LMFDB - Embedded newform 354.4.c.a.353.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,4,Mod(353,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("354.353");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	354.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$20.8866761420$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			353.6
Character	$\chi$	$=$	354.353
Dual form			354.4.c.a.353.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} +(-4.66792 + 2.28265i) q^{3} +4.00000 q^{4} +8.40010i q^{5} +(9.33585 - 4.56530i) q^{6} +31.0296 q^{7} -8.00000 q^{8} +(16.5790 - 21.3105i) q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +(-4.66792 + 2.28265i) q^{3} +4.00000 q^{4} +8.40010i q^{5} +(9.33585 - 4.56530i) q^{6} +31.0296 q^{7} -8.00000 q^{8} +(16.5790 - 21.3105i) q^{9} -16.8002i q^{10} +8.36506 q^{11} +(-18.6717 + 9.13060i) q^{12} -33.8590i q^{13} -62.0592 q^{14} +(-19.1745 - 39.2110i) q^{15} +16.0000 q^{16} -52.8462i q^{17} +(-33.1580 + 42.6210i) q^{18} -13.4852 q^{19} +33.6004i q^{20} +(-144.844 + 70.8297i) q^{21} -16.7301 q^{22} -124.185 q^{23} +(37.3434 - 18.2612i) q^{24} +54.4384 q^{25} +67.7180i q^{26} +(-28.7452 + 137.320i) q^{27} +124.118 q^{28} -146.756i q^{29} +(38.3490 + 78.4220i) q^{30} -205.242i q^{31} -32.0000 q^{32} +(-39.0475 + 19.0945i) q^{33} +105.692i q^{34} +260.651i q^{35} +(66.3160 - 85.2419i) q^{36} -278.619i q^{37} +26.9704 q^{38} +(77.2882 + 158.051i) q^{39} -67.2008i q^{40} +402.984i q^{41} +(289.687 - 141.659i) q^{42} -466.280i q^{43} +33.4602 q^{44} +(179.010 + 139.265i) q^{45} +248.370 q^{46} +513.624 q^{47} +(-74.6868 + 36.5224i) q^{48} +619.835 q^{49} -108.877 q^{50} +(120.629 + 246.682i) q^{51} -135.436i q^{52} -100.658i q^{53} +(57.4903 - 274.640i) q^{54} +70.2673i q^{55} -248.237 q^{56} +(62.9478 - 30.7820i) q^{57} +293.512i q^{58} +(-339.656 - 300.022i) q^{59} +(-76.6980 - 156.844i) q^{60} -413.290i q^{61} +410.483i q^{62} +(514.440 - 661.255i) q^{63} +64.0000 q^{64} +284.419 q^{65} +(78.0949 - 38.1890i) q^{66} +771.385i q^{67} -211.385i q^{68} +(579.686 - 283.471i) q^{69} -521.303i q^{70} -262.065i q^{71} +(-132.632 + 170.484i) q^{72} +355.978i q^{73} +557.238i q^{74} +(-254.114 + 124.264i) q^{75} -53.9408 q^{76} +259.564 q^{77} +(-154.576 - 316.102i) q^{78} +942.458 q^{79} +134.402i q^{80} +(-179.273 - 706.613i) q^{81} -805.969i q^{82} +1153.17 q^{83} +(-579.375 + 283.319i) q^{84} +443.913 q^{85} +932.560i q^{86} +(334.993 + 685.046i) q^{87} -66.9205 q^{88} +109.139 q^{89} +(-358.020 - 278.531i) q^{90} -1050.63i q^{91} -496.740 q^{92} +(468.495 + 958.052i) q^{93} -1027.25 q^{94} -113.277i q^{95} +(149.374 - 73.0448i) q^{96} +1052.48i q^{97} -1239.67 q^{98} +(138.684 - 178.263i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 60 q^{2} + 5 q^{3} + 120 q^{4} - 10 q^{6} + 6 q^{7} - 240 q^{8} + 27 q^{9}+O(q^{10}) $ 30 * q - 60 * q^2 + 5 * q^3 + 120 * q^4 - 10 * q^6 + 6 * q^7 - 240 * q^8 + 27 * q^9	$ 30 q - 60 q^{2} + 5 q^{3} + 120 q^{4} - 10 q^{6} + 6 q^{7} - 240 q^{8} + 27 q^{9} - 60 q^{11} + 20 q^{12} - 12 q^{14} + 20 q^{15} + 480 q^{16} - 54 q^{18} + 90 q^{19} + 132 q^{21} + 120 q^{22} + 24 q^{23} - 40 q^{24} - 1080 q^{25} - 55 q^{27} + 24 q^{28} - 40 q^{30} - 960 q^{32} + 336 q^{33} + 108 q^{36} - 180 q^{38} + 652 q^{39} - 264 q^{42} - 240 q^{44} - 878 q^{45} - 48 q^{46} + 792 q^{47} + 80 q^{48} + 2016 q^{49} + 2160 q^{50} + 650 q^{51} + 110 q^{54} - 48 q^{56} + 846 q^{57} - 480 q^{59} + 80 q^{60} + 887 q^{63} + 1920 q^{64} - 1416 q^{65} - 672 q^{66} - 590 q^{69} - 216 q^{72} - 952 q^{75} + 360 q^{76} + 864 q^{77} - 1304 q^{78} + 738 q^{79} - 1217 q^{81} + 876 q^{83} + 528 q^{84} + 1176 q^{85} + 534 q^{87} + 480 q^{88} - 300 q^{89} + 1756 q^{90} + 96 q^{92} + 1684 q^{93} - 1584 q^{94} - 160 q^{96} - 4032 q^{98} + 730 q^{99}+O(q^{100}) $ 30 * q - 60 * q^2 + 5 * q^3 + 120 * q^4 - 10 * q^6 + 6 * q^7 - 240 * q^8 + 27 * q^9 - 60 * q^11 + 20 * q^12 - 12 * q^14 + 20 * q^15 + 480 * q^16 - 54 * q^18 + 90 * q^19 + 132 * q^21 + 120 * q^22 + 24 * q^23 - 40 * q^24 - 1080 * q^25 - 55 * q^27 + 24 * q^28 - 40 * q^30 - 960 * q^32 + 336 * q^33 + 108 * q^36 - 180 * q^38 + 652 * q^39 - 264 * q^42 - 240 * q^44 - 878 * q^45 - 48 * q^46 + 792 * q^47 + 80 * q^48 + 2016 * q^49 + 2160 * q^50 + 650 * q^51 + 110 * q^54 - 48 * q^56 + 846 * q^57 - 480 * q^59 + 80 * q^60 + 887 * q^63 + 1920 * q^64 - 1416 * q^65 - 672 * q^66 - 590 * q^69 - 216 * q^72 - 952 * q^75 + 360 * q^76 + 864 * q^77 - 1304 * q^78 + 738 * q^79 - 1217 * q^81 + 876 * q^83 + 528 * q^84 + 1176 * q^85 + 534 * q^87 + 480 * q^88 - 300 * q^89 + 1756 * q^90 + 96 * q^92 + 1684 * q^93 - 1584 * q^94 - 160 * q^96 - 4032 * q^98 + 730 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−2.00000			−0.707107
$2$	−2.00000			−0.707107
$3$	−4.66792	+	2.28265i	−0.898342	+	0.439296i
$3$	−4.66792	+	2.28265i	−0.898342	+	0.439296i
$4$	4.00000			0.500000
$5$			8.40010i			0.751328i	0.926756	+	0.375664i	$0.122585\pi$
$5$			8.40010i			0.751328i	−0.926756	+	0.375664i	$0.877415\pi$
$6$	9.33585	−	4.56530i	0.635224	−	0.310629i
$7$	31.0296			1.67544			0.837720	−	0.546100i	$-0.183888\pi$
$7$	31.0296			1.67544			0.837720	+	0.546100i	$0.183888\pi$
$8$	−8.00000			−0.353553
$9$	16.5790	−	21.3105i	0.614037	−	0.789277i
$10$		−	16.8002i		−	0.531269i
$11$	8.36506			0.229287			0.114644	−	0.993407i	$-0.463427\pi$
$11$	8.36506			0.229287			0.114644	+	0.993407i	$0.463427\pi$
$12$	−18.6717	+	9.13060i	−0.449171	+	0.219648i
$13$		−	33.8590i		−	0.722368i	−0.932494	−	0.361184i	$-0.882373\pi$
$13$		−	33.8590i		−	0.722368i	0.932494	−	0.361184i	$-0.117627\pi$
$14$	−62.0592			−1.18471
$15$	−19.1745	−	39.2110i	−0.330055	−	0.674949i
$16$	16.0000			0.250000
$17$		−	52.8462i		−	0.753946i	−0.926224	−	0.376973i	$-0.876965\pi$
$17$		−	52.8462i		−	0.753946i	0.926224	−	0.376973i	$-0.123035\pi$
$18$	−33.1580	+	42.6210i	−0.434190	+	0.558103i
$19$	−13.4852			−0.162827			−0.0814135	−	0.996680i	$-0.525943\pi$
$19$	−13.4852			−0.162827			−0.0814135	+	0.996680i	$0.525943\pi$
$20$			33.6004i			0.375664i
$21$	−144.844	+	70.8297i	−1.50512	+	0.736015i
$22$	−16.7301			−0.162131
$23$	−124.185			−1.12584			−0.562921	−	0.826511i	$-0.690323\pi$
$23$	−124.185			−1.12584			−0.562921	+	0.826511i	$0.690323\pi$
$24$	37.3434	−	18.2612i	0.317612	−	0.155315i
$25$	54.4384			0.435507
$26$			67.7180i			0.510792i
$27$	−28.7452	+	137.320i	−0.204889	+	0.978785i
$28$	124.118			0.837720
$29$		−	146.756i		−	0.939722i	−0.882740	−	0.469861i	$-0.844304\pi$
$29$		−	146.756i		−	0.939722i	0.882740	−	0.469861i	$-0.155696\pi$
$30$	38.3490	+	78.4220i	0.233384	+	0.477261i
$31$		−	205.242i		−	1.18911i	−0.804054	−	0.594556i	$-0.797328\pi$
$31$		−	205.242i		−	1.18911i	0.804054	−	0.594556i	$-0.202672\pi$
$32$	−32.0000			−0.176777
$33$	−39.0475	+	19.0945i	−0.205979	+	0.100725i
$34$			105.692i			0.533120i
$35$			260.651i			1.25880i
$36$	66.3160	−	85.2419i	0.307019	−	0.394638i
$37$		−	278.619i		−	1.23796i	−0.785405	−	0.618982i	$-0.787545\pi$
$37$		−	278.619i		−	1.23796i	0.785405	−	0.618982i	$-0.212455\pi$
$38$	26.9704			0.115136
$39$	77.2882	+	158.051i	0.317334	+	0.648934i
$40$		−	67.2008i		−	0.265634i
$41$			402.984i			1.53501i	0.641040	+	0.767507i	$0.278503\pi$
$41$			402.984i			1.53501i	−0.641040	+	0.767507i	$0.721497\pi$
$42$	289.687	−	141.659i	1.06428	−	0.520441i
$43$		−	466.280i		−	1.65365i	−0.562457	−	0.826826i	$-0.690144\pi$
$43$		−	466.280i		−	1.65365i	0.562457	−	0.826826i	$-0.309856\pi$
$44$	33.4602			0.114644
$45$	179.010	+	139.265i	0.593006	+	0.461343i
$46$	248.370			0.796091
$47$	513.624			1.59404			0.797019	−	0.603954i	$-0.206409\pi$
$47$	513.624			1.59404			0.797019	+	0.603954i	$0.206409\pi$
$48$	−74.6868	+	36.5224i	−0.224586	+	0.109824i
$49$	619.835			1.80710
$50$	−108.877			−0.307950
$51$	120.629	+	246.682i	0.331206	+	0.677301i
$52$		−	135.436i		−	0.361184i
$53$		−	100.658i		−	0.260877i	−0.991456	−	0.130438i	$-0.958361\pi$
$53$		−	100.658i		−	0.260877i	0.991456	−	0.130438i	$-0.0416385\pi$
$54$	57.4903	−	274.640i	0.144879	−	0.692106i
$55$			70.2673i			0.172270i
$56$	−248.237			−0.592357
$57$	62.9478	−	30.7820i	0.146274	−	0.0715293i
$58$			293.512i			0.664484i
$59$	−339.656	−	300.022i	−0.749481	−	0.662026i
$59$	−339.656	−	300.022i	−0.749481	−	0.662026i
$60$	−76.6980	−	156.844i	−0.165028	−	0.337475i
$61$		−	413.290i		−	0.867481i	−0.901038	−	0.433740i	$-0.857193\pi$
$61$		−	413.290i		−	0.867481i	0.901038	−	0.433740i	$-0.142807\pi$
$62$			410.483i			0.840829i
$63$	514.440	−	661.255i	1.02878	−	1.32239i
$64$	64.0000			0.125000
$65$	284.419			0.542735
$66$	78.0949	−	38.1890i	0.145649	−	0.0712234i
$67$			771.385i			1.40656i	0.710911	+	0.703282i	$0.248283\pi$
$67$			771.385i			1.40656i	−0.710911	+	0.703282i	$0.751717\pi$
$68$		−	211.385i		−	0.376973i
$69$	579.686	−	283.471i	1.01139	−	0.494578i
$70$		−	521.303i		−	0.890109i
$71$		−	262.065i		−	0.438048i	−0.975720	−	0.219024i	$-0.929713\pi$
$71$		−	262.065i		−	0.438048i	0.975720	−	0.219024i	$-0.0702873\pi$
$72$	−132.632	+	170.484i	−0.217095	+	0.279052i
$73$			355.978i			0.570740i	0.958417	+	0.285370i	$0.0921166\pi$
$73$			355.978i			0.570740i	−0.958417	+	0.285370i	$0.907883\pi$
$74$			557.238i			0.875373i
$75$	−254.114	+	124.264i	−0.391234	+	0.191317i
$76$	−53.9408			−0.0814135
$77$	259.564			0.384157
$78$	−154.576	−	316.102i	−0.224389	−	0.458866i
$79$	942.458			1.34221			0.671106	−	0.741361i	$-0.265819\pi$
$79$	942.458			1.34221			0.671106	+	0.741361i	$0.265819\pi$
$80$			134.402i			0.187832i
$81$	−179.273	−	706.613i	−0.245916	−	0.969291i
$82$		−	805.969i		−	1.08542i
$83$	1153.17			1.52502			0.762510	−	0.646976i	$-0.223967\pi$
$83$	1153.17			1.52502			0.762510	+	0.646976i	$0.223967\pi$
$84$	−579.375	+	283.319i	−0.752559	+	0.368007i
$85$	443.913			0.566460
$86$			932.560i			1.16931i
$87$	334.993	+	685.046i	0.412816	+	0.844192i
$88$	−66.9205			−0.0810653
$89$	109.139			0.129985			0.0649925	−	0.997886i	$-0.479298\pi$
$89$	109.139			0.129985			0.0649925	+	0.997886i	$0.479298\pi$
$90$	−358.020	−	278.531i	−0.419318	−	0.326219i
$91$		−	1050.63i		−	1.21028i
$92$	−496.740			−0.562921
$93$	468.495	+	958.052i	0.522373	+	1.06823i
$94$	−1027.25			−1.12716
$95$		−	113.277i		−	0.122336i
$96$	149.374	−	73.0448i	0.158806	−	0.0776574i
$97$			1052.48i			1.10168i	0.834610	+	0.550842i	$0.185693\pi$
$97$			1052.48i			1.10168i	−0.834610	+	0.550842i	$0.814307\pi$
$98$	−1239.67			−1.27781
$99$	138.684	−	178.263i	0.140791	−	0.180971i
$100$	217.753			0.217753
$101$	−525.404			−0.517621			−0.258810	−	0.965928i	$-0.583330\pi$
$101$	−525.404			−0.517621			−0.258810	+	0.965928i	$0.583330\pi$
$102$	−241.259	−	493.364i	−0.234198	−	0.478924i
$103$			1421.58i			1.35993i	0.733245	+	0.679964i	$0.238005\pi$
$103$			1421.58i			1.35993i	−0.733245	+	0.679964i	$0.761995\pi$
$104$			270.872i			0.255396i
$105$	−594.976	−	1216.70i	−0.552988	−	1.13084i
$106$			201.317i			0.184468i
$107$		−	1116.93i		−	1.00914i	−0.863370	−	0.504571i	$-0.831651\pi$
$107$		−	1116.93i		−	1.00914i	0.863370	−	0.504571i	$-0.168349\pi$
$108$	−114.981	+	549.279i	−0.102445	+	0.489393i
$109$		−	981.827i		−	0.862771i	−0.902168	−	0.431385i	$-0.858025\pi$
$109$		−	981.827i		−	0.862771i	0.902168	−	0.431385i	$-0.141975\pi$
$110$		−	140.535i		−	0.121813i
$111$	635.990	+	1300.57i	0.543833	+	1.11212i
$112$	496.473			0.418860
$113$	408.043			0.339694			0.169847	−	0.985470i	$-0.445673\pi$
$113$	408.043			0.339694			0.169847	+	0.985470i	$0.445673\pi$
$114$	−125.896	+	61.5640i	−0.103432	+	0.0505789i
$115$		−	1043.17i		−	0.845876i
$116$		−	587.025i		−	0.469861i
$117$	−721.551	−	561.348i	−0.570149	−	0.443561i
$118$	679.311	+	600.044i	0.529963	+	0.468123i
$119$		−	1639.79i		−	1.26319i
$120$	153.396	+	313.688i	0.116692	+	0.238631i
$121$	−1261.03			−0.947427
$122$			826.580i			0.613402i
$123$	−919.873	−	1881.10i	−0.674326	−	1.37897i
$124$		−	820.966i		−	0.594556i
$125$			1507.30i			1.07854i
$126$	−1028.88	+	1322.51i	−0.727459	+	0.935068i
$127$	1285.44			0.898147			0.449073	−	0.893495i	$-0.351754\pi$
$127$	1285.44			0.898147			0.449073	+	0.893495i	$0.351754\pi$
$128$	−128.000			−0.0883883
$129$	1064.35	+	2176.56i	0.726444	+	1.48555i
$130$	−568.837			−0.383772
$131$	258.622			0.172488			0.0862439	−	0.996274i	$-0.472514\pi$
$131$	258.622			0.172488			0.0862439	+	0.996274i	$0.472514\pi$
$132$	−156.190	+	76.3781i	−0.102989	+	0.0503626i
$133$	−418.440			−0.272807
$134$		−	1542.77i		−	0.994590i
$135$	−1153.50	−	241.462i	−0.735388	−	0.153939i
$136$			422.769i			0.266560i
$137$			1367.24i			0.852635i	0.904574	+	0.426317i	$0.140189\pi$
$137$			1367.24i			0.852635i	−0.904574	+	0.426317i	$0.859811\pi$
$138$	−1159.37	+	566.942i	−0.715162	+	0.349720i
$139$	−610.063			−0.372265			−0.186133	−	0.982525i	$-0.559595\pi$
$139$	−610.063			−0.372265			−0.186133	+	0.982525i	$0.559595\pi$
$140$			1042.61i			0.629402i
$141$	−2397.56	+	1172.43i	−1.43199	+	0.700255i
$142$			524.130i			0.309747i
$143$		−	283.232i		−	0.165630i
$144$	265.264	−	340.968i	0.153509	−	0.197319i
$145$	1232.77			0.706039
$146$		−	711.956i		−	0.403574i
$147$	−2893.34	+	1414.87i	−1.62339	+	0.793852i
$148$		−	1114.48i		−	0.618982i
$149$	−1743.66			−0.958697			−0.479348	−	0.877625i	$-0.659127\pi$
$149$	−1743.66			−0.958697			−0.479348	+	0.877625i	$0.659127\pi$
$150$	508.228	−	248.528i	0.276644	−	0.135281i
$151$			1657.12i			0.893075i	0.894765	+	0.446538i	$0.147343\pi$
$151$			1657.12i			0.893075i	−0.894765	+	0.446538i	$0.852657\pi$
$152$	107.882			0.0575681
$153$	−1126.18	−	876.137i	−0.595072	−	0.462951i
$154$	−519.129			−0.271640
$155$	1724.05			0.893413
$156$	309.153	+	632.204i	0.158667	+	0.324467i
$157$		−	2682.20i		−	1.36346i	−0.731605	−	0.681729i	$-0.761228\pi$
$157$		−	2682.20i		−	1.36346i	0.731605	−	0.681729i	$-0.238772\pi$
$158$	−1884.92			−0.949088
$159$	229.768	+	469.865i	0.114602	+	0.234357i
$160$		−	268.803i		−	0.132817i
$161$	−3853.41			−1.88628
$162$	358.546	+	1413.23i	0.173889	+	0.685392i
$163$	1503.49			0.722471			0.361236	−	0.932475i	$-0.382355\pi$
$163$	1503.49			0.722471			0.361236	+	0.932475i	$0.382355\pi$
$164$			1611.94i			0.767507i
$165$	−160.396	−	328.002i	−0.0756775	−	0.154757i
$166$	−2306.34			−1.07835
$167$		−	1242.64i		−	0.575799i	−0.957661	−	0.287899i	$-0.907043\pi$
$167$		−	1242.64i		−	0.575799i	0.957661	−	0.287899i	$-0.0929569\pi$
$168$	1158.75	−	566.638i	0.532140	−	0.260220i
$169$	1050.57			0.478184
$170$	−887.826			−0.400548
$171$	−223.571	+	287.376i	−0.0999819	+	0.128516i
$172$		−	1865.12i		−	0.826826i
$173$	−2533.15			−1.11325			−0.556624	−	0.830764i	$-0.687904\pi$
$173$	−2533.15			−1.11325			−0.556624	+	0.830764i	$0.687904\pi$
$174$	−669.986	−	1370.09i	−0.291905	−	0.596934i
$175$	1689.20			0.729666
$176$	133.841			0.0573218
$177$	2270.33	+	625.163i	0.964116	+	0.265481i
$178$	−218.277			−0.0919133
$179$	1900.69			0.793656			0.396828	−	0.917893i	$-0.370111\pi$
$179$	1900.69			0.793656			0.396828	+	0.917893i	$0.370111\pi$
$180$	716.040	+	557.061i	0.296503	+	0.230672i
$181$	−3907.44			−1.60463			−0.802313	−	0.596903i	$-0.796398\pi$
$181$	−3907.44			−1.60463			−0.802313	+	0.596903i	$0.796398\pi$
$182$			2101.26i			0.855801i
$183$	943.396	+	1929.20i	0.381081	+	0.779295i
$184$	993.480			0.398045
$185$	2340.43			0.930117
$186$	−936.990	−	1916.10i	−0.369373	−	0.755353i
$187$		−	442.061i		−	0.172870i
$188$	2054.50			0.797019
$189$	−891.950	+	4260.97i	−0.343279	+	1.63990i
$190$			226.554i			0.0865049i
$191$	1208.73			0.457909			0.228954	−	0.973437i	$-0.426469\pi$
$191$	1208.73			0.457909			0.228954	+	0.973437i	$0.426469\pi$
$192$	−298.747	+	146.090i	−0.112293	+	0.0549120i
$193$	−520.796			−0.194237			−0.0971184	−	0.995273i	$-0.530963\pi$
$193$	−520.796			−0.194237			−0.0971184	+	0.995273i	$0.530963\pi$
$194$		−	2104.96i		−	0.779008i
$195$	−1327.64	+	649.229i	−0.487562	+	0.238422i
$196$	2479.34			0.903549
$197$			199.705i			0.0722253i	0.999348	+	0.0361126i	$0.0114975\pi$
$197$			199.705i			0.0722253i	−0.999348	+	0.0361126i	$0.988502\pi$
$198$	−277.369	+	356.527i	−0.0995543	+	0.127966i
$199$	3735.08			1.33052			0.665258	−	0.746614i	$-0.268322\pi$
$199$	3735.08			1.33052			0.665258	+	0.746614i	$0.268322\pi$
$200$	−435.507			−0.153975
$201$	−1760.80	−	3600.77i	−0.617898	−	1.26357i
$202$	1050.81			0.366013
$203$		−	4553.78i		−	1.57445i
$204$	482.517	+	986.727i	0.165603	+	0.338651i
$205$	−3385.11			−1.15330
$206$		−	2843.16i		−	0.961615i
$207$	−2058.86	+	2646.44i	−0.691309	+	0.888601i
$208$		−	541.744i		−	0.180592i
$209$	−112.804			−0.0373342
$210$	1189.95	+	2433.40i	0.391022	+	0.799622i
$211$			5577.94i			1.81991i	0.414707	+	0.909955i	$0.363884\pi$
$211$			5577.94i			1.81991i	−0.414707	+	0.909955i	$0.636116\pi$
$212$		−	402.633i		−	0.130438i
$213$	598.203	+	1223.30i	0.192433	+	0.393517i
$214$			2233.87i			0.713571i
$215$	3916.80			1.24243
$216$	229.961	−	1098.56i	0.0724393	−	0.346053i
$217$		−	6368.56i		−	1.99229i
$218$			1963.65i			0.610071i
$219$	−812.573	−	1661.68i	−0.250724	−	0.512720i
$220$			281.069i			0.0861350i
$221$	−1789.32			−0.544627
$222$	−1271.98	−	2601.14i	−0.384548	−	0.786384i
$223$	645.411			0.193811			0.0969056	−	0.995294i	$-0.469106\pi$
$223$	645.411			0.193811			0.0969056	+	0.995294i	$0.469106\pi$
$224$	−992.947			−0.296179
$225$	902.534	−	1160.11i	0.267418	−	0.343736i
$226$	−816.086			−0.240200
$227$	4962.92			1.45111			0.725553	−	0.688167i	$-0.241584\pi$
$227$	4962.92			1.45111			0.725553	+	0.688167i	$0.241584\pi$
$228$	251.791	−	123.128i	0.0731372	−	0.0357647i
$229$			1665.45i			0.480594i	0.970699	+	0.240297i	$0.0772448\pi$
$229$			1665.45i			0.480594i	−0.970699	+	0.240297i	$0.922755\pi$
$230$			2086.33i			0.598125i
$231$	−1211.63	+	592.495i	−0.345105	+	0.168759i
$232$			1174.05i			0.332242i
$233$	1081.65			0.304126			0.152063	−	0.988371i	$-0.451408\pi$
$233$	1081.65			0.304126			0.152063	+	0.988371i	$0.451408\pi$
$234$	1443.10	+	1122.70i	0.403156	+	0.313645i
$235$			4314.50i			1.19765i
$236$	−1358.62	−	1200.09i	−0.374741	−	0.331013i
$237$	−4399.32	+	2151.30i	−1.20577	+	0.589629i
$238$			3279.59i			0.893211i
$239$		−	3631.44i		−	0.982837i	−0.870923	−	0.491419i	$-0.836478\pi$
$239$		−	3631.44i		−	0.982837i	0.870923	−	0.491419i	$-0.163522\pi$
$240$	−306.792	−	627.376i	−0.0825139	−	0.168737i
$241$	−196.304			−0.0524692			−0.0262346	−	0.999656i	$-0.508352\pi$
$241$	−196.304			−0.0524692			−0.0262346	+	0.999656i	$0.508352\pi$
$242$	2522.05			0.669932
$243$	2449.78	+	2889.20i	0.646723	+	0.762725i
$244$		−	1653.16i		−	0.433740i
$245$			5206.67i			1.35772i
$246$	1839.75	+	3762.20i	0.476821	+	0.975078i
$247$			456.595i			0.117621i
$248$			1641.93i			0.420415i
$249$	−5382.90	+	2632.28i	−1.36999	+	0.669936i
$250$		−	3014.60i		−	0.762640i
$251$		−	4710.90i		−	1.18466i	−0.805696	−	0.592330i	$-0.798208\pi$
$251$		−	4710.90i		−	1.18466i	0.805696	−	0.592330i	$-0.201792\pi$
$252$	2057.76	−	2645.02i	0.514391	−	0.661193i
$253$	−1038.82			−0.258141
$254$	−2570.89			−0.635086
$255$	−2072.15	+	1013.30i	−0.508875	+	0.248844i
$256$	256.000			0.0625000
$257$		−	7251.98i		−	1.76018i	−0.474807	−	0.880090i	$-0.657482\pi$
$257$		−	7251.98i		−	1.76018i	0.474807	−	0.880090i	$-0.342518\pi$
$258$	−2128.71	−	4353.12i	−0.513673	−	1.05044i
$259$		−	8645.43i		−	2.07413i
$260$	1137.67			0.271368
$261$	−3127.44	−	2433.07i	−0.741701	−	0.577024i
$262$	−517.244			−0.121967
$263$		−	5336.53i		−	1.25119i	−0.780146	−	0.625597i	$-0.784855\pi$
$263$		−	5336.53i		−	1.25119i	0.780146	−	0.625597i	$-0.215145\pi$
$264$	312.380	−	152.756i	0.0728244	−	0.0356117i
$265$	845.539			0.196004
$266$	836.879			0.192904
$267$	−509.451	+	249.125i	−0.116771	+	0.0571020i
$268$			3085.54i			0.703282i
$269$	−4621.19			−1.04743			−0.523715	−	0.851893i	$-0.675454\pi$
$269$	−4621.19			−1.04743			−0.523715	+	0.851893i	$0.675454\pi$
$270$	2307.00	+	482.924i	0.519998	+	0.108851i
$271$	−1948.39			−0.436740			−0.218370	−	0.975866i	$-0.570074\pi$
$271$	−1948.39			−0.436740			−0.218370	+	0.975866i	$0.570074\pi$
$272$		−	845.539i		−	0.188486i
$273$	2398.22	+	4904.26i	0.531674	+	1.08725i
$274$		−	2734.47i		−	0.602904i
$275$	455.380			0.0998562
$276$	2318.74	−	1133.88i	0.505696	−	0.247289i
$277$	6091.03			1.32121			0.660603	−	0.750735i	$-0.270300\pi$
$277$	6091.03			1.32121			0.660603	+	0.750735i	$0.270300\pi$
$278$	1220.13			0.263231
$279$	−4373.80	−	3402.70i	−0.938539	−	0.730159i
$280$		−	2085.21i		−	0.445054i
$281$			236.625i			0.0502343i	0.999685	+	0.0251172i	$0.00799588\pi$
$281$			236.625i			0.0502343i	−0.999685	+	0.0251172i	$0.992004\pi$
$282$	4795.12	−	2344.85i	1.01257	−	0.495155i
$283$			4957.63i			1.04135i	0.853756	+	0.520673i	$0.174319\pi$
$283$			4957.63i			1.04135i	−0.853756	+	0.520673i	$0.825681\pi$
$284$		−	1048.26i		−	0.219024i
$285$	258.572	+	528.768i	0.0537420	+	0.109900i
$286$			566.465i			0.117118i
$287$			12504.4i			2.57182i
$288$	−530.528	+	681.935i	−0.108547	+	0.139526i
$289$	2120.28			0.431566
$290$	−2465.53			−0.499245
$291$	−2402.45	−	4912.90i	−0.483966	−	0.989689i
$292$			1423.91i			0.285370i
$293$			697.323i			0.139038i	0.997581	+	0.0695188i	$0.0221464\pi$
$293$			697.323i			0.139038i	−0.997581	+	0.0695188i	$0.977854\pi$
$294$	5786.68	−	2829.73i	1.14791	−	0.561338i
$295$	2520.21	−	2853.14i	0.497398	−	0.563106i
$296$			2228.95i			0.437686i
$297$	−240.455	+	1148.69i	−0.0469785	+	0.224423i
$298$	3487.31			0.677901
$299$			4204.78i			0.813273i
$300$	−1016.46	+	497.055i	−0.195617	+	0.0956583i
$301$		−	14468.5i		−	2.77060i
$302$		−	3314.24i		−	0.631499i
$303$	2452.55	−	1199.31i	0.465001	−	0.227389i
$304$	−215.763			−0.0407068
$305$	3471.67			0.651762
$306$	2252.35	+	1752.27i	0.420780	+	0.327356i
$307$	4472.31			0.831428			0.415714	−	0.909495i	$-0.363532\pi$
$307$	4472.31			0.831428			0.415714	+	0.909495i	$0.363532\pi$
$308$	1038.26			0.192079
$309$	−3244.98	−	6635.84i	−0.597412	−	1.22168i
$310$	−3448.10			−0.631738
$311$			1640.56i			0.299125i	0.988752	+	0.149562i	$0.0477865\pi$
$311$			1640.56i			0.299125i	−0.988752	+	0.149562i	$0.952214\pi$
$312$	−618.306	−	1264.41i	−0.112194	−	0.229433i
$313$		−	1328.32i		−	0.239875i	−0.992781	−	0.119938i	$-0.961731\pi$
$313$		−	1328.32i		−	0.239875i	0.992781	−	0.119938i	$-0.0382695\pi$
$314$			5364.40i			0.964110i
$315$	5554.61	+	4321.34i	0.993545	+	0.772953i
$316$	3769.83			0.671106
$317$			4577.13i			0.810970i	0.914102	+	0.405485i	$0.132897\pi$
$317$			4577.13i			0.810970i	−0.914102	+	0.405485i	$0.867103\pi$
$318$	−459.535	−	939.730i	−0.0810361	−	0.165715i
$319$		−	1227.62i		−	0.215466i
$320$			537.606i			0.0939159i
$321$	2549.57	+	5213.76i	0.443312	+	0.906554i
$322$	7706.82			1.33380
$323$			712.641i			0.122763i
$324$	−717.092	−	2826.45i	−0.122958	−	0.484646i
$325$		−	1843.23i		−	0.314596i
$326$	−3006.99			−0.510864
$327$	2241.17	+	4583.09i	0.379012	+	0.775063i
$328$		−	3223.88i		−	0.542710i
$329$	15937.5			2.67072
$330$	320.792	+	656.005i	0.0535121	+	0.109430i
$331$	−3063.70			−0.508751			−0.254375	−	0.967106i	$-0.581870\pi$
$331$	−3063.70			−0.508751			−0.254375	+	0.967106i	$0.581870\pi$
$332$	4612.68			0.762510
$333$	−5937.50	−	4619.23i	−0.977097	−	0.760156i
$334$			2485.28i			0.407151i
$335$	−6479.71			−1.05679
$336$	−2317.50	+	1133.28i	−0.376280	+	0.184004i
$337$			1397.94i			0.225966i	0.993597	+	0.112983i	$0.0360405\pi$
$337$			1397.94i			0.225966i	−0.993597	+	0.112983i	$0.963959\pi$
$338$	−2101.14			−0.338127
$339$	−1904.71	+	931.420i	−0.305162	+	0.149227i
$340$	1775.65			0.283230
$341$		−	1716.86i		−	0.272648i
$342$	447.142	−	574.752i	0.0706979	−	0.0908743i
$343$	8590.07			1.35224
$344$			3730.24i			0.584654i
$345$	2381.18	+	4869.42i	0.371590	+	0.759886i
$346$	5066.31			0.787186
$347$	5532.97			0.855982			0.427991	−	0.903783i	$-0.359222\pi$
$347$	5532.97			0.855982			0.427991	+	0.903783i	$0.359222\pi$
$348$	1339.97	+	2740.19i	0.206408	+	0.422096i
$349$			5299.70i			0.812856i	0.913683	+	0.406428i	$0.133226\pi$
$349$			5299.70i			0.812856i	−0.913683	+	0.406428i	$0.866774\pi$
$350$	−3378.40			−0.515952
$351$	4649.51	+	973.282i	0.707044	+	0.148005i
$352$	−267.682			−0.0405327
$353$	9723.93			1.46615			0.733077	−	0.680145i	$-0.238083\pi$
$353$	9723.93			1.46615			0.733077	+	0.680145i	$0.238083\pi$
$354$	−4540.66	−	1250.33i	−0.681733	−	0.187724i
$355$	2201.37			0.329117
$356$	436.555			0.0649925
$357$	3743.08	+	7654.43i	0.554915	+	1.13478i
$358$	−3801.39			−0.561200
$359$		−	1512.83i		−	0.222407i	−0.993798	−	0.111204i	$-0.964529\pi$
$359$		−	1512.83i		−	0.222407i	0.993798	−	0.111204i	$-0.0354705\pi$
$360$	−1432.08	−	1114.12i	−0.209659	−	0.163109i
$361$	−6677.15			−0.973487
$362$	7814.87			1.13464
$363$	5886.37	−	2878.48i	0.851114	−	0.416201i
$364$		−	4202.52i		−	0.605142i
$365$	−2990.25			−0.428813
$366$	−1886.79	−	3858.41i	−0.269465	−	0.551045i
$367$		−	4626.41i		−	0.658029i	−0.944325	−	0.329014i	$-0.893284\pi$
$367$		−	4626.41i		−	0.658029i	0.944325	−	0.329014i	$-0.106716\pi$
$368$	−1986.96			−0.281461
$369$	8587.79	+	6681.08i	1.21155	+	0.942556i
$370$	−4680.85			−0.657692
$371$		−	3123.38i		−	0.437084i
$372$	1873.98	+	3832.21i	0.261186	+	0.534115i
$373$	−3438.22			−0.477277			−0.238638	−	0.971109i	$-0.576701\pi$
$373$	−3438.22			−0.477277			−0.238638	+	0.971109i	$0.576701\pi$
$374$			884.123i			0.122238i
$375$	−3440.64	−	7035.96i	−0.473797	−	0.968894i
$376$	−4109.00			−0.563578
$377$	−4969.01			−0.678825
$378$	1783.90	−	8521.95i	0.242735	−	1.15958i
$379$	−13480.0			−1.82697			−0.913485	−	0.406871i	$-0.866620\pi$
$379$	−13480.0			−1.82697			−0.913485	+	0.406871i	$0.866620\pi$
$380$		−	453.108i		−	0.0611682i
$381$	−6000.35	+	2934.22i	−0.806843	+	0.394553i
$382$	−2417.46			−0.323791
$383$			4288.91i			0.572202i	0.958200	+	0.286101i	$0.0923592\pi$
$383$			4288.91i			0.572202i	−0.958200	+	0.286101i	$0.907641\pi$
$384$	597.494	−	292.179i	0.0794030	−	0.0388287i
$385$			2180.37i			0.288628i
$386$	1041.59			0.137346
$387$	−9936.65	−	7730.46i	−1.30519	−	1.01540i
$388$			4209.93i			0.550842i
$389$			2244.88i			0.292596i	0.989241	+	0.146298i	$0.0467359\pi$
$389$			2244.88i			0.292596i	−0.989241	+	0.146298i	$0.953264\pi$
$390$	2655.29	−	1298.46i	0.344758	−	0.168590i
$391$			6562.70i			0.848824i
$392$	−4958.68			−0.638906
$393$	−1207.23	+	590.344i	−0.154953	+	0.0757733i
$394$		−	399.410i		−	0.0510710i
$395$			7916.74i			1.00844i
$396$	554.738	−	713.054i	0.0703955	−	0.0904856i
$397$		−	10293.5i		−	1.30131i	−0.759375	−	0.650653i	$-0.774495\pi$
$397$		−	10293.5i		−	1.30131i	0.759375	−	0.650653i	$-0.225505\pi$
$398$	−7470.16			−0.940817
$399$	1953.24	−	955.152i	0.245074	−	0.119843i
$400$	871.014			0.108877
$401$	−14430.6			−1.79708			−0.898540	−	0.438892i	$-0.855371\pi$
$401$	−14430.6			−1.79708			−0.898540	+	0.438892i	$0.855371\pi$
$402$	3521.61	+	7201.54i	0.436920	+	0.893482i
$403$	−6949.27			−0.858977
$404$	−2101.62			−0.258810
$405$	5935.62	−	1505.91i	0.728255	−	0.184764i
$406$			9107.56i			1.11330i
$407$		−	2330.66i		−	0.283850i
$408$	−965.035	−	1973.45i	−0.117099	−	0.239462i
$409$			7892.13i			0.954133i	0.878867	+	0.477067i	$0.158300\pi$
$409$			7892.13i			0.954133i	−0.878867	+	0.477067i	$0.841700\pi$
$410$	6770.22			0.815505
$411$	−3120.93	−	6382.16i	−0.374559	−	0.765958i
$412$			5686.33i			0.679964i
$413$	−10539.4	−	9309.55i	−1.25571	−	1.10918i
$414$	4117.73	−	5292.88i	0.488829	−	0.628336i
$415$			9686.73i			1.14579i
$416$			1083.49i			0.127698i
$417$	2847.73	−	1392.56i	0.334422	−	0.163535i
$418$	225.609			0.0263993
$419$	−2953.47			−0.344359			−0.172180	−	0.985066i	$-0.555081\pi$
$419$	−2953.47			−0.344359			−0.172180	+	0.985066i	$0.555081\pi$
$420$	−2379.91	−	4866.80i	−0.276494	−	0.565418i
$421$			13002.4i			1.50522i	0.658465	+	0.752611i	$0.271206\pi$
$421$			13002.4i			1.50522i	−0.658465	+	0.752611i	$0.728794\pi$
$422$		−	11155.9i		−	1.28687i
$423$	8515.38	−	10945.6i	0.978799	−	1.25814i
$424$			805.266i			0.0922339i
$425$		−	2876.86i		−	0.328349i
$426$	−1196.41	−	2446.60i	−0.136071	−	0.278258i
$427$		−	12824.2i		−	1.45341i
$428$		−	4467.74i		−	0.504571i
$429$	646.521	+	1322.11i	0.0727606	+	0.148792i
$430$	−7833.60			−0.878534
$431$	−10132.3			−1.13238			−0.566192	−	0.824273i	$-0.691584\pi$
$431$	−10132.3			−1.13238			−0.566192	+	0.824273i	$0.691584\pi$
$432$	−459.922	+	2197.12i	−0.0512223	+	0.244696i
$433$	−4114.22			−0.456621			−0.228310	−	0.973588i	$-0.573320\pi$
$433$	−4114.22			−0.456621			−0.228310	+	0.973588i	$0.573320\pi$
$434$			12737.1i			1.40876i
$435$	−5754.46	+	2813.97i	−0.634265	+	0.310160i
$436$		−	3927.31i		−	0.431385i
$437$	1674.66			0.183318
$438$	1625.15	+	3323.35i	0.177289	+	0.362548i
$439$	−5508.75			−0.598902			−0.299451	−	0.954112i	$-0.596804\pi$
$439$	−5508.75			−0.598902			−0.299451	+	0.954112i	$0.596804\pi$
$440$		−	562.139i		−	0.0609066i
$441$	10276.2	−	13209.0i	1.10963	−	1.42630i
$442$	3578.63			0.385109
$443$	1630.71			0.174893			0.0874464	−	0.996169i	$-0.472129\pi$
$443$	1630.71			0.174893			0.0874464	+	0.996169i	$0.472129\pi$
$444$	2543.96	+	5202.29i	0.271917	+	0.556058i
$445$			916.775i			0.0976614i
$446$	−1290.82			−0.137045
$447$	8139.25	−	3980.16i	0.861238	−	0.421152i
$448$	1985.89			0.209430
$449$			4257.32i			0.447473i	0.974650	+	0.223736i	$0.0718254\pi$
$449$			4257.32i			0.447473i	−0.974650	+	0.223736i	$0.928175\pi$
$450$	−1805.07	+	2320.22i	−0.189093	+	0.243058i
$451$			3370.99i			0.351959i
$452$	1632.17			0.169847
$453$	−3782.62	−	7735.30i	−0.392325	−	0.802287i
$454$	−9925.85			−1.02609
$455$	8825.39			0.909320
$456$	−503.583	+	246.256i	−0.0517158	+	0.0252894i
$457$			3275.73i			0.335300i	0.985847	+	0.167650i	$0.0536179\pi$
$457$			3275.73i			0.335300i	−0.985847	+	0.167650i	$0.946382\pi$
$458$		−	3330.90i		−	0.339831i
$459$	7256.82	+	1519.07i	0.737951	+	0.154475i
$460$		−	4172.67i		−	0.422938i
$461$			6732.01i			0.680132i	0.940402	+	0.340066i	$0.110449\pi$
$461$			6732.01i			0.680132i	−0.940402	+	0.340066i	$0.889551\pi$
$462$	2423.25	−	1184.99i	0.244026	−	0.119331i
$463$			4773.68i			0.479161i	0.970876	+	0.239581i	$0.0770100\pi$
$463$			4773.68i			0.479161i	−0.970876	+	0.239581i	$0.922990\pi$
$464$		−	2348.10i		−	0.234930i
$465$	−8047.73	+	3935.40i	−0.802590	+	0.392473i
$466$	−2163.30			−0.215050
$467$	−18623.8			−1.84541			−0.922704	−	0.385509i	$-0.874026\pi$
$467$	−18623.8			−1.84541			−0.922704	+	0.385509i	$0.874026\pi$
$468$	−2886.20	−	2245.39i	−0.285074	−	0.221781i
$469$			23935.8i			2.35661i
$470$		−	8628.99i		−	0.846863i
$471$	6122.52	+	12520.3i	0.598962	+	1.22485i
$472$	2717.24	+	2400.17i	0.264982	+	0.234061i
$473$		−	3900.46i		−	0.379162i
$474$	8798.64	−	4302.61i	0.852606	−	0.416931i
$475$	−734.112			−0.0709123
$476$		−	6559.18i		−	0.631595i
$477$	−2145.08	−	1668.81i	−0.205904	−	0.160188i
$478$			7262.87i			0.694971i
$479$			2379.76i			0.227002i	0.993538	+	0.113501i	$0.0362066\pi$
$479$			2379.76i			0.227002i	−0.993538	+	0.113501i	$0.963793\pi$
$480$	613.584	+	1254.75i	0.0583461	+	0.119315i
$481$	−9433.75			−0.894266
$482$	392.609			0.0371013
$483$	17987.4	−	8795.99i	1.69453	−	0.828636i
$484$	−5044.10			−0.473714
$485$	−8840.95			−0.827725
$486$	−4899.57	−	5778.40i	−0.457302	−	0.539328i
$487$	−14744.7			−1.37196			−0.685982	−	0.727618i	$-0.740627\pi$
$487$	−14744.7			−1.37196			−0.685982	+	0.727618i	$0.740627\pi$
$488$			3306.32i			0.306701i
$489$	−7018.20	+	3431.95i	−0.649026	+	0.317379i
$490$		−	10413.3i		−	0.960055i
$491$		−	19027.8i		−	1.74891i	−0.485111	−	0.874453i	$-0.661221\pi$
$491$		−	19027.8i		−	1.74891i	0.485111	−	0.874453i	$-0.338779\pi$
$492$	−3679.49	−	7524.40i	−0.337163	−	0.689484i
$493$	−7755.50			−0.708499
$494$		−	913.189i		−	0.0831707i
$495$	1497.43	+	1164.96i	0.135969	+	0.105780i
$496$		−	3283.87i		−	0.297278i
$497$		−	8131.76i		−	0.733923i
$498$	10765.8	−	5264.56i	0.968730	−	0.473716i
$499$	−17377.1			−1.55893			−0.779465	−	0.626446i	$-0.784509\pi$
$499$	−17377.1			−1.55893			−0.779465	+	0.626446i	$0.784509\pi$
$500$			6029.20i			0.539268i
$501$	2836.51	+	5800.55i	0.252946	+	0.517264i
$502$			9421.81i			0.837681i
$503$	12024.8			1.06592			0.532960	−	0.846140i	$-0.321080\pi$
$503$	12024.8			1.06592			0.532960	+	0.846140i	$0.321080\pi$
$504$	−4115.52	+	5290.04i	−0.363730	+	0.467534i
$505$		−	4413.45i		−	0.388903i
$506$	2077.63			0.182534
$507$	−4903.98	+	2398.08i	−0.429573	+	0.210064i
$508$	5141.77			0.449073
$509$	−306.241			−0.0266677			−0.0133339	−	0.999911i	$-0.504244\pi$
$509$	−306.241			−0.0266677			−0.0133339	+	0.999911i	$0.504244\pi$
$510$	4144.30	−	2026.60i	0.359829	−	0.175959i
$511$			11045.8i			0.956241i
$512$	−512.000			−0.0441942
$513$	387.634	−	1851.78i	0.0333615	−	0.159373i
$514$			14504.0i			1.24463i
$515$	−11941.4			−1.02175
$516$	4257.42	+	8706.24i	0.363222	+	0.742773i
$517$	4296.50			0.365493
$518$			17290.9i			1.46663i
$519$	11824.6	−	5782.30i	1.00008	−	0.489046i
$520$	−2275.35			−0.191886
$521$		−	3176.70i		−	0.267128i	−0.991040	−	0.133564i	$-0.957358\pi$
$521$		−	3176.70i		−	0.267128i	0.991040	−	0.133564i	$-0.0426421\pi$
$522$	6254.89	+	4866.14i	0.524462	+	0.408018i
$523$	−2353.51			−0.196772			−0.0983861	−	0.995148i	$-0.531368\pi$
$523$	−2353.51			−0.196772			−0.0983861	+	0.995148i	$0.531368\pi$
$524$	1034.49			0.0862439
$525$	−7885.05	+	3855.85i	−0.655489	+	0.320539i
$526$			10673.1i			0.884728i
$527$	−10846.2			−0.896526
$528$	−624.759	+	305.512i	−0.0514946	+	0.0251813i
$529$	3254.92			0.267520
$530$	−1691.08			−0.138596
$531$	−12024.8	+	2264.16i	−0.982731	+	0.185040i
$532$	−1673.76			−0.136403
$533$	13644.6			1.10885
$534$	1018.90	−	498.251i	0.0825696	−	0.0403772i
$535$	9382.36			0.758196
$536$		−	6171.08i		−	0.497295i
$537$	−8872.29	+	4338.62i	−0.712975	+	0.348650i
$538$	9242.38			0.740645
$539$	5184.96			0.414345
$540$	−4614.00	−	965.848i	−0.367694	−	0.0769694i
$541$			402.038i			0.0319500i	0.999872	+	0.0159750i	$0.00508522\pi$
$541$			402.038i			0.0319500i	−0.999872	+	0.0159750i	$0.994915\pi$
$542$	3896.79			0.308822
$543$	18239.6	−	8919.31i	1.44150	−	0.704907i
$544$			1691.08i			0.133280i
$545$	8247.44			0.648223
$546$	−4796.44	−	9808.52i	−0.375950	−	0.768802i
$547$	3875.34			0.302920			0.151460	−	0.988463i	$-0.451602\pi$
$547$	3875.34			0.302920			0.151460	+	0.988463i	$0.451602\pi$
$548$			5468.95i			0.426317i
$549$	−8807.40	−	6851.94i	−0.684683	−	0.532666i
$550$	−910.761			−0.0706090
$551$			1979.03i			0.153012i
$552$	−4637.49	+	2267.77i	−0.357581	+	0.174860i
$553$	29244.1			2.24880
$554$	−12182.1			−0.934234
$555$	−10924.9	+	5342.38i	−0.835563	+	0.408597i
$556$	−2440.25			−0.186133
$557$			14688.1i			1.11733i	0.829392	+	0.558667i	$0.188687\pi$
$557$			14688.1i			1.11733i	−0.829392	+	0.558667i	$0.811313\pi$
$558$	8747.59	+	6805.41i	0.663647	+	0.516301i
$559$	−15787.8			−1.19455
$560$			4170.42i			0.314701i
$561$	1009.07	+	2063.51i	0.0759413	+	0.155297i
$562$		−	473.249i		−	0.0355210i
$563$	26307.9			1.96935			0.984676	−	0.174392i	$-0.0557960\pi$
$563$	26307.9			1.96935			0.984676	+	0.174392i	$0.0557960\pi$
$564$	−9590.24	+	4689.70i	−0.715996	+	0.350128i
$565$			3427.60i			0.255222i
$566$		−	9915.27i		−	0.736343i
$567$	−5562.76	−	21925.9i	−0.412018	−	1.62399i
$568$			2096.52i			0.154873i
$569$	−7713.03			−0.568272			−0.284136	−	0.958784i	$-0.591707\pi$
$569$	−7713.03			−0.568272			−0.284136	+	0.958784i	$0.591707\pi$
$570$	−517.143	−	1057.54i	−0.0380013	−	0.0777110i
$571$		−	17912.5i		−	1.31281i	−0.754409	−	0.656405i	$-0.772076\pi$
$571$		−	17912.5i		−	1.31281i	0.754409	−	0.656405i	$-0.227924\pi$
$572$		−	1132.93i		−	0.0828150i
$573$	−5642.26	+	2759.11i	−0.411359	+	0.201158i
$574$		−	25008.9i		−	1.81855i
$575$	−6760.43			−0.490312
$576$	1061.06	−	1363.87i	0.0767547	−	0.0986596i
$577$	−21753.0			−1.56948			−0.784740	−	0.619825i	$-0.787204\pi$
$577$	−21753.0			−1.56948			−0.784740	+	0.619825i	$0.787204\pi$
$578$	−4240.56			−0.305163
$579$	2431.03	−	1188.79i	0.174491	−	0.0853275i
$580$	4931.06			0.353019
$581$	35782.3			2.55508
$582$	4804.90	+	9825.81i	0.342215	+	0.699816i
$583$		−	842.013i		−	0.0598158i
$584$		−	2847.82i		−	0.201787i
$585$	4715.38	−	6061.10i	0.333260	−	0.428368i
$586$		−	1394.65i		−	0.0983145i
$587$	9628.83			0.677043			0.338522	−	0.940959i	$-0.390073\pi$
$587$	9628.83			0.677043			0.338522	+	0.940959i	$0.390073\pi$
$588$	−11573.4	+	5659.47i	−0.811696	+	0.396926i
$589$			2767.72i			0.193620i
$590$	−5040.42	+	5706.28i	−0.351714	+	0.398176i
$591$	−455.856	−	932.207i	−0.0317283	−	0.0648830i
$592$		−	4457.90i		−	0.309491i
$593$			21483.0i			1.48769i	0.668352	+	0.743846i	$0.267000\pi$
$593$			21483.0i			1.48769i	−0.668352	+	0.743846i	$0.733000\pi$
$594$	480.910	−	2297.38i	0.0332188	−	0.158691i
$595$	13774.4			0.949070
$596$	−6974.62			−0.479348
$597$	−17435.1	+	8525.88i	−1.19526	+	0.584491i
$598$		−	8409.56i		−	0.575071i
$599$		−	19057.7i		−	1.29996i	−0.759951	−	0.649980i	$-0.774777\pi$
$599$		−	19057.7i		−	1.29996i	0.759951	−	0.649980i	$-0.225223\pi$
$600$	2032.91	−	994.110i	0.138322	−	0.0676406i
$601$			5559.07i			0.377303i	0.982044	+	0.188651i	$0.0604116\pi$
$601$			5559.07i			0.377303i	−0.982044	+	0.188651i	$0.939588\pi$
$602$			28937.0i			1.95911i
$603$	16438.6	+	12788.8i	1.11017	+	0.863682i
$604$			6628.47i			0.446538i
$605$		−	10592.7i		−	0.711828i
$606$	−4905.09	+	2398.63i	−0.328805	+	0.160788i
$607$	15577.0			1.04160			0.520801	−	0.853678i	$-0.325633\pi$
$607$	15577.0			1.04160			0.520801	+	0.853678i	$0.325633\pi$
$608$	431.526			0.0287840
$609$	10394.7	+	21256.7i	0.691649	+	1.41439i
$610$	−6943.35			−0.460866
$611$		−	17390.8i		−	1.15148i
$612$	−4504.71	−	3504.55i	−0.297536	−	0.231475i
$613$		−	4461.15i		−	0.293938i	−0.989141	−	0.146969i	$-0.953048\pi$
$613$		−	4461.15i		−	0.293938i	0.989141	−	0.146969i	$-0.0469518\pi$
$614$	−8944.62			−0.587908
$615$	15801.4	−	7727.02i	1.03606	−	0.506640i
$616$	−2076.51			−0.135820
$617$		−	6488.60i		−	0.423373i	−0.977338	−	0.211687i	$-0.932104\pi$
$617$		−	6488.60i		−	0.423373i	0.977338	−	0.211687i	$-0.0678956\pi$
$618$	6489.95	+	13271.7i	0.422434	+	0.863859i
$619$	6925.70			0.449705			0.224853	−	0.974393i	$-0.427810\pi$
$619$	6925.70			0.449705			0.224853	+	0.974393i	$0.427810\pi$
$620$	6896.20			0.446706
$621$	3569.72	−	17053.1i	0.230673	−	1.10196i
$622$		−	3281.13i		−	0.211513i
$623$	3386.53			0.217782
$624$	1236.61	+	2528.82i	0.0793335	+	0.162234i
$625$	−5856.67			−0.374827
$626$			2656.64i			0.169617i
$627$	526.562	−	257.493i	0.0335389	−	0.0164008i
$628$		−	10728.8i		−	0.681729i
$629$	−14723.9			−0.933358
$630$	−11109.2	−	8642.69i	−0.702542	−	0.546560i
$631$	657.435			0.0414772			0.0207386	−	0.999785i	$-0.493398\pi$
$631$	657.435			0.0414772			0.0207386	+	0.999785i	$0.493398\pi$
$632$	−7539.66			−0.474544
$633$	−12732.5	−	26037.4i	−0.799480	−	1.63490i
$634$		−	9154.27i		−	0.573442i
$635$			10797.9i			0.674803i
$636$	919.071	+	1879.46i	0.0573012	+	0.117178i
$637$		−	20987.0i		−	1.30539i
$638$			2455.25i			0.152358i
$639$	−5584.73	−	4344.78i	−0.345741	−	0.268978i
$640$		−	1075.21i		−	0.0664086i
$641$		−	9656.95i		−	0.595049i	−0.954714	−	0.297525i	$-0.903839\pi$
$641$		−	9656.95i		−	0.595049i	0.954714	−	0.297525i	$-0.0961610\pi$
$642$	−5099.14	−	10427.5i	−0.313469	−	0.641031i
$643$	28412.0			1.74255			0.871275	−	0.490796i	$-0.163294\pi$
$643$	28412.0			1.74255			0.871275	+	0.490796i	$0.163294\pi$
$644$	−15413.6			−0.943140
$645$	−18283.3	+	8940.68i	−1.11613	+	0.545797i
$646$		−	1425.28i		−	0.0868064i
$647$			26332.7i			1.60007i	0.599955	+	0.800034i	$0.295185\pi$
$647$			26332.7i			1.60007i	−0.599955	+	0.800034i	$0.704815\pi$
$648$	1434.18	+	5652.91i	0.0869445	+	0.342696i
$649$	−2841.24	−	2509.70i	−0.171847	−	0.151794i
$650$			3686.45i			0.222453i
$651$	14537.2	+	29728.0i	0.875204	+	1.78975i
$652$	6013.98			0.361236
$653$		−	15577.3i		−	0.933516i	−0.884385	−	0.466758i	$-0.845422\pi$
$653$		−	15577.3i		−	0.933516i	0.884385	−	0.466758i	$-0.154578\pi$
$654$	−4482.34	−	9166.19i	−0.268002	−	0.548052i
$655$			2172.45i			0.129595i
$656$			6447.75i			0.383754i
$657$	7586.06	+	5901.76i	0.450472	+	0.350456i
$658$	−31875.1			−1.88848
$659$	6819.10			0.403087			0.201543	−	0.979480i	$-0.435404\pi$
$659$	6819.10			0.403087			0.201543	+	0.979480i	$0.435404\pi$
$660$	−641.583	−	1312.01i	−0.0378388	−	0.0773787i
$661$	−1640.37			−0.0965252			−0.0482626	−	0.998835i	$-0.515368\pi$
$661$	−1640.37			−0.0965252			−0.0482626	+	0.998835i	$0.515368\pi$
$662$	6127.41			0.359741
$663$	8352.39	−	4084.39i	0.489261	−	0.239253i
$664$	−9225.35			−0.539176
$665$		−	3514.93i		−	0.204967i
$666$	11875.0	+	9238.45i	0.690912	+	0.537512i
$667$			18224.9i			1.05798i
$668$		−	4970.56i		−	0.287899i
$669$	−3012.73	+	1473.25i	−0.174109	+	0.0851406i
$670$	12959.4			0.747263
$671$		−	3457.19i		−	0.198902i
$672$	4635.00	−	2266.55i	0.266070	−	0.130110i
$673$		−	13220.3i		−	0.757214i	−0.925557	−	0.378607i	$-0.876403\pi$
$673$		−	13220.3i		−	0.757214i	0.925557	−	0.378607i	$-0.123597\pi$
$674$		−	2795.87i		−	0.159782i
$675$	−1564.84	+	7475.46i	−0.0892307	+	0.426268i
$676$	4202.28			0.239092
$677$		−	11227.9i		−	0.637403i	−0.947855	−	0.318702i	$-0.896753\pi$
$677$		−	11227.9i		−	0.637403i	0.947855	−	0.318702i	$-0.103247\pi$
$678$	3809.43	−	1862.84i	0.215782	−	0.105519i
$679$			32658.1i			1.84580i
$680$	−3551.30			−0.200274
$681$	−23166.5	+	11328.6i	−1.30359	+	0.637465i
$682$			3433.72i			0.192792i
$683$	22495.5			1.26027			0.630136	−	0.776485i	$-0.282999\pi$
$683$	22495.5			1.26027			0.630136	+	0.776485i	$0.282999\pi$
$684$	−894.284	+	1149.50i	−0.0499910	+	0.0642578i
$685$	−11484.9			−0.640608
$686$	−17180.1			−0.956182
$687$	−3801.64	−	7774.19i	−0.211123	−	0.431738i
$688$		−	7460.48i		−	0.413413i
$689$	−3408.19			−0.188449
$690$	−4762.37	−	9738.84i	−0.262754	−	0.537321i
$691$			23380.9i			1.28719i	0.765364	+	0.643597i	$0.222559\pi$
$691$			23380.9i			1.28719i	−0.765364	+	0.643597i	$0.777441\pi$
$692$	−10132.6			−0.556624
$693$	4303.32	−	5531.44i	0.235887	−	0.303206i
$694$	−11065.9			−0.605270
$695$		−	5124.59i		−	0.279693i
$696$	−2679.94	−	5480.37i	−0.145953	−	0.298467i
$697$	21296.2			1.15732
$698$		−	10599.4i		−	0.574776i
$699$	−5049.07	+	2469.03i	−0.273209	+	0.133601i
$700$	6756.80			0.364833
$701$	7108.69			0.383012			0.191506	−	0.981491i	$-0.438663\pi$
$701$	7108.69			0.383012			0.191506	+	0.981491i	$0.438663\pi$
$702$	−9299.01	−	1946.56i	−0.499955	−	0.104656i
$703$			3757.23i			0.201574i
$704$	535.364			0.0286609
$705$	−9848.49	−	20139.7i	−0.526121	−	1.07590i
$706$	−19447.9			−1.03673
$707$	−16303.1			−0.867242
$708$	9081.32	+	2500.65i	0.482058	+	0.132741i
$709$	−26463.3			−1.40177			−0.700883	−	0.713276i	$-0.747210\pi$
$709$	−26463.3			−1.40177			−0.700883	+	0.713276i	$0.747210\pi$
$710$	−4402.74			−0.232721
$711$	15625.0	−	20084.2i	0.824169	−	1.05938i
$712$	−873.109			−0.0459567
$713$			25487.9i			1.33875i
$714$	−7486.16	−	15308.9i	−0.392384	−	0.802409i
$715$	2379.18			0.124442
$716$	7602.77			0.396828
$717$	8289.30	+	16951.3i	0.431757	+	0.882924i
$718$			3025.66i			0.157266i
$719$	10353.4			0.537022			0.268511	−	0.963277i	$-0.413469\pi$
$719$	10353.4			0.537022			0.268511	+	0.963277i	$0.413469\pi$
$720$	2864.16	+	2228.24i	0.148251	+	0.115336i
$721$			44111.1i			2.27848i
$722$	13354.3			0.688360
$723$	916.333	−	448.094i	0.0471353	−	0.0230495i
$724$	−15629.7			−0.802313
$725$		−	7989.17i		−	0.409255i
$726$	−11772.7	+	5756.96i	−0.601828	+	0.294299i
$727$	9760.73			0.497944			0.248972	−	0.968511i	$-0.419907\pi$
$727$	9760.73			0.497944			0.248972	+	0.968511i	$0.419907\pi$
$728$			8405.04i			0.427900i
$729$	−18030.4	−	7894.56i	−0.916041	−	0.401085i
$730$	5980.50			0.303217
$731$	−24641.1			−1.24676
$732$	3773.59	+	7716.82i	0.190541	+	0.389647i
$733$	25960.4			1.30814			0.654071	−	0.756433i	$-0.273060\pi$
$733$	25960.4			1.30814			0.654071	+	0.756433i	$0.273060\pi$
$734$			9252.82i			0.465297i
$735$	−11885.0	−	24304.3i	−0.596443	−	1.21970i
$736$	3973.92			0.199023
$737$			6452.69i			0.322507i
$738$	−17175.6	−	13362.2i	−0.856696	−	0.666488i
$739$			14687.1i			0.731090i	0.930794	+	0.365545i	$0.119117\pi$
$739$			14687.1i			0.731090i	−0.930794	+	0.365545i	$0.880883\pi$
$740$	9361.71			0.465058
$741$	−1042.25	−	2131.35i	−0.0516705	−	0.105664i
$742$			6246.77i			0.309065i
$743$			14225.4i			0.702397i	0.936301	+	0.351198i	$0.114226\pi$
$743$			14225.4i			0.702397i	−0.936301	+	0.351198i	$0.885774\pi$
$744$	−3747.96	−	7664.42i	−0.184687	−	0.377676i
$745$		−	14646.9i		−	0.720295i
$746$	6876.44			0.337486
$747$	19118.4	−	24574.6i	0.936420	−	1.20366i
$748$		−	1768.25i		−	0.0864351i
$749$		−	34658.0i		−	1.69076i
$750$	6881.28	+	14071.9i	0.335025	+	0.685112i
$751$		−	38067.6i		−	1.84967i	−0.380364	−	0.924837i	$-0.624201\pi$
$751$		−	38067.6i		−	1.84967i	0.380364	−	0.924837i	$-0.375799\pi$
$752$	8217.99			0.398510
$753$	10753.3	+	21990.1i	0.520417	+	1.06423i
$754$	9938.03			0.480002
$755$	−13920.0			−0.670992
$756$	−3567.80	+	17043.9i	−0.171640	+	0.819948i
$757$	−8768.72			−0.421010			−0.210505	−	0.977593i	$-0.567511\pi$
$757$	−8768.72			−0.421010			−0.210505	+	0.977593i	$0.567511\pi$
$758$	26960.0			1.29186
$759$	4849.11	−	2371.25i	0.231899	−	0.113401i
$760$			906.215i			0.0432525i
$761$			29912.6i			1.42487i	0.701736	+	0.712437i	$0.252409\pi$
$761$			29912.6i			1.42487i	−0.701736	+	0.712437i	$0.747591\pi$
$762$	12000.7	−	5868.44i	0.570524	−	0.278991i
$763$		−	30465.7i		−	1.44552i
$764$	4834.92			0.228954
$765$	7359.64	−	9460.00i	0.347828	−	0.447094i
$766$		−	8577.82i		−	0.404608i
$767$	−10158.4	+	11500.4i	−0.478226	+	0.541402i
$768$	−1194.99	+	584.359i	−0.0561464	+	0.0274560i
$769$		−	27505.9i		−	1.28984i	−0.764250	−	0.644920i	$-0.776891\pi$
$769$		−	27505.9i		−	1.28984i	0.764250	−	0.644920i	$-0.223109\pi$
$770$		−	4360.73i		−	0.204091i
$771$	16553.7	+	33851.7i	0.773241	+	1.58124i
$772$	−2083.18			−0.0971184
$773$	−10827.2			−0.503787			−0.251893	−	0.967755i	$-0.581053\pi$
$773$	−10827.2			−0.503787			−0.251893	+	0.967755i	$0.581053\pi$
$774$	19873.3	+	15460.9i	0.922909	+	0.717999i
$775$		−	11173.0i		−	0.517867i
$776$		−	8419.85i		−	0.389504i
$777$	19734.5	+	40356.2i	0.911160	+	1.86328i
$778$		−	4489.76i		−	0.206897i
$779$		−	5434.32i		−	0.249942i
$780$	−5310.58	+	2596.91i	−0.243781	+	0.119211i
$781$		−	2192.19i		−	0.100439i
$782$		−	13125.4i		−	0.600209i
$783$	20152.5	+	4218.53i	0.919786	+	0.192539i
$784$	9917.36			0.451775
$785$	22530.7			1.02440
$786$	2414.46	−	1180.69i	0.109568	−	0.0535798i
$787$	14752.6			0.668201			0.334101	−	0.942537i	$-0.391567\pi$
$787$	14752.6			0.668201			0.334101	+	0.942537i	$0.391567\pi$
$788$			798.819i			0.0361126i
$789$	12181.4	+	24910.5i	0.549645	+	1.12400i
$790$		−	15833.5i		−	0.713076i
$791$	12661.4			0.569137
$792$	−1109.48	+	1426.11i	−0.0497771	+	0.0639830i
$793$	−13993.6			−0.626641
$794$			20587.1i			0.920162i
$795$	−3946.91	+	1930.07i	−0.176079	+	0.0861039i
$796$	14940.3			0.665258
$797$	32488.0			1.44389			0.721947	−	0.691948i	$-0.243247\pi$
$797$	32488.0			1.44389			0.721947	+	0.691948i	$0.243247\pi$
$798$	−3906.49	+	1910.30i	−0.173293	+	0.0847419i
$799$		−	27143.1i		−	1.20182i
$800$	−1742.03			−0.0769875
$801$	1809.41	−	2325.80i	0.0798157	−	0.102594i
$802$	28861.2			1.27073
$803$			2977.78i			0.130864i
$804$	−7043.21	−	14403.1i	−0.308949	−	0.631787i
$805$		−	32369.0i		−	1.41721i
$806$	13898.5			0.607389
$807$	21571.3	−	10548.6i	0.940951	−	0.460132i
$808$	4203.24			0.183007
$809$	17534.8			0.762042			0.381021	−	0.924566i	$-0.375573\pi$
$809$	17534.8			0.762042			0.381021	+	0.924566i	$0.375573\pi$
$810$	−11871.2	+	3011.82i	−0.514954	+	0.130648i
$811$			8326.69i			0.360530i	0.983618	+	0.180265i	$0.0576955\pi$
$811$			8326.69i			0.360530i	−0.983618	+	0.180265i	$0.942305\pi$
$812$		−	18215.1i		−	0.787224i
$813$	9094.95	−	4447.50i	0.392342	−	0.191858i
$814$			4661.33i			0.200712i
$815$			12629.5i			0.542812i
$816$	1930.07	+	3946.91i	0.0828014	+	0.169325i
$817$			6287.88i			0.269259i
$818$		−	15784.3i		−	0.674674i
$819$	−22389.4	−	17418.4i	−0.955250	−	0.743160i
$820$	−13540.4			−0.576649
$821$	−13785.7			−0.586021			−0.293010	−	0.956109i	$-0.594657\pi$
$821$	−13785.7			−0.586021			−0.293010	+	0.956109i	$0.594657\pi$
$822$	6241.85	+	12764.3i	0.264853	+	0.541614i
$823$		−	1766.43i		−	0.0748164i	−0.999300	−	0.0374082i	$-0.988090\pi$
$823$		−	1766.43i		−	0.0748164i	0.999300	−	0.0374082i	$-0.0119102\pi$
$824$		−	11372.7i		−	0.480807i
$825$	−2125.68	+	1039.47i	−0.0897051	+	0.0438665i
$826$	21078.7	+	18619.1i	0.887922	+	0.784312i
$827$		−	32816.5i		−	1.37985i	−0.723878	−	0.689927i	$-0.757642\pi$
$827$		−	32816.5i		−	1.37985i	0.723878	−	0.689927i	$-0.242358\pi$
$828$	−8235.46	+	10585.8i	−0.345655	+	0.444301i
$829$	32527.6			1.36276			0.681382	−	0.731928i	$-0.261379\pi$
$829$	32527.6			1.36276			0.681382	+	0.731928i	$0.261379\pi$
$830$		−	19373.5i		−	0.810196i
$831$	−28432.4	+	13903.7i	−1.18690	+	0.580401i
$832$		−	2166.97i		−	0.0902961i
$833$		−	32755.9i		−	1.36245i
$834$	−5695.46	+	2785.12i	−0.236472	+	0.115637i
$835$	10438.3			0.432613
$836$	−451.218			−0.0186671
$837$	28183.7	+	5899.70i	1.16389	+	0.243636i
$838$	5906.95			0.243499
$839$	16461.3			0.677364			0.338682	−	0.940901i	$-0.390019\pi$
$839$	16461.3			0.677364			0.338682	+	0.940901i	$0.390019\pi$
$840$	4759.81	+	9733.61i	0.195511	+	0.399811i
$841$	2851.63			0.116923
$842$		−	26004.8i		−	1.06435i
$843$	−540.132	−	1104.55i	−0.0220678	−	0.0451276i
$844$			22311.8i			0.909955i
$845$			8824.89i			0.359273i
$846$	−17030.8	+	21891.2i	−0.692116	+	0.889638i
$847$	−39129.1			−1.58736
$848$		−	1610.53i		−	0.0652192i
$849$	−11316.6	−	23141.9i	−0.457459	−	0.935485i
$850$			5753.72i			0.232178i
$851$			34600.3i			1.39375i
$852$	2392.81	+	4893.20i	0.0962164	+	0.196758i
$853$	34952.5			1.40299			0.701496	−	0.712674i	$-0.252516\pi$
$853$	34952.5			1.40299			0.701496	+	0.712674i	$0.252516\pi$
$854$			25648.4i			1.02772i
$855$	−2413.98	−	1878.02i	−0.0965574	−	0.0751192i
$856$			8935.47i			0.356785i
$857$	−48998.5			−1.95304			−0.976521	−	0.215423i	$-0.930887\pi$
$857$	−48998.5			−1.95304			−0.976521	+	0.215423i	$0.930887\pi$
$858$	−1293.04	−	2644.21i	−0.0514495	−	0.105212i
$859$		−	3465.97i		−	0.137669i	−0.997628	−	0.0688343i	$-0.978072\pi$
$859$		−	3465.97i		−	0.137669i	0.997628	−	0.0688343i	$-0.0219280\pi$
$860$	15667.2			0.621217
$861$	−28543.3	−	58369.8i	−1.12979	−	2.31038i
$862$	20264.7			0.800717
$863$	−47401.2			−1.86970			−0.934852	−	0.355037i	$-0.884468\pi$
$863$	−47401.2			−1.86970			−0.934852	+	0.355037i	$0.884468\pi$
$864$	919.845	−	4394.23i	0.0362196	−	0.173026i
$865$		−	21278.7i		−	0.836414i
$866$	8228.44			0.322880
$867$	−9897.31	+	4839.86i	−0.387694	+	0.189585i
$868$		−	25474.2i		−	0.996143i
$869$	7883.72			0.307752
$870$	11508.9	−	5627.95i	0.448493	−	0.219316i
$871$	26118.3			1.01606
$872$			7854.62i			0.305035i
$873$	22428.9	+	17449.1i	0.869533	+	0.676475i
$874$	−3349.32			−0.129625
$875$			46770.9i			1.80702i
$876$	−3250.29	−	6646.71i	−0.125362	−	0.256360i
$877$	−35986.2			−1.38559			−0.692797	−	0.721132i	$-0.743622\pi$
$877$	−35986.2			−1.38559			−0.692797	+	0.721132i	$0.743622\pi$
$878$	11017.5			0.423488
$879$	−1591.74	−	3255.05i	−0.0610787	−	0.124903i
$880$			1124.28i			0.0430675i
$881$	41577.0			1.58997			0.794986	−	0.606627i	$-0.207478\pi$
$881$	41577.0			1.58997			0.794986	+	0.606627i	$0.207478\pi$
$882$	−20552.5	+	26417.9i	−0.784624	+	1.00855i
$883$	−27141.5			−1.03441			−0.517206	−	0.855861i	$-0.673028\pi$
$883$	−27141.5			−1.03441			−0.517206	+	0.855861i	$0.673028\pi$
$884$	−7157.27			−0.272313
$885$	−5251.43	+	19071.0i	−0.199463	+	0.724367i
$886$	−3261.43			−0.123668
$887$	−16474.1			−0.623616			−0.311808	−	0.950145i	$-0.600935\pi$
$887$	−16474.1			−0.623616			−0.311808	+	0.950145i	$0.600935\pi$
$888$	−5087.92	−	10404.6i	−0.192274	−	0.393192i
$889$	39886.8			1.50479
$890$		−	1833.55i		−	0.0690570i
$891$	−1499.63	−	5910.86i	−0.0563855	−	0.222246i
$892$	2581.64			0.0969056
$893$	−6926.32			−0.259553
$894$	−16278.5	+	7960.31i	−0.608987	+	0.297799i
$895$			15966.0i			0.596296i
$896$	−3971.79			−0.148089
$897$	−9598.04	−	19627.6i	−0.357268	−	0.730597i
$898$		−	8514.63i		−	0.316411i
$899$	−30120.5			−1.11743
$900$	3610.14	−	4640.43i	0.133709	−	0.171868i
$901$	−5319.41			−0.196687
$902$		−	6741.98i		−	0.248873i
$903$	33026.5	+	67537.7i	1.21711	+	2.48894i
$904$	−3264.34			−0.120100
$905$		−	32822.8i		−	1.20560i
$906$	7565.24	+	15470.6i	0.277415	+	0.567303i
$907$	7623.06			0.279073			0.139537	−	0.990217i	$-0.455439\pi$
$907$	7623.06			0.279073			0.139537	+	0.990217i	$0.455439\pi$
$908$	19851.7			0.725553
$909$	−8710.69	+	11196.6i	−0.317838	+	0.408546i
$910$	−17650.8			−0.642987
$911$		−	41097.5i		−	1.49465i	−0.664461	−	0.747323i	$-0.731339\pi$
$911$		−	41097.5i		−	1.49465i	0.664461	−	0.747323i	$-0.268661\pi$
$912$	1007.17	−	492.512i	0.0365686	−	0.0178823i
$913$	9646.33			0.349668
$914$		−	6551.46i		−	0.237093i
$915$	−16205.5	+	7924.62i	−0.585506	+	0.286317i
$916$			6661.80i			0.240297i
$917$	8024.93			0.288993
$918$	−14513.6	−	3038.14i	−0.521810	−	0.109231i
$919$			16473.5i			0.591307i	0.955295	+	0.295653i	$0.0955373\pi$
$919$			16473.5i			0.591307i	−0.955295	+	0.295653i	$0.904463\pi$
$920$			8345.33i			0.299062i
$921$	−20876.4	+	10208.7i	−0.746907	+	0.365243i
$922$		−	13464.0i		−	0.480926i
$923$	−8873.25			−0.316432
$924$	−4846.51	+	2369.98i	−0.172552	+	0.0843794i
$925$		−	15167.6i		−	0.539142i
$926$		−	9547.36i		−	0.338818i
$927$	30294.6	+	23568.4i	1.07336	+	0.835047i
$928$			4696.20i			0.166121i
$929$	−41311.2			−1.45896			−0.729482	−	0.684000i	$-0.760239\pi$
$929$	−41311.2			−1.45896			−0.729482	+	0.684000i	$0.760239\pi$
$930$	16095.5	−	7870.81i	0.567517	−	0.277520i
$931$	−8358.59			−0.294245
$932$	4326.61			0.152063
$933$	−3744.83	−	7658.02i	−0.131404	−	0.268716i
$934$	37247.5			1.30490
$935$	3713.36			0.129882
$936$	5772.41	+	4490.79i	0.201578	+	0.156823i
$937$		−	4002.69i		−	0.139554i	−0.997563	−	0.0697771i	$-0.977771\pi$
$937$		−	4002.69i		−	0.139554i	0.997563	−	0.0697771i	$-0.0222288\pi$
$938$		−	47871.5i		−	1.66638i
$939$	3032.09	+	6200.49i	0.105376	+	0.215490i
$940$			17258.0i			0.598823i
$941$	9974.29			0.345539			0.172770	−	0.984962i	$-0.444728\pi$
$941$	9974.29			0.345539			0.172770	+	0.984962i	$0.444728\pi$
$942$	−12245.0	−	25040.6i	−0.423530	−	0.866101i
$943$		−	50044.6i		−	1.72818i
$944$	−5434.49	−	4800.35i	−0.187370	−	0.165506i
$945$	−35792.6	−	7492.47i	−1.23210	−	0.257915i
$946$			7800.92i			0.268108i
$947$			52622.0i			1.80569i	0.429969	+	0.902844i	$0.358524\pi$
$947$			52622.0i			1.80569i	−0.429969	+	0.902844i	$0.641476\pi$
$948$	−17597.3	+	8605.21i	−0.602883	+	0.294815i
$949$	12053.0			0.412285
$950$	1468.22			0.0501426
$951$	−10448.0	−	21365.7i	−0.356256	−	0.728528i
$952$			13118.4i			0.446605i
$953$			29557.9i			1.00470i	0.864665	+	0.502348i	$0.167530\pi$
$953$			29557.9i			1.00470i	−0.864665	+	0.502348i	$0.832470\pi$
$954$	4290.15	+	3337.63i	0.145596	+	0.113270i
$955$			10153.4i			0.344040i
$956$		−	14525.7i		−	0.491419i
$957$	2802.24	+	5730.46i	0.0946536	+	0.193563i
$958$		−	4759.53i		−	0.160515i
$959$			42424.8i			1.42854i
$960$	−1227.17	−	2509.50i	−0.0412569	−	0.0843687i
$961$	−12333.1			−0.413988
$962$	18867.5			0.632342
$963$	−23802.4	−	18517.7i	−0.796492	−	0.619650i
$964$	−785.217			−0.0262346
$965$		−	4374.73i		−	0.145935i
$966$	−35974.8	+	17592.0i	−1.19821	+	0.585934i
$967$			2245.69i			0.0746810i	0.999303	+	0.0373405i	$0.0118886\pi$
$967$			2245.69i			0.0746810i	−0.999303	+	0.0373405i	$0.988111\pi$
$968$	10088.2			0.334966
$969$	−1626.71	−	3326.55i	−0.0539293	−	0.110283i
$970$	17681.9			0.585290
$971$		−	44353.4i		−	1.46588i	−0.680294	−	0.732939i	$-0.738148\pi$
$971$		−	44353.4i		−	1.46588i	0.680294	−	0.732939i	$-0.261852\pi$
$972$	9799.13	+	11556.8i	0.323361	+	0.381362i
$973$	−18930.0			−0.623708
$974$	29489.4			0.970125
$975$	4207.44	+	8604.04i	0.138201	+	0.282615i
$976$		−	6612.64i		−	0.216870i
$977$	−1724.31			−0.0564643			−0.0282321	−	0.999601i	$-0.508988\pi$
$977$	−1724.31			−0.0564643			−0.0282321	+	0.999601i	$0.508988\pi$
$978$	14036.4	−	6863.91i	0.458931	−	0.224421i
$979$	912.951			0.0298039
$980$			20826.7i			0.678861i
$981$	−20923.2	−	16277.7i	−0.680965	−	0.529773i
$982$			38055.6i			1.23666i
$983$	−4199.15			−0.136248			−0.0681241	−	0.997677i	$-0.521701\pi$
$983$	−4199.15			−0.136248			−0.0681241	+	0.997677i	$0.521701\pi$
$984$	7358.98	+	15048.8i	0.238410	+	0.487539i
$985$	−1677.54			−0.0542648
$986$	15511.0			0.500985
$987$	−74395.3	+	36379.9i	−2.39922	+	1.17324i
$988$			1826.38i			0.0588106i
$989$			57905.0i			1.86175i
$990$	−2994.86	−	2329.93i	−0.0961444	−	0.0747979i
$991$		−	18156.4i		−	0.581994i	−0.956724	−	0.290997i	$-0.906013\pi$
$991$		−	18156.4i		−	0.581994i	0.956724	−	0.290997i	$-0.0939869\pi$
$992$			6567.73i			0.210207i
$993$	14301.1	−	6993.37i	0.457032	−	0.223492i
$994$			16263.5i			0.518962i
$995$			31375.0i			0.999653i
$996$	−21531.6	+	10529.1i	−0.684995	+	0.334968i
$997$	20085.1			0.638017			0.319008	−	0.947752i	$-0.396650\pi$
$997$	20085.1			0.638017			0.319008	+	0.947752i	$0.396650\pi$
$998$	34754.2			1.10233
$999$	38259.9	+	8008.95i	1.21170	+	0.253645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.4.c.a.353.6	yes	30
3.2	odd	2		354.4.c.b.353.5	yes	30
59.58	odd	2		354.4.c.b.353.6	yes	30
177.176	even	2	inner	354.4.c.a.353.5	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.4.c.a.353.5	✓	30	177.176	even	2	inner
354.4.c.a.353.6	yes	30	1.1	even	1	trivial
354.4.c.b.353.5	yes	30	3.2	odd	2
354.4.c.b.353.6	yes	30	59.58	odd	2

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	354.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +(-4.66792 + 2.28265i) q^{3} +4.00000 q^{4} +8.40010i q^{5} +(9.33585 - 4.56530i) q^{6} +31.0296 q^{7} -8.00000 q^{8} +(16.5790 - 21.3105i) q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +(-4.66792 + 2.28265i) q^{3} +4.00000 q^{4} +8.40010i q^{5} +(9.33585 - 4.56530i) q^{6} +31.0296 q^{7} -8.00000 q^{8} +(16.5790 - 21.3105i) q^{9} -16.8002i q^{10} +8.36506 q^{11} +(-18.6717 + 9.13060i) q^{12} -33.8590i q^{13} -62.0592 q^{14} +(-19.1745 - 39.2110i) q^{15} +16.0000 q^{16} -52.8462i q^{17} +(-33.1580 + 42.6210i) q^{18} -13.4852 q^{19} +33.6004i q^{20} +(-144.844 + 70.8297i) q^{21} -16.7301 q^{22} -124.185 q^{23} +(37.3434 - 18.2612i) q^{24} +54.4384 q^{25} +67.7180i q^{26} +(-28.7452 + 137.320i) q^{27} +124.118 q^{28} -146.756i q^{29} +(38.3490 + 78.4220i) q^{30} -205.242i q^{31} -32.0000 q^{32} +(-39.0475 + 19.0945i) q^{33} +105.692i q^{34} +260.651i q^{35} +(66.3160 - 85.2419i) q^{36} -278.619i q^{37} +26.9704 q^{38} +(77.2882 + 158.051i) q^{39} -67.2008i q^{40} +402.984i q^{41} +(289.687 - 141.659i) q^{42} -466.280i q^{43} +33.4602 q^{44} +(179.010 + 139.265i) q^{45} +248.370 q^{46} +513.624 q^{47} +(-74.6868 + 36.5224i) q^{48} +619.835 q^{49} -108.877 q^{50} +(120.629 + 246.682i) q^{51} -135.436i q^{52} -100.658i q^{53} +(57.4903 - 274.640i) q^{54} +70.2673i q^{55} -248.237 q^{56} +(62.9478 - 30.7820i) q^{57} +293.512i q^{58} +(-339.656 - 300.022i) q^{59} +(-76.6980 - 156.844i) q^{60} -413.290i q^{61} +410.483i q^{62} +(514.440 - 661.255i) q^{63} +64.0000 q^{64} +284.419 q^{65} +(78.0949 - 38.1890i) q^{66} +771.385i q^{67} -211.385i q^{68} +(579.686 - 283.471i) q^{69} -521.303i q^{70} -262.065i q^{71} +(-132.632 + 170.484i) q^{72} +355.978i q^{73} +557.238i q^{74} +(-254.114 + 124.264i) q^{75} -53.9408 q^{76} +259.564 q^{77} +(-154.576 - 316.102i) q^{78} +942.458 q^{79} +134.402i q^{80} +(-179.273 - 706.613i) q^{81} -805.969i q^{82} +1153.17 q^{83} +(-579.375 + 283.319i) q^{84} +443.913 q^{85} +932.560i q^{86} +(334.993 + 685.046i) q^{87} -66.9205 q^{88} +109.139 q^{89} +(-358.020 - 278.531i) q^{90} -1050.63i q^{91} -496.740 q^{92} +(468.495 + 958.052i) q^{93} -1027.25 q^{94} -113.277i q^{95} +(149.374 - 73.0448i) q^{96} +1052.48i q^{97} -1239.67 q^{98} +(138.684 - 178.263i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 60 q^{2} + 5 q^{3} + 120 q^{4} - 10 q^{6} + 6 q^{7} - 240 q^{8} + 27 q^{9}+O(q^{10}) \) 30 * q - 60 * q^2 + 5 * q^3 + 120 * q^4 - 10 * q^6 + 6 * q^7 - 240 * q^8 + 27 * q^9	\( 30 q - 60 q^{2} + 5 q^{3} + 120 q^{4} - 10 q^{6} + 6 q^{7} - 240 q^{8} + 27 q^{9} - 60 q^{11} + 20 q^{12} - 12 q^{14} + 20 q^{15} + 480 q^{16} - 54 q^{18} + 90 q^{19} + 132 q^{21} + 120 q^{22} + 24 q^{23} - 40 q^{24} - 1080 q^{25} - 55 q^{27} + 24 q^{28} - 40 q^{30} - 960 q^{32} + 336 q^{33} + 108 q^{36} - 180 q^{38} + 652 q^{39} - 264 q^{42} - 240 q^{44} - 878 q^{45} - 48 q^{46} + 792 q^{47} + 80 q^{48} + 2016 q^{49} + 2160 q^{50} + 650 q^{51} + 110 q^{54} - 48 q^{56} + 846 q^{57} - 480 q^{59} + 80 q^{60} + 887 q^{63} + 1920 q^{64} - 1416 q^{65} - 672 q^{66} - 590 q^{69} - 216 q^{72} - 952 q^{75} + 360 q^{76} + 864 q^{77} - 1304 q^{78} + 738 q^{79} - 1217 q^{81} + 876 q^{83} + 528 q^{84} + 1176 q^{85} + 534 q^{87} + 480 q^{88} - 300 q^{89} + 1756 q^{90} + 96 q^{92} + 1684 q^{93} - 1584 q^{94} - 160 q^{96} - 4032 q^{98} + 730 q^{99}+O(q^{100}) \) 30 * q - 60 * q^2 + 5 * q^3 + 120 * q^4 - 10 * q^6 + 6 * q^7 - 240 * q^8 + 27 * q^9 - 60 * q^11 + 20 * q^12 - 12 * q^14 + 20 * q^15 + 480 * q^16 - 54 * q^18 + 90 * q^19 + 132 * q^21 + 120 * q^22 + 24 * q^23 - 40 * q^24 - 1080 * q^25 - 55 * q^27 + 24 * q^28 - 40 * q^30 - 960 * q^32 + 336 * q^33 + 108 * q^36 - 180 * q^38 + 652 * q^39 - 264 * q^42 - 240 * q^44 - 878 * q^45 - 48 * q^46 + 792 * q^47 + 80 * q^48 + 2016 * q^49 + 2160 * q^50 + 650 * q^51 + 110 * q^54 - 48 * q^56 + 846 * q^57 - 480 * q^59 + 80 * q^60 + 887 * q^63 + 1920 * q^64 - 1416 * q^65 - 672 * q^66 - 590 * q^69 - 216 * q^72 - 952 * q^75 + 360 * q^76 + 864 * q^77 - 1304 * q^78 + 738 * q^79 - 1217 * q^81 + 876 * q^83 + 528 * q^84 + 1176 * q^85 + 534 * q^87 + 480 * q^88 - 300 * q^89 + 1756 * q^90 + 96 * q^92 + 1684 * q^93 - 1584 * q^94 - 160 * q^96 - 4032 * q^98 + 730 * q^99

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