LMFDB - Embedded newform 169.4.e.h.23.7

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			23.7
Character	$\chi$	$=$	169.23
Dual form			169.4.e.h.147.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49617 + 0.863817i) q^{2} +(-3.44796 - 5.97204i) q^{3} +(-2.50764 + 4.34336i) q^{4} +20.8281i q^{5} +(10.3175 + 5.95681i) q^{6} +(6.55206 + 3.78283i) q^{7} -22.4856i q^{8} +(-10.2768 + 17.8000i) q^{9} +O(q^{10})$	\(q+(-1.49617 + 0.863817i) q^{2} +(-3.44796 - 5.97204i) q^{3} +(-2.50764 + 4.34336i) q^{4} +20.8281i q^{5} +(10.3175 + 5.95681i) q^{6} +(6.55206 + 3.78283i) q^{7} -22.4856i q^{8} +(-10.2768 + 17.8000i) q^{9} +(-17.9916 - 31.1624i) q^{10} +(3.81307 - 2.20147i) q^{11} +34.5850 q^{12} -13.0707 q^{14} +(124.386 - 71.8143i) q^{15} +(-0.637664 - 1.10447i) q^{16} +(-36.5043 + 63.2274i) q^{17} -35.5091i q^{18} +(-48.4475 - 27.9712i) q^{19} +(-90.4639 - 52.2293i) q^{20} -52.1722i q^{21} +(-3.80334 + 6.58758i) q^{22} +(-16.8122 - 29.1196i) q^{23} +(-134.285 + 77.5295i) q^{24} -308.809 q^{25} -44.4536 q^{27} +(-32.8604 + 18.9720i) q^{28} +(-60.7146 - 105.161i) q^{29} +(-124.069 + 214.893i) q^{30} -84.1320i q^{31} +(157.693 + 91.0442i) q^{32} +(-26.2946 - 15.1812i) q^{33} -126.132i q^{34} +(-78.7891 + 136.467i) q^{35} +(-51.5411 - 89.2719i) q^{36} +(-148.710 + 85.8578i) q^{37} +96.6479 q^{38} +468.332 q^{40} +(81.0352 - 46.7857i) q^{41} +(45.0672 + 78.0586i) q^{42} +(220.888 - 382.589i) q^{43} +22.0820i q^{44} +(-370.739 - 214.046i) q^{45} +(50.3080 + 29.0453i) q^{46} -272.528i q^{47} +(-4.39727 + 7.61630i) q^{48} +(-142.880 - 247.476i) q^{49} +(462.032 - 266.754i) q^{50} +503.461 q^{51} -480.202 q^{53} +(66.5103 - 38.3998i) q^{54} +(45.8525 + 79.4188i) q^{55} +(85.0594 - 147.327i) q^{56} +385.774i q^{57} +(181.679 + 104.893i) q^{58} +(303.572 + 175.267i) q^{59} +720.338i q^{60} +(242.233 - 419.560i) q^{61} +(72.6746 + 125.876i) q^{62} +(-134.669 + 77.7509i) q^{63} -304.379 q^{64} +52.4550 q^{66} +(-837.925 + 483.776i) q^{67} +(-183.080 - 317.103i) q^{68} +(-115.936 + 200.806i) q^{69} -272.237i q^{70} +(348.791 + 201.375i) q^{71} +(400.244 + 231.081i) q^{72} +351.621i q^{73} +(148.331 - 256.916i) q^{74} +(1064.76 + 1844.22i) q^{75} +(242.978 - 140.283i) q^{76} +33.3112 q^{77} -820.078 q^{79} +(23.0039 - 13.2813i) q^{80} +(430.748 + 746.078i) q^{81} +(-80.8285 + 139.999i) q^{82} +192.314i q^{83} +(226.603 + 130.829i) q^{84} +(-1316.90 - 760.315i) q^{85} +763.226i q^{86} +(-418.683 + 725.180i) q^{87} +(-49.5016 - 85.7392i) q^{88} +(704.573 - 406.786i) q^{89} +739.587 q^{90} +168.636 q^{92} +(-502.439 + 290.083i) q^{93} +(235.414 + 407.750i) q^{94} +(582.586 - 1009.07i) q^{95} -1255.67i q^{96} +(-682.682 - 394.146i) q^{97} +(427.548 + 246.845i) q^{98} +90.4966i 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 $

$2$	−1.49617	+	0.863817i	−0.528978	+	0.305405i	−0.740600	−	0.671946i	$-0.765459\pi$
$2$	−1.49617	+	0.863817i	−0.528978	+	0.305405i	0.211622	+	0.977351i	$0.432125\pi$
$3$	−3.44796	−	5.97204i	−0.663560	−	1.14932i	−0.979674	−	0.200598i	$-0.935712\pi$
$3$	−3.44796	−	5.97204i	−0.663560	−	1.14932i	0.316114	−	0.948721i	$-0.397622\pi$
$4$	−2.50764	+	4.34336i	−0.313455	+	0.542920i
$5$			20.8281i			1.86292i	0.363844	+	0.931460i	$0.381464\pi$
$5$			20.8281i			1.86292i	−0.363844	+	0.931460i	$0.618536\pi$
$6$	10.3175	+	5.95681i	0.702016	+	0.405309i
$7$	6.55206	+	3.78283i	0.353778	+	0.204254i	0.666348	−	0.745641i	$-0.267857\pi$
$7$	6.55206	+	3.78283i	0.353778	+	0.204254i	−0.312570	+	0.949895i	$0.601190\pi$
$8$		−	22.4856i		−	0.993734i
$9$	−10.2768	+	17.8000i	−0.380623	+	0.659258i
$10$	−17.9916	−	31.1624i	−0.568946	−	0.985443i
$11$	3.81307	−	2.20147i	0.104517	−	0.0603427i	−0.446831	−	0.894619i	$-0.647447\pi$
$11$	3.81307	−	2.20147i	0.104517	−	0.0603427i	0.551347	+	0.834276i	$0.314114\pi$
$12$	34.5850			0.831985
$13$		0			0
$13$		0			0
$14$	−13.0707			−0.249521
$15$	124.386	−	71.8143i	2.14109	−	1.23616i
$16$	−0.637664	−	1.10447i	−0.00996349	−	0.0172573i
$17$	−36.5043	+	63.2274i	−0.520800	+	0.902052i	0.478907	+	0.877865i	$0.341033\pi$
$17$	−36.5043	+	63.2274i	−0.520800	+	0.902052i	−0.999707	+	0.0241867i	$0.992300\pi$
$18$		−	35.5091i		−	0.464977i
$19$	−48.4475	−	27.9712i	−0.584980	−	0.337738i	0.178130	−	0.984007i	$-0.442995\pi$
$19$	−48.4475	−	27.9712i	−0.584980	−	0.337738i	−0.763110	+	0.646269i	$0.776329\pi$
$20$	−90.4639	−	52.2293i	−1.01142	−	0.583942i
$21$		−	52.1722i		−	0.542138i
$22$	−3.80334	+	6.58758i	−0.0368580	+	0.0638398i
$23$	−16.8122	−	29.1196i	−0.152417	−	0.263994i	0.779699	−	0.626155i	$-0.215372\pi$
$23$	−16.8122	−	29.1196i	−0.152417	−	0.263994i	−0.932115	+	0.362161i	$0.882039\pi$
$24$	−134.285	+	77.5295i	−1.14212	+	0.659402i
$25$	−308.809			−2.47047
$26$		0			0
$27$	−44.4536			−0.316855
$28$	−32.8604	+	18.9720i	−0.221787	+	0.128049i
$29$	−60.7146	−	105.161i	−0.388773	−	0.673375i	0.603512	−	0.797354i	$-0.293768\pi$
$29$	−60.7146	−	105.161i	−0.388773	−	0.673375i	−0.992285	+	0.123979i	$0.960434\pi$
$30$	−124.069	+	214.893i	−0.755059	+	1.30780i
$31$		−	84.1320i		−	0.487437i	−0.969846	−	0.243719i	$-0.921633\pi$
$31$		−	84.1320i		−	0.487437i	0.969846	−	0.243719i	$-0.0783673\pi$
$32$	157.693	+	91.0442i	0.871140	+	0.502953i
$33$	−26.2946	−	15.1812i	−0.138706	−	0.0800819i
$34$		−	126.132i		−	0.636220i
$35$	−78.7891	+	136.467i	−0.380508	+	0.659059i
$36$	−51.5411	−	89.2719i	−0.238616	−	0.413296i
$37$	−148.710	+	85.8578i	−0.660751	+	0.381485i	−0.792563	−	0.609790i	$-0.791254\pi$
$37$	−148.710	+	85.8578i	−0.660751	+	0.381485i	0.131812	+	0.991275i	$0.457920\pi$
$38$	96.6479			0.412588
$39$		0			0
$40$	468.332			1.85125
$41$	81.0352	−	46.7857i	0.308673	−	0.178212i	−0.337660	−	0.941268i	$-0.609635\pi$
$41$	81.0352	−	46.7857i	0.308673	−	0.178212i	0.646332	+	0.763056i	$0.276302\pi$
$42$	45.0672	+	78.0586i	0.165572	+	0.286779i
$43$	220.888	−	382.589i	0.783374	−	1.35684i	−0.146592	−	0.989197i	$-0.546830\pi$
$43$	220.888	−	382.589i	0.783374	−	1.35684i	0.929966	−	0.367646i	$-0.119836\pi$
$44$			22.0820i			0.0756589i
$45$	−370.739	−	214.046i	−1.22814	−	0.709070i
$46$	50.3080	+	29.0453i	0.161250	+	0.0930978i
$47$		−	272.528i		−	0.845794i	−0.906178	−	0.422897i	$-0.861013\pi$
$47$		−	272.528i		−	0.845794i	0.906178	−	0.422897i	$-0.138987\pi$
$48$	−4.39727	+	7.61630i	−0.0132227	+	0.0229025i
$49$	−142.880	−	247.476i	−0.416561	−	0.721505i
$50$	462.032	−	266.754i	1.30682	−	0.754494i
$51$	503.461			1.38233
$52$		0			0
$53$	−480.202			−1.24454			−0.622272	−	0.782801i	$-0.713790\pi$
$53$	−480.202			−1.24454			−0.622272	+	0.782801i	$0.713790\pi$
$54$	66.5103	−	38.3998i	0.167609	−	0.0967694i
$55$	45.8525	+	79.4188i	0.112414	+	0.194706i
$56$	85.0594	−	147.327i	0.202974	−	0.351561i
$57$			385.774i			0.896438i
$58$	181.679	+	104.893i	0.411305	+	0.237467i
$59$	303.572	+	175.267i	0.669859	+	0.386743i	0.796023	−	0.605266i	$-0.206933\pi$
$59$	303.572	+	175.267i	0.669859	+	0.386743i	−0.126164	+	0.992009i	$0.540267\pi$
$60$			720.338i			1.54992i
$61$	242.233	−	419.560i	0.508439	−	0.880643i	−0.491513	−	0.870870i	$-0.663556\pi$
$61$	242.233	−	419.560i	0.508439	−	0.880643i	0.999952	−	0.00977232i	$-0.00311068\pi$
$62$	72.6746	+	125.876i	0.148866	+	0.257843i
$63$	−134.669	+	77.7509i	−0.269312	+	0.155487i
$64$	−304.379			−0.594491
$65$		0			0
$66$	52.4550			0.0978298
$67$	−837.925	+	483.776i	−1.52789	+	0.882129i	−0.528442	+	0.848969i	$0.677224\pi$
$67$	−837.925	+	483.776i	−1.52789	+	0.882129i	−0.999450	+	0.0331598i	$0.989443\pi$
$68$	−183.080	−	317.103i	−0.326495	−	0.565506i
$69$	−115.936	+	200.806i	−0.202275	+	0.350351i
$70$		−	272.237i		−	0.464837i
$71$	348.791	+	201.375i	0.583013	+	0.336603i	0.762330	−	0.647189i	$-0.224055\pi$
$71$	348.791	+	201.375i	0.583013	+	0.336603i	−0.179317	+	0.983791i	$0.557389\pi$
$72$	400.244	+	231.081i	0.655127	+	0.378238i
$73$			351.621i			0.563754i	0.959450	+	0.281877i	$0.0909571\pi$
$73$			351.621i			0.563754i	−0.959450	+	0.281877i	$0.909043\pi$
$74$	148.331	−	256.916i	0.233015	−	0.403594i
$75$	1064.76	+	1844.22i	1.63930	+	2.83936i
$76$	242.978	−	140.283i	0.366730	−	0.211732i
$77$	33.3112			0.0493009
$78$		0			0
$79$	−820.078			−1.16792			−0.583962	−	0.811781i	$-0.698498\pi$
$79$	−820.078			−1.16792			−0.583962	+	0.811781i	$0.698498\pi$
$80$	23.0039	−	13.2813i	0.0321489	−	0.0185612i
$81$	430.748	+	746.078i	0.590875	+	1.02343i
$82$	−80.8285	+	139.999i	−0.108854	+	0.188540i
$83$			192.314i			0.254328i	0.991882	+	0.127164i	$0.0405875\pi$
$83$			192.314i			0.254328i	−0.991882	+	0.127164i	$0.959413\pi$
$84$	226.603	+	130.829i	0.294338	+	0.169936i
$85$	−1316.90	−	760.315i	−1.68045	−	0.970209i
$86$			763.226i			0.956986i
$87$	−418.683	+	725.180i	−0.515948	+	0.893649i
$88$	−49.5016	−	85.7392i	−0.0599646	−	0.103862i
$89$	704.573	−	406.786i	0.839153	−	0.484485i	−0.0178232	−	0.999841i	$-0.505674\pi$
$89$	704.573	−	406.786i	0.839153	−	0.484485i	0.856976	+	0.515356i	$0.172340\pi$
$90$	739.587			0.866215
$91$		0			0
$92$	168.636			0.191103
$93$	−502.439	+	290.083i	−0.560221	+	0.323444i
$94$	235.414	+	407.750i	0.258310	+	0.447406i
$95$	582.586	−	1009.07i	0.629180	−	1.08977i
$96$		−	1255.67i		−	1.33496i
$97$	−682.682	−	394.146i	−0.714596	−	0.412572i	0.0981645	−	0.995170i	$-0.468703\pi$
$97$	−682.682	−	394.146i	−0.714596	−	0.412572i	−0.812760	+	0.582598i	$0.802036\pi$
$98$	427.548	+	246.845i	0.440703	+	0.254440i
$99$			90.4966i			0.0918712i
$100$	774.381	−	1341.27i	0.774381	−	1.34127i
$101$	−796.530	−	1379.63i	−0.784730	−	1.35919i	−0.929160	−	0.369677i	$-0.879468\pi$
$101$	−796.530	−	1379.63i	−0.784730	−	1.35919i	0.144430	−	0.989515i	$-0.453865\pi$
$102$	−753.266	+	434.898i	−0.731220	+	0.422170i
$103$	134.659			0.128819			0.0644094	−	0.997924i	$-0.479484\pi$
$103$	134.659			0.128819			0.0644094	+	0.997924i	$0.479484\pi$
$104$		0			0
$105$	1086.65			1.00996
$106$	718.466	−	414.806i	0.658335	−	0.380090i
$107$	389.609	+	674.823i	0.352009	+	0.609697i	0.986601	−	0.163150i	$-0.0521653\pi$
$107$	389.609	+	674.823i	0.352009	+	0.609697i	−0.634592	+	0.772847i	$0.718832\pi$
$108$	111.474	−	193.078i	0.0993200	−	0.172027i
$109$			1341.63i			1.17894i	0.807789	+	0.589472i	$0.200664\pi$
$109$			1341.63i			1.17894i	−0.807789	+	0.589472i	$0.799336\pi$
$110$	−137.207	−	79.2163i	−0.118928	−	0.0686634i
$111$	1025.49	+	592.068i	0.876895	+	0.506276i
$112$		−	9.64870i		−	0.00814032i
$113$	−611.069	+	1058.40i	−0.508712	+	0.881116i	0.491237	+	0.871026i	$0.336545\pi$
$113$	−611.069	+	1058.40i	−0.508712	+	0.881116i	−0.999949	+	0.0100896i	$0.996788\pi$
$114$	−333.238	−	577.185i	−0.273777	−	0.474196i
$115$	606.505	−	350.166i	0.491799	−	0.283940i
$116$	609.002			0.487452
$117$		0			0
$118$	−605.595			−0.472454
$119$	−478.357	+	276.179i	−0.368495	+	0.212751i
$120$	−1614.79	−	2796.90i	−1.22841	−	2.12767i
$121$	−655.807	+	1135.89i	−0.492718	+	0.853412i
$122$			836.981i			0.621120i
$123$	−558.812	−	322.630i	−0.409645	−	0.236509i
$124$	365.416	+	210.973i	0.264639	+	0.152790i
$125$		−	3828.38i		−	2.73937i
$126$	134.325	−	232.658i	0.0949733	−	0.164498i
$127$	224.443	+	388.747i	0.156820	+	0.271620i	0.933720	−	0.358004i	$-0.116542\pi$
$127$	224.443	+	388.747i	0.156820	+	0.271620i	−0.776900	+	0.629624i	$0.783209\pi$
$128$	−806.141	+	465.426i	−0.556668	+	0.321392i
$129$	−3046.45			−2.07926
$130$		0			0
$131$	1787.67			1.19229			0.596144	−	0.802877i	$-0.296699\pi$
$131$	1787.67			1.19229			0.596144	+	0.802877i	$0.296699\pi$
$132$	131.875	−	76.1379i	0.0869562	−	0.0502042i
$133$	−211.621	−	366.538i	−0.137969	−	0.238969i
$134$	835.788	−	1447.63i	0.538814	−	0.933253i
$135$		−	925.883i		−	0.590276i
$136$	1421.71	+	820.823i	0.896400	+	0.517537i
$137$	718.830	+	415.017i	0.448276	+	0.258812i	0.707102	−	0.707112i	$-0.250002\pi$
$137$	718.830	+	415.017i	0.448276	+	0.258812i	−0.258826	+	0.965924i	$0.583336\pi$
$138$		−	400.588i		−	0.247104i
$139$	−494.673	+	856.799i	−0.301854	+	0.522826i	−0.976556	−	0.215264i	$-0.930939\pi$
$139$	−494.673	+	856.799i	−0.301854	+	0.522826i	0.674702	+	0.738090i	$0.264272\pi$
$140$	−395.150	−	684.419i	−0.238545	−	0.413171i
$141$	−1627.55	+	939.666i	−0.972088	+	0.561235i
$142$	−695.803			−0.411201
$143$		0			0
$144$	26.2126			0.0151693
$145$	2190.30	−	1264.57i	1.25444	−	0.724253i
$146$	−303.736	−	526.086i	−0.172174	−	0.298213i
$147$	−985.291	+	1706.57i	−0.552826	+	0.957523i
$148$		−	861.202i		−	0.478313i
$149$	406.663	+	234.787i	0.223592	+	0.129091i	0.607612	−	0.794234i	$-0.292127\pi$
$149$	406.663	+	234.787i	0.223592	+	0.129091i	−0.384021	+	0.923325i	$0.625461\pi$
$150$	−3186.13	−	1839.51i	−1.73431	−	1.00130i
$151$			1936.82i			1.04382i	0.853002	+	0.521908i	$0.174780\pi$
$151$			1936.82i			1.04382i	−0.853002	+	0.521908i	$0.825220\pi$
$152$	−628.950	+	1089.37i	−0.335622	+	0.581315i
$153$	−750.297	−	1299.55i	−0.396457	−	0.686683i
$154$	−49.8394	+	28.7748i	−0.0260790	+	0.0150567i
$155$	1752.31			0.908056
$156$		0			0
$157$	−2891.58			−1.46989			−0.734946	−	0.678125i	$-0.762793\pi$
$157$	−2891.58			−1.46989			−0.734946	+	0.678125i	$0.762793\pi$
$158$	1226.98	−	708.397i	0.617806	−	0.356690i
$159$	1655.72	+	2867.78i	0.825829	+	1.43038i
$160$	−1896.28	+	3284.45i	−0.936961	+	1.62286i
$161$		−	254.391i		−	0.124527i
$162$	−1288.95	−	744.175i	−0.625120	−	0.360913i
$163$	−1986.64	−	1146.99i	−0.954638	−	0.551160i	−0.0601193	−	0.998191i	$-0.519148\pi$
$163$	−1986.64	−	1146.99i	−0.954638	−	0.551160i	−0.894519	+	0.447031i	$0.852481\pi$
$164$			469.287i			0.223446i
$165$	316.195	−	547.665i	0.149186	−	0.258398i
$166$	−166.124	−	287.736i	−0.0776732	−	0.134534i
$167$	−975.703	+	563.322i	−0.452109	+	0.261025i	−0.708720	−	0.705490i	$-0.750727\pi$
$167$	−975.703	+	563.322i	−0.452109	+	0.261025i	0.256612	+	0.966515i	$0.417394\pi$
$168$	−1173.12			−0.538741
$169$		0			0
$170$	2627.09			1.18523
$171$	995.773	−	574.910i	0.445314	−	0.257102i
$172$	1107.81	+	1918.79i	0.491105	+	0.850619i
$173$	−255.950	+	443.318i	−0.112483	+	0.194826i	−0.916771	−	0.399414i	$-0.869214\pi$
$173$	−255.950	+	443.318i	−0.112483	+	0.194826i	0.804288	+	0.594240i	$0.202547\pi$
$174$		−	1446.66i		−	0.630293i
$175$	−2023.33	−	1168.17i	−0.873997	−	0.504602i
$176$	−4.86291	−	2.80760i	−0.00208270	−	0.00120245i
$177$		−	2417.26i		−	1.02651i
$178$	−702.776	+	1217.24i	−0.295929	+	0.512564i
$179$	181.695	+	314.706i	0.0758690	+	0.131409i	0.901464	−	0.432854i	$-0.142494\pi$
$179$	181.695	+	314.706i	0.0758690	+	0.131409i	−0.825595	+	0.564263i	$0.809160\pi$
$180$	1859.36	−	1073.50i	0.769937	−	0.444523i
$181$	−780.933			−0.320698			−0.160349	−	0.987060i	$-0.551262\pi$
$181$	−780.933			−0.320698			−0.160349	+	0.987060i	$0.551262\pi$
$182$		0			0
$183$	−3340.84			−1.34952
$184$	−654.773	+	378.033i	−0.262340	+	0.151462i
$185$	−1788.25	−	3097.34i	−0.710675	−	1.23093i
$186$	501.158	−	868.031i	0.197563	−	0.342189i
$187$			321.453i			0.125706i
$188$	1183.69	+	683.403i	0.459199	+	0.265119i
$189$	−291.262	−	168.160i	−0.112096	−	0.0647189i
$190$			2012.99i			0.768619i
$191$	2004.87	−	3472.54i	0.759515	−	1.31552i	−0.183584	−	0.983004i	$-0.558770\pi$
$191$	2004.87	−	3472.54i	0.759515	−	1.31552i	0.943098	−	0.332514i	$-0.107897\pi$
$192$	1049.49	+	1817.76i	0.394480	+	0.683260i
$193$	143.168	−	82.6579i	0.0533960	−	0.0308282i	−0.473064	−	0.881028i	$-0.656852\pi$
$193$	143.168	−	82.6579i	0.0533960	−	0.0308282i	0.526460	+	0.850200i	$0.323519\pi$
$194$	1361.88			0.504007
$195$		0			0
$196$	1433.17			0.522293
$197$	711.246	−	410.638i	0.257229	−	0.148511i	−0.365841	−	0.930677i	$-0.619219\pi$
$197$	711.246	−	410.638i	0.257229	−	0.148511i	0.623070	+	0.782166i	$0.285885\pi$
$198$	−78.1725	−	135.399i	−0.0280580	−	0.0485978i
$199$	−19.2851	+	33.4028i	−0.00686978	+	0.0118988i	−0.869440	−	0.494039i	$-0.835520\pi$
$199$	−19.2851	+	33.4028i	−0.00686978	+	0.0118988i	0.862570	+	0.505938i	$0.168853\pi$
$200$			6943.76i			2.45499i
$201$	5778.26	+	3336.08i	2.02770	+	1.17069i
$202$	2383.50	+	1376.11i	0.830209	+	0.479322i
$203$		−	918.693i		−	0.317633i
$204$	−1262.50	+	2186.72i	−0.433298	+	0.750494i
$205$	974.456	+	1687.81i	0.331995	+	0.575032i
$206$	−201.473	+	116.321i	−0.0681423	+	0.0393419i
$207$	691.104			0.232053
$208$		0			0
$209$	−246.311			−0.0815202
$210$	−1625.81	+	938.663i	−0.534246	+	0.308447i
$211$	−2522.00	−	4368.24i	−0.822853	−	1.42522i	−0.903549	−	0.428484i	$-0.859048\pi$
$211$	−2522.00	−	4368.24i	−0.822853	−	1.42522i	0.0806966	−	0.996739i	$-0.474286\pi$
$212$	1204.17	−	2085.69i	0.390108	−	0.675688i
$213$		−	2777.33i		−	0.893423i
$214$	−1165.85	−	673.102i	−0.372410	−	0.215011i
$215$	7968.59	+	4600.67i	2.52769	+	1.45936i
$216$			999.567i			0.314870i
$217$	318.257	−	551.237i	0.0995608	−	0.172444i
$218$	−1158.92	−	2007.31i	−0.360056	−	0.623635i
$219$	2099.89	−	1212.37i	0.647934	−	0.374085i
$220$	−459.926			−0.140946
$221$		0			0
$222$	−2045.75			−0.618477
$223$	−5306.81	+	3063.89i	−1.59359	+	0.920059i	−0.600905	+	0.799321i	$0.705193\pi$
$223$	−5306.81	+	3063.89i	−1.59359	+	0.920059i	−0.992684	+	0.120738i	$0.961474\pi$
$224$	688.810	+	1193.05i	0.205460	+	0.355867i
$225$	3173.57	−	5496.78i	0.940317	−	1.62868i
$226$		−	2111.41i		−	0.621454i
$227$	−5493.13	−	3171.46i	−1.60613	−	0.927300i	−0.990225	−	0.139481i	$-0.955457\pi$
$227$	−5493.13	−	3171.46i	−1.60613	−	0.927300i	−0.615907	−	0.787819i	$-0.711210\pi$
$228$	−1675.56	−	967.382i	−0.486695	−	0.280993i
$229$			1334.67i			0.385141i	0.981283	+	0.192571i	$0.0616825\pi$
$229$			1334.67i			0.385141i	−0.981283	+	0.192571i	$0.938318\pi$
$230$	−604.958	+	1047.82i	−0.173434	+	0.300396i
$231$	−114.856	−	198.936i	−0.0327141	−	0.0566624i
$232$	−2364.61	+	1365.21i	−0.669156	+	0.386337i
$233$	5392.39			1.51617			0.758084	−	0.652157i	$-0.226136\pi$
$233$	5392.39			1.51617			0.758084	+	0.652157i	$0.226136\pi$
$234$		0			0
$235$	5676.24			1.57565
$236$	−1522.50	+	879.015i	−0.419941	+	0.242453i
$237$	2827.59	+	4897.54i	0.774987	+	1.34232i
$238$	477.137	−	826.425i	0.129950	−	0.225081i
$239$			3748.70i			1.01458i	0.861777	+	0.507288i	$0.169352\pi$
$239$			3748.70i			1.01458i	−0.861777	+	0.507288i	$0.830648\pi$
$240$	−158.633	−	91.5867i	−0.0426655	−	0.0246329i
$241$	−3316.42	−	1914.74i	−0.886429	−	0.511780i	−0.0136563	−	0.999907i	$-0.504347\pi$
$241$	−3316.42	−	1914.74i	−0.886429	−	0.511780i	−0.872773	+	0.488127i	$0.837680\pi$
$242$		−	2265.99i		−	0.601914i
$243$	2370.28	−	4105.44i	0.625734	−	1.08380i
$244$	1214.87	+	2104.21i	0.318746	+	0.552084i
$245$	5154.45	−	2975.92i	1.34410	−	0.776019i
$246$	1114.77			0.288924
$247$		0			0
$248$	−1891.76			−0.484383
$249$	1148.51	−	663.091i	0.292304	−	0.168762i
$250$	3307.02	+	5727.92i	0.836617	+	1.44906i
$251$	−238.289	+	412.728i	−0.0599229	+	0.103790i	−0.894431	−	0.447207i	$-0.852419\pi$
$251$	−238.289	+	412.728i	−0.0599229	+	0.103790i	0.834508	+	0.550996i	$0.185752\pi$
$252$		−	779.886i		−	0.194953i
$253$	−128.212	−	74.0233i	−0.0318602	−	0.0183945i
$254$	−671.612	−	387.756i	−0.165908	−	0.0957872i
$255$			10486.1i			2.57517i
$256$	2021.60	−	3501.52i	0.493555	−	0.854863i
$257$	127.338	+	220.556i	0.0309071	+	0.0535327i	0.881065	−	0.472995i	$-0.156827\pi$
$257$	127.338	+	220.556i	0.0309071	+	0.0535327i	−0.850158	+	0.526527i	$0.823494\pi$
$258$	4558.01	−	2631.57i	1.09988	−	0.635017i
$259$	−1299.14			−0.311679
$260$		0			0
$261$	2495.81			0.591904
$262$	−2674.67	+	1544.22i	−0.630694	+	0.364131i
$263$	−1122.48	−	1944.20i	−0.263176	−	0.455834i	0.703908	−	0.710291i	$-0.251437\pi$
$263$	−1122.48	−	1944.20i	−0.263176	−	0.455834i	−0.967084	+	0.254457i	$0.918103\pi$
$264$	−341.358	+	591.250i	−0.0795802	+	0.137837i
$265$		−	10001.7i		−	2.31848i
$266$	633.243	+	365.603i	0.145965	+	0.0842727i
$267$	−4858.68	−	2805.16i	−1.11366	−	0.642970i
$268$		−	4852.55i		−	1.10603i
$269$	−2292.66	+	3971.00i	−0.519650	+	0.900060i	0.480089	+	0.877220i	$0.340604\pi$
$269$	−2292.66	+	3971.00i	−0.519650	+	0.900060i	−0.999739	+	0.0228404i	$0.992729\pi$
$270$	799.793	+	1385.28i	0.180274	+	0.312243i
$271$	−6904.64	+	3986.40i	−1.54770	+	0.893566i	−0.549385	+	0.835569i	$0.685138\pi$
$271$	−6904.64	+	3986.40i	−1.54770	+	0.893566i	−0.998317	+	0.0579969i	$0.981529\pi$
$272$	93.1099			0.0207560
$273$		0			0
$274$	−1433.99			−0.316171
$275$	−1177.51	+	679.834i	−0.258205	+	0.149075i
$276$	−581.450	−	1007.10i	−0.126809	−	0.219639i
$277$	2654.40	−	4597.55i	0.575766	−	0.997256i	−0.420192	−	0.907435i	$-0.638037\pi$
$277$	2654.40	−	4597.55i	0.575766	−	0.997256i	0.995958	−	0.0898206i	$-0.0286294\pi$
$278$		−	1709.23i		−	0.368751i
$279$	1497.55	+	864.609i	0.321347	+	0.185530i
$280$	3068.54	+	1771.62i	0.654930	+	0.378124i
$281$			6534.86i			1.38732i	0.720302	+	0.693661i	$0.244003\pi$
$281$			6534.86i			1.38732i	−0.720302	+	0.693661i	$0.755997\pi$
$282$	1623.40	−	2811.81i	0.342808	−	0.593761i
$283$	2096.30	+	3630.90i	0.440326	+	0.762667i	0.997713	−	0.0675855i	$-0.0215296\pi$
$283$	2096.30	+	3630.90i	0.440326	+	0.762667i	−0.557388	+	0.830252i	$0.688196\pi$
$284$	−1749.29	+	1009.95i	−0.365497	+	0.211020i
$285$	−8034.93			−1.66999
$286$		0			0
$287$	707.930			0.145602
$288$	−3241.17	+	1871.29i	−0.663152	+	0.382871i
$289$	−208.633	−	361.362i	−0.0424654	−	0.0735523i
$290$	−2184.71	+	3784.03i	−0.442381	+	0.766227i
$291$			5436.00i			1.09506i
$292$	−1527.22	−	881.738i	−0.306074	−	0.176712i
$293$	2073.17	+	1196.95i	0.413365	+	0.238656i	0.692235	−	0.721673i	$-0.256626\pi$
$293$	2073.17	+	1196.95i	0.413365	+	0.238656i	−0.278870	+	0.960329i	$0.589960\pi$
$294$		−	3404.44i		−	0.675344i
$295$	−3650.48	+	6322.81i	−0.720471	+	1.24789i
$296$	1930.57	+	3343.84i	0.379094	+	0.656611i
$297$	−169.504	+	97.8635i	−0.0331167	+	0.0191199i
$298$	−811.253			−0.157700
$299$		0			0
$300$	−10680.1			−2.05539
$301$	2894.54	−	1671.16i	0.554280	−	0.320014i
$302$	−1673.06	−	2897.82i	−0.318787	−	0.552156i
$303$	−5492.81	+	9513.82i	−1.04143	+	1.80381i
$304$			71.3448i			0.0134602i
$305$	8738.63	+	5045.25i	1.64057	+	0.947181i
$306$	2245.15	+	1296.24i	0.419433	+	0.242160i
$307$		−	821.783i		−	0.152774i	−0.997078	−	0.0763870i	$-0.975662\pi$
$307$		−	821.783i		−	0.152774i	0.997078	−	0.0763870i	$-0.0243385\pi$
$308$	−83.5326	+	144.683i	−0.0154536	+	0.0267664i
$309$	−464.298	−	804.188i	−0.0854790	−	0.148054i
$310$	−2621.76	+	1513.67i	−0.480341	+	0.277325i
$311$	5490.98			1.00117			0.500587	−	0.865686i	$-0.333118\pi$
$311$	5490.98			1.00117			0.500587	+	0.865686i	$0.333118\pi$
$312$		0			0
$313$	−315.481			−0.0569714			−0.0284857	−	0.999594i	$-0.509069\pi$
$313$	−315.481			−0.0569714			−0.0284857	+	0.999594i	$0.509069\pi$
$314$	4326.31	−	2497.79i	0.777540	−	0.448913i
$315$	−1619.40	−	2804.89i	−0.289660	−	0.501706i
$316$	2056.46	−	3561.90i	0.366092	−	0.634090i
$317$			8295.72i			1.46982i	0.678163	+	0.734912i	$0.262777\pi$
$317$			8295.72i			1.46982i	−0.678163	+	0.734912i	$0.737223\pi$
$318$	−4954.48	−	2860.47i	−0.873690	−	0.504425i
$319$	−463.018	−	267.323i	−0.0812665	−	0.0469192i
$320$		−	6339.64i		−	1.10749i
$321$	2686.71	−	4653.52i	0.467158	−	0.809141i
$322$	219.747	+	380.613i	0.0380311	+	0.0658719i
$323$	3537.09	−	2042.14i	0.609315	−	0.351788i
$324$	−4320.65			−0.740852
$325$		0			0
$326$	3963.15			0.673309
$327$	8012.27	−	4625.88i	1.35498	−	0.782300i
$328$	−1052.01	−	1822.13i	−0.177096	−	0.306738i
$329$	1030.93	−	1785.62i	0.172757	−	0.299223i
$330$			1092.54i			0.182249i
$331$	740.510	+	427.534i	0.122967	+	0.0709951i	0.560222	−	0.828343i	$-0.310716\pi$
$331$	740.510	+	427.534i	0.122967	+	0.0709951i	−0.437255	+	0.899338i	$0.644049\pi$
$332$	−835.291	−	482.255i	−0.138080	−	0.0797205i
$333$		−	3529.38i		−	0.580807i
$334$	973.214	−	1685.66i	0.159437	−	0.276153i
$335$	−10076.1	−	17452.4i	−1.64334	−	2.84634i
$336$	−57.6224	+	33.2683i	−0.00935583	+	0.00540159i
$337$	3400.09			0.549598			0.274799	−	0.961502i	$-0.411389\pi$
$337$	3400.09			0.549598			0.274799	+	0.961502i	$0.411389\pi$
$338$		0			0
$339$	8427.75			1.35024
$340$	6604.65	−	3813.19i	1.05349	−	0.608234i
$341$	−185.214	−	320.801i	−0.0294133	−	0.0509453i
$342$	−993.233	+	1720.33i	−0.157041	+	0.272002i
$343$		−	4756.99i		−	0.748844i
$344$	−8602.75	−	4966.80i	−1.34834	−	0.778465i
$345$	−4182.41	−	2414.71i	−0.652676	−	0.376823i
$346$		−	884.375i		−	0.137411i
$347$	−1772.16	+	3069.48i	−0.274164	+	0.474865i	−0.969924	−	0.243409i	$-0.921734\pi$
$347$	−1772.16	+	3069.48i	−0.274164	+	0.474865i	0.695760	+	0.718274i	$0.255068\pi$
$348$	−2099.81	−	3636.98i	−0.323453	−	0.560238i
$349$	7221.96	−	4169.60i	1.10769	−	0.639523i	0.169458	−	0.985537i	$-0.445798\pi$
$349$	7221.96	−	4169.60i	1.10769	−	0.639523i	0.938229	+	0.346014i	$0.112465\pi$
$350$	4036.34			0.616433
$351$		0			0
$352$	801.726			0.121398
$353$	−3742.92	+	2160.97i	−0.564349	+	0.325827i	−0.754889	−	0.655852i	$-0.772309\pi$
$353$	−3742.92	+	2160.97i	−0.564349	+	0.325827i	0.190540	+	0.981679i	$0.438976\pi$
$354$	2088.07	+	3616.64i	0.313501	+	0.543000i
$355$	−4194.25	+	7264.65i	−0.627063	+	1.08611i
$356$			4080.29i			0.607458i
$357$	3298.71	+	1904.51i	0.489037	+	0.282346i
$358$	−543.696	−	313.903i	−0.0802660	−	0.0463416i
$359$		−	4535.87i		−	0.666836i	−0.942779	−	0.333418i	$-0.891798\pi$
$359$		−	4535.87i		−	0.666836i	0.942779	−	0.333418i	$-0.108202\pi$
$360$	−4812.97	+	8336.30i	−0.704627	+	1.22045i
$361$	−1864.73	−	3229.80i	−0.271865	−	0.470885i
$362$	1168.41	−	674.583i	0.169642	−	0.0979428i
$363$	9044.78			1.30779
$364$		0			0
$365$	−7323.58			−1.05023
$366$	4998.48	−	2885.87i	0.713865	−	0.412150i
$367$	−112.681	−	195.170i	−0.0160270	−	0.0277596i	0.857901	−	0.513816i	$-0.171768\pi$
$367$	−112.681	−	195.170i	−0.0160270	−	0.0277596i	−0.873928	+	0.486056i	$0.838435\pi$
$368$	−21.4411	+	37.1370i	−0.00303721	+	0.00526060i
$369$			1923.23i			0.271326i
$370$	5351.07	+	3089.44i	0.751862	+	0.434088i
$371$	−3146.31	−	1816.52i	−0.440292	−	0.254203i
$372$		−	2909.70i		−	0.405540i
$373$	−1464.63	+	2536.81i	−0.203313	+	0.352148i	−0.949594	−	0.313483i	$-0.898504\pi$
$373$	−1464.63	+	2536.81i	−0.203313	+	0.352148i	0.746281	+	0.665631i	$0.231837\pi$
$374$	−277.677	−	480.950i	−0.0383912	−	0.0664956i
$375$	−22863.2	+	13200.1i	−3.14840	+	1.81773i
$376$	−6127.97			−0.840495
$377$		0			0
$378$	581.039			0.0790620
$379$	6764.32	−	3905.38i	0.916780	−	0.529303i	0.0341735	−	0.999416i	$-0.489120\pi$
$379$	6764.32	−	3905.38i	0.916780	−	0.529303i	0.882606	+	0.470113i	$0.155787\pi$
$380$	2921.83	+	5060.76i	0.394439	+	0.683189i
$381$	1547.74	−	2680.77i	0.208119	−	0.360472i
$382$			6927.36i			0.927839i
$383$	−4829.08	−	2788.07i	−0.644268	−	0.371968i	0.141989	−	0.989868i	$-0.454650\pi$
$383$	−4829.08	−	2788.07i	−0.644268	−	0.371968i	−0.786257	+	0.617900i	$0.787984\pi$
$384$	5559.08	+	3209.54i	0.738764	+	0.426526i
$385$			693.809i			0.0918435i
$386$	−142.802	+	247.341i	−0.0188302	+	0.0326149i
$387$	4540.05	+	7863.59i	0.596340	+	1.03289i
$388$	3423.84	−	1976.76i	0.447988	−	0.258646i
$389$	−12425.7			−1.61956			−0.809778	−	0.586737i	$-0.800412\pi$
$389$	−12425.7			−1.61956			−0.809778	+	0.586737i	$0.800412\pi$
$390$		0			0
$391$	2454.87			0.317515
$392$	−5564.66	+	3212.76i	−0.716984	+	0.413951i
$393$	−6163.82	−	10676.1i	−0.791154	−	1.37032i
$394$	−709.432	+	1228.77i	−0.0907123	+	0.157118i
$395$		−	17080.6i		−	2.17575i
$396$	−393.060	−	226.933i	−0.0498787	−	0.0287975i
$397$	−5558.86	−	3209.41i	−0.702748	−	0.405732i	0.105622	−	0.994406i	$-0.466317\pi$
$397$	−5558.86	−	3209.41i	−0.702748	−	0.405732i	−0.808370	+	0.588674i	$0.799650\pi$
$398$		−	66.6353i		−	0.00839227i
$399$	−1459.32	+	2527.61i	−0.183101	+	0.317140i
$400$	196.916	+	341.069i	0.0246145	+	0.0426336i
$401$	−1345.26	+	776.687i	−0.167529	+	0.0967230i	−0.581420	−	0.813603i	$-0.697503\pi$
$401$	−1345.26	+	776.687i	−0.167529	+	0.0967230i	0.413891	+	0.910326i	$0.364169\pi$
$402$	−11527.0			−1.43014
$403$		0			0
$404$	7989.65			0.983911
$405$	−15539.4	+	8971.65i	−1.90656	+	1.10075i
$406$	793.582	+	1374.52i	0.0970069	+	0.168021i
$407$	−378.027	+	654.763i	−0.0460396	+	0.0797430i
$408$		−	11320.7i		−	1.37367i
$409$	7587.72	+	4380.77i	0.917331	+	0.529622i	0.882783	−	0.469782i	$-0.155667\pi$
$409$	7587.72	+	4380.77i	0.917331	+	0.529622i	0.0345486	+	0.999403i	$0.489001\pi$
$410$	−2915.91	−	1683.50i	−0.351236	−	0.202786i
$411$		−	5723.84i		−	0.686949i
$412$	−337.676	+	584.872i	−0.0403789	+	0.0699383i
$413$	1326.01	+	2296.72i	0.157987	+	0.273642i
$414$	−1034.01	+	596.987i	−0.122751	+	0.0708703i
$415$	−4005.54			−0.473793
$416$		0			0
$417$	6822.45			0.801191
$418$	368.525	−	212.768i	0.0431223	−	0.0248967i
$419$	−4130.85	−	7154.85i	−0.481636	−	0.834218i	0.518142	−	0.855295i	$-0.326624\pi$
$419$	−4130.85	−	7154.85i	−0.481636	−	0.834218i	−0.999778	+	0.0210768i	$0.993291\pi$
$420$	−2724.92	+	4719.70i	−0.316577	+	0.548328i
$421$			4431.95i			0.513064i	0.966536	+	0.256532i	$0.0825799\pi$
$421$			4431.95i			0.513064i	−0.966536	+	0.256532i	$0.917420\pi$
$422$	7546.72	+	4357.10i	0.870541	+	0.502607i
$423$	4851.00	+	2800.72i	0.557597	+	0.321929i
$424$			10797.6i			1.23674i
$425$	11272.9	−	19525.2i	1.28662	−	2.22849i
$426$	2399.10	+	4155.36i	0.272856	+	0.472601i
$427$	3174.25	−	1832.66i	0.359749	−	0.207701i
$428$	−3908.00			−0.441356
$429$		0			0
$430$	−15896.5			−1.78279
$431$	8726.09	−	5038.01i	0.975223	−	0.563045i	0.0743985	−	0.997229i	$-0.476296\pi$
$431$	8726.09	−	5038.01i	0.975223	−	0.563045i	0.900825	+	0.434183i	$0.142963\pi$
$432$	28.3464	+	49.0975i	0.00315699	+	0.00546806i
$433$	49.8380	−	86.3220i	0.00553132	−	0.00958053i	−0.863246	−	0.504783i	$-0.831573\pi$
$433$	49.8380	−	86.3220i	0.00553132	−	0.00958053i	0.868778	+	0.495202i	$0.164906\pi$
$434$			1099.66i			0.121626i
$435$	−15104.1	−	8720.36i	−1.66480	−	0.961170i
$436$	−5827.19	−	3364.33i	−0.640073	−	0.369546i
$437$			1881.03i			0.205908i
$438$	−2094.54	+	3627.84i	−0.228495	+	0.395765i
$439$	5714.38	+	9897.60i	0.621258	+	1.07605i	0.989252	+	0.146223i	$0.0467116\pi$
$439$	5714.38	+	9897.60i	0.621258	+	1.07605i	−0.367993	+	0.929828i	$0.619955\pi$
$440$	1785.78	−	1031.02i	0.193486	−	0.111709i
$441$	5873.42			0.634210
$442$		0			0
$443$	−4786.94			−0.513396			−0.256698	−	0.966492i	$-0.582635\pi$
$443$	−4786.94			−0.513396			−0.256698	+	0.966492i	$0.582635\pi$
$444$	−5143.13	+	2969.39i	−0.549735	+	0.317389i
$445$	8472.56	+	14674.9i	0.902557	+	1.56327i
$446$	5293.28	−	9168.22i	0.561982	−	0.973381i
$447$		−	3238.15i		−	0.342638i
$448$	−1994.31	−	1151.42i	−0.210318	−	0.121427i
$449$	5608.69	+	3238.18i	0.589511	+	0.340355i	0.764904	−	0.644144i	$-0.222786\pi$
$449$	5608.69	+	3238.18i	0.589511	+	0.340355i	−0.175393	+	0.984499i	$0.556120\pi$
$450$			10965.5i			1.14871i
$451$	205.995	−	356.794i	0.0215076	−	0.0372523i
$452$	−3064.68	−	5308.19i	−0.318917	−	0.552381i
$453$	11566.8	−	6678.08i	1.19968	−	0.692635i
$454$	10958.2			1.13281
$455$		0			0
$456$	8674.37			0.890822
$457$	803.985	−	464.181i	0.0822950	−	0.0475131i	−0.458288	−	0.888804i	$-0.651537\pi$
$457$	803.985	−	464.181i	0.0822950	−	0.0475131i	0.540583	+	0.841291i	$0.318204\pi$
$458$	−1152.91	−	1996.90i	−0.117624	−	0.203731i
$459$	1622.75	−	2810.68i	0.165018	−	0.285820i
$460$			3512.36i			0.356010i
$461$	−9127.22	−	5269.60i	−0.922119	−	0.532386i	−0.0378085	−	0.999285i	$-0.512038\pi$
$461$	−9127.22	−	5269.60i	−0.922119	−	0.532386i	−0.884310	+	0.466899i	$0.845371\pi$
$462$	343.688	+	198.428i	0.0346100	+	0.0199821i
$463$		−	4928.72i		−	0.494724i	−0.968923	−	0.247362i	$-0.920436\pi$
$463$		−	4928.72i		−	0.494724i	0.968923	−	0.247362i	$-0.0795637\pi$
$464$	−77.4310	+	134.114i	−0.00774708	+	0.0134183i
$465$	−6041.88	−	10464.8i	−0.602549	−	1.04365i
$466$	−8067.96	+	4658.04i	−0.802019	+	0.463046i
$467$	−326.459			−0.0323484			−0.0161742	−	0.999869i	$-0.505149\pi$
$467$	−326.459			−0.0323484			−0.0161742	+	0.999869i	$0.505149\pi$
$468$		0			0
$469$	−7320.17			−0.720712
$470$	−8492.64	+	4903.23i	−0.833482	+	0.481211i
$471$	9970.04	+	17268.6i	0.975361	+	1.68938i
$472$	3941.00	−	6826.00i	0.384320	−	0.665662i
$473$		−	1945.12i		−	0.189083i
$474$	−8461.15	−	4885.05i	−0.819902	−	0.473371i
$475$	14961.0	+	8637.74i	1.44518	+	0.834372i
$476$		−	2770.24i		−	0.266751i
$477$	4934.95	−	8547.58i	0.473702	−	0.820475i
$478$	−3238.19	−	5608.71i	−0.309857	−	0.536687i
$479$	1613.85	−	931.754i	0.153943	−	0.0888787i	−0.421050	−	0.907037i	$-0.638338\pi$
$479$	1613.85	−	931.754i	0.153943	−	0.0888787i	0.574992	+	0.818159i	$0.305005\pi$
$480$	26153.1			2.48692
$481$		0			0
$482$	6615.92			0.625201
$483$	−1519.23	+	877.129i	−0.143121	+	0.0826310i
$484$	−3289.06	−	5696.82i	−0.308890	−	0.535013i
$485$	8209.31	−	14218.9i	0.768589	−	1.33123i
$486$			8189.94i			0.764410i
$487$	15050.8	+	8689.58i	1.40045	+	0.808548i	0.994438	−	0.105322i	$-0.0335874\pi$
$487$	15050.8	+	8689.58i	1.40045	+	0.808548i	0.406007	+	0.913870i	$0.366921\pi$
$488$	−9434.08	−	5446.77i	−0.875125	−	0.505253i
$489$			15819.1i			1.46291i
$490$	−5141.30	+	8905.00i	−0.474001	+	0.820994i
$491$	9629.10	+	16678.1i	0.885041	+	1.53294i	0.845666	+	0.533712i	$0.179203\pi$
$491$	9629.10	+	16678.1i	0.885041	+	1.53294i	0.0393748	+	0.999225i	$0.487463\pi$
$492$	2802.60	−	1618.08i	0.256811	−	0.148270i
$493$	8865.39			0.809892
$494$		0			0
$495$	−1884.87			−0.171149
$496$	−92.9209	+	53.6479i	−0.00841184	+	0.00485658i
$497$	1523.53	+	2638.84i	0.137505	+	0.238165i
$498$	−1145.58	+	1984.20i	−0.103082	+	0.178543i
$499$			13088.2i			1.17416i	0.809528	+	0.587082i	$0.199723\pi$
$499$			13088.2i			1.17416i	−0.809528	+	0.587082i	$0.800277\pi$
$500$	16628.0	+	9600.20i	1.48726	+	0.858668i
$501$	6728.36	+	3884.62i	0.600002	+	0.346411i
$502$		−	823.351i		−	0.0732031i
$503$	−9418.49	+	16313.3i	−0.834890	+	1.44607i	0.0592291	+	0.998244i	$0.481136\pi$
$503$	−9418.49	+	16313.3i	−0.834890	+	1.44607i	−0.894120	+	0.447828i	$0.852198\pi$
$504$	1748.28	+	3028.11i	0.154513	+	0.267624i
$505$	28735.1	−	16590.2i	2.53207	−	1.46189i
$506$	255.770			0.0224711
$507$		0			0
$508$	−2251.29			−0.196624
$509$	−132.670	+	76.5973i	−0.0115531	+	0.00667017i	−0.505765	−	0.862671i	$-0.668790\pi$
$509$	−132.670	+	76.5973i	−0.0115531	+	0.00667017i	0.494212	+	0.869341i	$0.335457\pi$
$510$	−9058.10	−	15689.1i	−0.786469	−	1.36220i
$511$	−1330.12	+	2303.84i	−0.115149	+	0.199444i
$512$		−	461.635i		−	0.0398468i
$513$	2153.67	+	1243.42i	0.185354	+	0.107014i
$514$	−381.040	−	219.993i	−0.0326983	−	0.0188784i
$515$			2804.69i			0.239979i
$516$	7639.40	−	13231.8i	0.651755	−	1.12887i
$517$	−599.964	−	1039.17i	−0.0510375	−	0.0883996i
$518$	1943.74	−	1122.22i	0.164871	−	0.0951883i
$519$	3530.02			0.298556
$520$		0			0
$521$	−10847.8			−0.912192			−0.456096	−	0.889931i	$-0.650753\pi$
$521$	−10847.8			−0.912192			−0.456096	+	0.889931i	$0.650753\pi$
$522$	−3734.17	+	2155.92i	−0.313104	+	0.180771i
$523$	−9924.94	−	17190.5i	−0.829804	−	1.43726i	−0.898192	−	0.439603i	$-0.855119\pi$
$523$	−9924.94	−	17190.5i	−0.829804	−	1.43726i	0.0683884	−	0.997659i	$-0.478214\pi$
$524$	−4482.84	+	7764.52i	−0.373729	+	0.647318i
$525$			16111.2i			1.33934i
$526$	3358.86	+	1939.24i	0.278428	+	0.160751i
$527$	5319.44	+	3071.18i	0.439694	+	0.253857i
$528$			38.7219i			0.00319158i
$529$	5518.20	−	9557.80i	0.453538	−	0.785551i
$530$	8639.62	+	14964.3i	0.708077	+	1.22643i
$531$	−6239.50	+	3602.38i	−0.509927	+	0.294407i
$532$	2122.67			0.172988
$533$		0			0
$534$	9692.57			0.785465
$535$	−14055.3	+	8114.81i	−1.13582	+	0.655764i
$536$	10878.0	+	18841.3i	0.876602	+	1.51832i
$537$	1252.96	−	2170.18i	0.100687	−	0.174395i
$538$		−	7921.75i		−	0.634815i
$539$	−1089.62	−	629.095i	−0.0870750	−	0.0502728i
$540$	4021.44	+	2321.78i	0.320473	+	0.185025i
$541$		−	15828.2i		−	1.25787i	−0.777457	−	0.628936i	$-0.783491\pi$
$541$		−	15828.2i		−	1.25787i	0.777457	−	0.628936i	$-0.216509\pi$
$542$	6887.03	−	11928.7i	0.545800	−	0.945353i
$543$	2692.62	+	4663.76i	0.212802	+	0.368584i
$544$	−11513.0	+	6647.02i	−0.907379	+	0.523876i
$545$	−27943.6			−2.19628
$546$		0			0
$547$	6963.82			0.544335			0.272168	−	0.962250i	$-0.412259\pi$
$547$	6963.82			0.544335			0.272168	+	0.962250i	$0.412259\pi$
$548$	−3605.14	+	2081.43i	−0.281029	+	0.162252i
$549$	4978.77	+	8623.49i	0.387047	+	0.670385i
$550$	1174.50	−	2034.30i	0.0910564	−	0.157714i
$551$			6793.04i			0.525215i
$552$	4515.26	+	2606.88i	0.348156	+	0.201008i
$553$	−5373.20	−	3102.22i	−0.413186	−	0.238553i
$554$			9171.64i			0.703368i
$555$	−12331.6	+	21359.0i	−0.943151	+	1.63359i
$556$	−2480.93	−	4297.09i	−0.189235	−	0.327765i
$557$	−16309.7	+	9416.39i	−1.24069	+	0.716311i	−0.969234	−	0.246140i	$-0.920838\pi$
$557$	−16309.7	+	9416.39i	−1.24069	+	0.716311i	−0.271453	+	0.962452i	$0.587504\pi$
$558$	−2987.45			−0.226647
$559$		0			0
$560$	200.964			0.0151648
$561$	1919.73	−	1108.36i	0.144476	−	0.0834134i
$562$	−5644.92	−	9777.30i	−0.423695	−	0.733862i
$563$	−9830.77	+	17027.4i	−0.735911	+	1.27463i	0.218412	+	0.975857i	$0.429912\pi$
$563$	−9830.77	+	17027.4i	−0.735911	+	1.27463i	−0.954323	+	0.298778i	$0.903421\pi$
$564$		−	9425.38i		−	0.703688i
$565$	−22044.5	−	12727.4i	−1.64145	−	0.947690i
$566$	−6272.87	−	3621.64i	−0.465845	−	0.268956i
$567$			6517.79i			0.482754i
$568$	4528.04	−	7842.79i	0.334493	−	0.579360i
$569$	1076.70	+	1864.90i	0.0793282	+	0.137400i	0.902960	−	0.429724i	$-0.141389\pi$
$569$	1076.70	+	1864.90i	0.0793282	+	0.137400i	−0.823632	+	0.567125i	$0.808056\pi$
$570$	12021.7	−	6940.70i	0.883389	−	0.510025i
$571$	−4437.31			−0.325212			−0.162606	−	0.986691i	$-0.551990\pi$
$571$	−4437.31			−0.325212			−0.162606	+	0.986691i	$0.551990\pi$
$572$		0			0
$573$	−27650.8			−2.01593
$574$	−1059.19	+	611.521i	−0.0770202	+	0.0444676i
$575$	5191.75	+	8992.38i	0.376541	+	0.652188i
$576$	3128.05	−	5417.94i	0.226277	−	0.391923i
$577$		−	14826.7i		−	1.06975i	−0.844933	−	0.534873i	$-0.820360\pi$
$577$		−	14826.7i		−	1.06975i	0.844933	−	0.534873i	$-0.179640\pi$
$578$	624.302	+	360.441i	0.0449265	+	0.0259383i
$579$	−987.272	−	570.002i	−0.0708629	−	0.0409127i
$580$			12684.3i			0.908084i
$581$	−727.493	+	1260.05i	−0.0519475	+	0.0899756i
$582$	−4695.71	−	8133.20i	−0.334439	−	0.579265i
$583$	−1831.04	+	1057.15i	−0.130075	+	0.0750991i
$584$	7906.41			0.560222
$585$		0			0
$586$	−4135.77			−0.291548
$587$	14730.8	−	8504.84i	1.03579	−	0.598011i	0.117149	−	0.993114i	$-0.462625\pi$
$587$	14730.8	−	8504.84i	1.03579	−	0.598011i	0.918637	+	0.395104i	$0.129291\pi$
$588$	−4941.51	−	8558.95i	−0.346572	−	0.600281i
$589$	−2353.27	+	4075.99i	−0.164626	+	0.285141i
$590$		−	12613.4i		−	0.880143i
$591$	−4904.69	−	2831.72i	−0.341374	−	0.197092i
$592$	189.654	+	109.497i	0.0131668	+	0.00760184i
$593$			9173.23i			0.635244i	0.948217	+	0.317622i	$0.102884\pi$
$593$			9173.23i			0.635244i	−0.948217	+	0.317622i	$0.897116\pi$
$594$	169.072	−	292.842i	0.0116786	−	0.0202280i
$595$	−5752.29	−	9963.25i	−0.396337	−	0.686476i
$596$	−2039.53	+	1177.52i	−0.140172	+	0.0809283i
$597$	265.977			0.0182340
$598$		0			0
$599$	2983.22			0.203491			0.101745	−	0.994810i	$-0.467557\pi$
$599$	2983.22			0.203491			0.101745	+	0.994810i	$0.467557\pi$
$600$	41468.4	−	23941.8i	2.82157	−	1.62903i
$601$	9098.00	+	15758.2i	0.617496	+	1.06953i	0.989941	+	0.141480i	$0.0451862\pi$
$601$	9098.00	+	15758.2i	0.617496	+	1.06953i	−0.372445	+	0.928054i	$0.621481\pi$
$602$	−2887.16	+	5000.70i	−0.195468	+	0.338560i
$603$		−	19886.7i		−	1.34303i
$604$	−8412.32	−	4856.86i	−0.566709	−	0.327190i
$605$	−23658.4	−	13659.2i	−1.58984	−	0.917893i
$606$		−	18979.1i		−	1.27223i
$607$	8336.28	−	14438.9i	0.557428	−	0.965494i	−0.440282	−	0.897860i	$-0.645121\pi$
$607$	8336.28	−	14438.9i	0.557428	−	0.965494i	0.997710	−	0.0676345i	$-0.0215452\pi$
$608$	−5093.23	−	8821.73i	−0.339733	−	0.588435i
$609$	−5486.47	+	3167.61i	−0.365062	+	0.210769i
$610$	−17432.7			−1.15710
$611$		0			0
$612$	7525.90			0.497086
$613$	−14511.9	+	8378.47i	−0.956168	+	0.552044i	−0.894992	−	0.446083i	$-0.852819\pi$
$613$	−14511.9	+	8378.47i	−0.956168	+	0.552044i	−0.0611768	+	0.998127i	$0.519485\pi$
$614$	709.870	+	1229.53i	0.0466580	+	0.0808141i
$615$	6719.76	−	11639.0i	0.440597	−	0.763136i
$616$		−	749.024i		−	0.0489920i
$617$	10379.7	+	5992.72i	0.677262	+	0.391017i	0.798823	−	0.601567i	$-0.205457\pi$
$617$	10379.7	+	5992.72i	0.677262	+	0.391017i	−0.121561	+	0.992584i	$0.538790\pi$
$618$	1389.34	+	802.137i	0.0904329	+	0.0522115i
$619$		−	22471.2i		−	1.45912i	−0.683917	−	0.729560i	$-0.739725\pi$
$619$		−	22471.2i		−	1.45912i	0.683917	−	0.729560i	$-0.260275\pi$
$620$	−4394.16	+	7610.90i	−0.284635	+	0.493002i
$621$	747.363	+	1294.47i	0.0482941	+	0.0836479i
$622$	−8215.46	+	4743.20i	−0.529598	+	0.305764i
$623$	6155.20			0.395832
$624$		0			0
$625$	41136.7			2.63275
$626$	472.015	−	272.518i	0.0301366	−	0.0173994i
$627$	849.271	+	1470.98i	0.0540935	+	0.0936927i
$628$	7251.04	−	12559.2i	0.460745	−	0.798035i
$629$		−	12536.7i		−	0.794709i
$630$	4845.82	+	2797.73i	0.306447	+	0.176928i
$631$	858.721	+	495.783i	0.0541762	+	0.0312786i	0.526843	−	0.849962i	$-0.323375\pi$
$631$	858.721	+	495.783i	0.0541762	+	0.0312786i	−0.472667	+	0.881241i	$0.656709\pi$
$632$			18440.0i			1.16061i
$633$	−17391.5	+	30123.0i	−1.09202	+	1.89144i
$634$	−7165.98	−	12411.8i	−0.448892	−	0.777504i
$635$	−8096.85	+	4674.72i	−0.506006	+	0.292143i
$636$	−16607.8			−1.03544
$637$		0			0
$638$	923.674			0.0573175
$639$	−7168.93	+	4138.98i	−0.443816	+	0.256237i
$640$	−9693.92	−	16790.4i	−0.598728	−	1.03703i
$641$	−4241.88	+	7347.15i	−0.261379	+	0.452722i	−0.966609	−	0.256257i	$-0.917511\pi$
$641$	−4241.88	+	7347.15i	−0.261379	+	0.452722i	0.705229	+	0.708979i	$0.250844\pi$
$642$			9283.31i			0.570690i
$643$	−19509.4	−	11263.8i	−1.19654	−	0.690823i	−0.236758	−	0.971569i	$-0.576085\pi$
$643$	−19509.4	−	11263.8i	−1.19654	−	0.690823i	−0.959782	+	0.280746i	$0.909418\pi$
$644$	1104.91	+	637.921i	0.0676081	+	0.0390336i
$645$		−	63451.6i		−	3.87350i
$646$	−3528.07	+	6110.79i	−0.214876	+	0.372176i
$647$	2743.08	+	4751.16i	0.166680	+	0.288698i	0.937251	−	0.348657i	$-0.113362\pi$
$647$	2743.08	+	4751.16i	0.166680	+	0.288698i	−0.770571	+	0.637354i	$0.780029\pi$
$648$	16776.0	−	9685.65i	1.01701	−	0.587173i
$649$	1543.39			0.0933485
$650$		0			0
$651$	−4389.35			−0.264258
$652$	9963.58	−	5752.48i	0.598472	−	0.345528i
$653$	−10218.1	−	17698.2i	−0.612348	−	1.06062i	−0.990844	−	0.135015i	$-0.956892\pi$
$653$	−10218.1	−	17698.2i	−0.612348	−	1.06062i	0.378495	−	0.925603i	$-0.376442\pi$
$654$	−7991.83	+	13842.3i	−0.477837	+	0.827638i
$655$			37233.8i			2.22114i
$656$	−103.346	−	59.6671i	−0.00615091	−	0.00355123i
$657$	−6258.83	−	3613.54i	−0.371660	−	0.214578i
$658$			3562.13i			0.211043i
$659$	4306.56	−	7459.18i	0.254567	−	0.440923i	−0.710211	−	0.703989i	$-0.751400\pi$
$659$	4306.56	−	7459.18i	0.254567	−	0.440923i	0.964778	+	0.263066i	$0.0847336\pi$
$660$	1585.81	+	2746.70i	0.0935264	+	0.161992i
$661$	−25347.5	+	14634.4i	−1.49153	+	0.861138i	−0.999953	−	0.00969383i	$-0.996914\pi$
$661$	−25347.5	+	14634.4i	−1.49153	+	0.861138i	−0.491581	+	0.870832i	$0.663581\pi$
$662$	−1477.24			−0.0867291
$663$		0			0
$664$	4324.31			0.252735
$665$	7634.27	−	4407.65i	0.445179	−	0.257024i
$666$	3048.74	+	5280.57i	0.177382	+	0.307234i
$667$	−2041.49	+	3535.97i	−0.118511	+	0.205267i
$668$		−	5650.44i		−	0.327279i
$669$	36595.3	+	21128.3i	2.11488	+	1.22103i
$670$	30151.3	+	17407.8i	1.73857	+	1.00377i
$671$		−	2133.08i		−	0.122722i
$672$	4749.97	−	8227.19i	0.272670	−	0.472278i
$673$	−11270.3	−	19520.7i	−0.645522	−	1.11808i	−0.984181	−	0.177168i	$-0.943306\pi$
$673$	−11270.3	−	19520.7i	−0.645522	−	1.11808i	0.338658	−	0.940909i	$-0.390027\pi$
$674$	−5087.12	+	2937.05i	−0.290725	+	0.167850i
$675$	13727.7			0.782782
$676$		0			0
$677$	−18727.0			−1.06313			−0.531563	−	0.847019i	$-0.678395\pi$
$677$	−18727.0			−1.06313			−0.531563	+	0.847019i	$0.678395\pi$
$678$	−12609.4	+	7280.03i	−0.714249	+	0.412372i
$679$	−2981.98	−	5164.94i	−0.168539	−	0.291918i
$680$	−17096.2	+	29611.4i	−0.964129	+	1.66992i
$681$			43740.2i			2.46128i
$682$	554.226	+	319.983i	0.0311179	+	0.0179659i
$683$	−4371.49	−	2523.88i	−0.244906	−	0.141396i	0.372524	−	0.928023i	$-0.378493\pi$
$683$	−4371.49	−	2523.88i	−0.244906	−	0.141396i	−0.617429	+	0.786626i	$0.711826\pi$
$684$			5766.67i			0.322360i
$685$	−8644.00	+	14971.8i	−0.482146	+	0.835102i
$686$	4109.17	+	7117.29i	0.228701	+	0.396121i
$687$	7970.69	−	4601.88i	0.442650	−	0.255564i
$688$	−563.408			−0.0312206
$689$		0			0
$690$	8343.48			0.460335
$691$	−14243.4	+	8223.46i	−0.784148	+	0.452728i	−0.837898	−	0.545826i	$-0.816216\pi$
$691$	−14243.4	+	8223.46i	−0.784148	+	0.452728i	0.0537505	+	0.998554i	$0.482882\pi$
$692$	−1283.66	−	2223.37i	−0.0705166	−	0.122138i
$693$	−342.333	+	592.939i	−0.0187650	+	0.0325020i
$694$		−	6123.30i		−	0.334924i
$695$	−17845.5	−	10303.1i	−0.973982	−	0.562329i
$696$	16306.1	+	9414.35i	0.888049	+	0.512716i
$697$			6831.52i			0.371252i
$698$	−7203.54	+	12476.9i	−0.390628	+	0.676587i
$699$	−18592.7	−	32203.6i	−1.00607	−	1.74256i
$700$	10147.6	−	5858.71i	0.547918	−	0.316340i
$701$	−14841.3			−0.799639			−0.399820	−	0.916594i	$-0.630927\pi$
$701$	−14841.3			−0.799639			−0.399820	+	0.916594i	$0.630927\pi$
$702$		0			0
$703$	9606.18			0.515368
$704$	−1160.62	+	670.083i	−0.0621342	+	0.0358732i
$705$	−19571.4	−	33898.7i	−1.04554	−	1.81092i
$706$	3733.37	−	6466.39i	0.199019	−	0.344711i
$707$		−	12052.6i		−	0.641136i
$708$	10499.0	+	6061.61i	0.557312	+	0.321764i
$709$	−16740.0	−	9664.87i	−0.886722	−	0.511949i	−0.0138529	−	0.999904i	$-0.504410\pi$
$709$	−16740.0	−	9664.87i	−0.886722	−	0.511949i	−0.872869	+	0.487955i	$0.837743\pi$
$710$		−	14492.2i		−	0.766034i
$711$	8427.79	−	14597.4i	0.444539	−	0.769963i
$712$	−9146.83	−	15842.8i	−0.481450	−	0.833895i
$713$	−2449.89	+	1414.44i	−0.128680	+	0.0742936i
$714$	−6580.59			−0.344919
$715$		0			0
$716$	−1822.51			−0.0951261
$717$	22387.4	−	12925.4i	1.16607	−	0.673231i
$718$	3918.16	+	6786.45i	0.203655	+	0.352741i
$719$	10670.0	−	18481.0i	0.553443	−	0.958591i	−0.444580	−	0.895739i	$-0.646647\pi$
$719$	10670.0	−	18481.0i	0.553443	−	0.958591i	0.998023	−	0.0628517i	$-0.0200195\pi$
$720$			545.958i			0.0282592i
$721$	882.293	+	509.392i	0.0455732	+	0.0263117i
$722$	5579.91	+	3221.56i	0.287621	+	0.166058i
$723$			26407.7i			1.35839i
$724$	1958.30	−	3391.88i	0.100524	−	0.174113i
$725$	18749.2	+	32474.6i	0.960452	+	1.66355i
$726$	−13532.6	+	7813.03i	−0.691791	+	0.399406i
$727$	15092.3			0.769934			0.384967	−	0.922930i	$-0.374213\pi$
$727$	15092.3			0.769934			0.384967	+	0.922930i	$0.374213\pi$
$728$		0			0
$729$	−9430.08			−0.479098
$730$	10957.4	−	6326.23i	0.555548	−	0.320746i
$731$	16126.7	+	27932.3i	0.815962	+	1.41329i
$732$	8377.63	−	14510.5i	0.423014	−	0.732681i
$733$		−	9108.56i		−	0.458980i	−0.973311	−	0.229490i	$-0.926294\pi$
$733$		−	9108.56i		−	0.458980i	0.973311	−	0.229490i	$-0.0737058\pi$
$734$	337.181	+	194.672i	0.0169558	+	0.00978946i
$735$	−35544.6	−	20521.7i	−1.78379	−	1.02987i
$736$		−	6122.62i		−	0.306634i
$737$	−2130.04	+	3689.34i	−0.106460	+	0.184394i
$738$	−1661.32	−	2877.49i	−0.0828645	−	0.143526i
$739$	16517.5	−	9536.37i	0.822200	−	0.474697i	−0.0289748	−	0.999580i	$-0.509224\pi$
$739$	16517.5	−	9536.37i	0.822200	−	0.474697i	0.851174	+	0.524883i	$0.175891\pi$
$740$	17937.2			0.891059
$741$		0			0
$742$	6276.57			0.310539
$743$	10631.8	−	6138.27i	0.524957	−	0.303084i	−0.214004	−	0.976833i	$-0.568650\pi$
$743$	10631.8	−	6138.27i	0.524957	−	0.303084i	0.738960	+	0.673749i	$0.235317\pi$
$744$	6522.71	+	11297.7i	0.321417	+	0.556710i
$745$	−4890.17	+	8470.02i	−0.240486	+	0.416533i
$746$		−	5060.68i		−	0.248371i
$747$	−3423.19	−	1976.38i	−0.167668	−	0.0968031i
$748$	−1396.19	−	806.090i	−0.0682483	−	0.0394032i
$749$			5895.30i			0.287596i
$750$	22804.9	−	39499.3i	1.11029	−	1.92308i
$751$	14332.8	+	24825.1i	0.696417	+	1.20623i	0.969701	+	0.244297i	$0.0785571\pi$
$751$	14332.8	+	24825.1i	0.696417	+	1.20623i	−0.273283	+	0.961934i	$0.588110\pi$
$752$	−300.998	+	173.781i	−0.0145961	+	0.00842707i
$753$	3286.44			0.159050
$754$		0			0
$755$	−40340.3			−1.94455
$756$	1460.76	−	843.372i	0.0702744	−	0.0405729i
$757$	14308.9	+	24783.7i	0.687008	+	1.18993i	0.972801	+	0.231642i	$0.0744096\pi$
$757$	14308.9	+	24783.7i	0.687008	+	1.18993i	−0.285793	+	0.958291i	$0.592257\pi$
$758$	−6747.06	+	11686.3i	−0.323304	+	0.559979i
$759$			1020.92i			0.0488233i
$760$	−22689.5	−	13099.8i	−1.08294	−	0.625237i
$761$	22878.0	+	13208.6i	1.08979	+	0.629189i	0.933520	−	0.358525i	$-0.116720\pi$
$761$	22878.0	+	13208.6i	1.08979	+	0.629189i	0.156268	+	0.987715i	$0.450054\pi$
$762$			5347.86i			0.254242i
$763$	−5075.16	+	8790.44i	−0.240804	+	0.417084i
$764$	10055.0	+	17415.8i	0.476148	+	0.824712i
$765$	27067.2	−	15627.2i	1.27924	−	0.738567i
$766$	9633.54			0.454404
$767$		0			0
$768$	−27881.6			−1.31001
$769$	27300.8	−	15762.1i	1.28022	−	0.739136i	0.303333	−	0.952885i	$-0.401901\pi$
$769$	27300.8	−	15762.1i	1.28022	−	0.739136i	0.976889	+	0.213748i	$0.0685673\pi$
$770$	−599.323	−	1038.06i	−0.0280495	−	0.0485832i
$771$	878.112	−	1520.93i	0.0410174	−	0.0710442i
$772$			829.105i			0.0386530i
$773$	−18763.8	−	10833.3i	−0.873077	−	0.504071i	−0.00470766	−	0.999989i	$-0.501499\pi$
$773$	−18763.8	−	10833.3i	−0.873077	−	0.504071i	−0.868370	+	0.495918i	$0.834832\pi$
$774$	−13585.4	−	7843.54i	−0.630901	−	0.364251i
$775$			25980.7i			1.20420i
$776$	−8862.63	+	15350.5i	−0.409987	+	0.710118i
$777$	4479.39	+	7758.52i	0.206817	+	0.358218i
$778$	18591.0	−	10733.5i	0.856708	−	0.494621i
$779$	−5234.61			−0.240756
$780$		0			0
$781$	1773.28			0.0812460
$782$	−3672.92	+	2120.56i	−0.167958	+	0.0969707i
$783$	2698.98	+	4674.78i	0.123185	+	0.213363i
$784$	−182.219	+	315.613i	−0.00830080	+	0.0143774i
$785$		−	60226.0i		−	2.73829i
$786$	18444.3	+	10648.8i	0.837006	+	0.483246i
$787$	22751.5	+	13135.6i	1.03050	+	0.594959i	0.917128	−	0.398593i	$-0.130501\pi$
$787$	22751.5	+	13135.6i	1.03050	+	0.594959i	0.113372	+	0.993553i	$0.463835\pi$
$788$			4118.93i			0.186207i
$789$	−7740.55	+	13407.0i	−0.349266	+	0.604946i
$790$	14754.5	+	25555.6i	0.664485	+	1.15092i
$791$	−8007.51	+	4623.14i	−0.359942	+	0.207813i
$792$	2034.87			0.0912956
$793$		0			0
$794$	11089.4			0.495651
$795$	−59730.4	+	34485.4i	−2.66468	+	1.53845i
$796$	−96.7204	−	167.525i	−0.00430674	−	0.00745949i
$797$	−168.492	+	291.836i	−0.00748843	+	0.0129703i	−0.869745	−	0.493501i	$-0.835717\pi$
$797$	−168.492	+	291.836i	−0.00748843	+	0.0129703i	0.862257	+	0.506471i	$0.169050\pi$
$798$		−	5042.33i		−	0.223680i
$799$	17231.2	+	9948.46i	0.762951	+	0.440490i
$800$	−48697.0	−	28115.2i	−2.15212	−	1.24253i
$801$			16721.8i			0.737625i
$802$	1341.83	−	2324.12i	0.0590794	−	0.102329i
$803$	774.084	+	1340.75i	0.0340185	+	0.0589217i
$804$	−28979.6	+	16731.4i	−1.27118	+	0.733918i
$805$	5298.47			0.231983
$806$		0			0
$807$	31619.9			1.37927
$808$	−31021.9	+	17910.5i	−1.35068	+	0.779813i
$809$	−3239.35	−	5610.72i	−0.140778	−	0.243835i	0.787012	−	0.616938i	$-0.211627\pi$
$809$	−3239.35	−	5610.72i	−0.140778	−	0.243835i	−0.927790	+	0.373103i	$0.878294\pi$
$810$	15499.7	−	26846.3i	0.672352	−	1.16455i
$811$			36823.2i			1.59437i	0.603734	+	0.797186i	$0.293679\pi$
$811$			36823.2i			1.59437i	−0.603734	+	0.797186i	$0.706321\pi$
$812$	3990.21	+	2303.75i	0.172450	+	0.0995638i
$813$	47613.8	+	27489.9i	2.05399	+	1.18587i
$814$		−	1306.19i		−	0.0562430i
$815$	23889.6	−	41378.0i	1.02677	−	1.77841i
$816$	−321.039	−	556.056i	−0.0137728	−	0.0238552i
$817$	−21402.9	+	12357.0i	−0.916516	+	0.529151i
$818$	−15136.7			−0.646997
$819$		0			0
$820$	−9774.34			−0.416262
$821$	−7382.46	+	4262.27i	−0.313824	+	0.181187i	−0.648636	−	0.761098i	$-0.724660\pi$
$821$	−7382.46	+	4262.27i	−0.313824	+	0.181187i	0.334812	+	0.942285i	$0.391327\pi$
$822$	4944.35	+	8563.86i	0.209798	+	0.363381i
$823$	−6656.54	+	11529.5i	−0.281935	+	0.488325i	−0.971861	−	0.235554i	$-0.924309\pi$
$823$	−6656.54	+	11529.5i	−0.281935	+	0.488325i	0.689927	+	0.723879i	$0.257643\pi$
$824$		−	3027.89i		−	0.128012i
$825$	8119.99	+	4688.08i	0.342669	+	0.197840i
$826$	−3967.89	−	2290.86i	−0.167144	−	0.0965004i
$827$			41849.9i			1.75969i	0.475261	+	0.879845i	$0.342354\pi$
$827$			41849.9i			1.75969i	−0.475261	+	0.879845i	$0.657646\pi$
$828$	−1733.04	+	3001.71i	−0.0727383	+	0.125986i
$829$	−6508.59	−	11273.2i	−0.272681	−	0.472298i	0.696866	−	0.717201i	$-0.254577\pi$
$829$	−6508.59	−	11273.2i	−0.272681	−	0.472298i	−0.969547	+	0.244903i	$0.921244\pi$
$830$	5992.98	−	3460.05i	0.250626	−	0.144699i
$831$	−36609.0			−1.52822
$832$		0			0
$833$	20863.0			0.867780
$834$	−10207.6	+	5893.35i	−0.423812	+	0.244688i
$835$	−11732.9	−	20322.0i	−0.486269	−	0.842242i
$836$	617.661	−	1069.82i	0.0255529	−	0.0442590i
$837$			3739.97i			0.154447i
$838$	12361.0	+	7136.60i	0.509549	+	0.294188i
$839$	17501.9	+	10104.7i	0.720181	+	0.415796i	0.814819	−	0.579715i	$-0.196836\pi$
$839$	17501.9	+	10104.7i	0.720181	+	0.415796i	−0.0946385	+	0.995512i	$0.530170\pi$
$840$		−	24433.9i		−	1.00363i
$841$	4821.97	−	8351.90i	0.197711	−	0.342445i
$842$	−3828.39	−	6630.97i	−0.156692	−	0.271399i
$843$	39026.4	−	22531.9i	1.59447	−	0.920570i
$844$	25297.1			1.03171
$845$		0			0
$846$	−9677.25			−0.393275
$847$	−8593.77	+	4961.61i	−0.348625	+	0.201279i
$848$	306.207	+	530.366i	0.0124000	+	0.0214774i
$849$	14455.9	−	25038.4i	0.584365	−	1.01215i
$850$			38950.7i			1.57176i
$851$	5000.29	+	2886.92i	0.201419	+	0.116289i
$852$	12062.9	+	6964.54i	0.485058	+	0.280048i
$853$			7958.24i			0.319443i	0.987162	+	0.159721i	$0.0510596\pi$
$853$			7958.24i			0.319443i	−0.987162	+	0.159721i	$0.948940\pi$
$854$	−3166.16	+	5483.94i	−0.126866	+	0.219738i
$855$	11974.3	+	20740.0i	0.478960	+	0.829583i
$856$	15173.8	−	8760.61i	0.605877	−	0.349803i
$857$	2144.65			0.0854840			0.0427420	−	0.999086i	$-0.486391\pi$
$857$	2144.65			0.0854840			0.0427420	+	0.999086i	$0.486391\pi$
$858$		0			0
$859$	−41723.5			−1.65726			−0.828632	−	0.559794i	$-0.810880\pi$
$859$	−41723.5			−1.65726			−0.828632	+	0.559794i	$0.810880\pi$
$860$	−39964.7	+	23073.6i	−1.58463	+	0.914889i
$861$	−2440.91	−	4227.78i	−0.0966156	−	0.167343i
$862$	−8703.84	+	15075.5i	−0.343914	+	0.595677i
$863$			10393.8i			0.409977i	0.978764	+	0.204989i	$0.0657157\pi$
$863$			10393.8i			0.409977i	−0.978764	+	0.204989i	$0.934284\pi$
$864$	−7010.03	−	4047.24i	−0.276025	−	0.159363i
$865$	−9233.47	−	5330.94i	−0.362945	−	0.209546i
$866$			172.204i			0.00675718i
$867$	−1438.71	+	2491.92i	−0.0563567	+	0.0976126i
$868$	1596.15	+	2764.61i	0.0624157	+	0.108107i
$869$	−3127.01	+	1805.38i	−0.122067	+	0.0704757i
$870$	30131.2			1.17419
$871$		0			0
$872$	30167.4			1.17156
$873$	14031.6	−	8101.14i	0.543983	−	0.314069i
$874$	−1624.86	−	2814.35i	−0.0628854	−	0.108921i
$875$	14482.1	−	25083.8i	0.559525	−	0.969127i
$876$			12160.8i			0.469035i
$877$	−4334.97	−	2502.79i	−0.166912	−	0.0963664i	0.414217	−	0.910178i	$-0.364055\pi$
$877$	−4334.97	−	2502.79i	−0.166912	−	0.0963664i	−0.581129	+	0.813812i	$0.697389\pi$
$878$	−17099.4	−	9872.35i	−0.657263	−	0.379471i
$879$		−	16508.1i		−	0.633451i
$880$	58.4769	−	101.285i	0.00224006	−	0.00387990i
$881$	−7298.57	−	12641.5i	−0.279109	−	0.483431i	0.692054	−	0.721845i	$-0.256706\pi$
$881$	−7298.57	−	12641.5i	−0.279109	−	0.483431i	−0.971164	+	0.238414i	$0.923372\pi$
$882$	−8787.66	+	5073.56i	−0.335483	+	0.193691i
$883$	5629.11			0.214535			0.107268	−	0.994230i	$-0.465790\pi$
$883$	5629.11			0.214535			0.107268	+	0.994230i	$0.465790\pi$
$884$		0			0
$885$	50346.8			1.91230
$886$	7162.09	−	4135.04i	0.271575	−	0.156794i
$887$	−8507.44	−	14735.3i	−0.322043	−	0.557794i	0.658867	−	0.752260i	$-0.271036\pi$
$887$	−8507.44	−	14735.3i	−0.322043	−	0.557794i	−0.980909	+	0.194465i	$0.937703\pi$
$888$	13313.0	−	23058.8i	0.503103	−	0.871401i
$889$			3396.12i			0.128124i
$890$	−25352.9	−	14637.5i	−0.954865	−	0.551291i
$891$	3284.94	+	1896.56i	0.123513	+	0.0713100i
$892$		−	30732.5i		−	1.15359i
$893$	−7622.94	+	13203.3i	−0.285657	+	0.494773i
$894$	2797.16	+	4844.83i	0.104643	+	0.181248i
$895$	−6554.71	+	3784.36i	−0.244804	+	0.141338i
$896$	−7042.51			−0.262582
$897$		0			0
$898$	−11188.8			−0.415784
$899$	−8847.39	+	5108.04i	−0.328228	+	0.189502i
$900$	15916.3	+	27567.9i	0.589494	+	1.02103i
$901$	17529.4	−	30361.9i	0.648158	−	1.12264i
$902$			711.768i			0.0262741i
$903$	−19960.5	−	11524.2i	−0.735596	−	0.424697i
$904$	23798.8	+	13740.3i	0.875595	+	0.505525i
$905$		−	16265.3i		−	0.597434i
$906$	−11537.3	+	19983.1i	−0.423069	+	0.732776i
$907$	−9592.67	−	16615.0i	−0.351179	−	0.608260i	0.635277	−	0.772284i	$-0.280886\pi$
$907$	−9592.67	−	16615.0i	−0.351179	−	0.608260i	−0.986456	+	0.164024i	$0.947552\pi$
$908$	27549.6	−	15905.8i	1.00690	−	0.581334i
$909$	32743.2			1.19474
$910$		0			0
$911$	30427.5			1.10659			0.553297	−	0.832984i	$-0.313369\pi$
$911$	30427.5			1.10659			0.553297	+	0.832984i	$0.313369\pi$
$912$	426.074	−	245.994i	0.0154701	−	0.00893166i
$913$	423.375	+	733.307i	0.0153468	+	0.0265815i
$914$	−801.934	+	1388.99i	−0.0290215	+	0.0502667i
$915$		−	69583.3i		−	2.51405i
$916$	−5796.95	−	3346.87i	−0.209101	−	0.120725i
$917$	11712.9	+	6762.47i	0.421805	+	0.243529i
$918$			5607.03i			0.201590i
$919$	19875.4	−	34425.2i	0.713415	−	1.23567i	−0.250153	−	0.968206i	$-0.580481\pi$
$919$	19875.4	−	34425.2i	0.713415	−	1.23567i	0.963568	−	0.267465i	$-0.0861859\pi$
$920$	−7873.70	−	13637.7i	−0.282161	−	0.488718i
$921$	−4907.72	+	2833.47i	−0.175586	+	0.101375i
$922$	18207.9			0.650374
$923$		0			0
$924$	1152.07			0.0410176
$925$	45922.9	−	26513.6i	1.63236	−	0.942446i
$926$	4257.51	+	7374.23i	0.151091	+	0.261698i
$927$	−1383.86	+	2396.92i	−0.0490314	+	0.0849248i
$928$		−	22110.9i		−	0.782138i
$929$	−5422.08	−	3130.44i	−0.191488	−	0.110556i	0.401191	−	0.915995i	$-0.368596\pi$
$929$	−5422.08	−	3130.44i	−0.191488	−	0.110556i	−0.592679	+	0.805439i	$0.701930\pi$
$930$	18079.4	+	10438.2i	0.637470	+	0.368044i
$931$			15986.1i			0.562755i
$932$	−13522.2	+	23421.1i	−0.475251	+	0.823159i
$933$	−18932.7	−	32792.3i	−0.664338	−	1.15067i
$934$	488.440	−	282.001i	0.0171116	−	0.00987939i
$935$	−6695.26			−0.234180
$936$		0			0
$937$	−24497.3			−0.854101			−0.427050	−	0.904228i	$-0.640447\pi$
$937$	−24497.3			−0.854101			−0.427050	+	0.904228i	$0.640447\pi$
$938$	10952.3	−	6323.29i	0.381241	−	0.220109i
$939$	1087.76	+	1884.06i	0.0378039	+	0.0654783i
$940$	−14234.0	+	24654.0i	−0.493895	+	0.855451i
$941$			10199.1i			0.353326i	0.984271	+	0.176663i	$0.0565303\pi$
$941$			10199.1i			0.353326i	−0.984271	+	0.176663i	$0.943470\pi$
$942$	−29833.8	−	17224.6i	−1.03189	−	0.595761i
$943$	−2724.76	−	1573.14i	−0.0940938	−	0.0543251i
$944$		−	447.046i		−	0.0154133i
$945$	3502.46	−	6066.44i	0.120566	−	0.208827i
$946$	1680.22	+	2910.23i	0.0577471	+	0.100021i
$947$	−87.5797	+	50.5642i	−0.00300523	+	0.00173507i	−0.501502	−	0.865157i	$-0.667219\pi$
$947$	−87.5797	+	50.5642i	−0.00300523	+	0.00173507i	0.498497	+	0.866892i	$0.333886\pi$
$948$	−28362.4			−0.971695
$949$		0			0
$950$	−29845.7			−1.01929
$951$	49542.4	−	28603.3i	1.68930	−	0.975316i
$952$	6210.07	+	10756.2i	0.211418	+	0.366186i
$953$	−21098.5	+	36543.7i	−0.717155	+	1.24215i	0.244968	+	0.969531i	$0.421223\pi$
$953$	−21098.5	+	36543.7i	−0.717155	+	1.24215i	−0.962122	+	0.272618i	$0.912111\pi$
$954$			17051.6i			0.578684i
$955$	72326.2	+	41757.6i	2.45070	+	1.41491i
$956$	−16282.0	−	9400.40i	−0.550833	−	0.318024i
$957$			3686.88i			0.124535i
$958$	−1609.73	+	2788.13i	−0.0542881	+	0.0940297i
$959$	3139.88	+	5438.43i	0.105727	+	0.183124i
$960$	−37860.5	+	21858.8i	−1.27286	+	0.734885i
$961$	22712.8			0.762405
$962$		0			0
$963$	−16015.8			−0.535931
$964$	16632.8	−	9602.94i	0.555712	−	0.320840i
$965$	1721.60	+	2981.91i	0.0574305	+	0.0994725i
$966$	1515.36	−	2624.68i	0.0504719	−	0.0874198i
$967$		−	1221.07i		−	0.0406069i	−0.999794	−	0.0203035i	$-0.993537\pi$
$967$		−	1221.07i		−	0.0406069i	0.999794	−	0.0203035i	$-0.00646324\pi$
$968$	25541.2	+	14746.2i	0.848064	+	0.489630i
$969$	−24391.5	−	14082.4i	−0.808634	−	0.466865i
$970$			28365.4i			0.938924i
$971$	21457.8	−	37166.1i	0.709181	−	1.22834i	−0.255980	−	0.966682i	$-0.582398\pi$
$971$	21457.8	−	37166.1i	0.709181	−	1.22834i	0.965161	−	0.261656i	$-0.0842684\pi$
$972$	11887.6	+	20590.0i	0.392279	+	0.679448i
$973$	−6482.25	+	3742.53i	−0.213578	+	0.123309i
$974$	−30024.8			−0.987739
$975$		0			0
$976$	−617.853			−0.0202633
$977$	−27066.4	+	15626.8i	−0.886315	+	0.511714i	−0.872735	−	0.488193i	$-0.837656\pi$
$977$	−27066.4	+	15626.8i	−0.886315	+	0.511714i	−0.0135799	+	0.999908i	$0.504323\pi$
$978$	−13664.8	−	23668.1i	−0.446781	−	0.773847i
$979$	1791.06	−	3102.20i	0.0584703	−	0.101273i
$980$			29850.2i			0.972989i
$981$	−23881.0	−	13787.7i	−0.777228	−	0.448733i
$982$	−28813.6	−	16635.6i	−0.936334	−	0.540593i
$983$		−	41688.2i		−	1.35264i	−0.736608	−	0.676320i	$-0.763574\pi$
$983$		−	41688.2i		−	1.35264i	0.736608	−	0.676320i	$-0.236426\pi$
$984$	−7254.54	+	12565.2i	−0.235027	+	0.407078i
$985$	8552.79	+	14813.9i	0.276665	+	0.479197i
$986$	−13264.2	+	7658.07i	−0.428415	+	0.247345i
$987$	−14218.4			−0.458537
$988$		0			0
$989$	−14854.4			−0.477597
$990$	2820.09	−	1628.18i	0.0905338	−	0.0522697i
$991$	−10186.0	−	17642.6i	−0.326506	−	0.565526i	0.655310	−	0.755360i	$-0.272538\pi$
$991$	−10186.0	−	17642.6i	−0.326506	−	0.565526i	−0.981816	+	0.189835i	$0.939205\pi$
$992$	7659.73	−	13267.0i	0.245158	−	0.424626i
$993$		−	5896.47i		−	0.188438i
$994$	−4558.94	−	2632.11i	−0.145474	−	0.0839893i
$995$	−695.717	−	401.672i	−0.0221665	−	0.0127979i
$996$			6651.18i			0.211597i
$997$	−9348.27	+	16191.7i	−0.296954	+	0.514339i	−0.975437	−	0.220277i	$-0.929304\pi$
$997$	−9348.27	+	16191.7i	−0.296954	+	0.514339i	0.678484	+	0.734615i	$0.262637\pi$
$998$	−11305.8	−	19582.2i	−0.358596	−	0.621106i
$999$	6610.70	−	3816.69i	0.209363	−	0.120876i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.e.h.23.7		36
13.2	odd	12		169.4.a.l.1.3	yes	9
13.3	even	3		169.4.b.g.168.7		18
13.4	even	6	inner	169.4.e.h.147.7		36
13.5	odd	4		169.4.c.k.146.7		18
13.6	odd	12		169.4.c.k.22.7		18
13.7	odd	12		169.4.c.l.22.3		18
13.8	odd	4		169.4.c.l.146.3		18
13.9	even	3	inner	169.4.e.h.147.12		36
13.10	even	6		169.4.b.g.168.12		18
13.11	odd	12		169.4.a.k.1.7	✓	9
13.12	even	2	inner	169.4.e.h.23.12		36
39.2	even	12		1521.4.a.bg.1.7		9
39.11	even	12		1521.4.a.bh.1.3		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.4.a.k.1.7	✓	9	13.11	odd	12
169.4.a.l.1.3	yes	9	13.2	odd	12
169.4.b.g.168.7		18	13.3	even	3
169.4.b.g.168.12		18	13.10	even	6
169.4.c.k.22.7		18	13.6	odd	12
169.4.c.k.146.7		18	13.5	odd	4
169.4.c.l.22.3		18	13.7	odd	12
169.4.c.l.146.3		18	13.8	odd	4
169.4.e.h.23.7		36	1.1	even	1	trivial
169.4.e.h.23.12		36	13.12	even	2	inner
169.4.e.h.147.7		36	13.4	even	6	inner
169.4.e.h.147.12		36	13.9	even	3	inner
1521.4.a.bg.1.7		9	39.2	even	12
1521.4.a.bh.1.3		9	39.11	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)

\(f(q)\)	\(=\)	\(q+(-1.49617 + 0.863817i) q^{2} +(-3.44796 - 5.97204i) q^{3} +(-2.50764 + 4.34336i) q^{4} +20.8281i q^{5} +(10.3175 + 5.95681i) q^{6} +(6.55206 + 3.78283i) q^{7} -22.4856i q^{8} +(-10.2768 + 17.8000i) q^{9} +O(q^{10})\)	\(q+(-1.49617 + 0.863817i) q^{2} +(-3.44796 - 5.97204i) q^{3} +(-2.50764 + 4.34336i) q^{4} +20.8281i q^{5} +(10.3175 + 5.95681i) q^{6} +(6.55206 + 3.78283i) q^{7} -22.4856i q^{8} +(-10.2768 + 17.8000i) q^{9} +(-17.9916 - 31.1624i) q^{10} +(3.81307 - 2.20147i) q^{11} +34.5850 q^{12} -13.0707 q^{14} +(124.386 - 71.8143i) q^{15} +(-0.637664 - 1.10447i) q^{16} +(-36.5043 + 63.2274i) q^{17} -35.5091i q^{18} +(-48.4475 - 27.9712i) q^{19} +(-90.4639 - 52.2293i) q^{20} -52.1722i q^{21} +(-3.80334 + 6.58758i) q^{22} +(-16.8122 - 29.1196i) q^{23} +(-134.285 + 77.5295i) q^{24} -308.809 q^{25} -44.4536 q^{27} +(-32.8604 + 18.9720i) q^{28} +(-60.7146 - 105.161i) q^{29} +(-124.069 + 214.893i) q^{30} -84.1320i q^{31} +(157.693 + 91.0442i) q^{32} +(-26.2946 - 15.1812i) q^{33} -126.132i q^{34} +(-78.7891 + 136.467i) q^{35} +(-51.5411 - 89.2719i) q^{36} +(-148.710 + 85.8578i) q^{37} +96.6479 q^{38} +468.332 q^{40} +(81.0352 - 46.7857i) q^{41} +(45.0672 + 78.0586i) q^{42} +(220.888 - 382.589i) q^{43} +22.0820i q^{44} +(-370.739 - 214.046i) q^{45} +(50.3080 + 29.0453i) q^{46} -272.528i q^{47} +(-4.39727 + 7.61630i) q^{48} +(-142.880 - 247.476i) q^{49} +(462.032 - 266.754i) q^{50} +503.461 q^{51} -480.202 q^{53} +(66.5103 - 38.3998i) q^{54} +(45.8525 + 79.4188i) q^{55} +(85.0594 - 147.327i) q^{56} +385.774i q^{57} +(181.679 + 104.893i) q^{58} +(303.572 + 175.267i) q^{59} +720.338i q^{60} +(242.233 - 419.560i) q^{61} +(72.6746 + 125.876i) q^{62} +(-134.669 + 77.7509i) q^{63} -304.379 q^{64} +52.4550 q^{66} +(-837.925 + 483.776i) q^{67} +(-183.080 - 317.103i) q^{68} +(-115.936 + 200.806i) q^{69} -272.237i q^{70} +(348.791 + 201.375i) q^{71} +(400.244 + 231.081i) q^{72} +351.621i q^{73} +(148.331 - 256.916i) q^{74} +(1064.76 + 1844.22i) q^{75} +(242.978 - 140.283i) q^{76} +33.3112 q^{77} -820.078 q^{79} +(23.0039 - 13.2813i) q^{80} +(430.748 + 746.078i) q^{81} +(-80.8285 + 139.999i) q^{82} +192.314i q^{83} +(226.603 + 130.829i) q^{84} +(-1316.90 - 760.315i) q^{85} +763.226i q^{86} +(-418.683 + 725.180i) q^{87} +(-49.5016 - 85.7392i) q^{88} +(704.573 - 406.786i) q^{89} +739.587 q^{90} +168.636 q^{92} +(-502.439 + 290.083i) q^{93} +(235.414 + 407.750i) q^{94} +(582.586 - 1009.07i) q^{95} -1255.67i q^{96} +(-682.682 - 394.146i) q^{97} +(427.548 + 246.845i) q^{98} +90.4966i 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

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Representations

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Database

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