LMFDB - Embedded newform 338.4.c.h.191.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [338,4,Mod(191,338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(338, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("338.191"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	338.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-4,3,-8,38] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$19.9426455819$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{217})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 55x^{2} + 54x + 2916 $ x^4 - x^3 + 55x^2 + 54x + 2916
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			191.2
Root			$3.93273 - 6.81169i$ of defining polynomial
Character	$\chi$	$=$	338.191
Dual form			338.4.c.h.315.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 1.73205i) q^{2} +(4.43273 - 7.67771i) q^{3} +(-2.00000 - 3.46410i) q^{4} +16.8655 q^{5} +(8.86546 + 15.3554i) q^{6} +(-5.43273 - 9.40976i) q^{7} +8.00000 q^{8} +(-25.7982 - 44.6838i) q^{9} +(-16.8655 + 29.2118i) q^{10} +(17.5964 - 30.4778i) q^{11} -35.4618 q^{12} +21.7309 q^{14} +(74.7600 - 129.488i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-15.1636 - 26.2642i) q^{17} +103.193 q^{18} +(14.1928 + 24.5826i) q^{19} +(-33.7309 - 58.4237i) q^{20} -96.3273 q^{21} +(35.1928 + 60.9556i) q^{22} +(12.3273 - 21.3515i) q^{23} +(35.4618 - 61.4217i) q^{24} +159.444 q^{25} -218.058 q^{27} +(-21.7309 + 37.6391i) q^{28} +(-145.058 + 251.248i) q^{29} +(149.520 + 258.976i) q^{30} +219.731 q^{31} +(-16.0000 - 27.7128i) q^{32} +(-156.000 - 270.200i) q^{33} +60.6546 q^{34} +(-91.6255 - 158.700i) q^{35} +(-103.193 + 178.735i) q^{36} +(-59.3564 + 102.808i) q^{37} -56.7710 q^{38} +134.924 q^{40} +(-41.8474 + 72.4818i) q^{41} +(96.3273 - 166.844i) q^{42} +(-146.818 - 254.297i) q^{43} -140.771 q^{44} +(-435.098 - 753.612i) q^{45} +(24.6546 + 42.7030i) q^{46} -166.211 q^{47} +(70.9237 + 122.843i) q^{48} +(112.471 - 194.805i) q^{49} +(-159.444 + 276.165i) q^{50} -268.865 q^{51} -76.3855 q^{53} +(218.058 - 377.688i) q^{54} +(296.771 - 514.023i) q^{55} +(-43.4618 - 75.2781i) q^{56} +251.651 q^{57} +(-290.116 - 502.496i) q^{58} +(-92.3454 - 159.947i) q^{59} -598.080 q^{60} +(-98.9056 - 171.309i) q^{61} +(-219.731 + 380.585i) q^{62} +(-280.309 + 485.510i) q^{63} +64.0000 q^{64} +624.000 q^{66} +(-160.636 + 278.231i) q^{67} +(-60.6546 + 105.057i) q^{68} +(-109.287 - 189.291i) q^{69} +366.502 q^{70} +(184.473 + 319.516i) q^{71} +(-206.386 - 357.470i) q^{72} +843.273 q^{73} +(-118.713 - 205.617i) q^{74} +(706.771 - 1224.16i) q^{75} +(56.7710 - 98.3303i) q^{76} -382.386 q^{77} +184.044 q^{79} +(-134.924 + 233.695i) q^{80} +(-270.042 + 467.727i) q^{81} +(-83.6947 - 144.964i) q^{82} +1274.16 q^{83} +(192.655 + 333.688i) q^{84} +(-255.742 - 442.958i) q^{85} +587.273 q^{86} +(1286.01 + 2227.43i) q^{87} +(140.771 - 243.823i) q^{88} +(683.717 - 1184.23i) q^{89} +1740.39 q^{90} -98.6184 q^{92} +(974.008 - 1687.03i) q^{93} +(166.211 - 287.886i) q^{94} +(239.367 + 414.597i) q^{95} -283.695 q^{96} +(345.120 + 597.766i) q^{97} +(224.942 + 389.611i) q^{98} -1815.82 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 3 q^{3} - 8 q^{4} + 38 q^{5} + 6 q^{6} - 7 q^{7} + 32 q^{8} - 59 q^{9} - 38 q^{10} - 18 q^{11} - 24 q^{12} + 28 q^{14} + 137 q^{15} - 32 q^{16} + 13 q^{17} + 236 q^{18} - 120 q^{19} - 76 q^{20}+ \cdots - 2844 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 3 * q^3 - 8 * q^4 + 38 * q^5 + 6 * q^6 - 7 * q^7 + 32 * q^8 - 59 * q^9 - 38 * q^10 - 18 * q^11 - 24 * q^12 + 28 * q^14 + 137 * q^15 - 32 * q^16 + 13 * q^17 + 236 * q^18 - 120 * q^19 - 76 * q^20 - 238 * q^21 - 36 * q^22 - 98 * q^23 + 24 * q^24 + 78 * q^25 - 666 * q^27 - 28 * q^28 - 374 * q^29 + 274 * q^30 + 820 * q^31 - 64 * q^32 - 624 * q^33 - 52 * q^34 - 175 * q^35 - 236 * q^36 + 13 * q^37 + 480 * q^38 + 304 * q^40 + 304 * q^41 + 238 * q^42 - 219 * q^43 + 144 * q^44 - 886 * q^45 - 196 * q^46 - 930 * q^47 + 48 * q^48 + 553 * q^49 - 78 * q^50 - 1046 * q^51 + 48 * q^53 + 666 * q^54 + 480 * q^55 - 56 * q^56 + 2244 * q^57 - 748 * q^58 - 664 * q^59 - 1096 * q^60 + 282 * q^61 - 820 * q^62 - 532 * q^63 + 256 * q^64 + 2496 * q^66 + 94 * q^67 + 52 * q^68 - 938 * q^69 + 700 * q^70 + 75 * q^71 - 472 * q^72 + 1900 * q^73 + 26 * q^74 + 2120 * q^75 - 480 * q^76 - 1176 * q^77 - 1444 * q^79 - 304 * q^80 + 334 * q^81 + 608 * q^82 + 2504 * q^83 + 476 * q^84 - 419 * q^85 + 876 * q^86 + 2080 * q^87 - 144 * q^88 + 702 * q^89 + 3544 * q^90 + 784 * q^92 + 832 * q^93 + 930 * q^94 + 162 * q^95 - 192 * q^96 - 564 * q^97 + 1106 * q^98 - 2844 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$3$	4.43273	−	7.67771i	0.853079	−	1.47758i	−0.0253362	−	0.999679i	$-0.508066\pi$
$3$	4.43273	−	7.67771i	0.853079	−	1.47758i	0.878416	−	0.477898i	$-0.158601\pi$
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	16.8655			1.50849			0.754246	−	0.656592i	$-0.228002\pi$
$5$	16.8655			1.50849			0.754246	+	0.656592i	$0.228002\pi$
$6$	8.86546	+	15.3554i	0.603218	+	1.04480i
$7$	−5.43273	−	9.40976i	−0.293340	−	0.508080i	0.681257	−	0.732044i	$-0.261433\pi$
$7$	−5.43273	−	9.40976i	−0.293340	−	0.508080i	−0.974597	+	0.223964i	$0.928100\pi$
$8$	8.00000			0.353553
$9$	−25.7982	−	44.6838i	−0.955489	−	1.65495i
$10$	−16.8655	+	29.2118i	−0.533333	+	0.923759i
$11$	17.5964	−	30.4778i	0.482319	−	0.835401i	−0.517475	−	0.855698i	$-0.673128\pi$
$11$	17.5964	−	30.4778i	0.482319	−	0.835401i	0.999794	+	0.0202974i	$0.00646131\pi$
$12$	−35.4618			−0.853079
$13$		0			0
$13$		0			0
$14$	21.7309			0.414845
$15$	74.7600	−	129.488i	1.28686	−	2.22891i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−15.1636	−	26.2642i	−0.216337	−	0.374706i	0.737348	−	0.675513i	$-0.236078\pi$
$17$	−15.1636	−	26.2642i	−0.216337	−	0.374706i	−0.953685	+	0.300806i	$0.902744\pi$
$18$	103.193			1.35126
$19$	14.1928	+	24.5826i	0.171371	+	0.296823i	0.938899	−	0.344192i	$-0.111847\pi$
$19$	14.1928	+	24.5826i	0.171371	+	0.296823i	−0.767529	+	0.641015i	$0.778514\pi$
$20$	−33.7309	−	58.4237i	−0.377123	−	0.653196i
$21$	−96.3273			−1.00097
$22$	35.1928	+	60.9556i	0.341051	+	0.590718i
$23$	12.3273	−	21.3515i	0.111757	−	0.193569i	−0.804722	−	0.593652i	$-0.797685\pi$
$23$	12.3273	−	21.3515i	0.111757	−	0.193569i	0.916479	+	0.400083i	$0.131019\pi$
$24$	35.4618	−	61.4217i	0.301609	−	0.522402i
$25$	159.444			1.27555
$26$		0			0
$27$	−218.058			−1.55427
$28$	−21.7309	+	37.6391i	−0.146670	+	0.254040i
$29$	−145.058	+	251.248i	−0.928849	+	1.60881i	−0.143599	+	0.989636i	$0.545868\pi$
$29$	−145.058	+	251.248i	−0.928849	+	1.60881i	−0.785250	+	0.619179i	$0.787466\pi$
$30$	149.520	+	258.976i	0.909950	+	1.57608i
$31$	219.731			1.27306			0.636530	−	0.771252i	$-0.280369\pi$
$31$	219.731			1.27306			0.636530	+	0.771252i	$0.280369\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$	−156.000	−	270.200i	−0.822913	−	1.42533i
$34$	60.6546			0.305946
$35$	−91.6255	−	158.700i	−0.442501	−	0.766434i
$36$	−103.193	+	178.735i	−0.477744	+	0.827477i
$37$	−59.3564	+	102.808i	−0.263733	+	0.456800i	−0.967231	−	0.253898i	$-0.918287\pi$
$37$	−59.3564	+	102.808i	−0.263733	+	0.456800i	0.703498	+	0.710698i	$0.251621\pi$
$38$	−56.7710			−0.242355
$39$		0			0
$40$	134.924			0.533333
$41$	−41.8474	+	72.4818i	−0.159401	+	0.276091i	−0.934653	−	0.355561i	$-0.884290\pi$
$41$	−41.8474	+	72.4818i	−0.159401	+	0.276091i	0.775252	+	0.631653i	$0.217623\pi$
$42$	96.3273	−	166.844i	0.353896	−	0.612966i
$43$	−146.818	−	254.297i	−0.520688	−	0.901858i	−0.999711	−	0.0240552i	$-0.992342\pi$
$43$	−146.818	−	254.297i	−0.520688	−	0.901858i	0.479023	−	0.877802i	$-0.340991\pi$
$44$	−140.771			−0.482319
$45$	−435.098	−	753.612i	−1.44135	−	2.49649i
$46$	24.6546	+	42.7030i	0.0790244	+	0.136874i
$47$	−166.211			−0.515837			−0.257919	−	0.966167i	$-0.583037\pi$
$47$	−166.211			−0.515837			−0.257919	+	0.966167i	$0.583037\pi$
$48$	70.9237	+	122.843i	0.213270	+	0.369394i
$49$	112.471	−	194.805i	0.327903	−	0.567945i
$50$	−159.444	+	276.165i	−0.450975	+	0.781112i
$51$	−268.865			−0.738210
$52$		0			0
$53$	−76.3855			−0.197969			−0.0989845	−	0.995089i	$-0.531559\pi$
$53$	−76.3855			−0.197969			−0.0989845	+	0.995089i	$0.531559\pi$
$54$	218.058	−	377.688i	0.549518	−	0.951793i
$55$	296.771	−	514.023i	0.727575	−	1.26020i
$56$	−43.4618	−	75.2781i	−0.103711	−	0.179633i
$57$	251.651			0.584771
$58$	−290.116	−	502.496i	−0.656796	−	1.13760i
$59$	−92.3454	−	159.947i	−0.203769	−	0.352938i	0.745971	−	0.665978i	$-0.231986\pi$
$59$	−92.3454	−	159.947i	−0.203769	−	0.352938i	−0.949740	+	0.313041i	$0.898652\pi$
$60$	−598.080			−1.28686
$61$	−98.9056	−	171.309i	−0.207599	−	0.359573i	0.743358	−	0.668893i	$-0.233232\pi$
$61$	−98.9056	−	171.309i	−0.207599	−	0.359573i	−0.950958	+	0.309321i	$0.899898\pi$
$62$	−219.731	+	380.585i	−0.450094	+	0.779586i
$63$	−280.309	+	485.510i	−0.560566	+	0.970928i
$64$	64.0000			0.125000
$65$		0			0
$66$	624.000			1.16377
$67$	−160.636	+	278.231i	−0.292909	+	0.507332i	−0.974496	−	0.224404i	$-0.927956\pi$
$67$	−160.636	+	278.231i	−0.292909	+	0.507332i	0.681588	+	0.731736i	$0.261290\pi$
$68$	−60.6546	+	105.057i	−0.108168	+	0.187353i
$69$	−109.287	−	189.291i	−0.190676	−	0.330260i
$70$	366.502			0.625791
$71$	184.473	+	319.516i	0.308351	+	0.534079i	0.978002	−	0.208597i	$-0.0668896\pi$
$71$	184.473	+	319.516i	0.308351	+	0.534079i	−0.669651	+	0.742676i	$0.733556\pi$
$72$	−206.386	−	357.470i	−0.337816	−	0.585115i
$73$	843.273			1.35202			0.676011	−	0.736891i	$-0.263707\pi$
$73$	843.273			1.35202			0.676011	+	0.736891i	$0.263707\pi$
$74$	−118.713	−	205.617i	−0.186488	−	0.323006i
$75$	706.771	−	1224.16i	1.08815	−	1.88472i
$76$	56.7710	−	98.3303i	0.0856853	−	0.148411i
$77$	−382.386			−0.565933
$78$		0			0
$79$	184.044			0.262109			0.131054	−	0.991375i	$-0.458164\pi$
$79$	184.044			0.262109			0.131054	+	0.991375i	$0.458164\pi$
$80$	−134.924	+	233.695i	−0.188562	+	0.326598i
$81$	−270.042	+	467.727i	−0.370428	+	0.641600i
$82$	−83.6947	−	144.964i	−0.112714	−	0.195226i
$83$	1274.16			1.68503			0.842514	−	0.538675i	$-0.181075\pi$
$83$	1274.16			1.68503			0.842514	+	0.538675i	$0.181075\pi$
$84$	192.655	+	333.688i	0.250242	+	0.433432i
$85$	−255.742	−	442.958i	−0.326342	−	0.565242i
$86$	587.273			0.736364
$87$	1286.01	+	2227.43i	1.58476	+	2.74489i
$88$	140.771	−	243.823i	0.170525	−	0.295359i
$89$	683.717	−	1184.23i	0.814313	−	1.41043i	−0.0955077	−	0.995429i	$-0.530447\pi$
$89$	683.717	−	1184.23i	0.814313	−	1.41043i	0.909820	−	0.415002i	$-0.136219\pi$
$90$	1740.39			2.03837
$91$		0			0
$92$	−98.6184			−0.111757
$93$	974.008	−	1687.03i	1.08602	−	1.88104i
$94$	166.211	−	287.886i	0.182376	−	0.315884i
$95$	239.367	+	414.597i	0.258511	+	0.447755i
$96$	−283.695			−0.301609
$97$	345.120	+	597.766i	0.361254	+	0.625711i	0.988168	−	0.153378i	$-0.0490153\pi$
$97$	345.120	+	597.766i	0.361254	+	0.625711i	−0.626913	+	0.779089i	$0.715682\pi$
$98$	224.942	+	389.611i	0.231863	+	0.401598i
$99$	−1815.82			−1.84340
$100$	−318.887	−	552.329i	−0.318887	−	0.552329i
$101$	−697.604	+	1208.29i	−0.687269	+	1.19039i	0.285448	+	0.958394i	$0.407857\pi$
$101$	−697.604	+	1208.29i	−0.687269	+	1.19039i	−0.972718	+	0.231992i	$0.925476\pi$
$102$	268.865	−	465.689i	0.260997	−	0.452059i
$103$	−1416.28			−1.35485			−0.677427	−	0.735590i	$-0.736905\pi$
$103$	−1416.28			−1.35485			−0.677427	+	0.735590i	$0.736905\pi$
$104$		0			0
$105$	−1624.60			−1.50995
$106$	76.3855	−	132.304i	0.0699926	−	0.121231i
$107$	−225.534	+	390.637i	−0.203768	+	0.352937i	−0.949740	−	0.313041i	$-0.898652\pi$
$107$	−225.534	+	390.637i	−0.203768	+	0.352937i	0.745971	+	0.665978i	$0.231986\pi$
$108$	436.116	+	755.376i	0.388568	+	0.673019i
$109$	−1386.13			−1.21805			−0.609024	−	0.793152i	$-0.708439\pi$
$109$	−1386.13			−1.21805			−0.609024	+	0.793152i	$0.708439\pi$
$110$	593.542	+	1028.05i	0.514473	+	0.891093i
$111$	526.222	+	911.443i	0.449971	+	0.779372i
$112$	173.847			0.146670
$113$	−764.389	−	1323.96i	−0.636351	−	1.10219i	−0.986227	−	0.165397i	$-0.947110\pi$
$113$	−764.389	−	1323.96i	−0.636351	−	1.10219i	0.349876	−	0.936796i	$-0.386224\pi$
$114$	−251.651	+	435.872i	−0.206748	+	0.358098i
$115$	207.906	−	360.103i	0.168585	−	0.291998i
$116$	1160.47			0.928849
$117$		0			0
$118$	369.382			0.288172
$119$	−164.760	+	285.373i	−0.126920	+	0.219833i
$120$	598.080	−	1035.91i	0.454975	−	0.788040i
$121$	46.2348	+	80.0811i	0.0347369	+	0.0601661i
$122$	395.622			0.293590
$123$	370.996	+	642.584i	0.271964	+	0.471056i
$124$	−439.462	−	761.170i	−0.318265	−	0.551251i
$125$	580.909			0.415665
$126$	−560.618	−	971.020i	−0.396380	−	0.686550i
$127$	723.833	−	1253.72i	0.505747	−	0.875979i	−0.494231	−	0.869330i	$-0.664550\pi$
$127$	723.833	−	1253.72i	0.505747	−	0.875979i	0.999978	−	0.00664827i	$-0.00211622\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$	−2603.22			−1.77675
$130$		0			0
$131$	631.877			0.421430			0.210715	−	0.977548i	$-0.432421\pi$
$131$	631.877			0.421430			0.210715	+	0.977548i	$0.432421\pi$
$132$	−624.000	+	1080.80i	−0.411456	+	0.712663i
$133$	154.211	−	267.101i	0.100540	−	0.174140i
$134$	−321.273	−	556.461i	−0.207118	−	0.358738i
$135$	−3677.65			−2.34461
$136$	−121.309	−	210.114i	−0.0764866	−	0.132479i
$137$	273.709	+	474.078i	0.170690	+	0.295644i	0.938661	−	0.344841i	$-0.112067\pi$
$137$	273.709	+	474.078i	0.170690	+	0.295644i	−0.767971	+	0.640484i	$0.778734\pi$
$138$	437.149			0.269656
$139$	338.535	+	586.360i	0.206577	+	0.357801i	0.950634	−	0.310315i	$-0.100434\pi$
$139$	338.535	+	586.360i	0.206577	+	0.357801i	−0.744057	+	0.668116i	$0.767101\pi$
$140$	−366.502	+	634.800i	−0.221250	+	0.383217i
$141$	−736.768	+	1276.12i	−0.440050	+	0.762189i
$142$	−737.891			−0.436074
$143$		0			0
$144$	825.542			0.477744
$145$	−2446.47	+	4237.42i	−1.40116	+	2.42688i
$146$	−843.273	+	1460.59i	−0.478012	+	0.827941i
$147$	−997.106	−	1727.04i	−0.559455	−	0.969005i
$148$	474.851			0.263733
$149$	142.167	+	246.240i	0.0781662	+	0.135388i	0.902459	−	0.430776i	$-0.141760\pi$
$149$	142.167	+	246.240i	0.0781662	+	0.135388i	−0.824293	+	0.566164i	$0.808427\pi$
$150$	1413.54	+	2448.33i	0.769435	+	1.33270i
$151$	2708.68			1.45980			0.729899	−	0.683555i	$-0.239567\pi$
$151$	2708.68			1.45980			0.729899	+	0.683555i	$0.239567\pi$
$152$	113.542	+	196.661i	0.0605887	+	0.104943i
$153$	−782.389	+	1355.14i	−0.413415	+	0.716055i
$154$	382.386	−	662.311i	0.200088	−	0.346562i
$155$	3705.86			1.92040
$156$		0			0
$157$	−883.775			−0.449254			−0.224627	−	0.974445i	$-0.572116\pi$
$157$	−883.775			−0.449254			−0.224627	+	0.974445i	$0.572116\pi$
$158$	−184.044	+	318.774i	−0.0926693	+	0.160508i
$159$	−338.596	+	586.466i	−0.168883	+	0.292514i
$160$	−269.847	−	467.389i	−0.133333	−	0.230940i
$161$	−267.884			−0.131132
$162$	−540.084	−	935.453i	−0.261932	−	0.453680i
$163$	1670.39	+	2893.20i	0.802669	+	1.39026i	0.917854	+	0.396919i	$0.129921\pi$
$163$	1670.39	+	2893.20i	0.802669	+	1.39026i	−0.115185	+	0.993344i	$0.536746\pi$
$164$	334.779			0.159401
$165$	−2631.01	−	4557.05i	−1.24136	−	2.15009i
$166$	−1274.16	+	2206.91i	−0.595747	+	1.03186i
$167$	−908.259	+	1573.15i	−0.420857	+	0.728946i	−0.996024	−	0.0890903i	$-0.971604\pi$
$167$	−908.259	+	1573.15i	−0.420857	+	0.728946i	0.575166	+	0.818037i	$0.304937\pi$
$168$	−770.618			−0.353896
$169$		0			0
$170$	1022.97			0.461518
$171$	732.295	−	1268.37i	0.327485	−	0.567221i
$172$	−587.273	+	1017.19i	−0.260344	+	0.450929i
$173$	492.120	+	852.377i	0.216273	+	0.374596i	0.953666	−	0.300869i	$-0.0972766\pi$
$173$	492.120	+	852.377i	0.216273	+	0.374596i	−0.737393	+	0.675464i	$0.763943\pi$
$174$	−5144.03			−2.24120
$175$	−866.215	−	1500.33i	−0.374170	−	0.648081i
$176$	281.542	+	487.645i	0.120580	+	0.208850i
$177$	−1637.37			−0.695323
$178$	1367.43	+	2368.46i	0.575806	+	0.997325i
$179$	1888.66	−	3271.25i	0.788631	−	1.36595i	−0.138174	−	0.990408i	$-0.544123\pi$
$179$	1888.66	−	3271.25i	0.788631	−	1.36595i	0.926805	−	0.375542i	$-0.122543\pi$
$180$	−1740.39	+	3014.45i	−0.720674	+	1.24824i
$181$	2329.80			0.956754			0.478377	−	0.878154i	$-0.341225\pi$
$181$	2329.80			0.956754			0.478377	+	0.878154i	$0.341225\pi$
$182$		0			0
$183$	−1753.69			−0.708395
$184$	98.6184	−	170.812i	0.0395122	−	0.0684371i
$185$	−1001.07	+	1733.91i	−0.397840	+	0.689079i
$186$	1948.02	+	3374.06i	0.767932	+	1.33010i
$187$	−1067.30			−0.417373
$188$	332.422	+	575.771i	0.128959	+	0.223364i
$189$	1184.65	+	2051.88i	0.455930	+	0.789693i
$190$	−957.470			−0.365590
$191$	2305.96	+	3994.05i	0.873579	+	1.51308i	0.858268	+	0.513201i	$0.171541\pi$
$191$	2305.96	+	3994.05i	0.873579	+	1.51308i	0.0153112	+	0.999883i	$0.495126\pi$
$192$	283.695	−	491.374i	0.106635	−	0.184697i
$193$	−476.400	+	825.148i	−0.177679	+	0.307749i	−0.941085	−	0.338170i	$-0.890192\pi$
$193$	−476.400	+	825.148i	−0.177679	+	0.307749i	0.763406	+	0.645919i	$0.223525\pi$
$194$	−1380.48			−0.510891
$195$		0			0
$196$	−899.767			−0.327903
$197$	−1025.27	+	1775.82i	−0.370799	+	0.642243i	−0.989689	−	0.143235i	$-0.954250\pi$
$197$	−1025.27	+	1775.82i	−0.370799	+	0.642243i	0.618889	+	0.785478i	$0.287583\pi$
$198$	1815.82	−	3145.09i	0.651741	−	1.12885i
$199$	1292.65	+	2238.94i	0.460472	+	0.797560i	0.998984	−	0.0450571i	$-0.0143470\pi$
$199$	1292.65	+	2238.94i	0.460472	+	0.797560i	−0.538513	+	0.842617i	$0.681014\pi$
$200$	1275.55			0.450975
$201$	1424.12	+	2466.64i	0.499748	+	0.865590i
$202$	−1395.21	−	2416.57i	−0.485973	−	0.841730i
$203$	3152.25			1.08987
$204$	537.731	+	931.377i	0.184552	+	0.319654i
$205$	−705.775	+	1222.44i	−0.240456	+	0.416482i
$206$	1416.28	−	2453.06i	0.479013	−	0.829675i
$207$	−1272.09			−0.427132
$208$		0			0
$209$	998.965			0.330621
$210$	1624.60	−	2813.90i	0.533849	−	0.924654i
$211$	878.113	−	1520.94i	0.286501	−	0.496235i	−0.686471	−	0.727157i	$-0.740841\pi$
$211$	878.113	−	1520.94i	0.286501	−	0.496235i	0.972972	+	0.230922i	$0.0741743\pi$
$212$	152.771	+	264.607i	0.0494923	+	0.0857231i
$213$	3270.87			1.05219
$214$	−451.068	−	781.274i	−0.144086	−	0.249564i
$215$	−2476.16	−	4288.83i	−0.785454	−	1.36045i
$216$	−1744.47			−0.549518
$217$	−1193.74	−	2067.62i	−0.373439	−	0.646815i
$218$	1386.13	−	2400.85i	0.430645	−	0.745899i
$219$	3738.00	−	6474.41i	1.15338	−	1.99772i
$220$	−2374.17			−0.727575
$221$		0			0
$222$	−2104.89			−0.636355
$223$	−1019.06	+	1765.07i	−0.306015	+	0.530034i	−0.977487	−	0.210996i	$-0.932329\pi$
$223$	−1019.06	+	1765.07i	−0.306015	+	0.530034i	0.671472	+	0.741030i	$0.265663\pi$
$224$	−173.847	+	301.112i	−0.0518556	+	0.0898166i
$225$	−4113.36	−	7124.55i	−1.21877	−	2.11098i
$226$	3057.56			0.899937
$227$	2345.93	+	4063.26i	0.685923	+	1.18805i	0.973146	+	0.230190i	$0.0739347\pi$
$227$	2345.93	+	4063.26i	0.685923	+	1.18805i	−0.287223	+	0.957864i	$0.592732\pi$
$228$	−503.301	−	871.744i	−0.146193	−	0.253213i
$229$	576.154			0.166259			0.0831296	−	0.996539i	$-0.473508\pi$
$229$	576.154			0.166259			0.0831296	+	0.996539i	$0.473508\pi$
$230$	415.811	+	720.206i	0.119208	+	0.206474i
$231$	−1695.01	+	2935.85i	−0.482786	+	0.836210i
$232$	−1160.47	+	2009.99i	−0.328398	+	0.568802i
$233$	724.319			0.203656			0.101828	−	0.994802i	$-0.467531\pi$
$233$	724.319			0.203656			0.101828	+	0.994802i	$0.467531\pi$
$234$		0			0
$235$	−2803.22			−0.778137
$236$	−369.382	+	639.788i	−0.101884	+	0.176469i
$237$	815.818	−	1413.04i	0.223599	−	0.387285i
$238$	−329.520	−	570.745i	−0.0897463	−	0.155445i
$239$	3137.80			0.849237			0.424619	−	0.905372i	$-0.360408\pi$
$239$	3137.80			0.849237			0.424619	+	0.905372i	$0.360408\pi$
$240$	1196.16	+	2071.81i	0.321716	+	0.557228i
$241$	881.869	+	1527.44i	0.235710	+	0.408262i	0.959479	−	0.281781i	$-0.0909250\pi$
$241$	881.869	+	1527.44i	0.235710	+	0.408262i	−0.723769	+	0.690043i	$0.757592\pi$
$242$	−184.939			−0.0491254
$243$	−549.739	−	952.175i	−0.145127	−	0.251367i
$244$	−395.622	+	685.238i	−0.103800	+	0.179786i
$245$	1896.87	−	3285.48i	0.494640	−	0.856742i
$246$	−1483.98			−0.384615
$247$		0			0
$248$	1757.85			0.450094
$249$	5648.01	−	9782.64i	1.43746	−	2.48976i
$250$	−580.909	+	1006.16i	−0.146960	+	0.254542i
$251$	823.004	+	1425.48i	0.206962	+	0.358469i	0.950756	−	0.309940i	$-0.100309\pi$
$251$	823.004	+	1425.48i	0.206962	+	0.358469i	−0.743794	+	0.668409i	$0.766976\pi$
$252$	2242.47			0.560566
$253$	−433.832	−	751.419i	−0.107805	−	0.186724i
$254$	1447.67	+	2507.43i	0.357617	+	0.619410i
$255$	−4534.54			−1.11358
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	3207.86	−	5556.18i	0.778603	−	1.34858i	−0.154144	−	0.988048i	$-0.549262\pi$
$257$	3207.86	−	5556.18i	0.778603	−	1.34858i	0.932747	−	0.360532i	$-0.117405\pi$
$258$	2603.22	−	4508.91i	0.628177	−	1.08803i
$259$	1289.87			0.309454
$260$		0			0
$261$	14969.0			3.55002
$262$	−631.877	+	1094.44i	−0.148998	+	0.258072i
$263$	1830.24	−	3170.07i	0.429116	−	0.743251i	−0.567679	−	0.823250i	$-0.692159\pi$
$263$	1830.24	−	3170.07i	0.429116	−	0.743251i	0.996795	+	0.0799995i	$0.0254919\pi$
$264$	−1248.00	−	2161.60i	−0.290944	−	0.503929i
$265$	−1288.28			−0.298635
$266$	308.422	+	534.202i	0.0710923	+	0.123135i
$267$	−6061.46	−	10498.8i	−1.38935	−	2.40642i
$268$	1285.09			0.292909
$269$	2822.65	+	4888.98i	0.639777	+	1.10813i	0.985481	+	0.169783i	$0.0543068\pi$
$269$	2822.65	+	4888.98i	0.639777	+	1.10813i	−0.345704	+	0.938344i	$0.612360\pi$
$270$	3677.65	−	6369.88i	0.828944	−	1.43577i
$271$	−3335.93	+	5778.01i	−0.747762	+	1.29516i	0.201131	+	0.979564i	$0.435538\pi$
$271$	−3335.93	+	5778.01i	−0.747762	+	1.29516i	−0.948893	+	0.315598i	$0.897795\pi$
$272$	485.237			0.108168
$273$		0			0
$274$	−1094.84			−0.241392
$275$	2805.63	−	4859.50i	0.615222	−	1.06560i
$276$	−437.149	+	757.164i	−0.0953379	+	0.165130i
$277$	1452.70	+	2516.14i	0.315105	+	0.545778i	0.979460	−	0.201640i	$-0.0646270\pi$
$277$	1452.70	+	2516.14i	0.315105	+	0.545778i	−0.664355	+	0.747417i	$0.731294\pi$
$278$	−1354.14			−0.292144
$279$	−5668.66	−	9818.41i	−1.21639	−	2.10686i
$280$	−733.004	−	1269.60i	−0.156448	−	0.270975i
$281$	−8009.76			−1.70044			−0.850218	−	0.526431i	$-0.823530\pi$
$281$	−8009.76			−1.70044			−0.850218	+	0.526431i	$0.823530\pi$
$282$	−1473.54	−	2552.24i	−0.311162	−	0.538949i
$283$	−1853.86	+	3210.97i	−0.389400	+	0.674461i	−0.992369	−	0.123304i	$-0.960651\pi$
$283$	−1853.86	+	3210.97i	−0.389400	+	0.674461i	0.602969	+	0.797765i	$0.293984\pi$
$284$	737.891	−	1278.07i	0.154175	−	0.267040i
$285$	4244.20			0.882123
$286$		0			0
$287$	909.382			0.187035
$288$	−825.542	+	1429.88i	−0.168908	+	0.292557i
$289$	1996.63	−	3458.26i	0.406397	−	0.703900i
$290$	−4892.95	−	8474.83i	−0.990772	−	1.71607i
$291$	6119.30			1.23271
$292$	−1686.55	−	2921.18i	−0.338006	−	0.585443i
$293$	−836.999	−	1449.73i	−0.166887	−	0.289058i	0.770437	−	0.637517i	$-0.220038\pi$
$293$	−836.999	−	1449.73i	−0.166887	−	0.289058i	−0.937324	+	0.348459i	$0.886705\pi$
$294$	3988.42			0.791189
$295$	−1557.45	−	2697.58i	−0.307383	−	0.532404i
$296$	−474.851	+	822.467i	−0.0932438	+	0.161503i
$297$	−3837.04	+	6645.94i	−0.749654	+	1.29844i
$298$	−568.667			−0.110544
$299$		0			0
$300$	−5654.17			−1.08815
$301$	−1595.25	+	2763.05i	−0.305477	+	0.529102i
$302$	−2708.68	+	4691.58i	−0.516117	+	0.893941i
$303$	6184.58	+	10712.0i	1.17259	+	2.03099i
$304$	−454.168			−0.0856853
$305$	−1668.09	−	2889.21i	−0.313162	−	0.542413i
$306$	−1564.78	−	2710.28i	−0.292328	−	0.506327i
$307$	−299.935			−0.0557597			−0.0278798	−	0.999611i	$-0.508876\pi$
$307$	−299.935			−0.0557597			−0.0278798	+	0.999611i	$0.508876\pi$
$308$	764.771	+	1324.62i	0.141483	+	0.245056i
$309$	−6277.97	+	10873.8i	−1.15580	+	2.00190i
$310$	−3705.86	+	6418.74i	−0.678964	+	1.17600i
$311$	−890.140			−0.162300			−0.0811498	−	0.996702i	$-0.525859\pi$
$311$	−890.140			−0.162300			−0.0811498	+	0.996702i	$0.525859\pi$
$312$		0			0
$313$	−1154.20			−0.208432			−0.104216	−	0.994555i	$-0.533233\pi$
$313$	−1154.20			−0.208432			−0.104216	+	0.994555i	$0.533233\pi$
$314$	883.775	−	1530.74i	0.158835	−	0.275111i
$315$	−4727.54	+	8188.35i	−0.845609	+	1.46464i
$316$	−368.088	−	637.547i	−0.0655271	−	0.113496i
$317$	2708.86			0.479951			0.239976	−	0.970779i	$-0.422861\pi$
$317$	2708.86			0.479951			0.239976	+	0.970779i	$0.422861\pi$
$318$	−677.193	−	1172.93i	−0.119419	−	0.206839i
$319$	5105.00	+	8842.12i	0.896003	+	1.55192i
$320$	1079.39			0.188562
$321$	1999.46	+	3463.17i	0.347661	+	0.602167i
$322$	267.884	−	463.988i	0.0463620	−	0.0803014i
$323$	430.428	−	745.523i	0.0741475	−	0.128427i
$324$	2160.34			0.370428
$325$		0			0
$326$	−6681.56			−1.13514
$327$	−6144.34	+	10642.3i	−1.03909	+	1.79976i
$328$	−334.779	+	579.854i	−0.0563569	+	0.0976131i
$329$	902.979	+	1564.01i	0.151316	+	0.262086i
$330$	10524.0			1.75554
$331$	−4093.56	−	7090.26i	−0.679766	−	1.17739i	−0.975051	−	0.221980i	$-0.928748\pi$
$331$	−4093.56	−	7090.26i	−0.679766	−	1.17739i	0.295285	−	0.955409i	$-0.404585\pi$
$332$	−2548.32	−	4413.82i	−0.421257	−	0.729638i
$333$	6125.15			1.00798
$334$	−1816.52	−	3146.30i	−0.297591	−	0.515443i
$335$	−2709.21	+	4692.49i	−0.441850	+	0.765307i
$336$	770.618	−	1334.75i	0.125121	−	0.216716i
$337$	−8770.94			−1.41776			−0.708878	−	0.705331i	$-0.750798\pi$
$337$	−8770.94			−1.41776			−0.708878	+	0.705331i	$0.750798\pi$
$338$		0			0
$339$	−13553.3			−2.17143
$340$	−1022.97	+	1771.83i	−0.163171	+	0.282621i
$341$	3866.47	−	6696.92i	0.614021	−	1.06351i
$342$	1464.59	+	2536.74i	0.231567	+	0.401086i
$343$	−6170.95			−0.971428
$344$	−1174.55	−	2034.37i	−0.184091	−	0.318855i
$345$	−1843.18	−	3192.48i	−0.287633	−	0.498195i
$346$	−1968.48			−0.305856
$347$	2139.48	+	3705.69i	0.330989	+	0.573290i	0.982706	−	0.185172i	$-0.0592843\pi$
$347$	2139.48	+	3705.69i	0.330989	+	0.573290i	−0.651717	+	0.758462i	$0.725951\pi$
$348$	5144.03	−	8909.72i	0.792382	−	1.37245i
$349$	−3090.73	+	5353.30i	−0.474049	+	0.821076i	−0.999559	−	0.0297111i	$-0.990541\pi$
$349$	−3090.73	+	5353.30i	−0.474049	+	0.821076i	0.525510	+	0.850788i	$0.323875\pi$
$350$	3464.86			0.529156
$351$		0			0
$352$	−1126.17			−0.170525
$353$	2735.80	−	4738.55i	0.412499	−	0.714469i	−0.582663	−	0.812714i	$-0.697989\pi$
$353$	2735.80	−	4738.55i	0.412499	−	0.714469i	0.995162	+	0.0982443i	$0.0313226\pi$
$354$	1637.37	−	2836.01i	0.245834	−	0.425797i
$355$	3111.22	+	5388.79i	0.465145	+	0.805654i
$356$	−5469.73			−0.814313
$357$	1460.67	+	2529.96i	0.216546	+	0.375069i
$358$	3777.32	+	6542.51i	0.557647	+	0.965872i
$359$	6398.77			0.940709			0.470354	−	0.882478i	$-0.344126\pi$
$359$	6398.77			0.940709			0.470354	+	0.882478i	$0.344126\pi$
$360$	−3480.79	−	6028.90i	−0.509593	−	0.882641i
$361$	3026.63	−	5242.28i	0.441264	−	0.764292i
$362$	−2329.80	+	4035.33i	−0.338264	+	0.585890i
$363$	819.786			0.118533
$364$		0			0
$365$	14222.2			2.03952
$366$	1753.69	−	3037.47i	0.250455	−	0.433802i
$367$	−4818.10	+	8345.19i	−0.685293	+	1.18696i	0.288052	+	0.957615i	$0.406993\pi$
$367$	−4818.10	+	8345.19i	−0.685293	+	1.18696i	−0.973345	+	0.229348i	$0.926341\pi$
$368$	197.237	+	341.624i	0.0279393	+	0.0483924i
$369$	4318.34			0.609225
$370$	−2002.15	−	3467.82i	−0.281315	−	0.487252i
$371$	414.982	+	718.770i	0.0580722	+	0.100584i
$372$	−7792.06			−1.08602
$373$	−4403.94	−	7627.84i	−0.611333	−	1.05886i	−0.991016	−	0.133743i	$-0.957300\pi$
$373$	−4403.94	−	7627.84i	−0.611333	−	1.05886i	0.379683	−	0.925117i	$-0.376033\pi$
$374$	1067.30	−	1848.62i	0.147564	−	0.255588i
$375$	2575.01	−	4460.06i	0.354595	−	0.614177i
$376$	−1329.69			−0.182376
$377$		0			0
$378$	−4738.61			−0.644782
$379$	4339.48	−	7516.19i	0.588137	−	1.01868i	−0.406339	−	0.913722i	$-0.633195\pi$
$379$	4339.48	−	7516.19i	0.588137	−	1.01868i	0.994476	−	0.104961i	$-0.0334718\pi$
$380$	957.470	−	1658.39i	0.129256	−	0.223877i
$381$	−6417.11	−	11114.8i	−0.862884	−	1.49456i
$382$	−9223.86			−1.23543
$383$	1356.15	+	2348.92i	0.180930	+	0.313380i	0.942197	−	0.335058i	$-0.108756\pi$
$383$	1356.15	+	2348.92i	0.180930	+	0.313380i	−0.761268	+	0.648438i	$0.775423\pi$
$384$	567.389	+	982.747i	0.0754023	+	0.130601i
$385$	−6449.11			−0.853706
$386$	−952.799	−	1650.30i	−0.125638	−	0.217611i
$387$	−7575.29	+	13120.8i	−0.995022	+	1.72343i
$388$	1380.48	−	2391.06i	0.180627	−	0.312855i
$389$	−290.941			−0.0379211			−0.0189605	−	0.999820i	$-0.506036\pi$
$389$	−290.941			−0.0379211			−0.0189605	+	0.999820i	$0.506036\pi$
$390$		0			0
$391$	−747.707			−0.0967089
$392$	899.767	−	1558.44i	0.115931	−	0.200799i
$393$	2800.94	−	4851.37i	0.359513	−	0.622696i
$394$	−2050.54	−	3551.64i	−0.262195	−	0.454134i
$395$	3103.99			0.395389
$396$	3631.64	+	6290.18i	0.460850	+	0.798216i
$397$	−7057.01	−	12223.1i	−0.892144	−	1.54524i	−0.837300	−	0.546743i	$-0.815867\pi$
$397$	−7057.01	−	12223.1i	−0.892144	−	1.54524i	−0.0548436	−	0.998495i	$-0.517466\pi$
$398$	−5170.62			−0.651205
$399$	−1367.15	−	2367.97i	−0.171537	−	0.297110i
$400$	−1275.55	+	2209.32i	−0.159444	+	0.276165i
$401$	5671.01	−	9822.47i	0.706226	−	1.22322i	−0.260022	−	0.965603i	$-0.583730\pi$
$401$	5671.01	−	9822.47i	0.706226	−	1.22322i	0.966247	−	0.257616i	$-0.0829369\pi$
$402$	−5696.47			−0.706751
$403$		0			0
$404$	5580.83			0.687269
$405$	−4554.38	+	7888.42i	−0.558788	+	0.967849i
$406$	−3152.25	+	5459.85i	−0.385329	+	0.667409i
$407$	2088.92	+	3618.11i	0.254407	+	0.440646i
$408$	−2150.92			−0.260997
$409$	−2343.47	−	4059.01i	−0.283318	−	0.490721i	0.688882	−	0.724874i	$-0.258102\pi$
$409$	−2343.47	−	4059.01i	−0.283318	−	0.490721i	−0.972200	+	0.234152i	$0.924769\pi$
$410$	−1411.55	−	2444.88i	−0.170028	−	0.294497i
$411$	4853.11			0.582448
$412$	2832.55	+	4906.13i	0.338713	+	0.586669i
$413$	−1003.38	+	1737.90i	−0.119547	+	0.207061i
$414$	1272.09	−	2203.32i	0.151014	−	0.261564i
$415$	21489.3			2.54185
$416$		0			0
$417$	6002.54			0.704905
$418$	−998.965	+	1730.26i	−0.116892	+	0.202463i
$419$	−5944.84	+	10296.8i	−0.693137	+	1.20055i	0.277668	+	0.960677i	$0.410438\pi$
$419$	−5944.84	+	10296.8i	−0.693137	+	1.20055i	−0.970805	+	0.239871i	$0.922895\pi$
$420$	3249.21	+	5627.79i	0.377488	+	0.653829i
$421$	−4755.64			−0.550536			−0.275268	−	0.961367i	$-0.588767\pi$
$421$	−4755.64			−0.550536			−0.275268	+	0.961367i	$0.588767\pi$
$422$	1756.23	+	3041.87i	0.202587	+	0.350891i
$423$	4287.94	+	7426.93i	0.492876	+	0.853687i
$424$	−611.084			−0.0699926
$425$	−2417.75	−	4187.66i	−0.275948	−	0.477957i
$426$	−3270.87	+	5665.32i	−0.372005	+	0.644332i
$427$	−1074.65	+	1861.36i	−0.121794	+	0.210954i
$428$	1804.27			0.203768
$429$		0			0
$430$	9904.63			1.11080
$431$	2189.06	−	3791.57i	0.244649	−	0.423744i	−0.717384	−	0.696678i	$-0.754661\pi$
$431$	2189.06	−	3791.57i	0.244649	−	0.423744i	0.962033	+	0.272934i	$0.0879941\pi$
$432$	1744.47	−	3021.50i	0.194284	−	0.336510i
$433$	−7788.16	−	13489.5i	−0.864377	−	1.49715i	−0.867664	−	0.497150i	$-0.834380\pi$
$433$	−7788.16	−	13489.5i	−0.864377	−	1.49715i	0.00328725	−	0.999995i	$-0.498954\pi$
$434$	4774.96			0.528123
$435$	21689.1	+	37566.6i	2.39061	+	4.14065i
$436$	2772.26	+	4801.70i	0.304512	+	0.527430i
$437$	699.834			0.0766077
$438$	7476.00	+	12948.8i	0.815564	+	1.41260i
$439$	6737.38	−	11669.5i	0.732477	−	1.26869i	−0.223345	−	0.974740i	$-0.571698\pi$
$439$	6737.38	−	11669.5i	0.732477	−	1.26869i	0.955822	−	0.293948i	$-0.0949692\pi$
$440$	2374.17	−	4112.18i	0.257236	−	0.445547i
$441$	−11606.2			−1.25323
$442$		0			0
$443$	−24.4564			−0.00262294			−0.00131147	−	0.999999i	$-0.500417\pi$
$443$	−24.4564			−0.00262294			−0.00131147	+	0.999999i	$0.500417\pi$
$444$	2104.89	−	3645.77i	0.224985	−	0.389686i
$445$	11531.2	−	19972.6i	1.22838	−	2.12762i
$446$	−2038.12	−	3530.13i	−0.216385	−	0.374791i
$447$	2520.75			0.266728
$448$	−347.695	−	602.225i	−0.0366675	−	0.0635099i
$449$	6818.36	+	11809.7i	0.716655	+	1.24128i	0.962318	+	0.271928i	$0.0876613\pi$
$449$	6818.36	+	11809.7i	0.716655	+	1.24128i	−0.245662	+	0.969356i	$0.579005\pi$
$450$	16453.4			1.72361
$451$	1472.72	+	2550.83i	0.153765	+	0.266328i
$452$	−3057.56	+	5295.85i	−0.318176	+	0.551096i
$453$	12006.9	−	20796.5i	1.24532	−	2.15696i
$454$	−9383.70			−0.970042
$455$		0			0
$456$	2013.21			0.206748
$457$	−6690.26	+	11587.9i	−0.684808	+	1.18612i	0.288689	+	0.957423i	$0.406781\pi$
$457$	−6690.26	+	11587.9i	−0.684808	+	1.18612i	−0.973497	+	0.228699i	$0.926553\pi$
$458$	−576.154	+	997.928i	−0.0587815	+	0.101812i
$459$	3306.56	+	5727.13i	0.336246	+	0.582395i
$460$	−1663.24			−0.168585
$461$	3391.27	+	5873.86i	0.342619	+	0.593434i	0.984918	−	0.173020i	$-0.0553526\pi$
$461$	3391.27	+	5873.86i	0.342619	+	0.593434i	−0.642299	+	0.766454i	$0.722019\pi$
$462$	−3390.02	−	5871.69i	−0.341381	−	0.591290i
$463$	−10966.2			−1.10074			−0.550368	−	0.834922i	$-0.685512\pi$
$463$	−10966.2			−1.10074			−0.550368	+	0.834922i	$0.685512\pi$
$464$	−2320.93	−	4019.97i	−0.232212	−	0.402204i
$465$	16427.1	−	28452.6i	1.63825	−	2.83754i
$466$	−724.319	+	1254.56i	−0.0720031	+	0.124713i
$467$	−609.640			−0.0604085			−0.0302043	−	0.999544i	$-0.509616\pi$
$467$	−609.640			−0.0604085			−0.0302043	+	0.999544i	$0.509616\pi$
$468$		0			0
$469$	3490.78			0.343687
$470$	2803.22	−	4855.32i	0.275113	−	0.476509i
$471$	−3917.54	+	6785.37i	−0.383250	+	0.663808i
$472$	−738.763	−	1279.58i	−0.0720431	−	0.124782i
$473$	−10333.9			−1.00455
$474$	1631.64	+	2826.07i	0.158109	+	0.273852i
$475$	2262.95	+	3919.54i	0.218592	+	0.378612i
$476$	1318.08			0.126920
$477$	1970.61	+	3413.19i	0.189157	+	0.327630i
$478$	−3137.80	+	5434.84i	−0.300251	+	0.520050i
$479$	−4202.64	+	7279.19i	−0.400884	+	0.694352i	−0.993833	−	0.110888i	$-0.964630\pi$
$479$	−4202.64	+	7279.19i	−0.400884	+	0.694352i	0.592949	+	0.805240i	$0.297964\pi$
$480$	−4784.64			−0.454975
$481$		0			0
$482$	−3527.48			−0.333345
$483$	−1187.46	+	2056.73i	−0.111866	+	0.193757i
$484$	184.939	−	320.324i	0.0173685	−	0.0300831i
$485$	5820.61	+	10081.6i	0.544949	+	0.943880i
$486$	2198.96			0.205240
$487$	−8080.22	−	13995.4i	−0.751848	−	1.30224i	−0.946926	−	0.321451i	$-0.895830\pi$
$487$	−8080.22	−	13995.4i	−0.751848	−	1.30224i	0.195079	−	0.980788i	$-0.437504\pi$
$488$	−791.245	−	1370.48i	−0.0733975	−	0.127128i
$489$	29617.5			2.73896
$490$	3793.75	+	6570.96i	0.349763	+	0.605808i
$491$	−3213.48	+	5565.91i	−0.295361	+	0.511581i	−0.975069	−	0.221903i	$-0.928773\pi$
$491$	−3213.48	+	5565.91i	−0.295361	+	0.511581i	0.679708	+	0.733483i	$0.262107\pi$
$492$	1483.98	−	2570.34i	0.135982	−	0.235528i
$493$	8798.45			0.803777
$494$		0			0
$495$	−30624.6			−2.78076
$496$	−1757.85	+	3044.68i	−0.159132	+	0.275625i
$497$	2004.38	−	3471.69i	0.180903	−	0.313333i
$498$	11296.0	+	19565.3i	1.01644	+	1.76052i
$499$	−15240.3			−1.36724			−0.683618	−	0.729840i	$-0.739595\pi$
$499$	−15240.3			−1.36724			−0.683618	+	0.729840i	$0.739595\pi$
$500$	−1161.82	−	2012.33i	−0.103916	−	0.179988i
$501$	8052.13	+	13946.7i	0.718049	+	1.24370i
$502$	−3292.02			−0.292689
$503$	−5202.00	−	9010.14i	−0.461125	−	0.798692i	0.537892	−	0.843014i	$-0.319221\pi$
$503$	−5202.00	−	9010.14i	−0.461125	−	0.798692i	−0.999017	+	0.0443215i	$0.985887\pi$
$504$	−2242.47	+	3884.08i	−0.198190	+	0.343275i
$505$	−11765.4	+	20378.3i	−1.03674	+	1.79569i
$506$	1735.33			0.152460
$507$		0			0
$508$	−5790.67			−0.505747
$509$	7311.67	−	12664.2i	0.636707	−	1.10281i	−0.349443	−	0.936957i	$-0.613629\pi$
$509$	7311.67	−	12664.2i	0.636707	−	1.10281i	0.986151	−	0.165852i	$-0.0530373\pi$
$510$	4534.54	−	7854.05i	0.393711	−	0.681928i
$511$	−4581.27	−	7935.00i	−0.396602	−	0.686935i
$512$	512.000			0.0441942
$513$	−3094.85	−	5360.43i	−0.266356	−	0.461343i
$514$	6415.73	+	11112.4i	0.550556	+	0.953590i
$515$	−23886.2			−2.04379
$516$	5206.45	+	9017.83i	0.444188	+	0.769356i
$517$	−2924.71	+	5065.75i	−0.248798	+	0.430931i
$518$	−1289.87	+	2234.12i	−0.109409	+	0.189501i
$519$	8725.75			0.737992
$520$		0			0
$521$	−19937.9			−1.67657			−0.838285	−	0.545232i	$-0.816442\pi$
$521$	−19937.9			−1.67657			−0.838285	+	0.545232i	$0.816442\pi$
$522$	−14969.0	+	25927.0i	−1.25512	+	2.17393i
$523$	−2163.50	+	3747.29i	−0.180886	+	0.313303i	−0.942182	−	0.335101i	$-0.891230\pi$
$523$	−2163.50	+	3747.29i	−0.180886	+	0.313303i	0.761297	+	0.648404i	$0.224563\pi$
$524$	−1263.75	−	2188.89i	−0.105358	−	0.182485i
$525$	−15358.8			−1.27679
$526$	3660.48	+	6340.14i	0.303431	+	0.525557i
$527$	−3331.92	−	5771.06i	−0.275410	−	0.477023i
$528$	4992.00			0.411456
$529$	5779.58	+	10010.5i	0.475021	+	0.822760i
$530$	1288.28	−	2231.36i	0.105583	−	0.182876i
$531$	−4764.69	+	8252.68i	−0.389397	+	0.674456i
$532$	−1233.69			−0.100540
$533$		0			0
$534$	24245.9			1.96483
$535$	−3803.74	+	6588.27i	−0.307383	+	0.532403i
$536$	−1285.09	+	2225.84i	−0.103559	+	0.179369i
$537$	−16743.8	−	29001.2i	−1.34553	−	2.33053i
$538$	−11290.6			−0.904782
$539$	−3958.16	−	6855.74i	−0.316308	−	0.547862i
$540$	7355.30	+	12739.8i	0.586152	+	1.01524i
$541$	−2602.93			−0.206855			−0.103428	−	0.994637i	$-0.532981\pi$
$541$	−2602.93			−0.206855			−0.103428	+	0.994637i	$0.532981\pi$
$542$	−6671.87	−	11556.0i	−0.528748	−	0.915818i
$543$	10327.4	−	17887.5i	0.816187	−	1.41368i
$544$	−485.237	+	840.455i	−0.0382433	+	0.0662393i
$545$	−23377.7			−1.83742
$546$		0			0
$547$	11225.3			0.877441			0.438720	−	0.898624i	$-0.355432\pi$
$547$	11225.3			0.877441			0.438720	+	0.898624i	$0.355432\pi$
$548$	1094.84	−	1896.31i	0.0853450	−	0.147822i
$549$	−5103.17	+	8838.95i	−0.396718	+	0.687135i
$550$	5611.27	+	9719.00i	0.435028	+	0.753490i
$551$	−8235.11			−0.636710
$552$	−874.297	−	1514.33i	−0.0674141	−	0.116765i
$553$	−999.862	−	1731.81i	−0.0768869	−	0.133172i
$554$	−5810.78			−0.445626
$555$	8874.97	+	15371.9i	0.678778	+	1.17568i
$556$	1354.14	−	2345.44i	0.103288	−	0.178901i
$557$	−4124.42	+	7143.70i	−0.313747	+	0.543426i	−0.979170	−	0.203040i	$-0.934918\pi$
$557$	−4124.42	+	7143.70i	−0.313747	+	0.543426i	0.665423	+	0.746466i	$0.268251\pi$
$558$	22674.6			1.72024
$559$		0			0
$560$	2932.02			0.221250
$561$	−4731.06	+	8194.43i	−0.356053	+	0.616701i
$562$	8009.76	−	13873.3i	0.601195	−	1.04130i
$563$	846.532	+	1466.24i	0.0633696	+	0.109759i	0.895970	−	0.444115i	$-0.146482\pi$
$563$	846.532	+	1466.24i	0.0633696	+	0.109759i	−0.832600	+	0.553875i	$0.813149\pi$
$564$	5894.14			0.440050
$565$	−12891.8	−	22329.2i	−0.959931	−	1.66265i
$566$	−3707.71	−	6421.94i	−0.275348	−	0.476916i
$567$	5868.26			0.434645
$568$	1475.78	+	2556.13i	0.109018	+	0.188825i
$569$	−4125.77	+	7146.05i	−0.303974	+	0.526499i	−0.977032	−	0.213091i	$-0.931647\pi$
$569$	−4125.77	+	7146.05i	−0.303974	+	0.526499i	0.673058	+	0.739590i	$0.264980\pi$
$570$	−4244.20	+	7351.18i	−0.311877	+	0.540188i
$571$	−23153.2			−1.69691			−0.848453	−	0.529271i	$-0.822466\pi$
$571$	−23153.2			−1.69691			−0.848453	+	0.529271i	$0.822466\pi$
$572$		0			0
$573$	40886.9			2.98093
$574$	−909.382	+	1575.10i	−0.0661269	+	0.114535i
$575$	1965.51	−	3404.36i	0.142552	−	0.246908i
$576$	−1651.08	−	2859.76i	−0.119436	−	0.206869i
$577$	2058.46			0.148518			0.0742590	−	0.997239i	$-0.476341\pi$
$577$	2058.46			0.148518			0.0742590	+	0.997239i	$0.476341\pi$
$578$	3993.25	+	6916.52i	0.287366	+	0.497732i
$579$	4223.50	+	7315.32i	0.303148	+	0.525068i
$580$	19571.8			1.40116
$581$	−6922.17	−	11989.5i	−0.494286	−	0.856128i
$582$	−6119.30	+	10598.9i	−0.435830	+	0.754880i
$583$	−1344.11	+	2328.06i	−0.0954842	+	0.165383i
$584$	6746.18			0.478012
$585$		0			0
$586$	3348.00			0.236014
$587$	−6430.86	+	11138.6i	−0.452180	+	0.783200i	−0.998521	−	0.0543635i	$-0.982687\pi$
$587$	−6430.86	+	11138.6i	−0.452180	+	0.783200i	0.546341	+	0.837563i	$0.316020\pi$
$588$	−3988.42	+	6908.15i	−0.279728	+	0.484503i
$589$	3118.59	+	5401.55i	0.218165	+	0.377873i
$590$	6229.79			0.434706
$591$	9089.49	+	15743.5i	0.632642	+	1.09577i
$592$	−949.703	−	1644.93i	−0.0659333	−	0.114200i
$593$	18098.4			1.25331			0.626653	−	0.779298i	$-0.284424\pi$
$593$	18098.4			1.25331			0.626653	+	0.779298i	$0.284424\pi$
$594$	−7674.07	−	13291.9i	−0.530086	−	0.918135i
$595$	−2778.75	+	4812.94i	−0.191458	+	0.331616i
$596$	568.667	−	984.961i	0.0390831	−	0.0676939i
$597$	22920.0			1.57128
$598$		0			0
$599$	−15338.0			−1.04623			−0.523115	−	0.852262i	$-0.675230\pi$
$599$	−15338.0			−1.04623			−0.523115	+	0.852262i	$0.675230\pi$
$600$	5654.17	−	9793.31i	0.384717	−	0.666350i
$601$	−11144.7	+	19303.2i	−0.756409	+	1.31014i	0.188262	+	0.982119i	$0.439715\pi$
$601$	−11144.7	+	19303.2i	−0.756409	+	1.31014i	−0.944671	+	0.328020i	$0.893619\pi$
$602$	−3190.50	−	5526.10i	−0.216005	−	0.374131i
$603$	16576.5			1.11948
$604$	−5417.37	−	9383.16i	−0.364950	−	0.632111i
$605$	779.772	+	1350.60i	0.0524004	+	0.0907601i
$606$	−24738.3			−1.65829
$607$	−3595.90	−	6228.29i	−0.240450	−	0.416472i	0.720392	−	0.693567i	$-0.243962\pi$
$607$	−3595.90	−	6228.29i	−0.240450	−	0.416472i	−0.960843	+	0.277095i	$0.910628\pi$
$608$	454.168	−	786.643i	0.0302943	−	0.0524713i
$609$	13973.1	−	24202.1i	0.929749	−	1.61037i
$610$	6672.35			0.442878
$611$		0			0
$612$	6259.12			0.413415
$613$	−398.529	+	690.272i	−0.0262584	+	0.0454810i	−0.878856	−	0.477087i	$-0.841693\pi$
$613$	−398.529	+	690.272i	−0.0262584	+	0.0454810i	0.852598	+	0.522568i	$0.175026\pi$
$614$	299.935	−	519.503i	0.0197140	−	0.0341457i
$615$	6257.02	+	10837.5i	0.410256	+	0.710584i
$616$	−3059.08			−0.200088
$617$	10454.1	+	18107.1i	0.682120	+	1.18147i	0.974333	+	0.225113i	$0.0722752\pi$
$617$	10454.1	+	18107.1i	0.682120	+	1.18147i	−0.292213	+	0.956353i	$0.594391\pi$
$618$	−12555.9	−	21747.5i	−0.817272	−	1.41556i
$619$	12309.9			0.799315			0.399658	−	0.916665i	$-0.369129\pi$
$619$	12309.9			0.799315			0.399658	+	0.916665i	$0.369129\pi$
$620$	−7411.73	−	12837.5i	−0.480100	−	0.831558i
$621$	−2688.07	+	4655.87i	−0.173701	+	0.300859i
$622$	890.140	−	1541.77i	0.0573816	−	0.0993879i
$623$	−14857.8			−0.955481
$624$		0			0
$625$	−10133.2			−0.648522
$626$	1154.20	−	1999.13i	0.0736918	−	0.127638i
$627$	4428.14	−	7669.77i	0.282046	−	0.488518i
$628$	1767.55	+	3061.49i	0.112314	+	0.194533i
$629$	3600.24			0.228221
$630$	−9455.09	−	16376.7i	−0.597936	−	1.03566i
$631$	5166.33	+	8948.35i	0.325940	+	0.564545i	0.981702	−	0.190422i	$-0.0609858\pi$
$631$	5166.33	+	8948.35i	0.325940	+	0.564545i	−0.655762	+	0.754968i	$0.727652\pi$
$632$	1472.35			0.0926693
$633$	−7784.88	−	13483.8i	−0.488817	−	0.846656i
$634$	−2708.86	+	4691.88i	−0.169688	+	0.293909i
$635$	12207.8	−	21144.5i	0.762915	−	1.32141i
$636$	2708.77			0.168883
$637$		0			0
$638$	−20420.0			−1.26714
$639$	9518.13	−	16485.9i	0.589251	−	1.02061i
$640$	−1079.39	+	1869.56i	−0.0666666	+	0.115470i
$641$	−338.433	−	586.184i	−0.0208539	−	0.0361199i	0.855410	−	0.517951i	$-0.173305\pi$
$641$	−338.433	−	586.184i	−0.0208539	−	0.0361199i	−0.876264	+	0.481831i	$0.839972\pi$
$642$	−7997.86			−0.491667
$643$	−13156.3	−	22787.4i	−0.806897	−	1.39759i	−0.915003	−	0.403448i	$-0.867812\pi$
$643$	−13156.3	−	22787.4i	−0.806897	−	1.39759i	0.108105	−	0.994139i	$-0.465522\pi$
$644$	535.767	+	927.976i	0.0327829	+	0.0567816i
$645$	−43904.5			−2.68022
$646$	860.856	+	1491.05i	0.0524302	+	0.0908118i
$647$	−84.9379	+	147.117i	−0.00516113	+	0.00893934i	−0.868594	−	0.495524i	$-0.834976\pi$
$647$	−84.9379	+	147.117i	−0.00516113	+	0.00893934i	0.863433	+	0.504463i	$0.168310\pi$
$648$	−2160.34	+	3741.81i	−0.130966	+	0.226840i
$649$	−6499.78			−0.393126
$650$		0			0
$651$	−21166.1			−1.27429
$652$	6681.56	−	11572.8i	0.401334	−	0.695131i
$653$	7213.30	−	12493.8i	0.432279	−	0.748729i	−0.564790	−	0.825235i	$-0.691043\pi$
$653$	7213.30	−	12493.8i	0.432279	−	0.748729i	0.997069	+	0.0765053i	$0.0243762\pi$
$654$	−12288.7	−	21284.6i	−0.734749	−	1.27262i
$655$	10656.9			0.635724
$656$	−669.558	−	1159.71i	−0.0398504	−	0.0690229i
$657$	−21754.9	−	37680.6i	−1.29184	−	2.23754i
$658$	−3611.91			−0.213993
$659$	12605.9	+	21834.1i	0.745155	+	1.29065i	0.950122	+	0.311877i	$0.100958\pi$
$659$	12605.9	+	21834.1i	0.745155	+	1.29065i	−0.204968	+	0.978769i	$0.565709\pi$
$660$	−10524.0	+	18228.2i	−0.620679	+	1.07505i
$661$	−11419.5	+	19779.2i	−0.671963	+	1.16387i	0.305384	+	0.952229i	$0.401215\pi$
$661$	−11419.5	+	19779.2i	−0.671963	+	1.16387i	−0.977347	+	0.211644i	$0.932118\pi$
$662$	16374.2			0.961334
$663$		0			0
$664$	10193.3			0.595747
$665$	2600.84	−	4504.78i	0.151663	−	0.262689i
$666$	−6125.15	+	10609.1i	−0.356374	+	0.617257i
$667$	3576.35	+	6194.42i	0.207612	+	0.359594i
$668$	7266.07			0.420857
$669$	9034.45	+	15648.1i	0.522111	+	0.904322i
$670$	−5418.42	−	9384.97i	−0.312435	−	0.541154i
$671$	−6961.52			−0.400516
$672$	1541.24	+	2669.50i	0.0884740	+	0.153241i
$673$	8354.10	−	14469.7i	0.478495	−	0.828777i	−0.521201	−	0.853434i	$-0.674516\pi$
$673$	8354.10	−	14469.7i	0.478495	−	0.828777i	0.999696	+	0.0246566i	$0.00784924\pi$
$674$	8770.94	−	15191.7i	0.501252	−	0.868195i
$675$	−34768.0			−1.98255
$676$		0			0
$677$	−15842.6			−0.899378			−0.449689	−	0.893185i	$-0.648465\pi$
$677$	−15842.6			−0.899378			−0.449689	+	0.893185i	$0.648465\pi$
$678$	13553.3	−	23475.1i	0.767717	−	1.32973i
$679$	3749.89	−	6495.00i	0.211941	−	0.367092i
$680$	−2045.94	−	3543.66i	−0.115379	−	0.199843i
$681$	41595.4			2.34059
$682$	7732.94	+	13393.8i	0.434178	+	0.752019i
$683$	−8233.63	−	14261.1i	−0.461275	−	0.798952i	0.537750	−	0.843105i	$-0.319275\pi$
$683$	−8233.63	−	14261.1i	−0.461275	−	0.798952i	−0.999025	+	0.0441525i	$0.985941\pi$
$684$	−5858.36			−0.327485
$685$	4616.23	+	7995.54i	0.257485	+	0.445976i
$686$	6170.95	−	10688.4i	0.343452	−	0.594876i
$687$	2553.94	−	4423.55i	0.141832	−	0.245661i
$688$	4698.18			0.260344
$689$		0			0
$690$	7372.71			0.406775
$691$	8265.50	−	14316.3i	0.455043	−	0.788157i	−0.543648	−	0.839313i	$-0.682957\pi$
$691$	8265.50	−	14316.3i	0.455043	−	0.788157i	0.998691	+	0.0511562i	$0.0162906\pi$
$692$	1968.48	−	3409.51i	0.108136	−	0.187298i
$693$	9864.85	+	17086.4i	0.540743	+	0.936594i
$694$	−8557.92			−0.468089
$695$	5709.55	+	9889.23i	0.311619	+	0.539741i
$696$	10288.1	+	17819.4i	0.560299	+	0.970466i
$697$	2538.23			0.137938
$698$	−6181.46	−	10706.6i	−0.335203	−	0.580589i
$699$	3210.71	−	5561.12i	0.173734	−	0.300917i
$700$	−3464.86	+	6001.31i	−0.187085	+	0.324040i
$701$	−11032.2			−0.594409			−0.297205	−	0.954814i	$-0.596054\pi$
$701$	−11032.2			−0.594409			−0.297205	+	0.954814i	$0.596054\pi$
$702$		0			0
$703$	−3369.72			−0.180785
$704$	1126.17	−	1950.58i	0.0602899	−	0.104425i
$705$	−12425.9	+	21522.3i	−0.663812	+	1.14976i
$706$	5471.61	+	9477.11i	0.291681	+	0.505206i
$707$	15159.6			0.806414
$708$	3274.74	+	5672.01i	0.173831	+	0.301084i
$709$	−10489.6	−	18168.5i	−0.555633	−	0.962385i	−0.997854	−	0.0654790i	$-0.979142\pi$
$709$	−10489.6	−	18168.5i	−0.555633	−	0.962385i	0.442220	−	0.896906i	$-0.354191\pi$
$710$	−12444.9			−0.657814
$711$	−4748.00	−	8223.78i	−0.250442	−	0.433778i
$712$	5469.73	−	9473.86i	0.287903	−	0.498663i
$713$	2708.69	−	4691.59i	0.142274	−	0.246425i
$714$	−5842.69			−0.306243
$715$		0			0
$716$	−15109.3			−0.788631
$717$	13909.0	−	24091.2i	0.724467	−	1.25481i
$718$	−6398.77	+	11083.0i	−0.332591	+	0.576064i
$719$	8849.89	+	15328.5i	0.459034	+	0.795070i	0.998910	−	0.0466744i	$-0.0148623\pi$
$719$	8849.89	+	15328.5i	0.459034	+	0.795070i	−0.539876	+	0.841744i	$0.681529\pi$
$720$	13923.1			0.720674
$721$	7694.25	+	13326.8i	0.397433	+	0.688373i
$722$	6053.26	+	10484.6i	0.312021	+	0.540436i
$723$	15636.4			0.804319
$724$	−4659.60	−	8070.66i	−0.239189	−	0.414287i
$725$	−23128.6	+	40060.0i	−1.18479	+	2.05212i
$726$	−819.786	+	1419.91i	−0.0419079	+	0.0725866i
$727$	33899.2			1.72937			0.864686	−	0.502313i	$-0.167518\pi$
$727$	33899.2			1.72937			0.864686	+	0.502313i	$0.167518\pi$
$728$		0			0
$729$	−24329.6			−1.23607
$730$	−14222.2	+	24633.6i	−0.721078	+	1.24894i
$731$	−4452.60	+	7712.13i	−0.225288	+	0.390210i
$732$	3507.37	+	6074.95i	0.177099	+	0.306744i
$733$	29937.3			1.50854			0.754270	−	0.656564i	$-0.227991\pi$
$733$	29937.3			1.50854			0.754270	+	0.656564i	$0.227991\pi$
$734$	−9636.19	−	16690.4i	−0.484575	−	0.839309i
$735$	−16816.7	−	29127.3i	−0.843934	−	1.46174i
$736$	−788.947			−0.0395122
$737$	5653.24	+	9791.70i	0.282551	+	0.489392i
$738$	−4318.34	+	7479.59i	−0.215394	+	0.373073i
$739$	8297.60	−	14371.9i	0.413034	−	0.715396i	−0.582186	−	0.813056i	$-0.697802\pi$
$739$	8297.60	−	14371.9i	0.413034	−	0.715396i	0.995220	+	0.0976599i	$0.0311357\pi$
$740$	8008.59			0.397840
$741$		0			0
$742$	−1659.93			−0.0821265
$743$	2464.54	−	4268.70i	0.121689	−	0.210772i	−0.798745	−	0.601670i	$-0.794502\pi$
$743$	2464.54	−	4268.70i	0.121689	−	0.210772i	0.920434	+	0.390898i	$0.127836\pi$
$744$	7792.06	−	13496.2i	0.383966	−	0.665049i
$745$	2397.71	+	4152.95i	0.117913	+	0.204231i
$746$	17615.8			0.864556
$747$	−32871.0	−	56934.3i	−1.61002	−	2.78864i
$748$	2134.60	+	3697.24i	0.104343	+	0.180728i
$749$	4901.07			0.239094
$750$	5150.03	+	8920.11i	0.250737	+	0.434289i
$751$	5343.83	−	9255.78i	0.259653	−	0.449732i	−0.706496	−	0.707717i	$-0.749725\pi$
$751$	5343.83	−	9255.78i	0.259653	−	0.449732i	0.966149	+	0.257985i	$0.0830586\pi$
$752$	1329.69	−	2303.09i	0.0644796	−	0.111682i
$753$	14592.6			0.706221
$754$		0			0
$755$	45683.2			2.20210
$756$	4738.61	−	8207.51i	0.227965	−	0.394847i
$757$	−14454.6	+	25036.1i	−0.694004	+	1.20205i	0.276511	+	0.961011i	$0.410822\pi$
$757$	−14454.6	+	25036.1i	−0.694004	+	1.20205i	−0.970515	+	0.241040i	$0.922512\pi$
$758$	8678.95	+	15032.4i	0.415876	+	0.720318i
$759$	−7692.23			−0.367866
$760$	1914.94	+	3316.77i	0.0913976	+	0.158305i
$761$	12699.9	+	21996.8i	0.604954	+	1.04781i	0.992059	+	0.125775i	$0.0401416\pi$
$761$	12699.9	+	21996.8i	0.604954	+	1.04781i	−0.387105	+	0.922036i	$0.626525\pi$
$762$	25668.5			1.22030
$763$	7530.47	+	13043.2i	0.357302	+	0.618865i
$764$	9223.86	−	15976.2i	0.436790	−	0.756542i
$765$	−13195.4	+	22855.0i	−0.623633	+	1.08016i
$766$	−5424.61			−0.255873
$767$		0			0
$768$	−2269.56			−0.106635
$769$	−11870.1	+	20559.7i	−0.556630	+	0.964111i	0.441145	+	0.897436i	$0.354572\pi$
$769$	−11870.1	+	20559.7i	−0.556630	+	0.964111i	−0.997775	+	0.0666752i	$0.978761\pi$
$770$	6449.11	−	11170.2i	0.301831	−	0.522786i
$771$	−28439.2	−	49258.1i	−1.32842	−	2.30089i
$772$	3811.20			0.177679
$773$	−18.6421	−	32.2891i	−0.000867413	−	0.00150240i	0.865591	−	0.500751i	$-0.166943\pi$
$773$	−18.6421	−	32.2891i	−0.000867413	−	0.00150240i	−0.866459	+	0.499249i	$0.833609\pi$
$774$	−15150.6	−	26241.6i	−0.703587	−	1.21865i
$775$	35034.7			1.62385
$776$	2760.96	+	4782.13i	0.127723	+	0.221222i
$777$	5717.64	−	9903.25i	0.263989	−	0.457242i
$778$	290.941	−	503.925i	0.0134071	−	0.0232218i
$779$	−2375.72			−0.109267
$780$		0			0
$781$	12984.2			0.594893
$782$	747.707	−	1295.07i	0.0341918	−	0.0592219i
$783$	31631.1	−	54786.7i	1.44368	−	2.50053i
$784$	1799.53	+	3116.88i	0.0819759	+	0.141986i
$785$	−14905.3			−0.677697
$786$	5601.88	+	9702.74i	0.254214	+	0.440312i
$787$	3486.17	+	6038.22i	0.157902	+	0.273493i	0.934112	−	0.356981i	$-0.116194\pi$
$787$	3486.17	+	6038.22i	0.157902	+	0.273493i	−0.776210	+	0.630474i	$0.782860\pi$
$788$	8202.16			0.370799
$789$	−16225.9	−	28104.1i	−0.732140	−	1.26810i
$790$	−3103.99	+	5376.26i	−0.139791	+	0.242125i
$791$	−8305.44	+	14385.4i	−0.373334	+	0.646634i
$792$	−14526.6			−0.651741
$793$		0			0
$794$	28228.0			1.26168
$795$	−5710.58	+	9891.02i	−0.254759	+	0.441256i
$796$	5170.62	−	8955.77i	0.230236	−	0.398780i
$797$	−6844.86	−	11855.6i	−0.304212	−	0.526911i	0.672873	−	0.739758i	$-0.265060\pi$
$797$	−6844.86	−	11855.6i	−0.304212	−	0.526911i	−0.977086	+	0.212846i	$0.931727\pi$
$798$	5468.60			0.242589
$799$	2520.36	+	4365.40i	0.111595	+	0.193287i
$800$	−2551.10	−	4418.63i	−0.112744	−	0.195278i
$801$	−70554.6			−3.11227
$802$	11342.0	+	19644.9i	0.499377	+	0.864946i
$803$	14838.6	−	25701.1i	0.652106	−	1.12948i
$804$	5696.47	−	9866.57i	0.249874	−	0.432795i
$805$	−4517.98			−0.197811
$806$		0			0
$807$	50048.2			2.18312
$808$	−5580.83	+	9666.29i	−0.242986	+	0.420865i
$809$	3549.44	−	6147.81i	0.154254	−	0.267176i	−0.778533	−	0.627604i	$-0.784036\pi$
$809$	3549.44	−	6147.81i	0.154254	−	0.267176i	0.932787	+	0.360427i	$0.117369\pi$
$810$	−9108.77	−	15776.8i	−0.395123	−	0.684373i
$811$	−24631.2			−1.06649			−0.533243	−	0.845962i	$-0.679027\pi$
$811$	−24631.2			−1.06649			−0.533243	+	0.845962i	$0.679027\pi$
$812$	−6304.50	−	10919.7i	−0.272469	−	0.471929i
$813$	29574.6	+	51224.7i	1.27580	+	2.20975i
$814$	−8355.66			−0.359786
$815$	28171.9	+	48795.1i	1.21082	+	2.09720i
$816$	2150.92	−	3725.51i	0.0922762	−	0.159827i
$817$	4167.51	−	7218.34i	0.178461	−	0.309104i
$818$	9373.87			0.400672
$819$		0			0
$820$	5646.20			0.240456
$821$	1145.05	−	1983.28i	0.0486753	−	0.0843081i	−0.840661	−	0.541561i	$-0.817833\pi$
$821$	1145.05	−	1983.28i	0.0486753	−	0.0843081i	0.889337	+	0.457253i	$0.151167\pi$
$822$	−4853.11	+	8405.83i	−0.205927	+	0.356675i
$823$	−18242.5	−	31596.9i	−0.772651	−	1.33827i	−0.936105	−	0.351720i	$-0.885597\pi$
$823$	−18242.5	−	31596.9i	−0.772651	−	1.33827i	0.163454	−	0.986551i	$-0.447736\pi$
$824$	−11330.2			−0.479013
$825$	−24873.2	−	43081.7i	−1.04967	−	1.81807i
$826$	−2006.75	−	3475.79i	−0.0845324	−	0.146414i
$827$	−3929.01			−0.165206			−0.0826028	−	0.996583i	$-0.526323\pi$
$827$	−3929.01			−0.165206			−0.0826028	+	0.996583i	$0.526323\pi$
$828$	2544.18	+	4406.64i	0.106783	+	0.184953i
$829$	−8700.85	+	15070.3i	−0.364527	+	0.631380i	−0.988700	−	0.149906i	$-0.952103\pi$
$829$	−8700.85	+	15070.3i	−0.364527	+	0.631380i	0.624173	+	0.781286i	$0.285436\pi$
$830$	−21489.3	+	37220.6i	−0.898680	+	1.55656i
$831$	25757.6			1.07524
$832$		0			0
$833$	−6821.88			−0.283750
$834$	−6002.54	+	10396.7i	−0.249222	+	0.431665i
$835$	−15318.2	+	26531.9i	−0.634860	+	1.09961i
$836$	−1997.93	−	3460.52i	−0.0826553	−	0.143163i
$837$	−47914.1			−1.97868
$838$	−11889.7	−	20593.5i	−0.490122	−	0.848915i
$839$	−19983.0	−	34611.5i	−0.822276	−	1.42422i	−0.903984	−	0.427567i	$-0.859371\pi$
$839$	−19983.0	−	34611.5i	−0.822276	−	1.42422i	0.0817082	−	0.996656i	$-0.473962\pi$
$840$	−12996.8			−0.533849
$841$	−29889.3	−	51769.7i	−1.22552	−	2.12267i
$842$	4755.64	−	8237.01i	0.194644	−	0.337133i
$843$	−35505.1	+	61496.7i	−1.45061	+	2.51252i
$844$	−7024.91			−0.286501
$845$		0			0
$846$	−17151.8			−0.697033
$847$	502.363	−	870.118i	0.0203794	−	0.0352982i
$848$	611.084	−	1058.43i	0.0247461	−	0.0428615i
$849$	16435.3	+	28466.7i	0.664378	+	1.15074i
$850$	9671.00			0.390250
$851$	1463.41	+	2534.70i	0.0589483	+	0.102101i
$852$	−6541.75	−	11330.6i	−0.263048	−	0.455612i
$853$	−7753.33			−0.311218			−0.155609	−	0.987819i	$-0.549734\pi$
$853$	−7753.33			−0.311218			−0.155609	+	0.987819i	$0.549734\pi$
$854$	−2149.31	−	3722.71i	−0.0861216	−	0.149167i
$855$	12350.5	−	21391.7i	0.494009	−	0.855649i
$856$	−1804.27	+	3125.09i	−0.0720430	+	0.124782i
$857$	−34346.7			−1.36903			−0.684515	−	0.728998i	$-0.739986\pi$
$857$	−34346.7			−1.36903			−0.684515	+	0.728998i	$0.739986\pi$
$858$		0			0
$859$	−23048.5			−0.915489			−0.457744	−	0.889084i	$-0.651342\pi$
$859$	−23048.5			−0.915489			−0.457744	+	0.889084i	$0.651342\pi$
$860$	−9904.63	+	17155.3i	−0.392727	+	0.680223i
$861$	4031.04	−	6981.97i	0.159556	−	0.276359i
$862$	4378.13	+	7583.14i	0.172993	+	0.299632i
$863$	8452.37			0.333398			0.166699	−	0.986008i	$-0.446689\pi$
$863$	8452.37			0.333398			0.166699	+	0.986008i	$0.446689\pi$
$864$	3488.93	+	6043.01i	0.137379	+	0.237948i
$865$	8299.84	+	14375.7i	0.326246	+	0.565075i
$866$	31152.7			1.22241
$867$	−17701.0	−	30659.1i	−0.693377	−	1.20096i
$868$	−4774.96	+	8270.46i	−0.186720	+	0.323408i
$869$	3238.51	−	5609.26i	0.126420	−	0.218966i
$870$	−86756.5			−3.38083
$871$		0			0
$872$	−11089.0			−0.430645
$873$	17807.0	−	30842.6i	0.690349	−	1.19572i
$874$	−699.834	+	1212.15i	−0.0270849	+	0.0469125i
$875$	−3155.92	−	5466.22i	−0.121931	−	0.211191i
$876$	−29904.0			−1.15338
$877$	−1685.53	−	2919.43i	−0.0648990	−	0.112408i	0.831750	−	0.555150i	$-0.187339\pi$
$877$	−1685.53	−	2919.43i	−0.0648990	−	0.112408i	−0.896649	+	0.442742i	$0.854006\pi$
$878$	13474.8	+	23339.0i	0.517939	+	0.897097i
$879$	−14840.8			−0.569473
$880$	4748.34	+	8224.36i	0.181894	+	0.315049i
$881$	−4965.18	+	8599.95i	−0.189877	+	0.328876i	−0.945209	−	0.326466i	$-0.894142\pi$
$881$	−4965.18	+	8599.95i	−0.189877	+	0.328876i	0.755332	+	0.655342i	$0.227475\pi$
$882$	11606.2	−	20102.5i	0.443084	−	0.767445i
$883$	38422.6			1.46435			0.732176	−	0.681116i	$-0.238505\pi$
$883$	38422.6			1.46435			0.732176	+	0.681116i	$0.238505\pi$
$884$		0			0
$885$	−27615.0			−1.04889
$886$	24.4564	−	42.3598i	0.000927348	−	0.00160621i
$887$	13039.1	−	22584.3i	0.493584	−	0.854913i	−0.506388	−	0.862305i	$-0.669020\pi$
$887$	13039.1	−	22584.3i	0.493584	−	0.854913i	0.999973	+	0.00739257i	$0.00235315\pi$
$888$	4209.77	+	7291.54i	0.159089	+	0.275550i
$889$	−15729.6			−0.593422
$890$	23062.4	+	39945.2i	0.868599	+	1.50446i
$891$	9503.53	+	16460.6i	0.357329	+	0.618912i
$892$	8152.49			0.306015
$893$	−2358.99	−	4085.89i	−0.0883993	−	0.153112i
$894$	−2520.75	+	4366.06i	−0.0943025	+	0.163337i
$895$	31853.1	−	55171.2i	1.18964	−	2.06052i
$896$	1390.78			0.0518556
$897$		0			0
$898$	−27273.4			−1.01350
$899$	−31873.8	+	55207.0i	−1.18248	+	2.04812i
$900$	−16453.4	+	28498.2i	−0.609387	+	1.05549i
$901$	1158.28	+	2006.21i	0.0428280	+	0.0741802i
$902$	−5890.90			−0.217456
$903$	14142.6	+	24495.7i	0.521192	+	0.902731i
$904$	−6115.12	−	10591.7i	−0.224984	−	0.389684i
$905$	39293.1			1.44326
$906$	24013.7	+	41593.0i	0.880577	+	1.52520i
$907$	−4494.45	+	7784.62i	−0.164538	+	0.284988i	−0.936491	−	0.350691i	$-0.885947\pi$
$907$	−4494.45	+	7784.62i	−0.164538	+	0.284988i	0.771953	+	0.635679i	$0.219280\pi$
$908$	9383.70	−	16253.0i	0.342962	−	0.594027i
$909$	71987.7			2.62671
$910$		0			0
$911$	28318.0			1.02988			0.514938	−	0.857227i	$-0.327815\pi$
$911$	28318.0			1.02988			0.514938	+	0.857227i	$0.327815\pi$
$912$	−2013.21	+	3486.97i	−0.0730964	+	0.126607i
$913$	22420.6	−	38833.6i	0.812721	−	1.40767i
$914$	−13380.5	−	23175.7i	−0.484232	−	0.838715i
$915$	−29576.7			−1.06861
$916$	−1152.31	−	1995.86i	−0.0415648	−	0.0719923i
$917$	−3432.82	−	5945.82i	−0.123622	−	0.214120i
$918$	−13226.2			−0.475524
$919$	6431.78	+	11140.2i	0.230865	+	0.399869i	0.958063	−	0.286558i	$-0.0925112\pi$
$919$	6431.78	+	11140.2i	0.230865	+	0.399869i	−0.727198	+	0.686428i	$0.759178\pi$
$920$	1663.24	−	2880.82i	0.0596039	−	0.103237i
$921$	−1329.53	+	2302.82i	−0.0475674	+	0.0823892i
$922$	−13565.1			−0.484537
$923$		0			0
$924$	13560.1			0.482786
$925$	−9464.01	+	16392.1i	−0.336405	+	0.582671i
$926$	10966.2	−	18993.9i	0.389169	−	0.674060i
$927$	36537.4	+	63284.6i	1.29455	+	2.24222i
$928$	9283.73			0.328398
$929$	949.747	+	1645.01i	0.0335416	+	0.0580958i	0.882309	−	0.470671i	$-0.155988\pi$
$929$	949.747	+	1645.01i	0.0335416	+	0.0580958i	−0.848767	+	0.528767i	$0.822655\pi$
$930$	32854.2	+	56905.1i	1.15842	+	2.00644i
$931$	6385.09			0.224772
$932$	−1448.64	−	2509.12i	−0.0509139	−	0.0881854i
$933$	−3945.75	+	6834.24i	−0.138455	+	0.239810i
$934$	609.640	−	1055.93i	0.0213576	−	0.0369925i
$935$	−18000.5			−0.629605
$936$		0			0
$937$	−35209.9			−1.22760			−0.613798	−	0.789463i	$-0.710359\pi$
$937$	−35209.9			−1.22760			−0.613798	+	0.789463i	$0.710359\pi$
$938$	−3490.78	+	6046.21i	−0.121512	+	0.210464i
$939$	−5116.25	+	8861.60i	−0.177809	+	0.307974i
$940$	5606.45	+	9710.65i	0.194534	+	0.336943i
$941$	56666.1			1.96308			0.981542	−	0.191247i	$-0.0612531\pi$
$941$	56666.1			1.96308			0.981542	+	0.191247i	$0.0612531\pi$
$942$	−7835.07	−	13570.7i	−0.270998	−	0.469383i
$943$	1031.73	+	1787.01i	0.0356286	+	0.0617105i
$944$	2955.05			0.101884
$945$	19979.7	+	34605.8i	0.687767	+	1.19125i
$946$	10333.9	−	17898.8i	0.355162	−	0.615159i
$947$	13668.2	−	23673.9i	0.469013	−	0.812354i	−0.530360	−	0.847773i	$-0.677943\pi$
$947$	13668.2	−	23673.9i	0.469013	−	0.812354i	0.999373	+	0.0354184i	$0.0112764\pi$
$948$	−6526.54			−0.223599
$949$		0			0
$950$	−9051.79			−0.309136
$951$	12007.6	−	20797.8i	0.409436	−	0.709165i
$952$	−1318.08	+	2282.98i	−0.0448731	+	0.0777226i
$953$	7217.54	+	12501.1i	0.245329	+	0.424923i	0.962224	−	0.272258i	$-0.0877706\pi$
$953$	7217.54	+	12501.1i	0.245329	+	0.424923i	−0.716895	+	0.697181i	$0.754437\pi$
$954$	−7882.43			−0.267509
$955$	38891.1	+	67361.4i	1.31779	+	2.28248i
$956$	−6275.61	−	10869.7i	−0.212309	−	0.367731i
$957$	90516.3			3.05745
$958$	−8405.28	−	14558.4i	−0.283468	−	0.490981i
$959$	2973.97	−	5151.07i	0.100140	−	0.173448i
$960$	4784.64	−	8287.24i	0.160858	−	0.278614i
$961$	18490.7			0.620680
$962$		0			0
$963$	23273.5			0.778793
$964$	3527.48	−	6109.77i	0.117855	−	0.204131i
$965$	−8034.70	+	13916.5i	−0.268027	+	0.464237i
$966$	−2374.91	−	4113.47i	−0.0791009	−	0.137007i
$967$	21556.9			0.716879			0.358440	−	0.933553i	$-0.383309\pi$
$967$	21556.9			0.716879			0.358440	+	0.933553i	$0.383309\pi$
$968$	369.879	+	640.649i	0.0122814	+	0.0212719i
$969$	−3815.94	−	6609.41i	−0.126507	−	0.219117i
$970$	−23282.5			−0.770675
$971$	1576.77	+	2731.05i	0.0521123	+	0.0902611i	0.890905	−	0.454190i	$-0.150071\pi$
$971$	1576.77	+	2731.05i	0.0521123	+	0.0902611i	−0.838793	+	0.544451i	$0.816738\pi$
$972$	−2198.96	+	3808.70i	−0.0725633	+	0.125683i
$973$	3678.34	−	6371.07i	0.121194	−	0.209915i
$974$	32320.9			1.06327
$975$		0			0
$976$	3164.98			0.103800
$977$	2464.81	−	4269.17i	0.0807125	−	0.139798i	−0.822844	−	0.568268i	$-0.807614\pi$
$977$	2464.81	−	4269.17i	0.0807125	−	0.139798i	0.903556	+	0.428470i	$0.140947\pi$
$978$	−29617.5	+	51299.1i	−0.968369	+	1.67726i
$979$	−24061.9	−	41676.4i	−0.785517	−	1.36056i
$980$	−15175.0			−0.494640
$981$	35759.7	+	61937.5i	1.16383	+	2.01581i
$982$	−6426.96	−	11131.8i	−0.208852	−	0.361742i
$983$	−15526.2			−0.503774			−0.251887	−	0.967757i	$-0.581051\pi$
$983$	−15526.2			−0.503774			−0.251887	+	0.967757i	$0.581051\pi$
$984$	2967.97	+	5140.67i	0.0961538	+	0.166543i
$985$	−17291.6	+	29950.0i	−0.559348	+	0.968819i
$986$	−8798.45	+	15239.4i	−0.284178	+	0.492211i
$987$	16010.6			0.516337
$988$		0			0
$989$	−7239.49			−0.232763
$990$	30624.6	−	53043.4i	0.983146	−	1.70286i
$991$	−14938.4	+	25874.1i	−0.478844	+	0.829381i	−0.999706	−	0.0242594i	$-0.992277\pi$
$991$	−14938.4	+	25874.1i	−0.478844	+	0.829381i	0.520862	+	0.853641i	$0.325611\pi$
$992$	−3515.69	−	6089.36i	−0.112524	−	0.194897i
$993$	−72582.6			−2.31958
$994$	4008.76	+	6943.38i	0.127918	+	0.221560i
$995$	21801.2	+	37760.8i	0.694618	+	1.20311i
$996$	−45184.1			−1.43746
$997$	−1300.23	−	2252.07i	−0.0413026	−	0.0715382i	0.844635	−	0.535342i	$-0.179817\pi$
$997$	−1300.23	−	2252.07i	−0.0413026	−	0.0715382i	−0.885938	+	0.463804i	$0.846484\pi$
$998$	15240.3	−	26397.0i	0.483391	−	0.837258i
$999$	12943.2	−	22418.2i	0.409913	−	0.709990i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.4.c.h.191.2		4
13.2	odd	12		338.4.e.g.23.2		8
13.3	even	3	inner	338.4.c.h.315.2		4
13.4	even	6		338.4.a.f.1.1		2
13.5	odd	4		338.4.e.g.147.4		8
13.6	odd	12		26.4.b.a.25.1	✓	4
13.7	odd	12		26.4.b.a.25.3	yes	4
13.8	odd	4		338.4.e.g.147.2		8
13.9	even	3		338.4.a.i.1.1		2
13.10	even	6		338.4.c.i.315.2		4
13.11	odd	12		338.4.e.g.23.4		8
13.12	even	2		338.4.c.i.191.2		4
39.20	even	12		234.4.b.b.181.1		4
39.32	even	12		234.4.b.b.181.4		4
52.7	even	12		208.4.f.d.129.4		4
52.19	even	12		208.4.f.d.129.3		4
65.7	even	12		650.4.c.e.649.4		4
65.19	odd	12		650.4.d.d.51.4		4
65.32	even	12		650.4.c.f.649.4		4
65.33	even	12		650.4.c.f.649.1		4
65.58	even	12		650.4.c.e.649.1		4
65.59	odd	12		650.4.d.d.51.2		4
104.19	even	12		832.4.f.h.129.2		4
104.45	odd	12		832.4.f.j.129.4		4
104.59	even	12		832.4.f.h.129.1		4
104.85	odd	12		832.4.f.j.129.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.4.b.a.25.1	✓	4	13.6	odd	12
26.4.b.a.25.3	yes	4	13.7	odd	12
208.4.f.d.129.3		4	52.19	even	12
208.4.f.d.129.4		4	52.7	even	12
234.4.b.b.181.1		4	39.20	even	12
234.4.b.b.181.4		4	39.32	even	12
338.4.a.f.1.1		2	13.4	even	6
338.4.a.i.1.1		2	13.9	even	3
338.4.c.h.191.2		4	1.1	even	1	trivial
338.4.c.h.315.2		4	13.3	even	3	inner
338.4.c.i.191.2		4	13.12	even	2
338.4.c.i.315.2		4	13.10	even	6
338.4.e.g.23.2		8	13.2	odd	12
338.4.e.g.23.4		8	13.11	odd	12
338.4.e.g.147.2		8	13.8	odd	4
338.4.e.g.147.4		8	13.5	odd	4
650.4.c.e.649.1		4	65.58	even	12
650.4.c.e.649.4		4	65.7	even	12
650.4.c.f.649.1		4	65.33	even	12
650.4.c.f.649.4		4	65.32	even	12
650.4.d.d.51.2		4	65.59	odd	12
650.4.d.d.51.4		4	65.19	odd	12
832.4.f.h.129.1		4	104.59	even	12
832.4.f.h.129.2		4	104.19	even	12
832.4.f.j.129.3		4	104.85	odd	12
832.4.f.j.129.4		4	104.45	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	338.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(4.43273 - 7.67771i) q^{3} +(-2.00000 - 3.46410i) q^{4} +16.8655 q^{5} +(8.86546 + 15.3554i) q^{6} +(-5.43273 - 9.40976i) q^{7} +8.00000 q^{8} +(-25.7982 - 44.6838i) q^{9} +(-16.8655 + 29.2118i) q^{10} +(17.5964 - 30.4778i) q^{11} -35.4618 q^{12} +21.7309 q^{14} +(74.7600 - 129.488i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-15.1636 - 26.2642i) q^{17} +103.193 q^{18} +(14.1928 + 24.5826i) q^{19} +(-33.7309 - 58.4237i) q^{20} -96.3273 q^{21} +(35.1928 + 60.9556i) q^{22} +(12.3273 - 21.3515i) q^{23} +(35.4618 - 61.4217i) q^{24} +159.444 q^{25} -218.058 q^{27} +(-21.7309 + 37.6391i) q^{28} +(-145.058 + 251.248i) q^{29} +(149.520 + 258.976i) q^{30} +219.731 q^{31} +(-16.0000 - 27.7128i) q^{32} +(-156.000 - 270.200i) q^{33} +60.6546 q^{34} +(-91.6255 - 158.700i) q^{35} +(-103.193 + 178.735i) q^{36} +(-59.3564 + 102.808i) q^{37} -56.7710 q^{38} +134.924 q^{40} +(-41.8474 + 72.4818i) q^{41} +(96.3273 - 166.844i) q^{42} +(-146.818 - 254.297i) q^{43} -140.771 q^{44} +(-435.098 - 753.612i) q^{45} +(24.6546 + 42.7030i) q^{46} -166.211 q^{47} +(70.9237 + 122.843i) q^{48} +(112.471 - 194.805i) q^{49} +(-159.444 + 276.165i) q^{50} -268.865 q^{51} -76.3855 q^{53} +(218.058 - 377.688i) q^{54} +(296.771 - 514.023i) q^{55} +(-43.4618 - 75.2781i) q^{56} +251.651 q^{57} +(-290.116 - 502.496i) q^{58} +(-92.3454 - 159.947i) q^{59} -598.080 q^{60} +(-98.9056 - 171.309i) q^{61} +(-219.731 + 380.585i) q^{62} +(-280.309 + 485.510i) q^{63} +64.0000 q^{64} +624.000 q^{66} +(-160.636 + 278.231i) q^{67} +(-60.6546 + 105.057i) q^{68} +(-109.287 - 189.291i) q^{69} +366.502 q^{70} +(184.473 + 319.516i) q^{71} +(-206.386 - 357.470i) q^{72} +843.273 q^{73} +(-118.713 - 205.617i) q^{74} +(706.771 - 1224.16i) q^{75} +(56.7710 - 98.3303i) q^{76} -382.386 q^{77} +184.044 q^{79} +(-134.924 + 233.695i) q^{80} +(-270.042 + 467.727i) q^{81} +(-83.6947 - 144.964i) q^{82} +1274.16 q^{83} +(192.655 + 333.688i) q^{84} +(-255.742 - 442.958i) q^{85} +587.273 q^{86} +(1286.01 + 2227.43i) q^{87} +(140.771 - 243.823i) q^{88} +(683.717 - 1184.23i) q^{89} +1740.39 q^{90} -98.6184 q^{92} +(974.008 - 1687.03i) q^{93} +(166.211 - 287.886i) q^{94} +(239.367 + 414.597i) q^{95} -283.695 q^{96} +(345.120 + 597.766i) q^{97} +(224.942 + 389.611i) q^{98} -1815.82 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 3 q^{3} - 8 q^{4} + 38 q^{5} + 6 q^{6} - 7 q^{7} + 32 q^{8} - 59 q^{9} - 38 q^{10} - 18 q^{11} - 24 q^{12} + 28 q^{14} + 137 q^{15} - 32 q^{16} + 13 q^{17} + 236 q^{18} - 120 q^{19} - 76 q^{20}+ \cdots - 2844 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 3 * q^3 - 8 * q^4 + 38 * q^5 + 6 * q^6 - 7 * q^7 + 32 * q^8 - 59 * q^9 - 38 * q^10 - 18 * q^11 - 24 * q^12 + 28 * q^14 + 137 * q^15 - 32 * q^16 + 13 * q^17 + 236 * q^18 - 120 * q^19 - 76 * q^20 - 238 * q^21 - 36 * q^22 - 98 * q^23 + 24 * q^24 + 78 * q^25 - 666 * q^27 - 28 * q^28 - 374 * q^29 + 274 * q^30 + 820 * q^31 - 64 * q^32 - 624 * q^33 - 52 * q^34 - 175 * q^35 - 236 * q^36 + 13 * q^37 + 480 * q^38 + 304 * q^40 + 304 * q^41 + 238 * q^42 - 219 * q^43 + 144 * q^44 - 886 * q^45 - 196 * q^46 - 930 * q^47 + 48 * q^48 + 553 * q^49 - 78 * q^50 - 1046 * q^51 + 48 * q^53 + 666 * q^54 + 480 * q^55 - 56 * q^56 + 2244 * q^57 - 748 * q^58 - 664 * q^59 - 1096 * q^60 + 282 * q^61 - 820 * q^62 - 532 * q^63 + 256 * q^64 + 2496 * q^66 + 94 * q^67 + 52 * q^68 - 938 * q^69 + 700 * q^70 + 75 * q^71 - 472 * q^72 + 1900 * q^73 + 26 * q^74 + 2120 * q^75 - 480 * q^76 - 1176 * q^77 - 1444 * q^79 - 304 * q^80 + 334 * q^81 + 608 * q^82 + 2504 * q^83 + 476 * q^84 - 419 * q^85 + 876 * q^86 + 2080 * q^87 - 144 * q^88 + 702 * q^89 + 3544 * q^90 + 784 * q^92 + 832 * q^93 + 930 * q^94 + 162 * q^95 - 192 * q^96 - 564 * q^97 + 1106 * q^98 - 2844 * q^99

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