LMFDB - Embedded newform 169.4.e.h.23.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,4,Mod(23,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("169.23");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	169.e (of order $6$, degree $2$, not 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:	$9.97132279097$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.6
Character	$\chi$	$=$	169.23
Dual form			169.4.e.h.147.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.92949 + 1.11399i) q^{2} +(4.87434 + 8.44260i) q^{3} +(-1.51803 + 2.62931i) q^{4} +8.20685i q^{5} +(-18.8100 - 10.8600i) q^{6} +(-7.23560 - 4.17747i) q^{7} -24.5882i q^{8} +(-34.0183 + 58.9214i) q^{9} +O(q^{10})$	\(q+(-1.92949 + 1.11399i) q^{2} +(4.87434 + 8.44260i) q^{3} +(-1.51803 + 2.62931i) q^{4} +8.20685i q^{5} +(-18.8100 - 10.8600i) q^{6} +(-7.23560 - 4.17747i) q^{7} -24.5882i q^{8} +(-34.0183 + 58.9214i) q^{9} +(-9.14239 - 15.8351i) q^{10} +(-8.39957 + 4.84949i) q^{11} -29.5976 q^{12} +18.6147 q^{14} +(-69.2872 + 40.0030i) q^{15} +(15.2469 + 26.4084i) q^{16} +(22.3109 - 38.6437i) q^{17} -151.585i q^{18} +(75.9867 + 43.8709i) q^{19} +(-21.5784 - 12.4583i) q^{20} -81.4497i q^{21} +(10.8046 - 18.7141i) q^{22} +(53.5263 + 92.7102i) q^{23} +(207.589 - 119.851i) q^{24} +57.6475 q^{25} -400.052 q^{27} +(21.9678 - 12.6831i) q^{28} +(7.02150 + 12.1616i) q^{29} +(89.1261 - 154.371i) q^{30} -171.090i q^{31} +(111.515 + 64.3831i) q^{32} +(-81.8846 - 47.2761i) q^{33} +99.4170i q^{34} +(34.2839 - 59.3815i) q^{35} +(-103.282 - 178.890i) q^{36} +(-358.495 + 206.977i) q^{37} -195.488 q^{38} +201.792 q^{40} +(-223.678 + 129.141i) q^{41} +(90.7344 + 157.157i) q^{42} +(30.5359 - 52.8897i) q^{43} -29.4468i q^{44} +(-483.560 - 279.183i) q^{45} +(-206.557 - 119.256i) q^{46} -68.7115i q^{47} +(-148.637 + 257.446i) q^{48} +(-136.597 - 236.594i) q^{49} +(-111.231 + 64.2190i) q^{50} +435.004 q^{51} +328.701 q^{53} +(771.899 - 445.656i) q^{54} +(-39.7991 - 68.9340i) q^{55} +(-102.717 + 177.911i) q^{56} +855.367i q^{57} +(-27.0959 - 15.6438i) q^{58} +(-127.431 - 73.5721i) q^{59} -242.904i q^{60} +(48.9041 - 84.7045i) q^{61} +(190.593 + 330.117i) q^{62} +(492.286 - 284.221i) q^{63} -530.839 q^{64} +210.661 q^{66} +(-586.817 + 338.799i) q^{67} +(67.7376 + 117.325i) q^{68} +(-521.810 + 903.802i) q^{69} +152.768i q^{70} +(681.360 + 393.383i) q^{71} +(1448.77 + 836.450i) q^{72} +997.675i q^{73} +(461.142 - 798.722i) q^{74} +(280.994 + 486.695i) q^{75} +(-230.701 + 133.195i) q^{76} +81.0345 q^{77} +383.897 q^{79} +(-216.729 + 125.129i) q^{80} +(-1031.50 - 1786.60i) q^{81} +(287.724 - 498.353i) q^{82} -519.718i q^{83} +(214.157 + 123.643i) q^{84} +(317.143 + 183.103i) q^{85} +136.067i q^{86} +(-68.4503 + 118.559i) q^{87} +(119.240 + 206.530i) q^{88} +(591.687 - 341.611i) q^{89} +1244.03 q^{90} -325.019 q^{92} +(1444.44 - 833.950i) q^{93} +(76.5442 + 132.578i) q^{94} +(-360.042 + 623.612i) q^{95} +1255.30i q^{96} +(-300.765 - 173.647i) q^{97} +(527.128 + 304.337i) q^{98} -659.886i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9}+O(q^{10}) $ 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9	$ 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9} - 294 q^{10} - 156 q^{12} - 588 q^{14} - 538 q^{16} - 110 q^{17} - 680 q^{22} - 408 q^{23} - 1228 q^{25} - 2672 q^{27} - 560 q^{29} + 1042 q^{30} - 40 q^{35} - 1818 q^{36} + 2956 q^{38} + 52 q^{40} + 8 q^{42} - 1066 q^{43} + 264 q^{48} + 806 q^{49} - 1880 q^{51} - 1112 q^{53} + 500 q^{55} + 500 q^{56} + 272 q^{61} + 4070 q^{62} - 1136 q^{64} + 13116 q^{66} + 3072 q^{68} - 4100 q^{69} + 3980 q^{74} + 4786 q^{75} + 2872 q^{77} + 1648 q^{79} + 1670 q^{81} + 5514 q^{82} + 1572 q^{87} - 1272 q^{88} + 5120 q^{90} + 16040 q^{92} + 5062 q^{94} - 3228 q^{95}+O(q^{100}) $ 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9 - 294 * q^10 - 156 * q^12 - 588 * q^14 - 538 * q^16 - 110 * q^17 - 680 * q^22 - 408 * q^23 - 1228 * q^25 - 2672 * q^27 - 560 * q^29 + 1042 * q^30 - 40 * q^35 - 1818 * q^36 + 2956 * q^38 + 52 * q^40 + 8 * q^42 - 1066 * q^43 + 264 * q^48 + 806 * q^49 - 1880 * q^51 - 1112 * q^53 + 500 * q^55 + 500 * q^56 + 272 * q^61 + 4070 * q^62 - 1136 * q^64 + 13116 * q^66 + 3072 * q^68 - 4100 * q^69 + 3980 * q^74 + 4786 * q^75 + 2872 * q^77 + 1648 * q^79 + 1670 * q^81 + 5514 * q^82 + 1572 * q^87 - 1272 * q^88 + 5120 * q^90 + 16040 * q^92 + 5062 * q^94 - 3228 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.92949	+	1.11399i	−0.682179	+	0.393856i	−0.800676	−	0.599098i	$-0.795526\pi$
$2$	−1.92949	+	1.11399i	−0.682179	+	0.393856i	0.118496	+	0.992954i	$0.462193\pi$
$3$	4.87434	+	8.44260i	0.938066	+	1.62478i	0.769072	+	0.639162i	$0.220719\pi$
$3$	4.87434	+	8.44260i	0.938066	+	1.62478i	0.168994	+	0.985617i	$0.445948\pi$
$4$	−1.51803	+	2.62931i	−0.189754	+	0.328664i
$5$			8.20685i			0.734043i	0.930212	+	0.367022i	$0.119623\pi$
$5$			8.20685i			0.734043i	−0.930212	+	0.367022i	$0.880377\pi$
$6$	−18.8100	−	10.8600i	−1.27986	−	0.738927i
$7$	−7.23560	−	4.17747i	−0.390686	−	0.225562i	0.291772	−	0.956488i	$-0.405755\pi$
$7$	−7.23560	−	4.17747i	−0.390686	−	0.225562i	−0.682457	+	0.730926i	$0.739089\pi$
$8$		−	24.5882i		−	1.08666i
$9$	−34.0183	+	58.9214i	−1.25994	+	2.18228i
$10$	−9.14239	−	15.8351i	−0.289108	−	0.500749i
$11$	−8.39957	+	4.84949i	−0.230233	+	0.132925i	−0.610680	−	0.791878i	$-0.709104\pi$
$11$	−8.39957	+	4.84949i	−0.230233	+	0.132925i	0.380446	+	0.924803i	$0.375770\pi$
$12$	−29.5976			−0.712009
$13$		0			0
$13$		0			0
$14$	18.6147			0.355357
$15$	−69.2872	+	40.0030i	−1.19266	+	0.688581i
$16$	15.2469	+	26.4084i	0.238232	+	0.412630i
$17$	22.3109	−	38.6437i	0.318306	−	0.551322i	−0.661829	−	0.749655i	$-0.730219\pi$
$17$	22.3109	−	38.6437i	0.318306	−	0.551322i	0.980135	+	0.198333i	$0.0635528\pi$
$18$		−	151.585i		−	1.98494i
$19$	75.9867	+	43.8709i	0.917502	+	0.529720i	0.882837	−	0.469679i	$-0.155630\pi$
$19$	75.9867	+	43.8709i	0.917502	+	0.529720i	0.0346647	+	0.999399i	$0.488964\pi$
$20$	−21.5784	−	12.4583i	−0.241254	−	0.139288i
$21$		−	81.4497i		−	0.846370i
$22$	10.8046	−	18.7141i	0.104707	−	0.181358i
$23$	53.5263	+	92.7102i	0.485261	+	0.840496i	0.999857	−	0.0169365i	$-0.00539131\pi$
$23$	53.5263	+	92.7102i	0.485261	+	0.840496i	−0.514596	+	0.857433i	$0.672058\pi$
$24$	207.589	−	119.851i	1.76558	−	1.01936i
$25$	57.6475			0.461180
$26$		0			0
$27$	−400.052			−2.85149
$28$	21.9678	−	12.6831i	0.148269	−	0.0856029i
$29$	7.02150	+	12.1616i	0.0449607	+	0.0778742i	0.887630	−	0.460557i	$-0.152350\pi$
$29$	7.02150	+	12.1616i	0.0449607	+	0.0778742i	−0.842669	+	0.538431i	$0.819017\pi$
$30$	89.1261	−	154.371i	0.542404	−	0.939472i
$31$		−	171.090i		−	0.991247i	−0.868537	−	0.495624i	$-0.834940\pi$
$31$		−	171.090i		−	0.991247i	0.868537	−	0.495624i	$-0.165060\pi$
$32$	111.515	+	64.3831i	0.616038	+	0.355670i
$33$	−81.8846	−	47.2761i	−0.431948	−	0.249385i
$34$			99.4170i			0.501467i
$35$	34.2839	−	59.3815i	0.165573	−	0.286780i
$36$	−103.282	−	178.890i	−0.478157	−	0.828192i
$37$	−358.495	+	206.977i	−1.59287	+	0.919643i	−0.600057	+	0.799957i	$0.704856\pi$
$37$	−358.495	+	206.977i	−1.59287	+	0.919643i	−0.992812	+	0.119686i	$0.961811\pi$
$38$	−195.488			−0.834534
$39$		0			0
$40$	201.792			0.797653
$41$	−223.678	+	129.141i	−0.852017	+	0.491912i	−0.861331	−	0.508044i	$-0.830369\pi$
$41$	−223.678	+	129.141i	−0.852017	+	0.491912i	0.00931374	+	0.999957i	$0.497035\pi$
$42$	90.7344	+	157.157i	0.333348	+	0.577376i
$43$	30.5359	−	52.8897i	0.108295	−	0.187572i	−0.806785	−	0.590845i	$-0.798794\pi$
$43$	30.5359	−	52.8897i	0.108295	−	0.187572i	0.915080	+	0.403273i	$0.132128\pi$
$44$		−	29.4468i		−	0.100892i
$45$	−483.560	−	279.183i	−1.60188	−	0.924849i
$46$	−206.557	−	119.256i	−0.662070	−	0.382246i
$47$		−	68.7115i		−	0.213247i	−0.994299	−	0.106623i	$-0.965996\pi$
$47$		−	68.7115i		−	0.213247i	0.994299	−	0.106623i	$-0.0340039\pi$
$48$	−148.637	+	257.446i	−0.446955	+	0.774150i
$49$	−136.597	−	236.594i	−0.398243	−	0.689777i
$50$	−111.231	+	64.2190i	−0.314608	+	0.181639i
$51$	435.004			1.19437
$52$		0			0
$53$	328.701			0.851896			0.425948	−	0.904748i	$-0.359941\pi$
$53$	328.701			0.851896			0.425948	+	0.904748i	$0.359941\pi$
$54$	771.899	−	445.656i	1.94522	−	1.12308i
$55$	−39.7991	−	68.9340i	−0.0975728	−	0.169001i
$56$	−102.717	+	177.911i	−0.245109	+	0.424541i
$57$			855.367i			1.98765i
$58$	−27.0959	−	15.6438i	−0.0613425	−	0.0354161i
$59$	−127.431	−	73.5721i	−0.281187	−	0.162344i	0.352773	−	0.935709i	$-0.385239\pi$
$59$	−127.431	−	73.5721i	−0.281187	−	0.162344i	−0.633961	+	0.773365i	$0.718572\pi$
$60$		−	242.904i		−	0.522645i
$61$	48.9041	−	84.7045i	0.102648	−	0.177792i	−0.810127	−	0.586255i	$-0.800602\pi$
$61$	48.9041	−	84.7045i	0.102648	−	0.177792i	0.912775	+	0.408463i	$0.133935\pi$
$62$	190.593	+	330.117i	0.390409	+	0.676208i
$63$	492.286	−	284.221i	0.984479	−	0.568389i
$64$	−530.839			−1.03680
$65$		0			0
$66$	210.661			0.392888
$67$	−586.817	+	338.799i	−1.07002	+	0.617774i	−0.928186	−	0.372117i	$-0.878632\pi$
$67$	−586.817	+	338.799i	−1.07002	+	0.617774i	−0.141830	+	0.989891i	$0.545299\pi$
$68$	67.7376	+	117.325i	0.120800	+	0.209231i
$69$	−521.810	+	903.802i	−0.910414	+	1.57688i
$70$			152.768i			0.260847i
$71$	681.360	+	393.383i	1.13891	+	0.657549i	0.946160	−	0.323699i	$-0.104926\pi$
$71$	681.360	+	393.383i	1.13891	+	0.657549i	0.192749	+	0.981248i	$0.438260\pi$
$72$	1448.77	+	836.450i	2.37138	+	1.36912i
$73$			997.675i			1.59958i	0.600282	+	0.799788i	$0.295055\pi$
$73$			997.675i			1.59958i	−0.600282	+	0.799788i	$0.704945\pi$
$74$	461.142	−	798.722i	0.724415	−	1.25472i
$75$	280.994	+	486.695i	0.432618	+	0.749316i
$76$	−230.701	+	133.195i	−0.348200	+	0.201033i
$77$	81.0345			0.119932
$78$		0			0
$79$	383.897			0.546731			0.273366	−	0.961910i	$-0.411863\pi$
$79$	383.897			0.546731			0.273366	+	0.961910i	$0.411863\pi$
$80$	−216.729	+	125.129i	−0.302889	+	0.174873i
$81$	−1031.50	−	1786.60i	−1.41495	−	2.45076i
$82$	287.724	−	498.353i	0.387486	−	0.671145i
$83$		−	519.718i		−	0.687307i	−0.939096	−	0.343654i	$-0.888335\pi$
$83$		−	519.718i		−	0.687307i	0.939096	−	0.343654i	$-0.111665\pi$
$84$	214.157	+	123.643i	0.278171	+	0.160602i
$85$	317.143	+	183.103i	0.404694	+	0.233650i
$86$			136.067i			0.170610i
$87$	−68.4503	+	118.559i	−0.0843522	+	0.146102i
$88$	119.240	+	206.530i	0.144444	+	0.250184i
$89$	591.687	−	341.611i	0.704705	−	0.406862i	−0.104393	−	0.994536i	$-0.533290\pi$
$89$	591.687	−	341.611i	0.704705	−	0.406862i	0.809097	+	0.587675i	$0.199956\pi$
$90$	1244.03			1.45703
$91$		0			0
$92$	−325.019			−0.368321
$93$	1444.44	−	833.950i	1.61056	−	0.929856i
$94$	76.5442	+	132.578i	0.0839887	+	0.145473i
$95$	−360.042	+	623.612i	−0.388837	+	0.673486i
$96$			1255.30i			1.33457i
$97$	−300.765	−	173.647i	−0.314826	−	0.181765i	0.334258	−	0.942482i	$-0.391514\pi$
$97$	−300.765	−	173.647i	−0.314826	−	0.181765i	−0.649084	+	0.760717i	$0.724848\pi$
$98$	527.128	+	304.337i	0.543346	+	0.313701i
$99$		−	659.886i		−	0.669909i
$100$	−87.5110	+	151.573i	−0.0875110	+	0.151573i
$101$	277.397	+	480.466i	0.273288	+	0.473348i	0.969702	−	0.244292i	$-0.0785556\pi$
$101$	277.397	+	480.466i	0.273288	+	0.473348i	−0.696414	+	0.717640i	$0.745222\pi$
$102$	−839.338	+	484.592i	−0.814773	+	0.470409i
$103$	−1137.13			−1.08781			−0.543905	−	0.839147i	$-0.683055\pi$
$103$	−1137.13			−1.08781			−0.543905	+	0.839147i	$0.683055\pi$
$104$		0			0
$105$	668.445			0.621272
$106$	−634.226	+	366.171i	−0.581146	+	0.335525i
$107$	778.069	+	1347.66i	0.702980	+	1.21760i	0.967416	+	0.253193i	$0.0814808\pi$
$107$	778.069	+	1347.66i	0.702980	+	1.21760i	−0.264436	+	0.964403i	$0.585186\pi$
$108$	607.293	−	1051.86i	0.541082	−	0.937181i
$109$			71.6448i			0.0629572i	0.999504	+	0.0314786i	$0.0100216\pi$
$109$			71.6448i			0.0629572i	−0.999504	+	0.0314786i	$0.989978\pi$
$110$	153.584	+	88.6719i	0.133124	+	0.0768594i
$111$	−3494.85	−	2017.75i	−2.98843	−	1.72537i
$112$		−	254.774i		−	0.214945i
$113$	490.436	−	849.460i	0.408286	−	0.707173i	−0.586411	−	0.810013i	$-0.699460\pi$
$113$	490.436	−	849.460i	0.408286	−	0.707173i	0.994698	+	0.102841i	$0.0327931\pi$
$114$	−952.873	−	1650.42i	−0.782849	−	1.35593i
$115$	−760.859	+	439.282i	−0.616961	+	0.356203i
$116$	−42.6355			−0.0341259
$117$		0			0
$118$	327.836			0.255760
$119$	−322.866	+	186.407i	−0.248715	+	0.143596i
$120$	983.602	+	1703.65i	0.748252	+	1.29601i
$121$	−618.465	+	1071.21i	−0.464662	+	0.804818i
$122$			217.916i			0.161714i
$123$	−2180.57	−	1258.95i	−1.59850	−	0.922893i
$124$	449.849	+	259.720i	0.325787	+	0.188093i
$125$			1498.96i			1.07257i
$126$	−633.241	+	1096.81i	−0.447727	+	0.775486i
$127$	−1088.65	−	1885.60i	−0.760649	−	1.31748i	−0.942517	−	0.334159i	$-0.891548\pi$
$127$	−1088.65	−	1885.60i	−0.760649	−	1.31748i	0.181868	−	0.983323i	$-0.441786\pi$
$128$	132.133	−	76.2873i	0.0912426	−	0.0526790i
$129$	595.369			0.406351
$130$		0			0
$131$	−1919.81			−1.28041			−0.640207	−	0.768202i	$-0.721152\pi$
$131$	−1919.81			−1.28041			−0.640207	+	0.768202i	$0.721152\pi$
$132$	248.607	−	143.534i	0.163928	−	0.0946438i
$133$	−366.539	−	634.865i	−0.238970	−	0.413908i
$134$	754.839	−	1307.42i	0.486628	−	0.842865i
$135$		−	3283.17i		−	2.09311i
$136$	−950.180	−	548.587i	−0.599098	−	0.345889i
$137$	644.334	+	372.006i	0.401819	+	0.231990i	0.687268	−	0.726404i	$-0.258810\pi$
$137$	644.334	+	372.006i	0.401819	+	0.231990i	−0.285450	+	0.958394i	$0.592143\pi$
$138$		−	2325.17i		−	1.43429i
$139$	−1410.00	+	2442.19i	−0.860392	+	1.49024i	0.0111596	+	0.999938i	$0.496448\pi$
$139$	−1410.00	+	2442.19i	−0.860392	+	1.49024i	−0.871551	+	0.490304i	$0.836886\pi$
$140$	104.088	+	180.286i	0.0628362	+	0.108836i
$141$	580.104	−	334.923i	0.346479	−	0.200040i
$142$	−1752.91			−1.03592
$143$		0			0
$144$	−2074.69			−1.20063
$145$	−99.8084	+	57.6244i	−0.0571630	+	0.0330031i
$146$	−1111.40	−	1925.01i	−0.630003	−	1.09120i
$147$	1331.64	−	2306.47i	0.747157	−	1.29411i
$148$		−	1256.79i		−	0.698025i
$149$	2506.80	+	1447.30i	1.37829	+	0.795755i	0.991953	−	0.126604i	$-0.0404077\pi$
$149$	2506.80	+	1447.30i	1.37829	+	0.795755i	0.386335	+	0.922359i	$0.373741\pi$
$150$	−1084.35	−	626.050i	−0.590246	−	0.340779i
$151$			494.004i			0.266235i	0.991100	+	0.133118i	$0.0424988\pi$
$151$			494.004i			0.266235i	−0.991100	+	0.133118i	$0.957501\pi$
$152$	1078.71	−	1868.38i	0.575624	−	0.997010i
$153$	1517.96	+	2629.19i	0.802091	+	1.38926i
$154$	−156.356	+	90.2720i	−0.0818149	+	0.0472359i
$155$	1404.11			0.727618
$156$		0			0
$157$	50.7450			0.0257955			0.0128977	−	0.999917i	$-0.495894\pi$
$157$	50.7450			0.0257955			0.0128977	+	0.999917i	$0.495894\pi$
$158$	−740.727	+	427.659i	−0.372969	+	0.215334i
$159$	1602.20	+	2775.09i	0.799135	+	1.38414i
$160$	−528.383	+	915.185i	−0.261077	+	0.452199i
$161$		−	894.419i		−	0.437826i
$162$	3980.53	+	2298.16i	1.93049	+	1.11457i
$163$	651.079	+	375.900i	0.312861	+	0.180631i	0.648206	−	0.761465i	$-0.275519\pi$
$163$	651.079	+	375.900i	0.312861	+	0.180631i	−0.335345	+	0.942095i	$0.608853\pi$
$164$		−	784.161i		−	0.373370i
$165$	387.988	−	672.015i	0.183060	−	0.317069i
$166$	578.963	+	1002.79i	0.270700	+	0.468867i
$167$	2575.84	−	1487.16i	1.19356	−	0.689102i	0.234448	−	0.972129i	$-0.424672\pi$
$167$	2575.84	−	1487.16i	1.19356	−	0.689102i	0.959112	+	0.283027i	$0.0913384\pi$
$168$	−2002.70			−0.919714
$169$		0			0
$170$	−815.901			−0.368099
$171$	−5169.88	+	2984.83i	−2.31199	+	1.33483i
$172$	92.7090	+	160.577i	0.0410988	+	0.0711852i
$173$	816.869	−	1414.86i	0.358991	−	0.621790i	−0.628802	−	0.777566i	$-0.716454\pi$
$173$	816.869	−	1414.86i	0.358991	−	0.621790i	0.987792	+	0.155775i	$0.0497876\pi$
$174$		−	305.013i		−	0.132891i
$175$	−417.114	−	240.821i	−0.180177	−	0.104025i
$176$	−256.134	−	147.879i	−0.109698	−	0.0633341i
$177$		−	1434.46i		−	0.609156i
$178$	−761.105	+	1318.27i	−0.320490	+	0.555105i
$179$	1696.32	+	2938.12i	0.708320	+	1.22685i	0.965480	+	0.260477i	$0.0838798\pi$
$179$	1696.32	+	2938.12i	0.708320	+	1.22685i	−0.257160	+	0.966369i	$0.582787\pi$
$180$	1468.12	−	847.620i	0.607929	−	0.350988i
$181$	3801.07			1.56095			0.780473	−	0.625190i	$-0.214979\pi$
$181$	3801.07			1.56095			0.780473	+	0.625190i	$0.214979\pi$
$182$		0			0
$183$	953.501			0.385163
$184$	2279.58	−	1316.12i	0.913331	−	0.527312i
$185$	−1698.63	−	2942.11i	−0.675058	−	1.16924i
$186$	−1858.03	+	3218.20i	−0.732459	+	1.26866i
$187$			432.787i			0.169243i
$188$	180.664	+	104.306i	0.0700866	+	0.0404645i
$189$	2894.62	+	1671.21i	1.11403	+	0.643188i
$190$		−	1604.34i		−	0.612584i
$191$	−632.755	+	1095.96i	−0.239710	+	0.415189i	−0.960631	−	0.277828i	$-0.910386\pi$
$191$	−632.755	+	1095.96i	−0.239710	+	0.415189i	0.720921	+	0.693017i	$0.243719\pi$
$192$	−2587.49	−	4481.66i	−0.972583	−	1.68456i
$193$	−1915.92	+	1106.16i	−0.714565	+	0.412555i	−0.812749	−	0.582614i	$-0.802030\pi$
$193$	−1915.92	+	1106.16i	−0.714565	+	0.412555i	0.0981838	+	0.995168i	$0.468697\pi$
$194$	773.767			0.286357
$195$		0			0
$196$	829.438			0.302273
$197$	3773.49	−	2178.63i	1.36472	−	0.787923i	0.374474	−	0.927238i	$-0.377823\pi$
$197$	3773.49	−	2178.63i	1.36472	−	0.787923i	0.990248	+	0.139315i	$0.0444901\pi$
$198$	735.109	+	1273.25i	0.263848	+	0.456998i
$199$	545.316	−	944.516i	0.194254	−	0.336457i	−0.752402	−	0.658704i	$-0.771105\pi$
$199$	545.316	−	944.516i	0.194254	−	0.336457i	0.946656	+	0.322247i	$0.104438\pi$
$200$		−	1417.45i		−	0.501145i
$201$	−5720.68	−	3302.84i	−2.00749	−	1.15903i
$202$	−1070.47	−	618.038i	−0.372862	−	0.215272i
$203$		−	117.329i		−	0.0405658i
$204$	−660.351	+	1143.76i	−0.226636	+	0.392546i
$205$	−1059.84	−	1835.70i	−0.361085	−	0.625418i
$206$	2194.08	−	1266.75i	0.742081	−	0.428441i
$207$	−7283.49			−2.44559
$208$		0			0
$209$	−851.007			−0.281652
$210$	−1289.76	+	744.644i	−0.423819	+	0.244692i
$211$	363.724	+	629.989i	0.118672	+	0.205546i	0.919242	−	0.393694i	$-0.128803\pi$
$211$	363.724	+	629.989i	0.118672	+	0.205546i	−0.800570	+	0.599240i	$0.795470\pi$
$212$	−498.979	+	864.257i	−0.161651	+	0.279988i
$213$			7669.93i			2.46730i
$214$	−3002.56	−	1733.53i	−0.959116	−	0.553746i
$215$	434.058	+	250.603i	0.137686	+	0.0794931i
$216$			9836.58i			3.09859i
$217$	−714.724	+	1237.94i	−0.223588	+	0.387266i
$218$	−79.8119	−	138.238i	−0.0247961	−	0.0429481i
$219$	−8422.97	+	4863.01i	−2.59896	+	1.50051i
$220$	241.665			0.0740595
$221$		0			0
$222$	8991.05			2.71820
$223$	879.405	−	507.725i	0.264078	−	0.152465i	−0.362116	−	0.932133i	$-0.617945\pi$
$223$	879.405	−	507.725i	0.264078	−	0.152465i	0.626193	+	0.779668i	$0.284612\pi$
$224$	−537.917	−	931.700i	−0.160451	−	0.277910i
$225$	−1961.07	+	3396.68i	−0.581058	+	1.00642i
$226$			2185.37i			0.643225i
$227$	4583.51	+	2646.29i	1.34017	+	0.773747i	0.986832	−	0.161748i	$-0.0517133\pi$
$227$	4583.51	+	2646.29i	1.34017	+	0.773747i	0.353338	+	0.935496i	$0.385047\pi$
$228$	−2249.03	−	1298.48i	−0.653269	−	0.377165i
$229$		−	3010.03i		−	0.868597i	−0.900769	−	0.434298i	$-0.856996\pi$
$229$		−	3010.03i		−	0.868597i	0.900769	−	0.434298i	$-0.143004\pi$
$230$	978.716	−	1695.19i	0.280585	−	0.485988i
$231$	394.989	+	684.142i	0.112504	+	0.194862i
$232$	299.032	−	172.646i	0.0846225	−	0.0488568i
$233$	2373.96			0.667482			0.333741	−	0.942665i	$-0.391689\pi$
$233$	2373.96			0.667482			0.333741	+	0.942665i	$0.391689\pi$
$234$		0			0
$235$	563.905			0.156532
$236$	386.888	−	223.370i	0.106713	−	0.0616108i
$237$	1871.24	+	3241.09i	0.512870	+	0.888318i
$238$	415.312	−	719.342i	0.113112	−	0.195916i
$239$			783.439i			0.212035i	0.994364	+	0.106018i	$0.0338100\pi$
$239$			783.439i			0.212035i	−0.994364	+	0.106018i	$0.966190\pi$
$240$	−2112.82	−	1219.84i	−0.568259	−	0.328085i
$241$	−3046.16	−	1758.70i	−0.814192	−	0.470074i	0.0342172	−	0.999414i	$-0.489106\pi$
$241$	−3046.16	−	1758.70i	−0.814192	−	0.470074i	−0.848410	+	0.529340i	$0.822440\pi$
$242$		−	2755.86i		−	0.732040i
$243$	4655.01	−	8062.71i	1.22888	−	2.12849i
$244$	148.476	+	257.169i	0.0389558	+	0.0674735i
$245$	1941.69	−	1121.04i	0.506327	−	0.292328i
$246$	5609.86			1.45395
$247$		0			0
$248$	−4206.80			−1.07715
$249$	4387.77	−	2533.28i	1.11672	−	0.644740i
$250$	−1669.83	−	2892.24i	−0.422438	−	0.731685i
$251$	708.480	−	1227.12i	0.178163	−	0.308587i	−0.763088	−	0.646294i	$-0.776318\pi$
$251$	708.480	−	1227.12i	0.178163	−	0.308587i	0.941251	+	0.337707i	$0.109651\pi$
$252$			1725.83i			0.431417i
$253$	−899.195	−	519.150i	−0.223446	−	0.129007i
$254$	4201.10	+	2425.51i	1.03780	+	0.599173i
$255$			3570.02i			0.876718i
$256$	1953.39	−	3383.37i	0.476902	−	0.826018i
$257$	−741.317	−	1284.00i	−0.179930	−	0.311648i	0.761926	−	0.647664i	$-0.224254\pi$
$257$	−741.317	−	1284.00i	−0.179930	−	0.311648i	−0.941856	+	0.336015i	$0.890921\pi$
$258$	−1148.76	+	663.237i	−0.277204	+	0.160044i
$259$	3458.56			0.829748
$260$		0			0
$261$	−955.438			−0.226591
$262$	3704.26	−	2138.65i	0.873473	−	0.504300i
$263$	−3614.82	−	6261.05i	−0.847526	−	1.46796i	−0.883409	−	0.468603i	$-0.844758\pi$
$263$	−3614.82	−	6261.05i	−0.847526	−	1.46796i	0.0358825	−	0.999356i	$-0.488576\pi$
$264$	−1162.44	+	2013.40i	−0.270996	+	0.469379i
$265$			2697.60i			0.625329i
$266$	1414.47	+	816.645i	0.326041	+	0.188240i
$267$	5768.17	+	3330.25i	1.32212	+	0.763326i
$268$		−	2057.23i		−	0.468901i
$269$	247.452	−	428.599i	0.0560870	−	0.0971456i	−0.836619	−	0.547786i	$-0.815471\pi$
$269$	247.452	−	428.599i	0.0560870	−	0.0971456i	0.892706	+	0.450640i	$0.148804\pi$
$270$	3657.43	+	6334.86i	0.824387	+	1.42788i
$271$	3642.14	−	2102.79i	0.816399	−	0.471348i	−0.0327741	−	0.999463i	$-0.510434\pi$
$271$	3642.14	−	2102.79i	0.816399	−	0.471348i	0.849173	+	0.528115i	$0.177101\pi$
$272$	1360.69			0.303323
$273$		0			0
$274$	−1657.65			−0.365483
$275$	−484.214	+	279.561i	−0.106179	+	0.0613025i
$276$	−1584.25	−	2744.00i	−0.345510	−	0.598441i
$277$	2104.27	−	3644.71i	0.456439	−	0.790575i	−0.542331	−	0.840165i	$-0.682458\pi$
$277$	2104.27	−	3644.71i	0.456439	−	0.790575i	0.998770	+	0.0495898i	$0.0157914\pi$
$278$		−	6282.92i		−	1.35548i
$279$	10080.9	+	5820.19i	2.16317	+	1.24891i
$280$	−1460.09	−	842.981i	−0.311632	−	0.179921i
$281$			4740.83i			1.00646i	0.864153	+	0.503228i	$0.167855\pi$
$281$			4740.83i			1.00646i	−0.864153	+	0.503228i	$0.832145\pi$
$282$	−746.205	+	1292.46i	−0.157574	+	0.272926i
$283$	−1871.41	−	3241.38i	−0.393088	−	0.680848i	0.599767	−	0.800175i	$-0.295260\pi$
$283$	−1871.41	−	3241.38i	−0.393088	−	0.680848i	−0.992855	+	0.119326i	$0.961927\pi$
$284$	−2068.66	+	1194.34i	−0.432226	+	0.249546i
$285$	−7019.87			−1.45902
$286$		0			0
$287$	2157.93			0.443828
$288$	−7587.09	+	4380.41i	−1.55234	+	0.896243i
$289$	1460.94	+	2530.43i	0.297363	+	0.515047i
$290$	128.387	−	222.372i	0.0259970	−	0.0450280i
$291$		−	3385.66i		−	0.682030i
$292$	−2623.20	−	1514.51i	−0.525723	−	0.303526i
$293$	4550.94	+	2627.49i	0.907402	+	0.523889i	0.879594	−	0.475725i	$-0.157814\pi$
$293$	4550.94	+	2627.49i	0.907402	+	0.523889i	0.0278075	+	0.999613i	$0.491147\pi$
$294$			5933.77i			1.17709i
$295$	603.795	−	1045.80i	0.119167	−	0.206404i
$296$	5089.20	+	8814.75i	0.999337	+	1.73090i
$297$	3360.27	−	1940.05i	0.656507	−	0.379034i
$298$	−6449.14			−1.25365
$299$		0			0
$300$	−1706.23			−0.328364
$301$	−441.891	+	255.126i	−0.0846185	+	0.0488545i
$302$	−550.318	−	953.179i	−0.104858	−	0.181620i
$303$	−2704.25	+	4683.91i	−0.512724	+	0.888064i
$304$			2675.58i			0.504786i
$305$	695.157	+	401.349i	0.130507	+	0.0753482i
$306$	−5857.79	−	3382.00i	−1.09434	−	0.631817i
$307$			252.464i			0.0469344i	0.999725	+	0.0234672i	$0.00747053\pi$
$307$			252.464i			0.0469344i	−0.999725	+	0.0234672i	$0.992529\pi$
$308$	−123.013	+	213.065i	−0.0227576	+	0.0394172i
$309$	−5542.74	−	9600.30i	−1.02044	−	1.76745i
$310$	−2709.22	+	1564.17i	−0.496366	+	0.286577i
$311$	−2561.20			−0.466986			−0.233493	−	0.972359i	$-0.575016\pi$
$311$	−2561.20			−0.466986			−0.233493	+	0.972359i	$0.575016\pi$
$312$		0			0
$313$	−695.893			−0.125668			−0.0628342	−	0.998024i	$-0.520014\pi$
$313$	−695.893			−0.125668			−0.0628342	+	0.998024i	$0.520014\pi$
$314$	−97.9122	+	56.5296i	−0.0175971	+	0.0101597i
$315$	2332.56	+	4040.12i	0.417222	+	0.722650i
$316$	−582.769	+	1009.39i	−0.103745	+	0.179691i
$317$		−	5747.37i		−	1.01831i	−0.860675	−	0.509155i	$-0.829958\pi$
$317$		−	5747.37i		−	1.01831i	0.860675	−	0.509155i	$-0.170042\pi$
$318$	−6182.86	−	3569.68i	−1.09031	−	0.629489i
$319$	−117.955	−	68.1014i	−0.0207029	−	0.0119528i
$320$		−	4356.52i		−	0.761053i
$321$	−7585.14	+	13137.9i	−1.31888	+	2.28437i
$322$	996.377	+	1725.78i	0.172441	+	0.298676i
$323$	3390.67	−	1957.60i	0.584092	−	0.337226i
$324$	6263.39			1.07397
$325$		0			0
$326$	−1675.00			−0.284570
$327$	−604.869	+	349.221i	−0.102291	+	0.0590580i
$328$	3175.34	+	5499.86i	0.534540	+	0.925850i
$329$	−287.041	+	497.169i	−0.0481005	+	0.0833125i
$330$			1728.87i			0.288397i
$331$	−3676.07	−	2122.38i	−0.610438	−	0.352437i	0.162699	−	0.986676i	$-0.447980\pi$
$331$	−3676.07	−	2122.38i	−0.610438	−	0.352437i	−0.773137	+	0.634239i	$0.781314\pi$
$332$	1366.50	+	788.950i	0.225893	+	0.130419i
$333$		−	28164.0i		−	4.63477i
$334$	−3313.38	+	5738.94i	−0.542815	+	0.940182i
$335$	−2780.47	−	4815.92i	−0.453473	−	0.785438i
$336$	2150.95	−	1241.85i	0.349238	−	0.201633i
$337$	7122.49			1.15130			0.575648	−	0.817698i	$-0.304750\pi$
$337$	7122.49			1.15130			0.575648	+	0.817698i	$0.304750\pi$
$338$		0			0
$339$	9562.20			1.53200
$340$	−962.868	+	555.912i	−0.153585	+	0.0886723i
$341$	829.699	+	1437.08i	0.131762	+	0.228218i
$342$	6650.16	−	11518.4i	1.05146	−	1.82118i
$343$			5148.28i			0.810440i
$344$	−1300.46	−	750.823i	−0.203827	−	0.117679i
$345$	−7417.37	−	4282.42i	−1.15750	−	0.668283i
$346$			3639.95i			0.565563i
$347$	1683.95	−	2916.69i	0.260517	−	0.451228i	−0.705863	−	0.708349i	$-0.749440\pi$
$347$	1683.95	−	2916.69i	0.260517	−	0.451228i	0.966379	+	0.257121i	$0.0827738\pi$
$348$	−207.820	−	359.954i	−0.0320124	−	0.0554471i
$349$	5265.18	−	3039.86i	0.807561	−	0.466246i	−0.0385471	−	0.999257i	$-0.512273\pi$
$349$	5265.18	−	3039.86i	0.807561	−	0.466246i	0.846108	+	0.533011i	$0.178940\pi$
$350$	1073.09			0.163884
$351$		0			0
$352$	−1248.90			−0.189110
$353$	−2798.12	+	1615.50i	−0.421895	+	0.243581i	−0.695888	−	0.718151i	$-0.744989\pi$
$353$	−2798.12	+	1615.50i	−0.421895	+	0.243581i	0.273993	+	0.961732i	$0.411656\pi$
$354$	1597.98	+	2767.78i	0.239920	+	0.415554i
$355$	−3228.44	+	5591.82i	−0.482670	+	0.836009i
$356$			2074.31i			0.308815i
$357$	−3147.52	−	1817.22i	−0.466622	−	0.269405i
$358$	−6546.10	−	3779.39i	−0.966402	−	0.557952i
$359$			5345.81i			0.785908i	0.919558	+	0.392954i	$0.128547\pi$
$359$			5345.81i			0.785908i	−0.919558	+	0.392954i	$0.871453\pi$
$360$	−6864.62	+	11889.9i	−1.00499	+	1.74070i
$361$	419.816	+	727.143i	0.0612066	+	0.106013i
$362$	−7334.14	+	4234.37i	−1.06484	+	0.614788i
$363$	−12058.4			−1.74353
$364$		0			0
$365$	−8187.78			−1.17416
$366$	−1839.77	+	1062.19i	−0.262750	+	0.151699i
$367$	6085.66	+	10540.7i	0.865583	+	1.49923i	0.866467	+	0.499234i	$0.166385\pi$
$367$	6085.66	+	10540.7i	0.865583	+	1.49923i	−0.000883749		1.00000i	$0.500281\pi$
$368$	−1632.22	+	2827.08i	−0.231210	+	0.400467i
$369$		−	17572.6i		−	2.47911i
$370$	6554.99	+	3784.53i	0.921021	+	0.531752i
$371$	−2378.35	−	1373.14i	−0.332824	−	0.192156i
$372$			5063.86i			0.705776i
$373$	2231.98	−	3865.90i	0.309832	−	0.536645i	−0.668493	−	0.743718i	$-0.733061\pi$
$373$	2231.98	−	3865.90i	0.309832	−	0.536645i	0.978325	+	0.207073i	$0.0663938\pi$
$374$	−482.122	−	835.060i	−0.0666576	−	0.115454i
$375$	−12655.1	+	7306.44i	−1.74269	+	1.00614i
$376$	−1689.49			−0.231726
$377$		0			0
$378$	−7446.87			−1.01330
$379$	−4649.74	+	2684.53i	−0.630188	+	0.363839i	−0.780825	−	0.624750i	$-0.785201\pi$
$379$	−4649.74	+	2684.53i	−0.630188	+	0.363839i	0.150637	+	0.988589i	$0.451868\pi$
$380$	−1093.11	−	1893.33i	−0.147567	−	0.255594i
$381$	10612.9	−	18382.1i	1.42708	−	2.47177i
$382$		−	2819.54i		−	0.377645i
$383$	168.948	+	97.5419i	0.0225400	+	0.0130135i	0.511228	−	0.859445i	$-0.329191\pi$
$383$	168.948	+	97.5419i	0.0225400	+	0.0130135i	−0.488688	+	0.872459i	$0.662524\pi$
$384$	1288.13	+	743.700i	0.171183	+	0.0988327i
$385$			665.038i			0.0880351i
$386$	2464.51	−	4268.65i	0.324974	−	0.562872i
$387$	2077.56	+	3598.44i	0.272889	+	0.472658i
$388$	913.145	−	527.204i	0.119479	−	0.0689813i
$389$	−9120.52			−1.18876			−0.594381	−	0.804183i	$-0.702603\pi$
$389$	−9120.52			−1.18876			−0.594381	+	0.804183i	$0.702603\pi$
$390$		0			0
$391$	4776.89			0.617845
$392$	−5817.42	+	3358.69i	−0.749551	+	0.432754i
$393$	−9357.79	−	16208.2i	−1.20111	−	2.08039i
$394$	−4853.95	+	8407.30i	−0.620657	+	1.07501i
$395$			3150.59i			0.401325i
$396$	1735.05	+	1001.73i	0.220175	+	0.127118i
$397$	5727.43	+	3306.73i	0.724059	+	0.418036i	0.816245	−	0.577706i	$-0.196052\pi$
$397$	5727.43	+	3306.73i	0.724059	+	0.418036i	−0.0921859	+	0.995742i	$0.529385\pi$
$398$			2429.92i			0.306032i
$399$	3573.27	−	6189.09i	0.448339	−	0.776546i
$400$	878.945	+	1522.38i	0.109868	+	0.190297i
$401$	7438.51	−	4294.63i	0.926338	−	0.534822i	0.0406868	−	0.999172i	$-0.487045\pi$
$401$	7438.51	−	4294.63i	0.926338	−	0.534822i	0.885652	+	0.464350i	$0.153712\pi$
$402$	14717.4			1.82596
$403$		0			0
$404$	−1684.39			−0.207430
$405$	14662.4	−	8465.34i	1.79896	−	1.03863i
$406$	130.703	+	226.385i	0.0159771	+	0.0276731i
$407$	2007.47	−	3477.03i	0.244487	−	0.423465i
$408$		−	10696.0i		−	1.29787i
$409$	6508.70	+	3757.80i	0.786881	+	0.454306i	0.838863	−	0.544342i	$-0.183221\pi$
$409$	6508.70	+	3757.80i	0.786881	+	0.454306i	−0.0519824	+	0.998648i	$0.516554\pi$
$410$	4089.91	+	2361.31i	0.492649	+	0.284431i
$411$			7253.14i			0.870489i
$412$	1726.20	−	2989.86i	0.206417	−	0.357524i
$413$	614.691	+	1064.68i	0.0732372	+	0.126851i
$414$	14053.5	−	8113.77i	1.66833	−	0.963212i
$415$	4265.25			0.504513
$416$		0			0
$417$	−27491.2			−3.22842
$418$	1642.01	−	948.016i	0.192137	−	0.110931i
$419$	2278.67	+	3946.76i	0.265680	+	0.460172i	0.967742	−	0.251945i	$-0.0810701\pi$
$419$	2278.67	+	3946.76i	0.265680	+	0.460172i	−0.702061	+	0.712117i	$0.747737\pi$
$420$	−1014.72	+	1757.55i	−0.117889	+	0.204190i
$421$		−	2225.19i		−	0.257599i	−0.991671	−	0.128800i	$-0.958888\pi$
$421$		−	2225.19i		−	0.257599i	0.991671	−	0.128800i	$-0.0411124\pi$
$422$	−1403.61	−	810.373i	−0.161911	−	0.0934795i
$423$	4048.58	+	2337.45i	0.465363	+	0.268678i
$424$		−	8082.17i		−	0.925719i
$425$	1286.17	−	2227.71i	0.146796	−	0.254259i
$426$	−8544.26	−	14799.1i	−0.971762	−	1.68314i
$427$	−707.701	+	408.592i	−0.0802063	+	0.0463071i
$428$	−4724.54			−0.533574
$429$		0			0
$430$	−1116.68			−0.125235
$431$	−342.970	+	198.014i	−0.0383302	+	0.0221299i	−0.519043	−	0.854748i	$-0.673711\pi$
$431$	−342.970	+	198.014i	−0.0383302	+	0.0221299i	0.480712	+	0.876878i	$0.340378\pi$
$432$	−6099.55	−	10564.7i	−0.679316	−	1.17661i
$433$	2594.03	−	4492.99i	0.287901	−	0.498659i	−0.685408	−	0.728159i	$-0.740376\pi$
$433$	2594.03	−	4492.99i	0.287901	−	0.498659i	0.973308	+	0.229501i	$0.0737093\pi$
$434$		−	3184.79i		−	0.352246i
$435$	−973.000	−	561.762i	−0.107245	−	0.0619182i
$436$	−188.377	−	108.759i	−0.0206918	−	0.0119464i
$437$			9392.99i			1.02821i
$438$	10834.7	−	18766.3i	1.18197	−	2.04723i
$439$	5664.93	+	9811.94i	0.615882	+	1.06674i	0.990229	+	0.139450i	$0.0445336\pi$
$439$	5664.93	+	9811.94i	0.615882	+	1.06674i	−0.374347	+	0.927289i	$0.622133\pi$
$440$	−1694.97	+	978.589i	−0.183646	+	0.106028i
$441$	18587.2			2.00705
$442$		0			0
$443$	15625.2			1.67579			0.837897	−	0.545828i	$-0.183785\pi$
$443$	15625.2			1.67579			0.837897	+	0.545828i	$0.183785\pi$
$444$	10610.6	−	6126.03i	1.13414	−	0.654794i
$445$	2803.55	+	4855.89i	0.298654	+	0.517284i
$446$	−1131.20	+	1959.30i	−0.120099	+	0.208017i
$447$			28218.5i			2.98588i
$448$	3840.94	+	2217.57i	0.405061	+	0.233862i
$449$	−11852.9	−	6843.29i	−1.24582	−	0.719276i	−0.275549	−	0.961287i	$-0.588860\pi$
$449$	−11852.9	−	6843.29i	−1.24582	−	0.719276i	−0.970273	+	0.242011i	$0.922193\pi$
$450$		−	8738.49i		−	0.915414i
$451$	1252.53	−	2169.45i	0.130775	−	0.226509i
$452$	1489.00	+	2579.02i	0.154948	+	0.268378i
$453$	−4170.68	+	2407.94i	−0.432573	+	0.249746i
$454$	−11791.8			−1.21898
$455$		0			0
$456$	21031.9			2.15989
$457$	−10975.2	+	6336.55i	−1.12341	+	0.648602i	−0.942270	−	0.334854i	$-0.891313\pi$
$457$	−10975.2	+	6336.55i	−1.12341	+	0.648602i	−0.181142	+	0.983457i	$0.557980\pi$
$458$	3353.16	+	5807.84i	0.342102	+	0.592539i
$459$	−8925.55	+	15459.5i	−0.907645	+	1.57209i
$460$		−	2667.38i		−	0.270364i
$461$	7928.34	+	4577.43i	0.800996	+	0.462456i	0.843819	−	0.536627i	$-0.180302\pi$
$461$	7928.34	+	4577.43i	0.800996	+	0.462456i	−0.0428230	+	0.999083i	$0.513635\pi$
$462$	−1524.26	−	880.032i	−0.153496	−	0.0886207i
$463$			6910.59i			0.693655i	0.937929	+	0.346827i	$0.112741\pi$
$463$			6910.59i			0.693655i	−0.937929	+	0.346827i	$0.887259\pi$
$464$	−214.112	+	370.852i	−0.0214222	+	0.0371043i
$465$	6844.11	+	11854.3i	0.682554	+	1.18222i
$466$	−4580.55	+	2644.58i	−0.455343	+	0.262892i
$467$	−2920.19			−0.289359			−0.144679	−	0.989479i	$-0.546215\pi$
$467$	−2920.19			−0.289359			−0.144679	+	0.989479i	$0.546215\pi$
$468$		0			0
$469$	5661.29			0.557386
$470$	−1088.05	+	628.187i	−0.106783	+	0.0616513i
$471$	247.348	+	428.420i	0.0241979	+	0.0419120i
$472$	−1809.01	+	3133.29i	−0.176412	+	0.305554i
$473$			592.334i			0.0575804i
$474$	−7221.10	−	4169.11i	−0.699739	−	0.403995i
$475$	4380.45	+	2529.05i	0.423134	+	0.244296i
$476$		−	1131.89i		−	0.108992i
$477$	−11181.8	+	19367.5i	−1.07334	+	1.85907i
$478$	−872.746	−	1511.64i	−0.0835115	−	0.144646i
$479$	−14799.2	+	8544.31i	−1.41167	+	0.815030i	−0.995546	−	0.0942761i	$-0.969946\pi$
$479$	−14799.2	+	8544.31i	−1.41167	+	0.815030i	−0.416128	+	0.909306i	$0.636613\pi$
$480$	−10302.1			−0.979630
$481$		0			0
$482$	7836.73			0.740567
$483$	7551.22	−	4359.70i	0.711371	−	0.410710i
$484$	−1877.70	−	3252.28i	−0.176343	−	0.305435i
$485$	1425.10	−	2468.34i	0.133423	−	0.231096i
$486$			20742.6i			1.93602i
$487$	−11962.4	−	6906.48i	−1.11307	−	0.642634i	−0.173450	−	0.984843i	$-0.555492\pi$
$487$	−11962.4	−	6906.48i	−1.11307	−	0.642634i	−0.939624	+	0.342209i	$0.888825\pi$
$488$	−2082.73	−	1202.47i	−0.193199	−	0.111543i
$489$			7329.06i			0.677774i
$490$	−2497.65	+	4326.06i	−0.230270	+	0.398840i
$491$	−5924.21	−	10261.0i	−0.544513	−	0.943125i	−0.998637	−	0.0521862i	$-0.983381\pi$
$491$	−5924.21	−	10261.0i	−0.544513	−	0.943125i	0.454124	−	0.890938i	$-0.349952\pi$
$492$	6620.35	−	3822.26i	0.606644	−	0.350246i
$493$	626.625			0.0572450
$494$		0			0
$495$	5415.59			0.491743
$496$	4518.20	−	2608.59i	0.409019	−	0.236147i
$497$	−3286.70	−	5692.73i	−0.296637	−	0.513790i
$498$	−5644.12	+	9775.90i	−0.507870	+	0.879656i
$499$			5224.46i			0.468696i	0.972153	+	0.234348i	$0.0752955\pi$
$499$			5224.46i			0.468696i	−0.972153	+	0.234348i	$0.924705\pi$
$500$	−3941.24	−	2275.48i	−0.352515	−	0.203525i
$501$	25111.0	+	14497.9i	2.23928	+	1.29285i
$502$			3156.97i			0.280682i
$503$	−3942.20	+	6828.08i	−0.349451	+	0.605267i	−0.986152	−	0.165844i	$-0.946965\pi$
$503$	−3942.20	+	6828.08i	−0.349451	+	0.605267i	0.636701	+	0.771111i	$0.280299\pi$
$504$	−6988.50	−	12104.4i	−0.617644	−	1.06979i
$505$	−3943.11	+	2276.56i	−0.347458	+	0.200605i
$506$	2313.32			0.203241
$507$		0			0
$508$	6610.45			0.577345
$509$	3487.10	−	2013.28i	0.303660	−	0.175318i	−0.340426	−	0.940271i	$-0.610571\pi$
$509$	3487.10	−	2013.28i	0.303660	−	0.175318i	0.644086	+	0.764953i	$0.277238\pi$
$510$	−3976.98	−	6888.33i	−0.345301	−	0.598079i
$511$	4167.76	−	7218.78i	0.360804	−	0.624931i
$512$			9924.86i			0.856681i
$513$	−30398.7	−	17550.7i	−2.61624	−	1.51049i
$514$	2860.73	+	1651.65i	0.245489	+	0.141733i
$515$		−	9332.23i		−	0.798499i
$516$	−903.790	+	1565.41i	−0.0771068	+	0.133553i
$517$	333.216	+	577.147i	0.0283459	+	0.0490965i
$518$	−6673.28	+	3852.82i	−0.566037	+	0.326802i
$519$	15926.8			1.34703
$520$		0			0
$521$	6196.12			0.521030			0.260515	−	0.965470i	$-0.416108\pi$
$521$	6196.12			0.521030			0.260515	+	0.965470i	$0.416108\pi$
$522$	1843.51	−	1064.35i	0.154575	−	0.0892441i
$523$	−3949.69	−	6841.07i	−0.330226	−	0.571968i	0.652330	−	0.757935i	$-0.273792\pi$
$523$	−3949.69	−	6841.07i	−0.330226	−	0.571968i	−0.982556	+	0.185967i	$0.940458\pi$
$524$	2914.33	−	5047.77i	0.242964	−	0.420826i
$525$		−	4695.37i		−	0.390329i
$526$	13949.6	+	8053.78i	1.15633	+	0.667607i
$527$	−6611.55	−	3817.18i	−0.546496	−	0.315520i
$528$		−	2883.25i		−	0.237646i
$529$	353.376	−	612.065i	0.0290438	−	0.0503053i
$530$	−3005.11	−	5205.00i	−0.246290	−	0.426586i
$531$	8669.95	−	5005.60i	0.708557	−	0.409085i
$532$	2225.68			0.181382
$533$		0			0
$534$	−14839.5			−1.20256
$535$	−11060.0	+	6385.50i	−0.893768	+	0.516017i
$536$	8330.46	+	14428.8i	0.671308	+	1.16274i
$537$	−16536.9	+	28642.8i	−1.32890	+	2.30173i
$538$			1102.64i			0.0883609i
$539$	2294.72	+	1324.86i	0.183378	+	0.105873i
$540$	8632.49	+	4983.97i	0.687932	+	0.397178i
$541$		−	6146.22i		−	0.488441i	−0.969720	−	0.244220i	$-0.921468\pi$
$541$		−	6146.22i		−	0.488441i	0.969720	−	0.244220i	$-0.0785320\pi$
$542$	−4684.99	+	8114.64i	−0.371287	+	0.643088i
$543$	18527.7	+	32090.9i	1.46427	+	2.53619i
$544$	4976.00	−	2872.89i	0.392177	−	0.226423i
$545$	−587.979			−0.0462133
$546$		0			0
$547$	5555.49			0.434252			0.217126	−	0.976144i	$-0.430332\pi$
$547$	5555.49			0.434252			0.217126	+	0.976144i	$0.430332\pi$
$548$	−1956.24	+	1129.44i	−0.152494	+	0.0880422i
$549$	3327.27	+	5763.00i	0.258660	+	0.448013i
$550$	622.859	−	1078.82i	0.0482887	−	0.0836385i
$551$			1232.16i			0.0952663i
$552$	22222.9	+	12830.4i	1.71353	+	0.989307i
$553$	−2777.72	−	1603.72i	−0.213600	−	0.123322i
$554$			9376.59i			0.719085i
$555$	16559.4	−	28681.7i	1.26650	−	2.19364i
$556$	−4280.85	−	7414.65i	−0.326526	−	0.565560i
$557$	6565.08	−	3790.35i	0.499410	−	0.288335i	−0.229060	−	0.973412i	$-0.573565\pi$
$557$	6565.08	−	3790.35i	0.499410	−	0.288335i	0.728470	+	0.685078i	$0.240232\pi$
$558$	−25934.6			−1.96756
$559$		0			0
$560$	2090.89			0.157779
$561$	−3653.85	+	2109.55i	−0.274983	+	0.158762i
$562$	−5281.26	−	9147.41i	−0.396399	−	0.686584i
$563$	−6797.30	+	11773.3i	−0.508831	+	0.881322i	0.491116	+	0.871094i	$0.336589\pi$
$563$	−6797.30	+	11773.3i	−0.508831	+	0.881322i	−0.999948	+	0.0102278i	$0.996744\pi$
$564$			2033.70i			0.151834i
$565$	6971.40	+	4024.94i	0.519095	+	0.299700i
$566$	7221.76	+	4169.48i	0.536313	+	0.309640i
$567$			17236.2i			1.27664i
$568$	9672.60	−	16753.4i	0.714530	−	1.23760i
$569$	2825.07	+	4893.16i	0.208143	+	0.360513i	0.951129	−	0.308793i	$-0.0999249\pi$
$569$	2825.07	+	4893.16i	0.208143	+	0.360513i	−0.742987	+	0.669306i	$0.766592\pi$
$570$	13544.8	−	7820.09i	0.995314	−	0.574645i
$571$	−6297.53			−0.461547			−0.230773	−	0.973008i	$-0.574126\pi$
$571$	−6297.53			−0.461547			−0.230773	+	0.973008i	$0.574126\pi$
$572$		0			0
$573$	−12337.0			−0.899454
$574$	−4163.71	+	2403.92i	−0.302770	+	0.174804i
$575$	3085.66	+	5344.52i	0.223793	+	0.387620i
$576$	18058.3	−	31277.8i	1.30630	−	2.26257i
$577$		−	17838.9i		−	1.28707i	−0.765415	−	0.643537i	$-0.777466\pi$
$577$		−	17838.9i		−	1.28707i	0.765415	−	0.643537i	$-0.222534\pi$
$578$	−5637.76	−	3254.96i	−0.405709	−	0.234236i
$579$	−18677.7	−	10783.6i	−1.34062	−	0.774007i
$580$		−	349.903i		−	0.0250499i
$581$	−2171.11	+	3760.47i	−0.155031	+	0.268521i
$582$	3771.60	+	6532.60i	0.268622	+	0.465266i
$583$	−2760.94	+	1594.03i	−0.196135	+	0.113238i
$584$	24531.1			1.73819
$585$		0			0
$586$	−11708.0			−0.825348
$587$	394.120	−	227.545i	0.0277122	−	0.0159997i	−0.486080	−	0.873914i	$-0.661574\pi$
$587$	394.120	−	227.545i	0.0277122	−	0.0159997i	0.513792	+	0.857915i	$0.328240\pi$
$588$	4042.96	+	7002.61i	0.283553	+	0.491127i
$589$	7505.87	−	13000.6i	0.525083	−	0.909471i
$590$			2690.50i			0.187739i
$591$	36786.5	+	21238.7i	2.56040	+	1.47825i
$592$	−10931.8	−	6311.50i	−0.758946	−	0.438178i
$593$		−	16240.6i		−	1.12466i	−0.826913	−	0.562330i	$-0.809905\pi$
$593$		−	16240.6i		−	1.12466i	0.826913	−	0.562330i	$-0.190095\pi$
$594$	−4322.41	+	7486.63i	−0.298570	+	0.517139i
$595$	−1529.81	−	2649.71i	−0.105405	−	0.182568i
$596$	−7610.81	+	4394.10i	−0.523072	+	0.301996i
$597$	10632.2			0.728891
$598$		0			0
$599$	−6704.05			−0.457296			−0.228648	−	0.973509i	$-0.573430\pi$
$599$	−6704.05			−0.457296			−0.228648	+	0.973509i	$0.573430\pi$
$600$	11967.0	−	6909.13i	0.814249	−	0.470107i
$601$	−13206.6	−	22874.5i	−0.896354	−	1.55253i	−0.832120	−	0.554596i	$-0.812873\pi$
$601$	−13206.6	−	22874.5i	−0.896354	−	1.55253i	−0.0642341	−	0.997935i	$-0.520460\pi$
$602$	568.417	−	984.527i	0.0384833	−	0.0666550i
$603$		−	46101.4i		−	3.11343i
$604$	−1298.89	−	749.916i	−0.0875019	−	0.0505193i
$605$	−8791.29	−	5075.65i	−0.590771	−	0.341082i
$606$		−	12050.1i		−	0.807758i
$607$	1663.19	−	2880.72i	0.111214	−	0.192628i	−0.805046	−	0.593212i	$-0.797860\pi$
$607$	1663.19	−	2880.72i	0.111214	−	0.192628i	0.916260	+	0.400584i	$0.131193\pi$
$608$	5649.09	+	9784.51i	0.376811	+	0.652655i
$609$	990.558	−	571.899i	0.0659104	−	0.0380534i
$610$	−1788.40			−0.118705
$611$		0			0
$612$	−9217.27			−0.608801
$613$	22740.7	−	13129.3i	1.49835	−	0.865072i	0.498351	−	0.866975i	$-0.333939\pi$
$613$	22740.7	−	13129.3i	1.49835	−	0.865072i	0.999998	+	0.00190303i	$0.000605753\pi$
$614$	−281.243	−	487.127i	−0.0184854	−	0.0320177i
$615$	10332.0	−	17895.6i	0.677443	−	1.17337i
$616$		−	1992.50i		−	0.130325i
$617$	−23688.3	−	13676.4i	−1.54563	−	0.892370i	−0.998467	−	0.0553441i	$-0.982374\pi$
$617$	−23688.3	−	13676.4i	−1.54563	−	0.892370i	−0.547163	−	0.837026i	$-0.684292\pi$
$618$	21389.4	+	12349.1i	1.39224	+	0.803812i
$619$			13056.5i			0.847795i	0.905710	+	0.423897i	$0.139338\pi$
$619$			13056.5i			0.847795i	−0.905710	+	0.423897i	$0.860662\pi$
$620$	−2131.49	+	3691.85i	−0.138069	+	0.239142i
$621$	−21413.3	−	37089.0i	−1.38371	−	2.39666i
$622$	4941.83	−	2853.17i	0.318568	−	0.183925i
$623$	−5708.28			−0.367091
$624$		0			0
$625$	−5095.82			−0.326132
$626$	1342.72	−	775.220i	0.0857283	−	0.0494953i
$627$	−4148.09	−	7184.71i	−0.264209	−	0.457623i
$628$	−77.0326	+	133.424i	−0.00489480	+	0.00847805i
$629$			18471.4i			1.17091i
$630$	−9001.33	−	5196.92i	−0.569241	−	0.328651i
$631$	5674.99	+	3276.46i	0.358031	+	0.206709i	0.668217	−	0.743967i	$-0.267058\pi$
$631$	5674.99	+	3276.46i	0.358031	+	0.206709i	−0.310186	+	0.950676i	$0.600391\pi$
$632$		−	9439.35i		−	0.594109i
$633$	−3545.83	+	6141.55i	−0.222645	+	0.385632i
$634$	6402.54	+	11089.5i	0.401068	+	0.694671i
$635$	15474.9	−	8934.42i	0.967089	−	0.558349i
$636$	−9728.76			−0.606557
$637$		0			0
$638$	303.458			0.0188308
$639$	−46357.4	+	26764.5i	−2.86991	+	1.65694i
$640$	626.079	+	1084.40i	0.0386686	+	0.0669760i
$641$	−2882.38	+	4992.44i	−0.177609	+	0.307628i	−0.941061	−	0.338237i	$-0.890170\pi$
$641$	−2882.38	+	4992.44i	−0.177609	+	0.307628i	0.763452	+	0.645864i	$0.223503\pi$
$642$		−	33799.2i		−	2.07780i
$643$	−10634.4	−	6139.75i	−0.652221	−	0.376560i	0.137086	−	0.990559i	$-0.456226\pi$
$643$	−10634.4	−	6139.75i	−0.652221	−	0.376560i	−0.789307	+	0.613999i	$0.789560\pi$
$644$	2351.71	+	1357.76i	0.143898	+	0.0830795i
$645$			4886.10i			0.298279i
$646$	−4361.52	+	7554.37i	−0.265637	+	0.460097i
$647$	−14512.1	−	25135.8i	−0.881810	−	1.52734i	−0.849327	−	0.527867i	$-0.822992\pi$
$647$	−14512.1	−	25135.8i	−0.881810	−	1.52734i	−0.0324826	−	0.999472i	$-0.510341\pi$
$648$	−43929.4	+	25362.7i	−2.66313	+	1.53756i
$649$	1427.15			0.0863182
$650$		0			0
$651$	−13935.2			−0.838962
$652$	−1976.72	+	1141.26i	−0.118734	+	0.0685509i
$653$	8583.57	+	14867.2i	0.514396	+	0.890961i	0.999860	+	0.0167042i	$0.00531736\pi$
$653$	8583.57	+	14867.2i	0.514396	+	0.890961i	−0.485464	+	0.874257i	$0.661349\pi$
$654$	778.060	−	1347.64i	0.0465207	−	0.0805763i
$655$		−	15755.6i		−	0.939880i
$656$	−6820.79	−	3937.99i	−0.405956	−	0.234379i
$657$	−58784.5	−	33939.2i	−3.49072	−	2.01537i
$658$		−	1279.05i		−	0.0757787i
$659$	−9156.49	+	15859.5i	−0.541254	+	0.937479i	0.457579	+	0.889169i	$0.348717\pi$
$659$	−9156.49	+	15859.5i	−0.541254	+	0.937479i	−0.998832	+	0.0483096i	$0.984617\pi$
$660$	1177.96	+	2040.28i	0.0694727	+	0.120330i
$661$	−5962.85	+	3442.65i	−0.350874	+	0.202577i	−0.665070	−	0.746781i	$-0.731598\pi$
$661$	−5962.85	+	3442.65i	−0.350874	+	0.202577i	0.314196	+	0.949358i	$0.398265\pi$
$662$	9457.28			0.555238
$663$		0			0
$664$	−12779.0			−0.746867
$665$	5210.24	−	3008.13i	0.303826	−	0.175414i
$666$	31374.6	+	54342.3i	1.82543	+	3.16175i
$667$	−751.669	+	1301.93i	−0.0436353	+	0.0755786i
$668$			9030.25i			0.523040i
$669$	8573.03	+	4949.64i	0.495445	+	0.286045i
$670$	10729.8	+	6194.86i	0.618699	+	0.357206i
$671$			948.641i			0.0545781i
$672$	5243.98	−	9082.84i	0.301028	−	0.521396i
$673$	3119.13	+	5402.50i	0.178653	+	0.309437i	0.941420	−	0.337238i	$-0.109493\pi$
$673$	3119.13	+	5402.50i	0.178653	+	0.309437i	−0.762766	+	0.646674i	$0.776159\pi$
$674$	−13742.8	+	7934.41i	−0.785390	+	0.453445i
$675$	−23062.0			−1.31505
$676$		0			0
$677$	25482.4			1.44663			0.723316	−	0.690517i	$-0.242617\pi$
$677$	25482.4			1.44663			0.723316	+	0.690517i	$0.242617\pi$
$678$	−18450.2	+	10652.2i	−1.04510	+	0.603388i
$679$	1450.81	+	2512.88i	0.0819986	+	0.142026i
$680$	4502.17	−	7797.99i	0.253898	−	0.439764i
$681$			51595.7i			2.90331i
$682$	−3201.80	−	1848.56i	−0.179770	−	0.103790i
$683$	−23752.0	−	13713.2i	−1.33067	−	0.768261i	−0.345266	−	0.938505i	$-0.612211\pi$
$683$	−23752.0	−	13713.2i	−1.33067	−	0.768261i	−0.985402	+	0.170243i	$0.945545\pi$
$684$		−	18124.3i		−	1.01316i
$685$	−3053.00	+	5287.95i	−0.170291	+	0.294952i
$686$	−5735.15	−	9933.57i	−0.319197	−	0.552865i
$687$	25412.5	−	14671.9i	1.41128	−	0.814802i
$688$	1862.31			0.103197
$689$		0			0
$690$	19082.4			1.05283
$691$	12025.9	−	6943.15i	0.662064	−	0.382243i	−0.130999	−	0.991383i	$-0.541818\pi$
$691$	12025.9	−	6943.15i	0.662064	−	0.382243i	0.793063	+	0.609140i	$0.208485\pi$
$692$	2480.07	+	4295.61i	0.136240	+	0.235975i
$693$	−2756.66	+	4774.67i	−0.151106	+	0.261724i
$694$			7503.65i			0.410425i
$695$	−20042.7	−	11571.6i	−1.09390	−	0.631565i
$696$	2915.17	+	1683.07i	0.158763	+	0.0916619i
$697$			11525.0i			0.626314i
$698$	−6772.76	+	11730.8i	−0.367268	+	0.636126i
$699$	11571.5	+	20042.4i	0.626143	+	1.08451i
$700$	1266.39	−	731.150i	0.0683785	−	0.0394784i
$701$	−15744.4			−0.848301			−0.424151	−	0.905592i	$-0.639427\pi$
$701$	−15744.4			−0.848301			−0.424151	+	0.905592i	$0.639427\pi$
$702$		0			0
$703$	−36321.1			−1.94861
$704$	4458.82	−	2574.30i	0.238705	−	0.137816i
$705$	2748.66	+	4760.83i	0.146838	+	0.254331i
$706$	3599.30	−	6234.18i	0.191872	−	0.332332i
$707$		−	4635.28i		−	0.246574i
$708$	3771.65	+	2177.56i	0.200208	+	0.115590i
$709$	24845.5	+	14344.6i	1.31607	+	0.759833i	0.983094	−	0.183102i	$-0.0586140\pi$
$709$	24845.5	+	14344.6i	1.31607	+	0.759833i	0.332976	+	0.942935i	$0.391947\pi$
$710$		−	14385.9i		−	0.760410i
$711$	−13059.5	+	22619.8i	−0.688847	+	1.19312i
$712$	−8399.61	−	14548.5i	−0.442119	−	0.765772i
$713$	15861.8	−	9157.81i	0.833140	−	0.481013i
$714$	8097.48			0.424427
$715$		0			0
$716$	−10300.3			−0.537627
$717$	−6614.26	+	3818.75i	−0.344511	+	0.198903i
$718$	−5955.20	−	10314.7i	−0.309535	−	0.536130i
$719$	−6309.54	+	10928.4i	−0.327269	+	0.566846i	−0.981969	−	0.189043i	$-0.939462\pi$
$719$	−6309.54	+	10928.4i	−0.327269	+	0.566846i	0.654700	+	0.755889i	$0.272795\pi$
$720$		−	17026.7i		−	0.881315i
$721$	8227.79	+	4750.32i	0.424991	+	0.245369i
$722$	−1620.07	−	935.345i	−0.0835078	−	0.0482132i
$723$		−	34290.0i		−	1.76384i
$724$	−5770.15	+	9994.19i	−0.296196	+	0.513027i
$725$	404.772	+	701.086i	0.0207350	+	0.0359140i
$726$	23266.7	−	13433.0i	1.18940	−	0.686702i
$727$	12644.5			0.645061			0.322531	−	0.946559i	$-0.395466\pi$
$727$	12644.5			0.645061			0.322531	+	0.946559i	$0.395466\pi$
$728$		0			0
$729$	35059.5			1.78121
$730$	15798.3	−	9121.13i	0.800986	−	0.462450i
$731$	−1362.57	−	2360.04i	−0.0689418	−	0.119411i
$732$	−1447.45	+	2507.05i	−0.0730863	+	0.126589i
$733$		−	19109.0i		−	0.962903i	−0.876473	−	0.481451i	$-0.840110\pi$
$733$		−	19109.0i		−	0.962903i	0.876473	−	0.481451i	$-0.159890\pi$
$734$	−23484.5	−	13558.8i	−1.18097	−	0.681831i
$735$	18928.9	+	10928.6i	0.949936	+	0.548446i
$736$			13784.7i			0.690370i
$737$	3286.00	−	5691.52i	0.164235	−	0.284464i
$738$	19575.8	+	33906.2i	0.976415	+	1.69120i
$739$	−12205.4	+	7046.78i	−0.607554	+	0.350771i	−0.772007	−	0.635614i	$-0.780747\pi$
$739$	−12205.4	+	7046.78i	−0.607554	+	0.350771i	0.164454	+	0.986385i	$0.447414\pi$
$740$	10314.3			0.512381
$741$		0			0
$742$	6118.67			0.302727
$743$	15231.1	−	8793.70i	0.752054	−	0.434198i	−0.0743817	−	0.997230i	$-0.523698\pi$
$743$	15231.1	−	8793.70i	0.752054	−	0.434198i	0.826436	+	0.563031i	$0.190365\pi$
$744$	−20505.4	−	35516.3i	−1.01043	−	1.75012i
$745$	−11877.8	+	20572.9i	−0.584119	+	1.01172i
$746$			9945.63i			0.488117i
$747$	30622.5	+	17679.9i	1.49989	+	0.865964i
$748$	−1137.93	−	656.985i	−0.0556242	−	0.0321147i
$749$		−	13001.5i		−	0.634263i
$750$	16278.7	−	28195.5i	0.792551	−	1.37274i
$751$	−8293.48	−	14364.7i	−0.402974	−	0.697971i	0.591109	−	0.806591i	$-0.298690\pi$
$751$	−8293.48	−	14364.7i	−0.402974	−	0.697971i	−0.994083	+	0.108620i	$0.965357\pi$
$752$	1814.56	−	1047.64i	0.0879922	−	0.0508023i
$753$	13813.5			0.668514
$754$		0			0
$755$	−4054.22			−0.195428
$756$	−8788.26	+	5073.91i	−0.422786	+	0.244095i
$757$	−16909.7	−	29288.5i	−0.811882	−	1.40622i	−0.911545	−	0.411199i	$-0.865110\pi$
$757$	−16909.7	−	29288.5i	−0.811882	−	1.40622i	0.0996637	−	0.995021i	$-0.468223\pi$
$758$	5981.10	−	10359.6i	0.286601	−	0.496407i
$759$		−	10122.1i		−	0.484068i
$760$	15333.5	+	8852.80i	0.731848	+	0.422533i
$761$	24362.4	+	14065.6i	1.16049	+	0.670011i	0.951422	−	0.307890i	$-0.0996229\pi$
$761$	24362.4	+	14065.6i	1.16049	+	0.670011i	0.209071	+	0.977901i	$0.432956\pi$
$762$			47290.9i			2.24825i
$763$	299.295	−	518.393i	0.0142008	−	0.0245965i
$764$	−1921.09	−	3327.42i	−0.0909719	−	0.157568i
$765$	−21577.3	+	12457.7i	−1.01978	+	0.588769i
$766$	−434.645			−0.0205018
$767$		0			0
$768$	38085.9			1.78946
$769$	−20555.1	+	11867.5i	−0.963897	+	0.556506i	−0.897370	−	0.441279i	$-0.854525\pi$
$769$	−20555.1	+	11867.5i	−0.963897	+	0.556506i	−0.0665267	+	0.997785i	$0.521192\pi$
$770$	−740.849	−	1283.19i	−0.0346732	−	0.0600557i
$771$	7226.86	−	12517.3i	0.337573	−	0.584694i
$772$		−	6716.75i		−	0.313136i
$773$	8258.64	+	4768.13i	0.384272	+	0.221860i	0.679675	−	0.733513i	$-0.262121\pi$
$773$	8258.64	+	4768.13i	0.384272	+	0.221860i	−0.295403	+	0.955373i	$0.595454\pi$
$774$	−8017.27	−	4628.77i	−0.372319	−	0.214958i
$775$		−	9862.92i		−	0.457144i
$776$	−4269.67	+	7395.29i	−0.197516	+	0.342108i
$777$	16858.2	+	29199.3i	0.778359	+	1.34816i
$778$	17598.0	−	10160.2i	0.810949	−	0.468202i
$779$	−22662.1			−1.04230
$780$		0			0
$781$	−7630.84			−0.349619
$782$	−9216.98	+	5321.42i	−0.421481	+	0.243342i
$783$	−2808.97	−	4865.28i	−0.128205	−	0.222057i
$784$	4165.37	−	7214.62i	0.189749	−	0.328655i
$785$			416.457i			0.0189350i
$786$	36111.6	+	20849.0i	1.63875	+	0.946133i
$787$	15325.4	+	8848.10i	0.694143	+	0.400763i	0.805162	−	0.593055i	$-0.202078\pi$
$787$	15325.4	+	8848.10i	0.694143	+	0.400763i	−0.111019	+	0.993818i	$0.535412\pi$
$788$			13228.9i			0.598047i
$789$	35239.7	−	61037.0i	1.59007	−	2.75409i
$790$	−3509.73	−	6079.04i	−0.158064	−	0.273775i
$791$	−7097.20	+	4097.57i	−0.319023	+	0.184188i
$792$	−16225.4			−0.727961
$793$		0			0
$794$	−14734.7			−0.658584
$795$	−22774.7	+	13149.0i	−1.01602	+	0.586600i
$796$	1655.62	+	2867.61i	0.0737209	+	0.127688i
$797$	−16283.4	+	28203.6i	−0.723696	+	1.25348i	0.235812	+	0.971799i	$0.424225\pi$
$797$	−16283.4	+	28203.6i	−0.723696	+	1.25348i	−0.959508	+	0.281680i	$0.909108\pi$
$798$			15922.4i			0.706325i
$799$	−2655.27	−	1533.02i	−0.117568	−	0.0678777i
$800$	6428.55	+	3711.53i	0.284105	+	0.164028i
$801$			46484.1i			2.05048i
$802$	−9568.38	+	16572.9i	−0.421286	+	0.729689i
$803$	−4838.22	−	8380.04i	−0.212624	−	0.368275i
$804$	17368.4	−	10027.6i	0.761860	−	0.439860i
$805$	7340.36			0.321384
$806$		0			0
$807$	4824.66			0.210453
$808$	11813.8	−	6820.71i	0.514367	−	0.296970i
$809$	−5811.13	−	10065.2i	−0.252544	−	0.437420i	0.711681	−	0.702502i	$-0.247934\pi$
$809$	−5811.13	−	10065.2i	−0.252544	−	0.437420i	−0.964226	+	0.265083i	$0.914601\pi$
$810$	−18860.7	+	32667.6i	−0.818144	+	1.41707i
$811$			6494.39i			0.281195i	0.990067	+	0.140597i	$0.0449023\pi$
$811$			6494.39i			0.281195i	−0.990067	+	0.140597i	$0.955098\pi$
$812$	308.493	+	178.109i	0.0133325	+	0.00769753i
$813$	35506.0	+	20499.4i	1.53167	+	0.884312i
$814$			8945.22i			0.385172i
$815$	−3084.96	+	5343.31i	−0.132591	+	0.229654i
$816$	6632.45	+	11487.7i	0.284537	+	0.492833i
$817$	4640.64	−	2679.27i	0.198721	−	0.114732i
$818$	−16744.7			−0.715725
$819$		0			0
$820$	6435.49			0.274070
$821$	30222.4	−	17448.9i	1.28474	−	0.741743i	0.307026	−	0.951701i	$-0.400666\pi$
$821$	30222.4	−	17448.9i	1.28474	−	0.741743i	0.977710	+	0.209959i	$0.0673329\pi$
$822$	−8079.95	−	13994.9i	−0.342847	−	0.593829i
$823$	751.307	−	1301.30i	0.0318213	−	0.0551161i	−0.849676	−	0.527305i	$-0.823203\pi$
$823$	751.307	−	1301.30i	0.0318213	−	0.0551161i	0.881497	+	0.472189i	$0.156536\pi$
$824$			27959.9i			1.18208i
$825$	−4720.45	−	2725.35i	−0.199206	−	0.115012i
$826$	−2372.09	−	1369.52i	−0.0999218	−	0.0576899i
$827$		−	27887.8i		−	1.17262i	−0.810088	−	0.586308i	$-0.800581\pi$
$827$		−	27887.8i		−	1.17262i	0.810088	−	0.586308i	$-0.199419\pi$
$828$	11056.6	−	19150.6i	0.464062	−	0.803779i
$829$	15421.8	+	26711.4i	0.646107	+	1.11909i	0.984045	+	0.177922i	$0.0569373\pi$
$829$	15421.8	+	26711.4i	0.646107	+	1.11909i	−0.337938	+	0.941168i	$0.609729\pi$
$830$	−8229.78	+	4751.47i	−0.344168	+	0.198706i
$831$	41027.8			1.71268
$832$		0			0
$833$	−12190.5			−0.507053
$834$	53044.1	−	30625.0i	2.20236	−	1.27153i
$835$	12204.9	+	21139.5i	0.505831	+	0.876125i
$836$	1291.86	−	2237.56i	0.0534448	−	0.0925690i
$837$			68445.0i			2.82653i
$838$	−8793.35	−	5076.84i	−0.362483	−	0.209280i
$839$	−31695.5	−	18299.4i	−1.30423	−	0.752997i	−0.323103	−	0.946364i	$-0.604726\pi$
$839$	−31695.5	−	18299.4i	−1.30423	−	0.752997i	−0.981127	+	0.193366i	$0.938059\pi$
$840$		−	16435.9i		−	0.675110i
$841$	12095.9	−	20950.7i	0.495957	−	0.859023i
$842$	2478.85	+	4293.50i	0.101457	+	0.175729i
$843$	−40024.9	+	23108.4i	−1.63527	+	0.944123i
$844$	−2208.58			−0.0900741
$845$		0			0
$846$	−10415.6			−0.423282
$847$	8949.93	−	5167.24i	0.363073	−	0.209620i
$848$	5011.66	+	8680.44i	0.202949	+	0.351518i
$849$	18243.8	−	31599.2i	0.737485	−	1.27736i
$850$			5731.15i			0.231267i
$851$	−38377.8	−	22157.4i	−1.54591	−	0.892534i
$852$	−20166.6	−	11643.2i	−0.810913	−	0.468181i
$853$		−	21578.4i		−	0.866155i	−0.901357	−	0.433077i	$-0.857428\pi$
$853$		−	21578.4i		−	0.866155i	0.901357	−	0.433077i	$-0.142572\pi$
$854$	910.337	−	1576.75i	0.0364767	−	0.0631795i
$855$	−24496.1	−	42428.4i	−0.979822	−	1.69710i
$856$	33136.5	−	19131.4i	1.32311	−	0.763897i
$857$	31199.6			1.24359			0.621795	−	0.783180i	$-0.286404\pi$
$857$	31199.6			1.24359			0.621795	+	0.783180i	$0.286404\pi$
$858$		0			0
$859$	8035.71			0.319179			0.159590	−	0.987183i	$-0.448983\pi$
$859$	8035.71			0.319179			0.159590	+	0.987183i	$0.448983\pi$
$860$	−1317.83	+	760.849i	−0.0522531	+	0.0301683i
$861$	10518.5	+	18218.5i	0.416340	+	0.721122i
$862$	441.173	−	764.134i	0.0174320	−	0.0301932i
$863$		−	8741.47i		−	0.344801i	−0.985027	−	0.172400i	$-0.944848\pi$
$863$		−	8741.47i		−	0.344801i	0.985027	−	0.172400i	$-0.0551523\pi$
$864$	−44611.8	−	25756.6i	−1.75662	−	1.01419i
$865$	11611.5	+	6703.93i	0.456421	+	0.263515i
$866$			11558.9i			0.453566i
$867$	−14242.3	+	24668.3i	−0.557892	+	0.966297i
$868$	−2169.95	−	3758.47i	−0.0848536	−	0.146971i
$869$	−3224.57	+	1861.71i	−0.125876	+	0.0726744i
$870$	2503.20			0.0975475
$871$		0			0
$872$	1761.62			0.0684128
$873$	20463.1	−	11814.4i	0.793321	−	0.458024i
$874$	−10463.7	−	18123.7i	−0.404967	−	0.701423i
$875$	6261.87	−	10845.9i	0.241931	−	0.419038i
$876$		−	29528.8i		−	1.13891i
$877$	1510.46	+	872.066i	0.0581582	+	0.0335776i	0.528797	−	0.848748i	$-0.322643\pi$
$877$	1510.46	+	872.066i	0.0581582	+	0.0335776i	−0.470639	+	0.882326i	$0.655977\pi$
$878$	−21860.9	−	12621.4i	−0.840284	−	0.485138i
$879$			51229.0i			1.96577i
$880$	1213.62	−	2102.06i	0.0464900	−	0.0805230i
$881$	−2844.40	−	4926.65i	−0.108775	−	0.188403i	0.806500	−	0.591235i	$-0.201359\pi$
$881$	−2844.40	−	4926.65i	−0.108775	−	0.188403i	−0.915274	+	0.402832i	$0.868026\pi$
$882$	−35864.0	+	20706.1i	−1.36916	+	0.790488i
$883$	3940.14			0.150165			0.0750827	−	0.997177i	$-0.476078\pi$
$883$	3940.14			0.150165			0.0750827	+	0.997177i	$0.476078\pi$
$884$		0			0
$885$	11772.4			0.447147
$886$	−30148.8	+	17406.4i	−1.14319	+	0.660022i
$887$	18440.2	+	31939.3i	0.698039	+	1.20904i	0.969145	+	0.246490i	$0.0792772\pi$
$887$	18440.2	+	31939.3i	0.698039	+	1.20904i	−0.271106	+	0.962549i	$0.587389\pi$
$888$	−49612.9	+	85932.1i	−1.87489	+	3.24740i
$889$			18191.3i			0.686295i
$890$	−10818.9	−	6246.28i	−0.407471	−	0.235254i
$891$	17328.2	+	10004.5i	0.651535	+	0.376164i
$892$			3082.97i			0.115724i
$893$	3014.44	−	5221.16i	0.112961	−	0.195654i
$894$	−31435.3	−	54447.5i	−1.17601	−	2.03691i
$895$	−24112.7	+	13921.5i	−0.900558	+	0.519937i
$896$	−1274.75			−0.0475296
$897$		0			0
$898$	30493.5			1.13317
$899$	2080.73	−	1201.31i	0.0771926	−	0.0445671i
$900$	−5953.95	−	10312.5i	−0.220517	−	0.381946i
$901$	7333.62	−	12702.2i	0.271164	−	0.469669i
$902$			5581.26i			0.206026i
$903$	−4307.85	−	2487.14i	−0.158755	−	0.0916575i
$904$	−20886.7	−	12059.0i	−0.768454	−	0.443667i
$905$			31194.8i			1.14580i
$906$	5364.87	−	9292.23i	0.196728	−	0.340743i
$907$	8955.99	+	15512.2i	0.327871	+	0.567889i	0.982089	−	0.188417i	$-0.0603357\pi$
$907$	8955.99	+	15512.2i	0.327871	+	0.567889i	−0.654219	+	0.756306i	$0.727002\pi$
$908$	−13915.9	+	8034.33i	−0.508606	+	0.293644i
$909$	−37746.3			−1.37730
$910$		0			0
$911$	51246.0			1.86373			0.931864	−	0.362807i	$-0.118181\pi$
$911$	51246.0			1.86373			0.931864	+	0.362807i	$0.118181\pi$
$912$	−22588.8	+	13041.7i	−0.820165	+	0.473523i
$913$	2520.37	+	4365.41i	0.0913604	+	0.158241i
$914$	14117.8	−	24452.7i	0.510912	−	0.884926i
$915$			7825.24i			0.282726i
$916$	7914.32	+	4569.34i	0.285477	+	0.164820i
$917$	13891.0	+	8019.95i	0.500240	+	0.288814i
$918$		−	39772.0i		−	1.42993i
$919$	−12748.3	+	22080.6i	−0.457591	+	0.792571i	−0.998833	−	0.0482959i	$-0.984621\pi$
$919$	−12748.3	+	22080.6i	−0.457591	+	0.792571i	0.541242	+	0.840867i	$0.317954\pi$
$920$	10801.2	+	18708.2i	0.387070	+	0.670425i
$921$	−2131.45	+	1230.59i	−0.0762580	+	0.0440276i
$922$	−20396.9			−0.728564
$923$		0			0
$924$	−2398.43			−0.0853924
$925$	−20666.3	+	11931.7i	−0.734600	+	0.424121i
$926$	−7698.35	−	13333.9i	−0.273200	−	0.473197i
$927$	38683.1	−	67001.1i	1.37057	−	2.37390i
$928$			1808.26i			0.0639646i
$929$	39013.2	+	22524.3i	1.37781	+	0.795477i	0.991895	−	0.127058i	$-0.0405535\pi$
$929$	39013.2	+	22524.3i	1.37781	+	0.795477i	0.385912	+	0.922536i	$0.373887\pi$
$930$	−26411.3	−	15248.6i	−0.931249	−	0.537657i
$931$		−	23970.6i		−	0.843830i
$932$	−3603.76	+	6241.89i	−0.126658	+	0.219378i
$933$	−12484.2	−	21623.2i	−0.438064	−	0.758748i
$934$	5634.50	−	3253.08i	0.197394	−	0.113966i
$935$	−3551.82			−0.124232
$936$		0			0
$937$	−2280.50			−0.0795099			−0.0397550	−	0.999209i	$-0.512658\pi$
$937$	−2280.50			−0.0795099			−0.0397550	+	0.999209i	$0.512658\pi$
$938$	−10923.4	+	6306.65i	−0.380237	+	0.219530i
$939$	−3392.02	−	5875.14i	−0.117885	−	0.204183i
$940$	−856.028	+	1482.68i	−0.0297027	+	0.0514466i
$941$		−	31174.8i		−	1.07999i	−0.841669	−	0.539994i	$-0.818427\pi$
$941$		−	31174.8i		−	1.07999i	0.841669	−	0.539994i	$-0.181573\pi$
$942$	−954.514	−	551.089i	−0.0330146	−	0.0190610i
$943$	−23945.3	−	13824.9i	−0.826901	−	0.477412i
$944$		−	4486.98i		−	0.154702i
$945$	−13715.4	+	23755.7i	−0.472128	+	0.817750i
$946$	−659.856	−	1142.90i	−0.0226784	−	0.0392802i
$947$	−24589.9	+	14197.0i	−0.843784	+	0.487159i	−0.858549	−	0.512732i	$-0.828634\pi$
$947$	−24589.9	+	14197.0i	−0.843784	+	0.487159i	0.0147644	+	0.999891i	$0.495300\pi$
$948$	−11362.4			−0.389277
$949$		0			0
$950$	−11269.4			−0.384871
$951$	48522.8	−	28014.6i	1.65453	−	0.955243i
$952$	4583.41	+	7938.71i	0.156039	+	0.270268i
$953$	−16958.4	+	29372.8i	−0.576429	+	0.998404i	0.419456	+	0.907776i	$0.362221\pi$
$953$	−16958.4	+	29372.8i	−0.576429	+	0.998404i	−0.995885	+	0.0906283i	$0.971112\pi$
$954$		−	49826.0i		−	1.69096i
$955$	−8994.42	−	5192.93i	−0.304767	−	0.175957i
$956$	−2059.91	−	1189.29i	−0.0696884	−	0.0402346i
$957$		−	1327.80i		−	0.0448501i
$958$	19036.6	−	32972.4i	0.642010	−	1.11199i
$959$	−3108.09	−	5383.38i	−0.104657	−	0.181270i
$960$	36780.4	−	21235.1i	1.23654	−	0.713918i
$961$	519.228			0.0174290
$962$		0			0
$963$	−105874.			−3.54284
$964$	9248.35	−	5339.54i	0.308993	−	0.178397i
$965$	−9078.08	−	15723.7i	−0.302833	−	0.524522i
$966$	−9713.35	+	16824.0i	−0.323522	+	0.560356i
$967$			10792.9i			0.358920i	0.983765	+	0.179460i	$0.0574350\pi$
$967$			10792.9i			0.358920i	−0.983765	+	0.179460i	$0.942565\pi$
$968$	26339.2	+	15207.0i	0.874561	+	0.504928i
$969$	33054.5	+	19084.0i	1.09584	+	0.632681i
$970$			6350.19i			0.210198i
$971$	−3715.56	+	6435.55i	−0.122799	+	0.212695i	−0.920871	−	0.389868i	$-0.872520\pi$
$971$	−3715.56	+	6435.55i	−0.122799	+	0.212695i	0.798071	+	0.602563i	$0.205854\pi$
$972$	14132.9	+	24478.9i	0.466372	+	0.807780i
$973$	20404.4	−	11780.5i	0.672285	−	0.388144i
$974$	30775.1			1.01242
$975$		0			0
$976$	2982.54			0.0978164
$977$	−10758.3	+	6211.30i	−0.352291	+	0.203395i	−0.665694	−	0.746225i	$-0.731864\pi$
$977$	−10758.3	+	6211.30i	−0.352291	+	0.203395i	0.313403	+	0.949620i	$0.398531\pi$
$978$	−8164.53	−	14141.4i	−0.266946	−	0.462364i
$979$	−3313.28	+	5738.77i	−0.108164	+	0.187346i
$980$			6807.08i			0.221882i
$981$	−4221.42	−	2437.24i	−0.137390	−	0.0793221i
$982$	22861.5	+	13199.1i	0.742911	+	0.428920i
$983$		−	38791.6i		−	1.25866i	−0.777140	−	0.629328i	$-0.783330\pi$
$983$		−	38791.6i		−	1.25866i	0.777140	−	0.629328i	$-0.216670\pi$
$984$	−30955.4	+	53616.3i	−1.00287	+	1.73702i
$985$	17879.7	+	30968.5i	0.578369	+	1.00177i
$986$	−1209.07	+	698.057i	−0.0390513	+	0.0225463i
$987$	−5596.53			−0.180486
$988$		0			0
$989$	6537.89			0.210205
$990$	−10449.3	+	6032.93i	−0.335457	+	0.193676i
$991$	533.253	+	923.621i	0.0170932	+	0.0296062i	0.874445	−	0.485124i	$-0.161225\pi$
$991$	533.253	+	923.621i	0.0170932	+	0.0296062i	−0.857352	+	0.514730i	$0.827892\pi$
$992$	11015.3	−	19079.1i	0.352557	−	0.610646i
$993$		−	41380.8i		−	1.32244i
$994$	12683.3	+	7322.72i	0.404719	+	0.233665i
$995$	7751.50	+	4475.33i	0.246974	+	0.142590i
$996$			15382.4i			0.489369i
$997$	15325.8	−	26545.0i	0.486833	−	0.843219i	−0.513053	−	0.858357i	$-0.671485\pi$
$997$	15325.8	−	26545.0i	0.486833	−	0.843219i	0.999885	+	0.0151382i	$0.00481881\pi$
$998$	−5820.02	−	10080.6i	−0.184599	−	0.319734i
$999$	143417.	−	82801.7i	4.54204	−	2.62235i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.e.h.23.6		36
13.2	odd	12		169.4.a.k.1.4	✓	9
13.3	even	3		169.4.b.g.168.6		18
13.4	even	6	inner	169.4.e.h.147.6		36
13.5	odd	4		169.4.c.l.146.6		18
13.6	odd	12		169.4.c.l.22.6		18
13.7	odd	12		169.4.c.k.22.4		18
13.8	odd	4		169.4.c.k.146.4		18
13.9	even	3	inner	169.4.e.h.147.13		36
13.10	even	6		169.4.b.g.168.13		18
13.11	odd	12		169.4.a.l.1.6	yes	9
13.12	even	2	inner	169.4.e.h.23.13		36
39.2	even	12		1521.4.a.bh.1.6		9
39.11	even	12		1521.4.a.bg.1.4		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.4.a.k.1.4	✓	9	13.2	odd	12
169.4.a.l.1.6	yes	9	13.11	odd	12
169.4.b.g.168.6		18	13.3	even	3
169.4.b.g.168.13		18	13.10	even	6
169.4.c.k.22.4		18	13.7	odd	12
169.4.c.k.146.4		18	13.8	odd	4
169.4.c.l.22.6		18	13.6	odd	12
169.4.c.l.146.6		18	13.5	odd	4
169.4.e.h.23.6		36	1.1	even	1	trivial
169.4.e.h.23.13		36	13.12	even	2	inner
169.4.e.h.147.6		36	13.4	even	6	inner
169.4.e.h.147.13		36	13.9	even	3	inner
1521.4.a.bg.1.4		9	39.11	even	12
1521.4.a.bh.1.6		9	39.2	even	12

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	169.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.92949 + 1.11399i) q^{2} +(4.87434 + 8.44260i) q^{3} +(-1.51803 + 2.62931i) q^{4} +8.20685i q^{5} +(-18.8100 - 10.8600i) q^{6} +(-7.23560 - 4.17747i) q^{7} -24.5882i q^{8} +(-34.0183 + 58.9214i) q^{9} +O(q^{10})\)	\(q+(-1.92949 + 1.11399i) q^{2} +(4.87434 + 8.44260i) q^{3} +(-1.51803 + 2.62931i) q^{4} +8.20685i q^{5} +(-18.8100 - 10.8600i) q^{6} +(-7.23560 - 4.17747i) q^{7} -24.5882i q^{8} +(-34.0183 + 58.9214i) q^{9} +(-9.14239 - 15.8351i) q^{10} +(-8.39957 + 4.84949i) q^{11} -29.5976 q^{12} +18.6147 q^{14} +(-69.2872 + 40.0030i) q^{15} +(15.2469 + 26.4084i) q^{16} +(22.3109 - 38.6437i) q^{17} -151.585i q^{18} +(75.9867 + 43.8709i) q^{19} +(-21.5784 - 12.4583i) q^{20} -81.4497i q^{21} +(10.8046 - 18.7141i) q^{22} +(53.5263 + 92.7102i) q^{23} +(207.589 - 119.851i) q^{24} +57.6475 q^{25} -400.052 q^{27} +(21.9678 - 12.6831i) q^{28} +(7.02150 + 12.1616i) q^{29} +(89.1261 - 154.371i) q^{30} -171.090i q^{31} +(111.515 + 64.3831i) q^{32} +(-81.8846 - 47.2761i) q^{33} +99.4170i q^{34} +(34.2839 - 59.3815i) q^{35} +(-103.282 - 178.890i) q^{36} +(-358.495 + 206.977i) q^{37} -195.488 q^{38} +201.792 q^{40} +(-223.678 + 129.141i) q^{41} +(90.7344 + 157.157i) q^{42} +(30.5359 - 52.8897i) q^{43} -29.4468i q^{44} +(-483.560 - 279.183i) q^{45} +(-206.557 - 119.256i) q^{46} -68.7115i q^{47} +(-148.637 + 257.446i) q^{48} +(-136.597 - 236.594i) q^{49} +(-111.231 + 64.2190i) q^{50} +435.004 q^{51} +328.701 q^{53} +(771.899 - 445.656i) q^{54} +(-39.7991 - 68.9340i) q^{55} +(-102.717 + 177.911i) q^{56} +855.367i q^{57} +(-27.0959 - 15.6438i) q^{58} +(-127.431 - 73.5721i) q^{59} -242.904i q^{60} +(48.9041 - 84.7045i) q^{61} +(190.593 + 330.117i) q^{62} +(492.286 - 284.221i) q^{63} -530.839 q^{64} +210.661 q^{66} +(-586.817 + 338.799i) q^{67} +(67.7376 + 117.325i) q^{68} +(-521.810 + 903.802i) q^{69} +152.768i q^{70} +(681.360 + 393.383i) q^{71} +(1448.77 + 836.450i) q^{72} +997.675i q^{73} +(461.142 - 798.722i) q^{74} +(280.994 + 486.695i) q^{75} +(-230.701 + 133.195i) q^{76} +81.0345 q^{77} +383.897 q^{79} +(-216.729 + 125.129i) q^{80} +(-1031.50 - 1786.60i) q^{81} +(287.724 - 498.353i) q^{82} -519.718i q^{83} +(214.157 + 123.643i) q^{84} +(317.143 + 183.103i) q^{85} +136.067i q^{86} +(-68.4503 + 118.559i) q^{87} +(119.240 + 206.530i) q^{88} +(591.687 - 341.611i) q^{89} +1244.03 q^{90} -325.019 q^{92} +(1444.44 - 833.950i) q^{93} +(76.5442 + 132.578i) q^{94} +(-360.042 + 623.612i) q^{95} +1255.30i q^{96} +(-300.765 - 173.647i) q^{97} +(527.128 + 304.337i) q^{98} -659.886i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9}+O(q^{10}) \) 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9	\( 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9} - 294 q^{10} - 156 q^{12} - 588 q^{14} - 538 q^{16} - 110 q^{17} - 680 q^{22} - 408 q^{23} - 1228 q^{25} - 2672 q^{27} - 560 q^{29} + 1042 q^{30} - 40 q^{35} - 1818 q^{36} + 2956 q^{38} + 52 q^{40} + 8 q^{42} - 1066 q^{43} + 264 q^{48} + 806 q^{49} - 1880 q^{51} - 1112 q^{53} + 500 q^{55} + 500 q^{56} + 272 q^{61} + 4070 q^{62} - 1136 q^{64} + 13116 q^{66} + 3072 q^{68} - 4100 q^{69} + 3980 q^{74} + 4786 q^{75} + 2872 q^{77} + 1648 q^{79} + 1670 q^{81} + 5514 q^{82} + 1572 q^{87} - 1272 q^{88} + 5120 q^{90} + 16040 q^{92} + 5062 q^{94} - 3228 q^{95}+O(q^{100}) \) 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9 - 294 * q^10 - 156 * q^12 - 588 * q^14 - 538 * q^16 - 110 * q^17 - 680 * q^22 - 408 * q^23 - 1228 * q^25 - 2672 * q^27 - 560 * q^29 + 1042 * q^30 - 40 * q^35 - 1818 * q^36 + 2956 * q^38 + 52 * q^40 + 8 * q^42 - 1066 * q^43 + 264 * q^48 + 806 * q^49 - 1880 * q^51 - 1112 * q^53 + 500 * q^55 + 500 * q^56 + 272 * q^61 + 4070 * q^62 - 1136 * q^64 + 13116 * q^66 + 3072 * q^68 - 4100 * q^69 + 3980 * q^74 + 4786 * q^75 + 2872 * q^77 + 1648 * q^79 + 1670 * q^81 + 5514 * q^82 + 1572 * q^87 - 1272 * q^88 + 5120 * q^90 + 16040 * q^92 + 5062 * q^94 - 3228 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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