{75} + 5588 q^{76} - 3492 q^{79} - 510 q^{80} + 1134 q^{81} - 1008 q^{84} - 1068 q^{85} + 2540 q^{86} + 4452 q^{89} + 432 q^{90} + 2144 q^{91} - 9472 q^{94} - 932 q^{95} + 450 q^{96} - 1386 q^{99}+O(q^{100}) $ 14 * q - 26 * q^4 - 14 * q^5 - 30 * q^6 - 126 * q^9 - 48 * q^10 + 154 * q^11 - 84 * q^14 - 86 * q^16 - 116 * q^19 + 442 * q^20 - 204 * q^21 + 450 * q^24 + 162 * q^25 - 400 * q^26 - 128 * q^29 + 246 * q^30 - 696 * q^31 - 412 * q^34 + 672 * q^35 + 234 * q^36 + 480 * q^39 + 1612 * q^40 - 664 * q^41 - 286 * q^44 + 126 * q^45 - 656 * q^46 + 834 * q^49 + 1908 * q^50 - 972 * q^51 + 270 * q^54 - 154 * q^55 - 3236 * q^56 + 664 * q^59 + 108 * q^60 + 44 * q^61 - 1122 * q^64 - 2328 * q^65 - 330 * q^66 + 1944 * q^69 + 1220 * q^70 - 1032 * q^71 - 3256 * q^74 + 84 * q^75 + 5588 * q^76 - 3492 * q^79 - 510 * q^80 + 1134 * q^81 - 1008 * q^84 - 1068 * q^85 + 2540 * q^86 + 4452 * q^89 + 432 * q^90 + 2144 * q^91 - 9472 * q^94 - 932 * q^95 + 450 * q^96 - 1386 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$			3.57884i			1.26531i	0.774434	+	0.632655i	$0.218035\pi$
$2$			3.57884i			1.26531i	−0.774434	+	0.632655i	$0.781965\pi$
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	−4.80807			−0.601008
$5$	−0.925309	+	11.1420i	−0.0827622	+	0.996569i
$5$	−0.925309	+	11.1420i	−0.0827622	+	0.996569i
$6$	10.7365			0.730527
$7$		−	7.85216i		−	0.423977i	−0.977272	−	0.211988i	$-0.932006\pi$
$7$		−	7.85216i		−	0.423977i	0.977272	−	0.211988i	$-0.0679939\pi$
$8$			11.4234i			0.504848i
$9$	−9.00000			−0.333333
$10$	−39.8753	−	3.31153i	−1.26097	−	0.104720i
$11$	11.0000			0.301511
$11$	11.0000			0.301511
$12$			14.4242i			0.346992i
$13$			74.4243i			1.58781i	0.608039	+	0.793907i	$0.291956\pi$
$13$			74.4243i			1.58781i	−0.608039	+	0.793907i	$0.708044\pi$
$14$	28.1016			0.536462
$15$	33.4260	+	2.77593i	0.575370	+	0.0477828i
$16$	−79.3470			−1.23980
$17$		−	45.2599i		−	0.645714i	−0.946448	−	0.322857i	$-0.895357\pi$
$17$		−	45.2599i		−	0.645714i	0.946448	−	0.322857i	$-0.104643\pi$
$18$		−	32.2095i		−	0.421770i
$19$	−126.908			−1.53236			−0.766178	−	0.642629i	$-0.777844\pi$
$19$	−126.908			−1.53236			−0.766178	+	0.642629i	$0.777844\pi$
$20$	4.44895	−	53.5714i	0.0497407	−	0.598946i
$21$	−23.5565			−0.244783
$22$			39.3672i			0.381505i
$23$			191.703i			1.73795i	0.494855	+	0.868976i	$0.335221\pi$
$23$			191.703i			1.73795i	−0.494855	+	0.868976i	$0.664779\pi$
$24$	34.2702			0.291474
$25$	−123.288	−	20.6196i	−0.986301	−	0.164956i
$26$	−266.352			−2.00908
$27$			27.0000i			0.192450i
$28$			37.7537i			0.254814i
$29$	38.0790			0.243831			0.121915	−	0.992540i	$-0.461096\pi$
$29$	38.0790			0.243831			0.121915	+	0.992540i	$0.461096\pi$
$30$	−9.93459	+	119.626i	−0.0604600	+	0.728021i
$31$	−10.1038			−0.0585385			−0.0292692	−	0.999572i	$-0.509318\pi$
$31$	−10.1038			−0.0585385			−0.0292692	+	0.999572i	$0.509318\pi$
$32$		−	192.583i		−	1.06388i
$33$		−	33.0000i		−	0.174078i
$34$	161.978			0.817028
$35$	87.4886	+	7.26568i	0.422522	+	0.0350892i
$36$	43.2726			0.200336
$37$		−	277.510i		−	1.23304i	−0.787341	−	0.616518i	$-0.788543\pi$
$37$		−	277.510i		−	1.23304i	0.787341	−	0.616518i	$-0.211457\pi$
$38$		−	454.184i		−	1.93890i
$39$	223.273			0.916725
$40$	−127.279	−	10.5702i	−0.503116	−	0.0417823i
$41$	42.1151			0.160421			0.0802107	−	0.996778i	$-0.474441\pi$
$41$	42.1151			0.160421			0.0802107	+	0.996778i	$0.474441\pi$
$42$		−	84.3048i		−	0.309726i
$43$			294.515i			1.04449i	0.852795	+	0.522245i	$0.174905\pi$
$43$			294.515i			1.04449i	−0.852795	+	0.522245i	$0.825095\pi$
$44$	−52.8887			−0.181211
$45$	8.32778	−	100.278i	0.0275874	−	0.332190i
$46$	−686.074			−2.19905
$47$			136.845i			0.424699i	0.977194	+	0.212350i	$0.0681116\pi$
$47$			136.845i			0.424699i	−0.977194	+	0.212350i	$0.931888\pi$
$48$			238.041i			0.715797i
$49$	281.344			0.820244
$50$	73.7940	−	441.226i	0.208721	−	1.24798i
$51$	−135.780			−0.372803
$52$		−	357.837i		−	0.954289i
$53$		−	404.781i		−	1.04907i	−0.851388	−	0.524537i	$-0.824239\pi$
$53$		−	404.781i		−	1.04907i	0.851388	−	0.524537i	$-0.175761\pi$
$54$	−96.6286			−0.243509
$55$	−10.1784	+	122.562i	−0.0249537	+	0.300477i
$56$	89.6984			0.214044
$57$			380.725i			0.884706i
$58$			136.278i			0.308521i
$59$	729.685			1.61012			0.805058	−	0.593196i	$-0.202134\pi$
$59$	729.685			1.61012			0.805058	+	0.593196i	$0.202134\pi$
$60$	−160.714	−	13.3468i	−0.345802	−	0.0287178i
$61$	388.529			0.815510			0.407755	−	0.913091i	$-0.366312\pi$
$61$	388.529			0.815510			0.407755	+	0.913091i	$0.366312\pi$
$62$		−	36.1598i		−	0.0740693i
$63$			70.6694i			0.141326i
$64$	54.4458			0.106339
$65$	−829.234	−	68.8655i	−1.58237	−	0.131411i
$66$	118.102			0.220262
$67$			1000.11i			1.82363i	0.410600	+	0.911815i	$0.365319\pi$
$67$			1000.11i			1.82363i	−0.410600	+	0.911815i	$0.634681\pi$
$68$			217.612i			0.388079i
$69$	575.109			1.00341
$70$	−26.0027	+	313.107i	−0.0443988	+	0.534621i
$71$	300.729			0.502675			0.251337	−	0.967900i	$-0.419130\pi$
$71$	300.729			0.502675			0.251337	+	0.967900i	$0.419130\pi$
$72$		−	102.811i		−	0.168283i
$73$			791.763i			1.26944i	0.772744	+	0.634718i	$0.218884\pi$
$73$			791.763i			1.26944i	−0.772744	+	0.634718i	$0.781116\pi$
$74$	993.163			1.56017
$75$	−61.8587	+	369.863i	−0.0952377	+	0.569441i
$76$	610.183			0.920958
$77$		−	86.3738i		−	0.127834i
$78$			799.057i			1.15994i
$79$	129.787			0.184838			0.0924189	−	0.995720i	$-0.470540\pi$
$79$	129.787			0.184838			0.0924189	+	0.995720i	$0.470540\pi$
$80$	73.4205	−	884.083i	0.102608	−	1.23554i
$81$	81.0000			0.111111
$82$			150.723i			0.202983i
$83$			757.192i			1.00136i	0.865633	+	0.500678i	$0.166916\pi$
$83$			757.192i			1.00136i	−0.865633	+	0.500678i	$0.833084\pi$
$84$	113.261			0.147117
$85$	504.285	+	41.8794i	0.643498	+	0.0534407i
$86$	−1054.02			−1.32160
$87$		−	114.237i		−	0.140776i
$88$			125.657i			0.152217i
$89$	545.691			0.649923			0.324962	−	0.945727i	$-0.394649\pi$
$89$	545.691			0.649923			0.324962	+	0.945727i	$0.394649\pi$
$90$	358.878	+	29.8038i	0.420323	+	0.0349066i
$91$	584.391			0.673196
$92$		−	921.721i		−	1.04452i
$93$			30.3114i			0.0337972i
$94$	−489.745			−0.537376
$95$	117.429	−	1414.01i	0.126821	−	1.52710i
$96$	−577.748			−0.614231
$97$		−	1426.70i		−	1.49340i	−0.665162	−	0.746699i	$-0.731637\pi$
$97$		−	1426.70i		−	1.49340i	0.665162	−	0.746699i	$-0.268363\pi$
$98$			1006.88i			1.03786i
$99$	−99.0000			−0.100504
$100$	592.775	+	99.1402i	0.592775	+	0.0991402i
$101$	2.33305			0.00229848			0.00114924	−	0.999999i	$-0.499634\pi$
$101$	2.33305			0.00229848			0.00114924	+	0.999999i	$0.499634\pi$
$102$		−	485.933i		−	0.471711i
$103$		−	1946.72i		−	1.86229i	−0.364647	−	0.931146i	$-0.618810\pi$
$103$		−	1946.72i		−	1.86229i	0.364647	−	0.931146i	$-0.381190\pi$
$104$	−850.179			−0.801605
$105$	21.7970	−	262.466i	0.0202588	−	0.243943i
$106$	1448.64			1.32740
$107$			950.981i			0.859203i	0.903018	+	0.429602i	$0.141346\pi$
$107$			950.981i			0.859203i	−0.903018	+	0.429602i	$0.858654\pi$
$108$		−	129.818i		−	0.115664i
$109$	383.999			0.337435			0.168718	−	0.985664i	$-0.446037\pi$
$109$	383.999			0.337435			0.168718	+	0.985664i	$0.446037\pi$
$110$	−438.629	−	36.4268i	−0.380196	−	0.0315742i
$111$	−832.530			−0.711894
$112$			623.046i			0.525645i
$113$		−	1003.99i		−	0.835816i	−0.908489	−	0.417908i	$-0.862763\pi$
$113$		−	1003.99i		−	0.835816i	0.908489	−	0.417908i	$-0.137237\pi$
$114$	−1362.55			−1.11943
$115$	−2135.95	−	177.385i	−1.73199	−	0.143837i
$116$	−183.086			−0.146544
$117$		−	669.819i		−	0.529271i
$118$			2611.42i			2.03730i
$119$	−355.388			−0.273768
$120$	−31.7106	+	381.838i	−0.0241230	+	0.290474i
$121$	121.000			0.0909091
$122$			1390.48i			1.03187i
$123$		−	126.345i		−	0.0926194i
$124$	48.5797			0.0351821
$125$	343.822	−	1354.59i	0.246019	−	0.969265i
$126$	−252.914			−0.178821
$127$		−	1731.81i		−	1.21002i	−0.796216	−	0.605012i	$-0.793168\pi$
$127$		−	1731.81i		−	1.21002i	0.796216	−	0.605012i	$-0.206832\pi$
$128$		−	1345.81i		−	0.929327i
$129$	883.544			0.603037
$130$	246.458	−	2967.69i	0.166276	−	2.00218i
$131$	1058.86			0.706207			0.353103	−	0.935584i	$-0.385126\pi$
$131$	1058.86			0.706207			0.353103	+	0.935584i	$0.385126\pi$
$132$			158.666i			0.104622i
$133$			996.504i			0.649683i
$134$	−3579.24			−2.30746
$135$	−300.834	−	24.9833i	−0.191790	−	0.0159276i
$136$	517.022			0.325987
$137$			267.694i			0.166939i	0.996510	+	0.0834696i	$0.0266001\pi$
$137$			267.694i			0.166939i	−0.996510	+	0.0834696i	$0.973400\pi$
$138$			2058.22i			1.26962i
$139$	−1351.75			−0.824847			−0.412424	−	0.910992i	$-0.635318\pi$
$139$	−1351.75			−0.824847			−0.412424	+	0.910992i	$0.635318\pi$
$140$	−420.651	−	34.9339i	−0.253939	−	0.0210889i
$141$	410.535			0.245200
$142$			1076.26i			0.636039i
$143$			818.667i			0.478744i
$144$	714.123			0.413266
$145$	−35.2348	+	424.276i	−0.0201800	+	0.242994i
$146$	−2833.59			−1.60623
$147$		−	844.031i		−	0.473568i
$148$			1334.29i			0.741065i
$149$	1020.64			0.561167			0.280583	−	0.959830i	$-0.409472\pi$
$149$	1020.64			0.561167			0.280583	+	0.959830i	$0.409472\pi$
$150$	−1323.68	−	221.382i	−0.720519	−	0.120505i
$151$	3147.14			1.69610			0.848049	−	0.529918i	$-0.177777\pi$
$151$	3147.14			1.69610			0.848049	+	0.529918i	$0.177777\pi$
$152$		−	1449.72i		−	0.773606i
$153$			407.339i			0.215238i
$154$	309.118			0.161749
$155$	9.34912	−	112.576i	0.00484477	−	0.0583377i
$156$	−1073.51			−0.550959
$157$		−	2836.95i		−	1.44212i	−0.692872	−	0.721060i	$-0.743655\pi$
$157$		−	2836.95i		−	1.44212i	0.692872	−	0.721060i	$-0.256345\pi$
$158$			464.487i			0.233877i
$159$	−1214.34			−0.605683
$160$	2145.75	+	178.199i	1.06023	+	0.0880490i
$161$	1505.28			0.736851
$162$			289.886i			0.140590i
$163$			3658.55i			1.75804i	0.476788	+	0.879019i	$0.341801\pi$
$163$			3658.55i			1.75804i	−0.476788	+	0.879019i	$0.658199\pi$
$164$	−202.492			−0.0964146
$165$	367.685	+	30.5352i	0.173480	+	0.0144070i
$166$	−2709.87			−1.26703
$167$			2551.66i			1.18236i	0.806541	+	0.591178i	$0.201337\pi$
$167$			2551.66i			1.18236i	−0.806541	+	0.591178i	$0.798663\pi$
$168$		−	269.095i		−	0.123578i
$169$	−3341.97			−1.52115
$170$	−149.879	+	1804.75i	−0.0676190	+	0.814225i
$171$	1142.17			0.510785
$172$		−	1416.05i		−	0.627747i
$173$			1770.65i			0.778150i	0.921206	+	0.389075i	$0.127205\pi$
$173$			1770.65i			0.778150i	−0.921206	+	0.389075i	$0.872795\pi$
$174$	408.835			0.178125
$175$	−161.908	+	968.074i	−0.0699377	+	0.418169i
$176$	−872.817			−0.373813
$177$		−	2189.05i		−	0.929601i
$178$			1952.94i			0.822354i
$179$	−669.558			−0.279582			−0.139791	−	0.990181i	$-0.544643\pi$
$179$	−669.558			−0.279582			−0.139791	+	0.990181i	$0.544643\pi$
$180$	−40.0405	+	482.143i	−0.0165802	+	0.199649i
$181$	−3568.19			−1.46531			−0.732657	−	0.680598i	$-0.761720\pi$
$181$	−3568.19			−1.46531			−0.732657	+	0.680598i	$0.761720\pi$
$182$			2091.44i			0.851802i
$183$		−	1165.59i		−	0.470835i
$184$	−2189.90			−0.877401
$185$	3092.01	+	256.783i	1.22881	+	0.102049i
$186$	−108.479			−0.0427639
$187$		−	497.859i		−	0.194690i
$188$		−	657.959i		−	0.255248i
$189$	212.008			0.0815944
$190$	5060.51	+	420.260i	1.93225	+	0.160468i
$191$	−2147.40			−0.813509			−0.406754	−	0.913538i	$-0.633340\pi$
$191$	−2147.40			−0.813509			−0.406754	+	0.913538i	$0.633340\pi$
$192$		−	163.337i		−	0.0613951i
$193$		−	1156.43i		−	0.431305i	−0.976470	−	0.215652i	$-0.930812\pi$
$193$		−	1156.43i		−	0.431305i	0.976470	−	0.215652i	$-0.0691878\pi$
$194$	5105.93			1.88961
$195$	−206.596	+	2487.70i	−0.0758701	+	0.913580i
$196$	−1352.72			−0.492973
$197$			3737.51i			1.35171i	0.737036	+	0.675854i	$0.236225\pi$
$197$			3737.51i			1.35171i	−0.737036	+	0.675854i	$0.763775\pi$
$198$		−	354.305i		−	0.127168i
$199$	−2862.04			−1.01952			−0.509760	−	0.860317i	$-0.670266\pi$
$199$	−2862.04			−1.01952			−0.509760	+	0.860317i	$0.670266\pi$
$200$	235.546	−	1408.36i	0.0832780	−	0.497932i
$201$	3000.34			1.05287
$202$			8.34959i			0.00290829i
$203$		−	299.002i		−	0.103379i
$204$	652.837			0.224058
$205$	−38.9695	+	469.246i	−0.0132768	+	0.159871i
$206$	6966.99			2.35638
$207$		−	1725.33i		−	0.579317i
$208$		−	5905.35i		−	1.96857i
$209$	−1395.99			−0.462022
$210$	939.322	+	78.0080i	0.308664	+	0.0256336i
$211$	1643.11			0.536095			0.268047	−	0.963406i	$-0.413622\pi$
$211$	1643.11			0.536095			0.268047	+	0.963406i	$0.413622\pi$
$212$			1946.21i			0.630502i
$213$		−	902.186i		−	0.290220i
$214$	−3403.40			−1.08716
$215$	−3281.48	−	272.517i	−1.04091	−	0.0864443i
$216$	−308.432			−0.0971581
$217$			79.3365i			0.0248190i
$218$			1374.27i			0.426960i
$219$	2375.29			0.732909
$220$	48.9384	−	589.285i	0.0149974	−	0.180589i
$221$	3368.43			1.02527
$222$		−	2979.49i		−	0.900766i
$223$		−	77.0948i		−	0.0231509i	−0.999933	−	0.0115754i	$-0.996315\pi$
$223$		−	77.0948i		−	0.0231509i	0.999933	−	0.0115754i	$-0.00368466\pi$
$224$	−1512.19			−0.451060
$225$	1109.59	+	185.576i	0.328767	+	0.0549855i
$226$	3593.11			1.05757
$227$		−	943.946i		−	0.276000i	−0.990432	−	0.138000i	$-0.955933\pi$
$227$		−	943.946i		−	0.276000i	0.990432	−	0.138000i	$-0.0440673\pi$
$228$		−	1830.55i		−	0.531715i
$229$	−2643.94			−0.762953			−0.381477	−	0.924378i	$-0.624584\pi$
$229$	−2643.94			−0.762953			−0.381477	+	0.924378i	$0.624584\pi$
$230$	634.831	−	7644.23i	0.181998	−	2.19150i
$231$	−259.121			−0.0738049
$232$			434.992i			0.123097i
$233$		−	632.308i		−	0.177785i	−0.996041	−	0.0888925i	$-0.971667\pi$
$233$		−	632.308i		−	0.177785i	0.996041	−	0.0888925i	$-0.0283327\pi$
$234$	2397.17			0.669692
$235$	−1524.72	−	126.624i	−0.423242	−	0.0351490i
$236$	−3508.37			−0.967693
$237$		−	389.361i		−	0.106716i
$238$		−	1271.87i		−	0.346401i
$239$	812.245			0.219832			0.109916	−	0.993941i	$-0.464942\pi$
$239$	812.245			0.219832			0.109916	+	0.993941i	$0.464942\pi$
$240$	−2652.25	−	220.262i	−0.713342	−	0.0592409i
$241$	−3163.83			−0.845645			−0.422822	−	0.906213i	$-0.638961\pi$
$241$	−3163.83			−0.845645			−0.422822	+	0.906213i	$0.638961\pi$
$242$			433.039i			0.115028i
$243$		−	243.000i		−	0.0641500i
$244$	−1868.08			−0.490128
$245$	−260.330	+	3134.73i	−0.0678851	+	0.817430i
$246$	452.170			0.117192
$247$		−	9445.06i		−	2.43310i
$248$		−	115.420i		−	0.0295530i
$249$	2271.58			0.578134
$250$	4847.85	+	1230.48i	1.22642	+	0.311290i
$251$	3838.24			0.965210			0.482605	−	0.875838i	$-0.339691\pi$
$251$	3838.24			0.965210			0.482605	+	0.875838i	$0.339691\pi$
$252$		−	339.783i		−	0.0849379i
$253$			2108.73i			0.524012i
$254$	6197.86			1.53106
$255$	125.638	−	1512.85i	0.0308540	−	0.371524i
$256$	5252.00			1.28223
$257$			2633.59i			0.639218i	0.947550	+	0.319609i	$0.103552\pi$
$257$			2633.59i			0.639218i	−0.947550	+	0.319609i	$0.896448\pi$
$258$			3162.06i			0.763028i
$259$	−2179.05			−0.522779
$260$	3987.01	+	331.110i	0.951016	+	0.0789791i
$261$	−342.711			−0.0812769
$262$			3789.49i			0.893570i
$263$			5867.74i			1.37574i	0.725833	+	0.687871i	$0.241455\pi$
$263$			5867.74i			1.37574i	−0.725833	+	0.687871i	$0.758545\pi$
$264$	376.972			0.0878828
$265$	4510.06	+	374.547i	1.04547	+	0.0868236i
$266$	−3566.32			−0.822050
$267$		−	1637.07i		−	0.375233i
$268$		−	4808.61i		−	1.09602i
$269$	5826.82			1.32070			0.660349	−	0.750959i	$-0.270408\pi$
$269$	5826.82			1.32070			0.660349	+	0.750959i	$0.270408\pi$
$270$	89.4113	−	1076.63i	0.0201533	−	0.242674i
$271$	−2802.97			−0.628296			−0.314148	−	0.949374i	$-0.601719\pi$
$271$	−2802.97			−0.628296			−0.314148	+	0.949374i	$0.601719\pi$
$272$			3591.24i			0.800554i
$273$		−	1753.17i		−	0.388670i
$274$	−958.034			−0.211230
$275$	−1356.16	−	226.815i	−0.297381	−	0.0497363i
$276$	−2765.16			−0.603056
$277$			3188.02i			0.691515i	0.938324	+	0.345757i	$0.112378\pi$
$277$			3188.02i			0.691515i	−0.938324	+	0.345757i	$0.887622\pi$
$278$		−	4837.69i		−	1.04369i
$279$	90.9341			0.0195128
$280$	−82.9988	+	999.418i	−0.0177147	+	0.213310i
$281$	−830.887			−0.176394			−0.0881968	−	0.996103i	$-0.528110\pi$
$281$	−830.887			−0.176394			−0.0881968	+	0.996103i	$0.528110\pi$
$282$			1469.24i			0.310254i
$283$		−	7372.66i		−	1.54862i	−0.632807	−	0.774310i	$-0.718097\pi$
$283$		−	7372.66i		−	1.54862i	0.632807	−	0.774310i	$-0.281903\pi$
$284$	−1445.92			−0.302112
$285$	−4242.03	−	352.288i	−0.881670	−	0.0732202i
$286$	−2929.88			−0.605759
$287$		−	330.695i		−	0.0680150i
$288$			1733.24i			0.354626i
$289$	2864.54			0.583054
$290$	−1518.41	−	126.100i	−0.307463	−	0.0255339i
$291$	−4280.11			−0.862214
$292$		−	3806.85i		−	0.762942i
$293$			3148.91i			0.627853i	0.949447	+	0.313927i	$0.101645\pi$
$293$			3148.91i			0.627853i	−0.949447	+	0.313927i	$0.898355\pi$
$294$	3020.65			0.599210
$295$	−675.184	+	8130.14i	−0.133257	+	1.60459i
$296$	3170.11			0.622496
$297$			297.000i			0.0580259i
$298$			3652.69i			0.710050i
$299$	−14267.4			−2.75954
$300$	297.421	−	1778.32i	0.0572386	−	0.342239i
$301$	2312.58			0.442840
$302$			11263.1i			2.14609i
$303$		−	6.99914i		−	0.00132703i
$304$	10069.8			1.89981
$305$	−359.510	+	4328.99i	−0.0674934	+	0.812712i
$306$	−1457.80			−0.272343
$307$			2643.59i			0.491459i	0.969339	+	0.245729i	$0.0790274\pi$
$307$			2643.59i			0.491459i	−0.969339	+	0.245729i	$0.920973\pi$
$308$			415.291i			0.0768292i
$309$	−5840.16			−1.07519
$310$	402.892	+	33.4590i	0.0738152	+	0.00613014i
$311$	−3608.92			−0.658017			−0.329009	−	0.944327i	$-0.606714\pi$
$311$	−3608.92			−0.658017			−0.329009	+	0.944327i	$0.606714\pi$
$312$			2550.54i			0.462807i
$313$			1044.35i			0.188596i	0.995544	+	0.0942978i	$0.0300606\pi$
$313$			1044.35i			0.188596i	−0.995544	+	0.0942978i	$0.969939\pi$
$314$	10153.0			1.82473
$315$	−787.398	−	65.3911i	−0.140841	−	0.0116964i
$316$	−624.025			−0.111089
$317$		−	2725.18i		−	0.482843i	−0.970420	−	0.241421i	$-0.922386\pi$
$317$		−	2725.18i		−	0.482843i	0.970420	−	0.241421i	$-0.0776136\pi$
$318$		−	4345.93i		−	0.766376i
$319$	418.869			0.0735177
$320$	−50.3792	+	606.634i	−0.00880088	+	0.105975i
$321$	2852.94			0.496061
$322$			5387.16i			0.932345i
$323$			5743.85i			0.989463i
$324$	−389.453			−0.0667787
$325$	1534.60	−	9175.59i	0.261920	−	1.56606i
$326$	−13093.4			−2.22446
$327$		−	1152.00i		−	0.194818i
$328$			481.098i			0.0809885i
$329$	1074.53			0.180063
$330$	−109.280	+	1315.89i	−0.0182294	+	0.219506i
$331$	84.3804			0.0140120			0.00700599	−	0.999975i	$-0.497770\pi$
$331$	84.3804			0.0140120			0.00700599	+	0.999975i	$0.497770\pi$
$332$		−	3640.63i		−	0.601824i
$333$			2497.59i			0.411012i
$334$	−9131.97			−1.49605
$335$	−11143.2	−	925.414i	−1.81737	−	0.150928i
$336$	1869.14			0.303481
$337$			6569.46i			1.06190i	0.847402	+	0.530951i	$0.178165\pi$
$337$			6569.46i			1.06190i	−0.847402	+	0.530951i	$0.821835\pi$
$338$		−	11960.4i		−	1.92473i
$339$	−3011.96			−0.482559
$340$	−2424.63	−	201.359i	−0.386748	−	0.0321183i
$341$	−111.142			−0.0176500
$342$			4087.65i			0.646301i
$343$		−	4902.45i		−	0.771741i
$344$	−3364.36			−0.527309
$345$	−532.154	+	6407.86i	−0.0830441	+	0.999964i
$346$	−6336.86			−0.984601
$347$			263.376i			0.0407457i	0.999792	+	0.0203729i	$0.00648533\pi$
$347$			263.376i			0.0407457i	−0.999792	+	0.0203729i	$0.993515\pi$
$348$			549.259i			0.0846074i
$349$	8742.08			1.34084			0.670419	−	0.741982i	$-0.266114\pi$
$349$	8742.08			1.34084			0.670419	+	0.741982i	$0.266114\pi$
$350$	−3464.58	−	579.443i	−0.529113	−	0.0884929i
$351$	−2009.46			−0.305575
$352$		−	2118.41i		−	0.320772i
$353$		−	9193.95i		−	1.38624i	−0.720820	−	0.693122i	$-0.756235\pi$
$353$		−	9193.95i		−	1.38624i	0.720820	−	0.693122i	$-0.243765\pi$
$354$	7834.27			1.17623
$355$	−278.267	+	3350.71i	−0.0416025	+	0.500950i
$356$	−2623.72			−0.390609
$357$			1066.16i			0.158060i
$358$		−	2396.24i		−	0.353757i
$359$	11580.0			1.70243			0.851213	−	0.524820i	$-0.175868\pi$
$359$	11580.0			1.70243			0.851213	+	0.524820i	$0.175868\pi$
$360$	1145.51	+	95.1317i	0.167705	+	0.0139274i
$361$	9246.70			1.34811
$362$		−	12770.0i		−	1.85407i
$363$		−	363.000i		−	0.0524864i
$364$	−2809.79			−0.404597
$365$	−8821.81	−	732.626i	−1.26508	−	0.105061i
$366$	4171.45			0.595752
$367$			3285.45i			0.467300i	0.972321	+	0.233650i	$0.0750670\pi$
$367$			3285.45i			0.467300i	−0.972321	+	0.233650i	$0.924933\pi$
$368$		−	15211.1i		−	2.15471i
$369$	−379.036			−0.0534738
$370$	−918.982	+	11065.8i	−0.129123	+	1.55482i
$371$	−3178.40			−0.444783
$372$		−	145.739i		−	0.0203124i
$373$			4512.30i			0.626376i	0.949691	+	0.313188i	$0.101397\pi$
$373$			4512.30i			0.626376i	−0.949691	+	0.313188i	$0.898603\pi$
$374$	1781.75			0.246343
$375$	−4063.77	−	1031.47i	−0.559605	−	0.142039i
$376$	−1563.23			−0.214409
$377$			2834.00i			0.387158i
$378$			758.743i			0.103242i
$379$	336.306			0.0455802			0.0227901	−	0.999740i	$-0.492745\pi$
$379$	336.306			0.0455802			0.0227901	+	0.999740i	$0.492745\pi$
$380$	−564.608	+	6798.65i	−0.0762205	+	0.917799i
$381$	−5195.42			−0.698608
$382$		−	7685.18i		−	1.02934i
$383$			6943.74i			0.926394i	0.886255	+	0.463197i	$0.153298\pi$
$383$			6943.74i			0.926394i	−0.886255	+	0.463197i	$0.846702\pi$
$384$	−4037.43			−0.536547
$385$	962.375	+	79.9224i	0.127395	+	0.0105798i
$386$	4138.68			0.545734
$387$		−	2650.63i		−	0.348163i
$388$			6859.68i			0.897545i
$389$	5075.14			0.661491			0.330745	−	0.943720i	$-0.392700\pi$
$389$	5075.14			0.661491			0.330745	+	0.943720i	$0.392700\pi$
$390$	−8903.08	−	739.375i	−1.15596	−	0.0959992i
$391$	8676.46			1.12222
$392$			3213.90i			0.414098i
$393$		−	3176.58i		−	0.407729i
$394$	−13375.9			−1.71033
$395$	−120.093	+	1446.09i	−0.0152976	+	0.184204i
$396$	475.999			0.0604036
$397$		−	10970.2i		−	1.38684i	−0.720533	−	0.693421i	$-0.756103\pi$
$397$		−	10970.2i		−	1.38684i	0.720533	−	0.693421i	$-0.243897\pi$
$398$		−	10242.8i		−	1.29001i
$399$	2989.51			0.375095
$400$	9782.51	+	1636.10i	1.22281	+	0.204513i
$401$	723.097			0.0900492			0.0450246	−	0.998986i	$-0.485663\pi$
$401$	723.097			0.0900492			0.0450246	+	0.998986i	$0.485663\pi$
$402$			10737.7i			1.33221i
$403$		−	751.967i		−	0.0929482i
$404$	−11.2174			−0.00138141
$405$	−74.9500	+	902.501i	−0.00919580	+	0.110730i
$406$	1070.08			0.130806
$407$		−	3052.61i		−	0.371775i
$408$		−	1551.07i		−	0.188209i
$409$	−10900.9			−1.31789			−0.658943	−	0.752193i	$-0.728996\pi$
$409$	−10900.9			−1.31789			−0.658943	+	0.752193i	$0.728996\pi$
$410$	−1679.36	−	139.466i	−0.202286	−	0.0167993i
$411$	803.083			0.0963824
$412$			9359.96i			1.11925i
$413$		−	5729.60i		−	0.682652i
$414$	6174.67			0.733015
$415$	−8436.62	−	700.637i	−0.997921	−	0.0828745i
$416$	14332.8			1.68924
$417$			4055.24i			0.476226i
$418$		−	4996.02i		−	0.584601i
$419$	5279.01			0.615505			0.307753	−	0.951466i	$-0.400423\pi$
$419$	5279.01			0.615505			0.307753	+	0.951466i	$0.400423\pi$
$420$	−104.802	+	1261.95i	−0.0121757	+	0.146612i
$421$	−1707.16			−0.197629			−0.0988144	−	0.995106i	$-0.531505\pi$
$421$	−1707.16			−0.197629			−0.0988144	+	0.995106i	$0.531505\pi$
$422$			5880.40i			0.678326i
$423$		−	1231.60i		−	0.141566i
$424$	4623.97			0.529623
$425$	−933.239	+	5579.98i	−0.106515	+	0.636868i
$426$	3228.78			0.367218
$427$		−	3050.80i		−	0.345757i
$428$		−	4572.38i		−	0.516388i
$429$	2456.00			0.276403
$430$	975.294	−	11743.9i	0.109379	−	1.31707i
$431$	−12859.1			−1.43712			−0.718560	−	0.695465i	$-0.755198\pi$
$431$	−12859.1			−1.43712			−0.718560	+	0.695465i	$0.755198\pi$
$432$		−	2142.37i		−	0.238599i
$433$		−	3785.01i		−	0.420083i	−0.977692	−	0.210041i	$-0.932640\pi$
$433$		−	3785.01i		−	0.420083i	0.977692	−	0.210041i	$-0.0673599\pi$
$434$	−283.932			−0.0314037
$435$	1272.83	+	105.705i	0.140293	+	0.0116509i
$436$	−1846.29			−0.202801
$437$		−	24328.7i		−	2.66316i
$438$			8500.77i			0.927357i
$439$	−2455.88			−0.266999			−0.133499	−	0.991049i	$-0.542621\pi$
$439$	−2455.88			−0.266999			−0.133499	+	0.991049i	$0.542621\pi$
$440$	−1400.07	−	116.272i	−0.151695	−	0.0125978i
$441$	−2532.09			−0.273415
$442$			12055.1i			1.29729i
$443$			9644.61i			1.03438i	0.855871	+	0.517189i	$0.173021\pi$
$443$			9644.61i			1.03438i	−0.855871	+	0.517189i	$0.826979\pi$
$444$	4002.86			0.427854
$445$	−504.933	+	6080.09i	−0.0537891	+	0.647694i
$446$	275.910			0.0292931
$447$		−	3061.91i		−	0.323990i
$448$		−	427.517i		−	0.0450854i
$449$	−4519.51			−0.475031			−0.237515	−	0.971384i	$-0.576333\pi$
$449$	−4519.51			−0.475031			−0.237515	+	0.971384i	$0.576333\pi$
$450$	−664.146	+	3971.03i	−0.0695737	+	0.415992i
$451$	463.267			0.0483689
$452$			4827.24i			0.502332i
$453$		−	9441.42i		−	0.979242i
$454$	3378.23			0.349225
$455$	−540.743	+	6511.28i	−0.0557152	+	0.670887i
$456$	−4349.17			−0.446642
$457$			6323.94i			0.647311i	0.946175	+	0.323656i	$0.104912\pi$
$457$			6323.94i			0.647311i	−0.946175	+	0.323656i	$0.895088\pi$
$458$		−	9462.22i		−	0.965372i
$459$	1222.02			0.124268
$460$	10269.8	+	852.877i	1.04094	+	0.0864470i
$461$	6128.99			0.619209			0.309605	−	0.950865i	$-0.399803\pi$
$461$	6128.99			0.619209			0.309605	+	0.950865i	$0.399803\pi$
$462$		−	927.353i		−	0.0933860i
$463$		−	14199.0i		−	1.42523i	−0.701554	−	0.712616i	$-0.747510\pi$
$463$		−	14199.0i		−	1.42523i	0.701554	−	0.712616i	$-0.252490\pi$
$464$	−3021.46			−0.302301
$465$	−337.729	−	28.0474i	−0.0336813	−	0.00279713i
$466$	2262.93			0.224953
$467$		−	10339.4i		−	1.02452i	−0.858830	−	0.512260i	$-0.828808\pi$
$467$		−	10339.4i		−	1.02452i	0.858830	−	0.512260i	$-0.171192\pi$
$468$			3220.53i			0.318096i
$469$	7853.05			0.773177
$470$	453.166	−	5456.73i	0.0444744	−	0.535533i
$471$	−8510.84			−0.832609
$472$			8335.49i			0.812864i
$473$			3239.66i			0.314926i
$474$	1393.46			0.135029
$475$	15646.2	+	2616.79i	1.51136	+	0.252772i
$476$	1708.73			0.164537
$477$			3643.02i			0.349691i
$478$			2906.89i			0.278155i
$479$	−17248.5			−1.64531			−0.822654	−	0.568542i	$-0.807508\pi$
$479$	−17248.5			−1.64531			−0.822654	+	0.568542i	$0.807508\pi$
$480$	534.596	−	6437.26i	0.0508351	−	0.612124i
$481$	20653.5			1.95783
$482$		−	11322.8i		−	1.07000i
$483$		−	4515.85i		−	0.425421i
$484$	−581.776			−0.0546371
$485$	15896.3	+	1320.14i	1.48828	+	0.123597i
$486$	869.657			0.0811696
$487$		−	2572.47i		−	0.239363i	−0.992812	−	0.119682i	$-0.961813\pi$
$487$		−	2572.47i		−	0.239363i	0.992812	−	0.119682i	$-0.0381874\pi$
$488$			4438.33i			0.411709i
$489$	10975.7			1.01500
$490$	−11218.7	−	931.678i	−1.03430	−	0.0858957i
$491$	2155.02			0.198075			0.0990375	−	0.995084i	$-0.468424\pi$
$491$	2155.02			0.198075			0.0990375	+	0.995084i	$0.468424\pi$
$492$			607.477i			0.0556650i
$493$		−	1723.45i		−	0.157445i
$494$	33802.3			3.07862
$495$	91.6056	−	1103.06i	0.00831791	−	0.100159i
$496$	801.705			0.0725759
$497$		−	2361.37i		−	0.213123i
$498$			8129.60i			0.731518i
$499$	−5300.90			−0.475553			−0.237776	−	0.971320i	$-0.576419\pi$
$499$	−5300.90			−0.475553			−0.237776	+	0.971320i	$0.576419\pi$
$500$	−1653.12	+	6512.95i	−0.147859	+	0.582536i
$501$	7654.98			0.682633
$502$			13736.4i			1.22129i
$503$			16731.1i			1.48311i	0.670891	+	0.741556i	$0.265912\pi$
$503$			16731.1i			1.48311i	−0.670891	+	0.741556i	$0.734088\pi$
$504$	−807.286			−0.0713480
$505$	−2.15879	+	25.9948i	−0.000190227	+	0.00229060i
$506$	−7546.82			−0.663037
$507$			10025.9i			0.878238i
$508$			8326.65i			0.727235i
$509$	8453.50			0.736139			0.368070	−	0.929798i	$-0.380019\pi$
$509$	8453.50			0.736139			0.368070	+	0.929798i	$0.380019\pi$
$510$	5414.26	+	449.638i	0.470093	+	0.0390398i
$511$	6217.05			0.538212
$512$			8029.56i			0.693086i
$513$		−	3426.52i		−	0.294902i
$514$	−9425.20			−0.808809
$515$	21690.3	+	1801.32i	1.85590	+	0.154127i
$516$	−4248.14			−0.362430
$517$			1505.29i			0.128052i
$518$		−	7798.47i		−	0.661477i
$519$	5311.95			0.449265
$520$	786.678	−	9472.68i	0.0663426	−	0.798855i
$521$	1966.07			0.165326			0.0826631	−	0.996578i	$-0.473657\pi$
$521$	1966.07			0.165326			0.0826631	+	0.996578i	$0.473657\pi$
$522$		−	1226.51i		−	0.102840i
$523$			3210.69i			0.268440i	0.990952	+	0.134220i	$0.0428528\pi$
$523$			3210.69i			0.268440i	−0.990952	+	0.134220i	$0.957147\pi$
$524$	−5091.07			−0.424436
$525$	2904.22	+	485.724i	0.241430	+	0.0403786i
$526$	−20999.7			−1.74074
$527$			457.296i			0.0377991i
$528$			2618.45i			0.215821i
$529$	−24583.1			−2.02047
$530$	−1340.44	+	16140.8i	−0.109859	+	1.32285i
$531$	−6567.16			−0.536706
$532$		−	4791.26i		−	0.390465i
$533$			3134.39i			0.254719i
$534$	5858.82			0.474786
$535$	−10595.8	−	879.951i	−0.856256	−	0.0711095i
$536$	−11424.7			−0.920657
$537$			2008.67i			0.161416i
$538$			20853.2i			1.67109i
$539$	3094.78			0.247313
$540$	1446.43	+	120.122i	0.115267	+	0.00957261i
$541$	18474.2			1.46815			0.734074	−	0.679069i	$-0.237616\pi$
$541$	18474.2			1.46815			0.734074	+	0.679069i	$0.237616\pi$
$542$		−	10031.4i		−	0.794989i
$543$			10704.6i			0.845999i
$544$	−8716.27			−0.686961
$545$	−355.318	+	4278.51i	−0.0279269	+	0.336278i
$546$	6274.32			0.491788
$547$			7728.31i			0.604093i	0.953293	+	0.302046i	$0.0976698\pi$
$547$			7728.31i			0.604093i	−0.953293	+	0.302046i	$0.902330\pi$
$548$		−	1287.09i		−	0.100332i
$549$	−3496.76			−0.271837
$550$	811.734	−	4853.49i	0.0629318	−	0.376279i
$551$	−4832.54			−0.373635
$552$			6569.71i			0.506568i
$553$		−	1019.11i		−	0.0783670i
$554$	−11409.4			−0.874981
$555$	770.348	−	9276.03i	0.0589179	−	0.709452i
$556$	6499.30			0.495740
$557$		−	22509.9i		−	1.71234i	−0.516692	−	0.856172i	$-0.672837\pi$
$557$		−	22509.9i		−	1.71234i	0.516692	−	0.856172i	$-0.327163\pi$
$558$			325.438i			0.0246898i
$559$	−21919.0			−1.65846
$560$	−6941.96	−	576.510i	−0.523842	−	0.0435035i
$561$	−1493.58			−0.112404
$562$		−	2973.61i		−	0.223192i
$563$		−	9173.84i		−	0.686734i	−0.939201	−	0.343367i	$-0.888433\pi$
$563$		−	9173.84i		−	0.686734i	0.939201	−	0.343367i	$-0.111567\pi$
$564$	−1973.88			−0.147367
$565$	11186.4	+	928.999i	0.832949	+	0.0691740i
$566$	26385.5			1.95948
$567$		−	636.025i		−	0.0471085i
$568$			3435.35i			0.253774i
$569$	−6653.89			−0.490238			−0.245119	−	0.969493i	$-0.578827\pi$
$569$	−6653.89			−0.490238			−0.245119	+	0.969493i	$0.578827\pi$
$570$	1260.78	−	15181.5i	0.0926462	−	1.11559i
$571$	−12590.3			−0.922743			−0.461372	−	0.887207i	$-0.652643\pi$
$571$	−12590.3			−0.922743			−0.461372	+	0.887207i	$0.652643\pi$
$572$		−	3936.21i		−	0.287729i
$573$			6442.19i			0.469680i
$574$	1183.50			0.0860600
$575$	3952.84	−	23634.6i	0.286686	−	1.71414i
$576$	−490.012			−0.0354465
$577$		−	11868.9i		−	0.856340i	−0.903698	−	0.428170i	$-0.859158\pi$
$577$		−	11868.9i		−	0.856340i	0.903698	−	0.428170i	$-0.140842\pi$
$578$			10251.7i			0.737744i
$579$	−3469.30			−0.249014
$580$	169.411	−	2039.94i	0.0121283	−	0.146042i
$581$	5945.59			0.424552
$582$		−	15317.8i		−	1.09097i
$583$		−	4452.59i		−	0.316307i
$584$	−9044.63			−0.640872
$585$	7463.11	+	619.789i	0.527456	+	0.0438036i
$586$	−11269.4			−0.794429
$587$			6133.10i			0.431244i	0.976477	+	0.215622i	$0.0691778\pi$
$587$			6133.10i			0.431244i	−0.976477	+	0.215622i	$0.930822\pi$
$588$			4058.16i			0.284618i
$589$	1282.25			0.0897018
$590$	−29096.4	−	2416.37i	−2.03031	−	0.168611i
$591$	11212.5			0.780409
$592$			22019.6i			1.52872i
$593$			7111.43i			0.492464i	0.969211	+	0.246232i	$0.0791925\pi$
$593$			7111.43i			0.492464i	−0.969211	+	0.246232i	$0.920807\pi$
$594$	−1062.91			−0.0734207
$595$	328.844	−	3959.73i	0.0226576	−	0.272828i
$596$	−4907.29			−0.337266
$597$			8586.11i			0.588620i
$598$		−	51060.6i		−	3.49168i
$599$	24497.0			1.67099			0.835494	−	0.549499i	$-0.185181\pi$
$599$	24497.0			1.67099			0.835494	+	0.549499i	$0.185181\pi$
$600$	−4225.09	−	706.637i	−0.287481	−	0.0480806i
$601$	1409.41			0.0956591			0.0478296	−	0.998856i	$-0.484770\pi$
$601$	1409.41			0.0956591			0.0478296	+	0.998856i	$0.484770\pi$
$602$			8276.33i			0.560329i
$603$		−	9001.02i		−	0.607877i
$604$	−15131.7			−1.01937
$605$	−111.962	+	1348.18i	−0.00752383	+	0.0905972i
$606$	25.0488			0.00167910
$607$		−	3569.00i		−	0.238651i	−0.992855	−	0.119326i	$-0.961927\pi$
$607$		−	3569.00i		−	0.238651i	0.992855	−	0.119326i	$-0.0380732\pi$
$608$			24440.3i			1.63024i
$609$	−897.007			−0.0596857
$610$	−15492.7	−	1286.63i	−1.02833	−	0.0854000i
$611$	−10184.6			−0.674344
$612$		−	1958.51i		−	0.129360i
$613$		−	6848.73i		−	0.451252i	−0.974214	−	0.225626i	$-0.927557\pi$
$613$		−	6848.73i		−	0.451252i	0.974214	−	0.225626i	$-0.0724428\pi$
$614$	−9460.98			−0.621847
$615$	1407.74	+	116.909i	0.0923016	+	0.00766538i
$616$	986.683			0.0645367
$617$		−	1365.14i		−	0.0890734i	−0.999008	−	0.0445367i	$-0.985819\pi$
$617$		−	1365.14i		−	0.0890734i	0.999008	−	0.0445367i	$-0.0141812\pi$
$618$		−	20901.0i		−	1.36045i
$619$	10475.0			0.680173			0.340087	−	0.940394i	$-0.389544\pi$
$619$	10475.0			0.680173			0.340087	+	0.940394i	$0.389544\pi$
$620$	−44.9512	+	541.274i	−0.00291175	+	0.0350614i
$621$	−5175.99			−0.334469
$622$		−	12915.7i		−	0.832595i
$623$		−	4284.86i		−	0.275552i
$624$	−17716.0			−1.13655
$625$	14774.7	+	5084.27i	0.945579	+	0.325393i
$626$	−3737.57			−0.238632
$627$			4187.97i			0.266749i
$628$			13640.2i			0.866726i
$629$	−12560.1			−0.796189
$630$	234.024	−	2817.97i	0.0147996	−	0.178207i
$631$	−13819.5			−0.871864			−0.435932	−	0.899980i	$-0.643581\pi$
$631$	−13819.5			−0.871864			−0.435932	+	0.899980i	$0.643581\pi$
$632$			1482.61i			0.0933150i
$633$		−	4929.32i		−	0.309515i
$634$	9752.96			0.610945
$635$	19295.8	+	1602.46i	1.20587	+	0.100144i
$636$	5838.63			0.364020
$637$			20938.8i			1.30239i
$638$			1499.06i			0.0930227i
$639$	−2706.56			−0.167558
$640$	14995.0	+	1245.29i	0.926139	+	0.0769131i
$641$	−15876.0			−0.978262			−0.489131	−	0.872210i	$-0.662686\pi$
$641$	−15876.0			−0.978262			−0.489131	+	0.872210i	$0.662686\pi$
$642$			10210.2i			0.627671i
$643$		−	8074.63i		−	0.495229i	−0.968859	−	0.247615i	$-0.920353\pi$
$643$		−	8074.63i		−	0.495229i	0.968859	−	0.247615i	$-0.0796467\pi$
$644$	−7237.51			−0.442854
$645$	−817.552	+	9844.43i	−0.0499086	+	0.600968i
$646$	−20556.3			−1.25198
$647$		−	20914.5i		−	1.27084i	−0.772166	−	0.635421i	$-0.780826\pi$
$647$		−	20914.5i		−	1.27084i	0.772166	−	0.635421i	$-0.219174\pi$
$648$			925.296i			0.0560942i
$649$	8026.53			0.485468
$650$	32837.9	+	5492.07i	1.98155	+	0.331410i
$651$	238.010			0.0143292
$652$		−	17590.6i		−	1.05659i
$653$			22089.9i			1.32380i	0.749591	+	0.661901i	$0.230250\pi$
$653$			22089.9i			1.32380i	−0.749591	+	0.661901i	$0.769750\pi$
$654$	4122.81			0.246506
$655$	−979.774	+	11797.8i	−0.0584472	+	0.703784i
$656$	−3341.71			−0.198890
$657$		−	7125.87i		−	0.423145i
$658$			3845.56i			0.227835i
$659$	−10282.0			−0.607784			−0.303892	−	0.952707i	$-0.598286\pi$
$659$	−10282.0			−0.607784			−0.303892	+	0.952707i	$0.598286\pi$
$660$	−1767.86	−	146.815i	−0.104263	−	0.00865875i
$661$	−19195.0			−1.12950			−0.564750	−	0.825262i	$-0.691027\pi$
$661$	−19195.0			−1.12950			−0.564750	+	0.825262i	$0.691027\pi$
$662$			301.984i			0.0177295i
$663$		−	10105.3i		−	0.591942i
$664$	−8649.71			−0.505533
$665$	−11103.0	−	922.074i	−0.647454	−	0.0537692i
$666$	−8938.46			−0.520058
$667$			7299.86i			0.423766i
$668$		−	12268.6i		−	0.710606i
$669$	−231.284			−0.0133662
$670$	3311.90	−	39879.8i	0.190970	−	2.29954i
$671$	4273.82			0.245885
$672$			4536.57i			0.260420i
$673$			29004.4i			1.66128i	0.556813	+	0.830638i	$0.312024\pi$
$673$			29004.4i			1.66128i	−0.556813	+	0.830638i	$0.687976\pi$
$674$	−23511.0			−1.34364
$675$	556.728	−	3328.77i	0.0317459	−	0.189814i
$676$	16068.4			0.914226
$677$		−	10560.1i		−	0.599494i	−0.954019	−	0.299747i	$-0.903098\pi$
$677$		−	10560.1i		−	0.599494i	0.954019	−	0.299747i	$-0.0969022\pi$
$678$		−	10779.3i		−	0.610586i
$679$	−11202.7			−0.633167
$680$	−478.405	+	5760.65i	−0.0269794	+	0.324869i
$681$	−2831.84			−0.159348
$682$		−	397.758i		−	0.0223327i
$683$			34535.0i			1.93477i	0.253317	+	0.967383i	$0.418478\pi$
$683$			34535.0i			1.93477i	−0.253317	+	0.967383i	$0.581522\pi$
$684$	−5491.65			−0.306986
$685$	−2982.64	−	247.700i	−0.166366	−	0.0138162i
$686$	17545.0			0.976491
$687$			7931.81i			0.440491i
$688$		−	23368.9i		−	1.29496i
$689$	30125.5			1.66573
$690$	−22932.7	−	1904.49i	−1.26526	−	0.105076i
$691$	33279.8			1.83216			0.916081	−	0.400993i	$-0.131335\pi$
$691$	33279.8			1.83216			0.916081	+	0.400993i	$0.131335\pi$
$692$		−	8513.40i		−	0.467675i
$693$			777.364i			0.0426113i
$694$	−942.580			−0.0515560
$695$	1250.79	−	15061.2i	0.0682662	−	0.822018i
$696$	1304.98			0.0710704
$697$		−	1906.13i		−	0.103586i
$698$			31286.5i			1.69658i
$699$	−1896.92			−0.102644
$700$	778.465	−	4654.56i	0.0420332	−	0.251323i
$701$	−32650.3			−1.75918			−0.879590	−	0.475732i	$-0.842183\pi$
$701$	−32650.3			−1.75918			−0.879590	+	0.475732i	$0.842183\pi$
$702$		−	7191.51i		−	0.386647i
$703$			35218.3i			1.88945i
$704$	598.903			0.0320625
$705$	−379.871	+	4574.17i	−0.0202933	+	0.244359i
$706$	32903.6			1.75403
$707$		−	18.3195i		−	0.000974504i
$708$			10525.1i			0.558698i
$709$	22836.3			1.20964			0.604820	−	0.796362i	$-0.293245\pi$
$709$	22836.3			1.20964			0.604820	+	0.796362i	$0.293245\pi$
$710$	−11991.7	−	995.872i	−0.633857	−	0.0526400i
$711$	−1168.08			−0.0616126
$712$			6233.66i			0.328113i
$713$		−	1936.93i		−	0.101737i
$714$	−3815.62			−0.199995
$715$	−9121.58	−	757.520i	−0.477102	−	0.0396219i
$716$	3219.28			0.168031
$717$		−	2436.73i		−	0.126920i
$718$			41443.0i			2.15410i
$719$	−34574.0			−1.79331			−0.896657	−	0.442726i	$-0.854011\pi$
$719$	−34574.0			−1.79331			−0.896657	+	0.442726i	$0.854011\pi$
$720$	−660.785	+	7956.75i	−0.0342028	+	0.411848i
$721$	−15286.0			−0.789568
$722$			33092.4i			1.70578i
$723$			9491.50i			0.488233i
$724$	17156.1			0.880665
$725$	−4694.67	−	785.172i	−0.240490	−	0.0402215i
$726$	1299.12			0.0664115
$727$		−	25552.1i		−	1.30354i	−0.758416	−	0.651771i	$-0.774026\pi$
$727$		−	25552.1i		−	1.30354i	0.758416	−	0.651771i	$-0.225974\pi$
$728$			6675.74i			0.339862i
$729$	−729.000			−0.0370370
$730$	2621.95	−	31571.8i	0.132935	−	1.60072i
$731$	13329.7			0.674441
$732$			5604.23i			0.282976i
$733$		−	34325.7i		−	1.72967i	−0.502056	−	0.864835i	$-0.667423\pi$
$733$		−	34325.7i		−	1.72967i	0.502056	−	0.864835i	$-0.332577\pi$
$734$	−11758.1			−0.591279
$735$	9404.18	+	780.989i	0.471943	+	0.0391935i
$736$	36918.7			1.84897
$737$			11001.2i			0.549845i
$738$		−	1356.51i		−	0.0676609i
$739$	7525.56			0.374604			0.187302	−	0.982302i	$-0.440026\pi$
$739$	7525.56			0.374604			0.187302	+	0.982302i	$0.440026\pi$
$740$	−14866.6	−	1234.63i	−0.738523	−	0.0613322i
$741$	−28335.2			−1.40475
$742$		−	11375.0i		−	0.562788i
$743$			17822.1i			0.879987i	0.898001	+	0.439993i	$0.145019\pi$
$743$			17822.1i			0.879987i	−0.898001	+	0.439993i	$0.854981\pi$
$744$	−346.259			−0.0170625
$745$	−944.405	+	11371.9i	−0.0464434	+	0.559242i
$746$	−16148.8			−0.792559
$747$		−	6814.73i		−	0.333786i
$748$			2393.74i			0.117010i
$749$	7467.25			0.364282
$750$	3691.45	−	14543.6i	0.179723	−	0.708074i
$751$	10469.9			0.508727			0.254363	−	0.967109i	$-0.418134\pi$
$751$	10469.9			0.508727			0.254363	+	0.967109i	$0.418134\pi$
$752$		−	10858.2i		−	0.526541i
$753$		−	11514.7i		−	0.557265i
$754$	−10142.4			−0.489875
$755$	−2912.08	+	35065.4i	−0.140373	+	1.69028i
$756$	−1019.35			−0.0490389
$757$		−	3183.05i		−	0.152827i	−0.997076	−	0.0764135i	$-0.975653\pi$
$757$		−	3183.05i		−	0.152827i	0.997076	−	0.0764135i	$-0.0243469\pi$
$758$			1203.59i			0.0576731i
$759$	6326.20			0.302538
$760$	16152.8	+	1341.44i	0.770952	+	0.0640254i
$761$	26723.4			1.27296			0.636481	−	0.771292i	$-0.280389\pi$
$761$	26723.4			1.27296			0.636481	+	0.771292i	$0.280389\pi$
$762$		−	18593.6i		−	0.883955i
$763$		−	3015.22i		−	0.143065i
$764$	10324.8			0.488926
$765$	−4538.56	−	376.914i	−0.214499	−	0.0178136i
$766$	−24850.5			−1.17217
$767$			54306.3i			2.55657i
$768$		−	15756.0i		−	0.740293i
$769$	29672.1			1.39142			0.695711	−	0.718322i	$-0.255090\pi$
$769$	29672.1			1.39142			0.695711	+	0.718322i	$0.255090\pi$
$770$	−286.029	+	3444.18i	−0.0133867	+	0.161194i
$771$	7900.78			0.369053
$772$			5560.20i			0.259218i
$773$			13.7392i			0.000639281i	1.00000		0.000319640i	$0.000101745\pi$
$773$			13.7392i			0.000639281i	−1.00000		0.000319640i	$0.999898\pi$
$774$	9486.18			0.440534
$775$	1245.67	+	208.336i	0.0577366	+	0.00965630i
$776$	16297.8			0.753940
$777$			6537.16i			0.301827i
$778$			18163.1i			0.836991i
$779$	−5344.76			−0.245823
$780$	993.329	−	11961.0i	0.0455986	−	0.549069i
$781$	3308.01			0.151562
$782$			31051.6i			1.41995i
$783$			1028.13i			0.0469252i
$784$	−22323.8			−1.01694
$785$	31609.2	+	2625.05i	1.43717	+	0.119353i
$786$	11368.5			0.515903
$787$		−	38903.5i		−	1.76208i	−0.473037	−	0.881042i	$-0.656842\pi$
$787$		−	38903.5i		−	1.76208i	0.473037	−	0.881042i	$-0.343158\pi$
$788$		−	17970.2i		−	0.812388i
$789$	17603.2			0.794285
$790$	−5175.30	−	429.794i	−0.233075	−	0.0193562i
$791$	−7883.47			−0.354367
$792$		−	1130.92i		−	0.0507391i
$793$			28916.0i			1.29488i
$794$	39260.4			1.75478
$795$	1123.64	−	13530.2i	0.0501276	−	0.603605i
$796$	13760.9			0.612740
$797$		−	27640.0i		−	1.22843i	−0.789138	−	0.614216i	$-0.789472\pi$
$797$		−	27640.0i		−	1.22843i	0.789138	−	0.614216i	$-0.210528\pi$
$798$			10699.0i			0.474611i
$799$	6193.58			0.274234
$800$	−3970.97	+	23743.1i	−0.175494	+	1.04931i
$801$	−4911.22			−0.216641
$802$			2587.84i			0.113940i
$803$			8709.39i			0.382749i
$804$	−14425.8			−0.632786
$805$	−1392.85	+	16771.9i	−0.0609834	+	0.734323i
$806$	2691.17			0.117608
$807$		−	17480.5i		−	0.762505i
$808$			26.6513i			0.00116038i
$809$	11892.2			0.516821			0.258411	−	0.966035i	$-0.416801\pi$
$809$	11892.2			0.516821			0.258411	+	0.966035i	$0.416801\pi$
$810$	−3229.90	−	268.234i	−0.140108	−	0.0116355i
$811$	12095.3			0.523705			0.261853	−	0.965108i	$-0.415667\pi$
$811$	12095.3			0.523705			0.261853	+	0.965108i	$0.415667\pi$
$812$			1437.62i			0.0621314i
$813$			8408.91i			0.362747i
$814$	10924.8			0.470410
$815$	−40763.5	−	3385.29i	−1.75201	−	0.145499i
$816$	10773.7			0.462200
$817$		−	37376.3i		−	1.60053i
$818$		−	39012.6i		−	1.66753i
$819$	−5259.52			−0.224399
$820$	187.368	−	2256.17i	0.00797948	−	0.0960839i
$821$	−37161.3			−1.57971			−0.789853	−	0.613296i	$-0.789843\pi$
$821$	−37161.3			−1.57971			−0.789853	+	0.613296i	$0.789843\pi$
$822$			2874.10i			0.121954i
$823$			16196.3i			0.685988i	0.939338	+	0.342994i	$0.111441\pi$
$823$			16196.3i			0.685988i	−0.939338	+	0.342994i	$0.888559\pi$
$824$	22238.2			0.940174
$825$	−680.446	+	4068.49i	−0.0287152	+	0.171693i
$826$	20505.3			0.863766
$827$		−	14131.0i		−	0.594175i	−0.954850	−	0.297088i	$-0.903985\pi$
$827$		−	14131.0i		−	0.594175i	0.954850	−	0.297088i	$-0.0960153\pi$
$828$			8295.49i			0.348174i
$829$	35608.7			1.49185			0.745923	−	0.666033i	$-0.232009\pi$
$829$	35608.7			1.49185			0.745923	+	0.666033i	$0.232009\pi$
$830$	2507.46	−	30193.3i	0.104862	−	1.26268i
$831$	9564.06			0.399246
$832$			4052.09i			0.168847i
$833$		−	12733.6i		−	0.529643i
$834$	−14513.1			−0.602573
$835$	−28430.6	−	2361.08i	−1.17830	−	0.0978543i
$836$	6712.02			0.277679
$837$		−	272.802i		−	0.0112657i
$838$			18892.7i			0.778804i
$839$	25822.1			1.06255			0.531274	−	0.847200i	$-0.321713\pi$
$839$	25822.1			1.06255			0.531274	+	0.847200i	$0.321713\pi$
$840$	2998.26	+	248.996i	0.123154	+	0.0102276i
$841$	−22939.0			−0.940547
$842$		−	6109.63i		−	0.250062i
$843$			2492.66i			0.101841i
$844$	−7900.16			−0.322197
$845$	3092.36	−	37236.2i	0.125894	−	1.51594i
$846$	4407.71			0.179125
$847$		−	950.111i		−	0.0385433i
$848$			32118.1i			1.30064i
$849$	−22118.0			−0.894096
$850$	−19969.8	−	3339.91i	−0.805835	−	0.134774i
$851$	53199.5			2.14296
$852$			4337.77i			0.174424i
$853$		−	46078.8i		−	1.84960i	−0.380454	−	0.924800i	$-0.624232\pi$
$853$		−	46078.8i		−	1.84960i	0.380454	−	0.924800i	$-0.375768\pi$
$854$	10918.3			0.437490
$855$	−1056.86	+	12726.1i	−0.0422737	+	0.509033i
$856$	−10863.4			−0.433767
$857$		−	49518.4i		−	1.97376i	−0.161447	−	0.986881i	$-0.551616\pi$
$857$		−	49518.4i		−	1.97376i	0.161447	−	0.986881i	$-0.448384\pi$
$858$			8789.63i			0.349735i
$859$	2523.51			0.100234			0.0501171	−	0.998743i	$-0.484041\pi$
$859$	2523.51			0.100234			0.0501171	+	0.998743i	$0.484041\pi$
$860$	15777.6	+	1310.28i	0.625594	+	0.0519537i
$861$	−992.084			−0.0392685
$862$		−	46020.4i		−	1.81840i
$863$			5487.12i			0.216435i	0.994127	+	0.108218i	$0.0345143\pi$
$863$			5487.12i			0.216435i	−0.994127	+	0.108218i	$0.965486\pi$
$864$	5199.73			0.204744
$865$	−19728.5	−	1638.40i	−0.775480	−	0.0644014i
$866$	13545.9			0.531535
$867$		−	8593.63i		−	0.336626i
$868$		−	381.455i		−	0.0149164i
$869$	1427.66			0.0557307
$870$	−378.299	+	4555.24i	−0.0147420	+	0.177514i
$871$	−74432.7			−2.89559
$872$			4386.58i			0.170354i
$873$			12840.3i			0.497800i
$874$	87068.5			3.36972
$875$	−10636.5	−	2699.75i	−0.410946	−	0.104306i
$876$	−11420.5			−0.440485
$877$			38507.4i			1.48267i	0.671135	+	0.741335i	$0.265807\pi$
$877$			38507.4i			1.48267i	−0.671135	+	0.741335i	$0.734193\pi$
$878$		−	8789.18i		−	0.337836i
$879$	9446.72			0.362491
$880$	807.626	−	9724.92i	0.0309376	−	0.372531i
$881$	−20408.0			−0.780433			−0.390216	−	0.920723i	$-0.627600\pi$
$881$	−20408.0			−0.780433			−0.390216	+	0.920723i	$0.627600\pi$
$882$		−	9061.94i		−	0.345954i
$883$			8284.22i			0.315726i	0.987461	+	0.157863i	$0.0504605\pi$
$883$			8284.22i			0.315726i	−0.987461	+	0.157863i	$0.949540\pi$
$884$	−16195.7			−0.616198
$885$	24390.4	+	2025.55i	0.926412	+	0.0769358i
$886$	−34516.5			−1.30881
$887$		−	29522.9i		−	1.11757i	−0.829313	−	0.558784i	$-0.811268\pi$
$887$		−	29522.9i		−	1.11757i	0.829313	−	0.558784i	$-0.188732\pi$
$888$		−	9510.33i		−	0.359398i
$889$	−13598.4			−0.513022
$890$	−21759.6	−	1807.07i	−0.819533	−	0.0680598i
$891$	891.000			0.0335013
$892$			370.677i			0.0139139i
$893$		−	17366.7i		−	0.650790i
$894$	10958.1			0.409948
$895$	619.548	−	7460.20i	0.0231388	−	0.278622i
$896$	−10567.5			−0.394013
$897$			42802.1i			1.59322i
$898$		−	16174.6i		−	0.601061i
$899$	−384.742			−0.0142735
$900$	−5334.97	−	892.262i	−0.197592	−	0.0330467i
$901$	−18320.3			−0.677401
$902$			1657.95i			0.0612016i
$903$		−	6937.73i		−	0.255674i
$904$	11469.0			0.421960
$905$	3301.68	−	39756.8i	0.121273	−	1.46029i
$906$	33789.3			1.23904
$907$			15994.9i			0.585561i	0.956180	+	0.292780i	$0.0945804\pi$
$907$			15994.9i			0.585561i	−0.956180	+	0.292780i	$0.905420\pi$
$908$			4538.56i			0.165878i
$909$	−20.9974			−0.000766161
$910$	−23302.8	−	1935.23i	−0.848880	−	0.0704970i
$911$	40778.1			1.48303			0.741514	−	0.670938i	$-0.234108\pi$
$911$	40778.1			1.48303			0.741514	+	0.670938i	$0.234108\pi$
$912$		−	30209.4i		−	1.09686i
$913$			8329.11i			0.301920i
$914$	−22632.3			−0.819049
$915$	12987.0	+	1078.53i	0.469220	+	0.0389673i
$916$	12712.2			0.458541
$917$		−	8314.34i		−	0.299415i
$918$			4373.40i			0.157237i
$919$	−11958.3			−0.429236			−0.214618	−	0.976698i	$-0.568851\pi$
$919$	−11958.3			−0.429236			−0.214618	+	0.976698i	$0.568851\pi$
$920$	2026.34	−	24399.9i	0.0726156	−	0.874391i
$921$	7930.78			0.283744
$922$			21934.6i			0.783491i
$923$			22381.5i			0.798154i
$924$	1245.87			0.0443573
$925$	−5722.13	+	34213.5i	−0.203397	+	1.21615i
$926$	50815.8			1.80336
$927$			17520.5i			0.620764i
$928$		−	7333.36i		−	0.259406i
$929$	8935.99			0.315587			0.157793	−	0.987472i	$-0.449562\pi$
$929$	8935.99			0.315587			0.157793	+	0.987472i	$0.449562\pi$
$930$	100.377	−	1208.68i	0.00353924	−	0.0426172i
$931$	−35704.8			−1.25690
$932$			3040.18i			0.106850i
$933$			10826.8i			0.379906i
$934$	37003.1			1.29634
$935$	5547.13	+	460.673i	0.194022	+	0.0161130i
$936$	7651.61			0.267202
$937$			49396.1i			1.72220i	0.508437	+	0.861099i	$0.330223\pi$
$937$			49396.1i			1.72220i	−0.508437	+	0.861099i	$0.669777\pi$
$938$			28104.8i			0.978309i
$939$	3133.06			0.108886
$940$	7330.97	+	608.816i	0.254372	+	0.0211249i
$941$	−42760.7			−1.48136			−0.740679	−	0.671859i	$-0.765496\pi$
$941$	−42760.7			−1.48136			−0.740679	+	0.671859i	$0.765496\pi$
$942$		−	30458.9i		−	1.05351i
$943$			8073.61i			0.278805i
$944$	−57898.3			−1.99622
$945$	−196.173	+	2362.19i	−0.00675293	+	0.0813145i
$946$	−11594.2			−0.398478
$947$		−	30415.1i		−	1.04367i	−0.853045	−	0.521837i	$-0.825247\pi$
$947$		−	30415.1i		−	1.04367i	0.853045	−	0.521837i	$-0.174753\pi$
$948$			1872.07i			0.0641373i
$949$	−58926.4			−2.01563
$950$	−9365.07	+	55995.2i	−0.319835	+	1.91234i
$951$	−8175.53			−0.278769
$952$		−	4059.74i		−	0.138211i
$953$		−	28926.2i		−	0.983223i	−0.870815	−	0.491611i	$-0.836408\pi$
$953$		−	28926.2i		−	0.983223i	0.870815	−	0.491611i	$-0.163592\pi$
$954$	−13037.8			−0.442467
$955$	1987.01	−	23926.3i	0.0673278	−	0.810718i
$956$	−3905.33			−0.132121
$957$		−	1256.61i		−	0.0424455i
$958$		−	61729.4i		−	2.08182i
$959$	2101.98			0.0707783
$960$	1819.90	+	151.137i	0.0611844	+	0.00508119i
$961$	−29688.9			−0.996573
$962$			73915.4i			2.47726i
$963$		−	8558.83i		−	0.286401i
$964$	15211.9			0.508239
$965$	12885.0	+	1070.06i	0.429825	+	0.0356957i
$966$	16161.5			0.538289
$967$			10872.9i			0.361582i	0.983522	+	0.180791i	$0.0578658\pi$
$967$			10872.9i			0.361582i	−0.983522	+	0.180791i	$0.942134\pi$
$968$			1382.23i			0.0458953i
$969$	17231.6			0.571266
$970$	−4724.57	+	56890.2i	−0.156388	+	1.88313i
$971$	−37009.8			−1.22317			−0.611586	−	0.791178i	$-0.709468\pi$
$971$	−37009.8			−1.22317			−0.611586	+	0.791178i	$0.709468\pi$
$972$			1168.36i			0.0385547i
$973$			10614.1i			0.349716i
$974$	9206.46			0.302869
$975$	−27526.8	−	4603.79i	−0.904167	−	0.151220i
$976$	−30828.7			−1.01107
$977$			52946.8i			1.73380i	0.498486	+	0.866898i	$0.333890\pi$
$977$			52946.8i			1.73380i	−0.498486	+	0.866898i	$0.666110\pi$
$978$			39280.1i			1.28429i
$979$	6002.61			0.195959
$980$	1251.68	−	15072.0i	0.0407995	−	0.491282i
$981$	−3455.99			−0.112478
$982$			7712.47i			0.250626i
$983$		−	42643.2i		−	1.38363i	−0.722075	−	0.691814i	$-0.756812\pi$
$983$		−	42643.2i		−	1.38363i	0.722075	−	0.691814i	$-0.243188\pi$
$984$	1443.30			0.0467587
$985$	−41643.3	−	3458.35i	−1.34707	−	0.111870i
$986$	6167.95			0.199216
$987$		−	3223.58i		−	0.103959i
$988$			45412.4i			1.46231i
$989$	−56459.4			−1.81527
$990$	3947.66	+	327.841i	0.126732	+	0.0105247i
$991$	36400.6			1.16680			0.583402	−	0.812183i	$-0.301721\pi$
$991$	36400.6			1.16680			0.583402	+	0.812183i	$0.301721\pi$
$992$			1945.81i			0.0622779i
$993$		−	253.141i		−	0.00808982i
$994$	8450.95			0.269666
$995$	2648.27	−	31888.8i	0.0843776	−	1.01602i
$996$	−10921.9			−0.347463
$997$			54980.2i			1.74648i	0.487291	+	0.873239i	$0.337985\pi$
$997$			54980.2i			1.74648i	−0.487291	+	0.873239i	$0.662015\pi$
$998$		−	18971.1i		−	0.601722i
$999$	7492.77			0.237298

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.4.c.b.34.12	yes	14
3.2	odd	2		495.4.c.d.199.3		14
5.2	odd	4		825.4.a.bd.1.1		7
5.3	odd	4		825.4.a.ba.1.7		7
5.4	even	2	inner	165.4.c.b.34.3	✓	14
15.2	even	4		2475.4.a.bo.1.7		7
15.8	even	4		2475.4.a.bs.1.1		7
15.14	odd	2		495.4.c.d.199.12		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.c.b.34.3	✓	14	5.4	even	2	inner
165.4.c.b.34.12	yes	14	1.1	even	1	trivial
495.4.c.d.199.3		14	3.2	odd	2
495.4.c.d.199.12		14	15.14	odd	2
825.4.a.ba.1.7		7	5.3	odd	4
825.4.a.bd.1.1		7	5.2	odd	4
2475.4.a.bo.1.7		7	15.2	even	4
2475.4.a.bs.1.1		7	15.8	even	4

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	165.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.57884i q^{2} -3.00000i q^{3} -4.80807 q^{4} +(-0.925309 + 11.1420i) q^{5} +10.7365 q^{6} -7.85216i q^{7} +11.4234i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+3.57884i q^{2} -3.00000i q^{3} -4.80807 q^{4} +(-0.925309 + 11.1420i) q^{5} +10.7365 q^{6} -7.85216i q^{7} +11.4234i q^{8} -9.00000 q^{9} +(-39.8753 - 3.31153i) q^{10} +11.0000 q^{11} +14.4242i q^{12} +74.4243i q^{13} +28.1016 q^{14} +(33.4260 + 2.77593i) q^{15} -79.3470 q^{16} -45.2599i q^{17} -32.2095i q^{18} -126.908 q^{19} +(4.44895 - 53.5714i) q^{20} -23.5565 q^{21} +39.3672i q^{22} +191.703i q^{23} +34.2702 q^{24} +(-123.288 - 20.6196i) q^{25} -266.352 q^{26} +27.0000i q^{27} +37.7537i q^{28} +38.0790 q^{29} +(-9.93459 + 119.626i) q^{30} -10.1038 q^{31} -192.583i q^{32} -33.0000i q^{33} +161.978 q^{34} +(87.4886 + 7.26568i) q^{35} +43.2726 q^{36} -277.510i q^{37} -454.184i q^{38} +223.273 q^{39} +(-127.279 - 10.5702i) q^{40} +42.1151 q^{41} -84.3048i q^{42} +294.515i q^{43} -52.8887 q^{44} +(8.32778 - 100.278i) q^{45} -686.074 q^{46} +136.845i q^{47} +238.041i q^{48} +281.344 q^{49} +(73.7940 - 441.226i) q^{50} -135.780 q^{51} -357.837i q^{52} -404.781i q^{53} -96.6286 q^{54} +(-10.1784 + 122.562i) q^{55} +89.6984 q^{56} +380.725i q^{57} +136.278i q^{58} +729.685 q^{59} +(-160.714 - 13.3468i) q^{60} +388.529 q^{61} -36.1598i q^{62} +70.6694i q^{63} +54.4458 q^{64} +(-829.234 - 68.8655i) q^{65} +118.102 q^{66} +1000.11i q^{67} +217.612i q^{68} +575.109 q^{69} +(-26.0027 + 313.107i) q^{70} +300.729 q^{71} -102.811i q^{72} +791.763i q^{73} +993.163 q^{74} +(-61.8587 + 369.863i) q^{75} +610.183 q^{76} -86.3738i q^{77} +799.057i q^{78} +129.787 q^{79} +(73.4205 - 884.083i) q^{80} +81.0000 q^{81} +150.723i q^{82} +757.192i q^{83} +113.261 q^{84} +(504.285 + 41.8794i) q^{85} -1054.02 q^{86} -114.237i q^{87} +125.657i q^{88} +545.691 q^{89} +(358.878 + 29.8038i) q^{90} +584.391 q^{91} -921.721i q^{92} +30.3114i q^{93} -489.745 q^{94} +(117.429 - 1414.01i) q^{95} -577.748 q^{96} -1426.70i q^{97} +1006.88i q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 26 q^{4} - 14 q^{5} - 30 q^{6} - 126 q^{9}+O(q^{10}) \) 14 * q - 26 * q^4 - 14 * q^5 - 30 * q^6 - 126 * q^9	\( 14 q - 26 q^{4} - 14 q^{5} - 30 q^{6} - 126 q^{9} - 48 q^{10} + 154 q^{11} - 84 q^{14} - 86 q^{16} - 116 q^{19} + 442 q^{20} - 204 q^{21} + 450 q^{24} + 162 q^{25} - 400 q^{26} - 128 q^{29} + 246 q^{30} - 696 q^{31} - 412 q^{34} + 672 q^{35} + 234 q^{36} + 480 q^{39} + 1612 q^{40} - 664 q^{41} - 286 q^{44} + 126 q^{45} - 656 q^{46} + 834 q^{49} + 1908 q^{50} - 972 q^{51} + 270 q^{54} - 154 q^{55} - 3236 q^{56} + 664 q^{59} + 108 q^{60} + 44 q^{61} - 1122 q^{64} - 2328 q^{65} - 330 q^{66} + 1944 q^{69} + 1220 q^{70} - 1032 q^{71} - 3256 q^{74} + 84 q^{75} + 5588 q^{76} - 3492 q^{79} - 510 q^{80} + 1134 q^{81} - 1008 q^{84} - 1068 q^{85} + 2540 q^{86} + 4452 q^{89} + 432 q^{90} + 2144 q^{91} - 9472 q^{94} - 932 q^{95} + 450 q^{96} - 1386 q^{99}+O(q^{100}) \) 14 * q - 26 * q^4 - 14 * q^5 - 30 * q^6 - 126 * q^9 - 48 * q^10 + 154 * q^11 - 84 * q^14 - 86 * q^16 - 116 * q^19 + 442 * q^20 - 204 * q^21 + 450 * q^24 + 162 * q^25 - 400 * q^26 - 128 * q^29 + 246 * q^30 - 696 * q^31 - 412 * q^34 + 672 * q^35 + 234 * q^36 + 480 * q^39 + 1612 * q^40 - 664 * q^41 - 286 * q^44 + 126 * q^45 - 656 * q^46 + 834 * q^49 + 1908 * q^50 - 972 * q^51 + 270 * q^54 - 154 * q^55 - 3236 * q^56 + 664 * q^59 + 108 * q^60 + 44 * q^61 - 1122 * q^64 - 2328 * q^65 - 330 * q^66 + 1944 * q^69 + 1220 * q^70 - 1032 * q^71 - 3256 * q^74 + 84 * q^75 + 5588 * q^76 - 3492 * q^79 - 510 * q^80 + 1134 * q^81 - 1008 * q^84 - 1068 * q^85 + 2540 * q^86 + 4452 * q^89 + 432 * q^90 + 2144 * q^91 - 9472 * q^94 - 932 * q^95 + 450 * q^96 - 1386 * q^99

Introduction

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