LMFDB - Embedded newform 242.4.c.d.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [242,4,Mod(3,242)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(242, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("242.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 242 = 2 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	242.c (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.2784622214$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 22)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			9.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	242.9
Dual form			242.4.c.d.27.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.618034 - 1.90211i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-3.23607 - 2.35114i) q^{4} +(-0.927051 - 2.85317i) q^{5} +(0.618034 + 1.90211i) q^{6} +(8.09017 + 5.87785i) q^{7} +(-6.47214 + 4.70228i) q^{8} +(-8.03444 + 24.7275i) q^{9} +O(q^{10})$	\(q+(0.618034 - 1.90211i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-3.23607 - 2.35114i) q^{4} +(-0.927051 - 2.85317i) q^{5} +(0.618034 + 1.90211i) q^{6} +(8.09017 + 5.87785i) q^{7} +(-6.47214 + 4.70228i) q^{8} +(-8.03444 + 24.7275i) q^{9} -6.00000 q^{10} +4.00000 q^{12} +(-4.94427 + 15.2169i) q^{13} +(16.1803 - 11.7557i) q^{14} +(2.42705 + 1.76336i) q^{15} +(4.94427 + 15.2169i) q^{16} +(12.9787 + 39.9444i) q^{17} +(42.0689 + 30.5648i) q^{18} +(-93.8460 + 68.1831i) q^{19} +(-3.70820 + 11.4127i) q^{20} -10.0000 q^{21} +189.000 q^{23} +(2.47214 - 7.60845i) q^{24} +(93.8460 - 68.1831i) q^{25} +(25.8885 + 18.8091i) q^{26} +(-16.3779 - 50.4060i) q^{27} +(-12.3607 - 38.0423i) q^{28} +(97.0820 + 70.5342i) q^{29} +(4.85410 - 3.52671i) q^{30} +(-50.3698 + 155.022i) q^{31} +32.0000 q^{32} +84.0000 q^{34} +(9.27051 - 28.5317i) q^{35} +(84.1378 - 61.1297i) q^{36} +(330.888 + 240.404i) q^{37} +(71.6919 + 220.645i) q^{38} +(-4.94427 - 15.2169i) q^{39} +(19.4164 + 14.1068i) q^{40} +(-378.620 + 275.083i) q^{41} +(-6.18034 + 19.0211i) q^{42} +110.000 q^{43} +78.0000 q^{45} +(116.808 - 359.499i) q^{46} +(-116.498 + 84.6411i) q^{47} +(-12.9443 - 9.40456i) q^{48} +(-75.0911 - 231.107i) q^{49} +(-71.6919 - 220.645i) q^{50} +(-33.9787 - 24.6870i) q^{51} +(51.7771 - 37.6183i) q^{52} +(27.8115 - 85.5951i) q^{53} -106.000 q^{54} -80.0000 q^{56} +(35.8460 - 110.323i) q^{57} +(194.164 - 141.068i) q^{58} +(366.485 + 266.267i) q^{59} +(-3.70820 - 11.4127i) q^{60} +(6.18034 + 19.0211i) q^{61} +(263.740 + 191.618i) q^{62} +(-210.344 + 152.824i) q^{63} +(19.7771 - 60.8676i) q^{64} +48.0000 q^{65} -97.0000 q^{67} +(51.9149 - 159.777i) q^{68} +(-152.904 + 111.091i) q^{69} +(-48.5410 - 35.2671i) q^{70} +(-143.693 - 442.241i) q^{71} +(-64.2755 - 197.820i) q^{72} +(-686.046 - 498.442i) q^{73} +(661.776 - 480.808i) q^{74} +(-35.8460 + 110.323i) q^{75} +464.000 q^{76} -32.0000 q^{78} +(-229.291 + 705.684i) q^{79} +(38.8328 - 28.2137i) q^{80} +(-525.052 - 381.473i) q^{81} +(289.240 + 890.189i) q^{82} +(135.349 + 416.563i) q^{83} +(32.3607 + 23.5114i) q^{84} +(101.936 - 74.0609i) q^{85} +(67.9837 - 209.232i) q^{86} -120.000 q^{87} -273.000 q^{89} +(48.2067 - 148.365i) q^{90} +(-129.443 + 94.0456i) q^{91} +(-611.617 - 444.366i) q^{92} +(-50.3698 - 155.022i) q^{93} +(88.9969 + 273.904i) q^{94} +(281.538 + 204.549i) q^{95} +(-25.8885 + 18.8091i) q^{96} +(235.162 - 723.754i) q^{97} -486.000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - q^{3} - 4 q^{4} + 3 q^{5} - 2 q^{6} + 10 q^{7} - 8 q^{8} + 26 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - q^3 - 4 * q^4 + 3 * q^5 - 2 * q^6 + 10 * q^7 - 8 * q^8 + 26 * q^9	\( 4 q - 2 q^{2} - q^{3} - 4 q^{4} + 3 q^{5} - 2 q^{6} + 10 q^{7} - 8 q^{8} + 26 q^{9} - 24 q^{10} + 16 q^{12} + 16 q^{13} + 20 q^{14} + 3 q^{15} - 16 q^{16} - 42 q^{17} + 52 q^{18} - 116 q^{19} + 12 q^{20} - 40 q^{21} + 756 q^{23} - 8 q^{24} + 116 q^{25} + 32 q^{26} + 53 q^{27} + 40 q^{28} + 120 q^{29} + 6 q^{30} + 163 q^{31} + 128 q^{32} + 336 q^{34} - 30 q^{35} + 104 q^{36} + 409 q^{37} - 232 q^{38} + 16 q^{39} + 24 q^{40} - 468 q^{41} + 20 q^{42} + 440 q^{43} + 312 q^{45} - 378 q^{46} - 144 q^{47} - 16 q^{48} + 243 q^{49} + 232 q^{50} - 42 q^{51} + 64 q^{52} - 90 q^{53} - 424 q^{54} - 320 q^{56} - 116 q^{57} + 240 q^{58} + 453 q^{59} + 12 q^{60} - 20 q^{61} + 326 q^{62} - 260 q^{63} - 64 q^{64} + 192 q^{65} - 388 q^{67} - 168 q^{68} - 189 q^{69} - 60 q^{70} + 465 q^{71} + 208 q^{72} - 848 q^{73} + 818 q^{74} + 116 q^{75} + 1856 q^{76} - 128 q^{78} + 742 q^{79} + 48 q^{80} - 649 q^{81} - 936 q^{82} - 438 q^{83} + 40 q^{84} + 126 q^{85} - 220 q^{86} - 480 q^{87} - 1092 q^{89} - 156 q^{90} - 160 q^{91} - 756 q^{92} + 163 q^{93} - 288 q^{94} + 348 q^{95} - 32 q^{96} - 761 q^{97} - 1944 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - q^3 - 4 * q^4 + 3 * q^5 - 2 * q^6 + 10 * q^7 - 8 * q^8 + 26 * q^9 - 24 * q^10 + 16 * q^12 + 16 * q^13 + 20 * q^14 + 3 * q^15 - 16 * q^16 - 42 * q^17 + 52 * q^18 - 116 * q^19 + 12 * q^20 - 40 * q^21 + 756 * q^23 - 8 * q^24 + 116 * q^25 + 32 * q^26 + 53 * q^27 + 40 * q^28 + 120 * q^29 + 6 * q^30 + 163 * q^31 + 128 * q^32 + 336 * q^34 - 30 * q^35 + 104 * q^36 + 409 * q^37 - 232 * q^38 + 16 * q^39 + 24 * q^40 - 468 * q^41 + 20 * q^42 + 440 * q^43 + 312 * q^45 - 378 * q^46 - 144 * q^47 - 16 * q^48 + 243 * q^49 + 232 * q^50 - 42 * q^51 + 64 * q^52 - 90 * q^53 - 424 * q^54 - 320 * q^56 - 116 * q^57 + 240 * q^58 + 453 * q^59 + 12 * q^60 - 20 * q^61 + 326 * q^62 - 260 * q^63 - 64 * q^64 + 192 * q^65 - 388 * q^67 - 168 * q^68 - 189 * q^69 - 60 * q^70 + 465 * q^71 + 208 * q^72 - 848 * q^73 + 818 * q^74 + 116 * q^75 + 1856 * q^76 - 128 * q^78 + 742 * q^79 + 48 * q^80 - 649 * q^81 - 936 * q^82 - 438 * q^83 + 40 * q^84 + 126 * q^85 - 220 * q^86 - 480 * q^87 - 1092 * q^89 - 156 * q^90 - 160 * q^91 - 756 * q^92 + 163 * q^93 - 288 * q^94 + 348 * q^95 - 32 * q^96 - 761 * q^97 - 1944 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/242\mathbb{Z}\right)^\times$.

$n$	$123$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.618034	−	1.90211i	0.218508	−	0.672499i
$2$	0.618034	−	1.90211i	0.218508	−	0.672499i
$3$	−0.809017	+	0.587785i	−0.155695	+	0.113119i	−0.662905	−	0.748703i	$-0.730677\pi$
$3$	−0.809017	+	0.587785i	−0.155695	+	0.113119i	0.507210	+	0.861822i	$0.330677\pi$
$4$	−3.23607	−	2.35114i	−0.404508	−	0.293893i
$5$	−0.927051	−	2.85317i	−0.0829180	−	0.255195i	0.900999	−	0.433821i	$-0.142835\pi$
$5$	−0.927051	−	2.85317i	−0.0829180	−	0.255195i	−0.983917	+	0.178626i	$0.942835\pi$
$6$	0.618034	+	1.90211i	0.0420519	+	0.129422i
$7$	8.09017	+	5.87785i	0.436828	+	0.317374i	0.784373	−	0.620289i	$-0.212985\pi$
$7$	8.09017	+	5.87785i	0.436828	+	0.317374i	−0.347545	+	0.937663i	$0.612985\pi$
$8$	−6.47214	+	4.70228i	−0.286031	+	0.207813i
$9$	−8.03444	+	24.7275i	−0.297572	+	0.915832i
$10$	−6.00000			−0.189737
$11$		0			0
$11$		0			0
$12$	4.00000			0.0962250
$13$	−4.94427	+	15.2169i	−0.105484	+	0.324647i	−0.989844	−	0.142159i	$-0.954595\pi$
$13$	−4.94427	+	15.2169i	−0.105484	+	0.324647i	0.884360	+	0.466806i	$0.154595\pi$
$14$	16.1803	−	11.7557i	0.308884	−	0.224417i
$15$	2.42705	+	1.76336i	0.0417775	+	0.0303531i
$16$	4.94427	+	15.2169i	0.0772542	+	0.237764i
$17$	12.9787	+	39.9444i	0.185165	+	0.569878i	0.999951	−	0.00988277i	$-0.00314583\pi$
$17$	12.9787	+	39.9444i	0.185165	+	0.569878i	−0.814786	+	0.579761i	$0.803146\pi$
$18$	42.0689	+	30.5648i	0.550874	+	0.400233i
$19$	−93.8460	+	68.1831i	−1.13314	+	0.823278i	−0.986149	−	0.165860i	$-0.946960\pi$
$19$	−93.8460	+	68.1831i	−1.13314	+	0.823278i	−0.146995	+	0.989137i	$0.546960\pi$
$20$	−3.70820	+	11.4127i	−0.0414590	+	0.127598i
$21$	−10.0000			−0.103913
$22$		0			0
$23$	189.000			1.71344			0.856722	−	0.515778i	$-0.172497\pi$
$23$	189.000			1.71344			0.856722	+	0.515778i	$0.172497\pi$
$24$	2.47214	−	7.60845i	0.0210259	−	0.0647112i
$25$	93.8460	−	68.1831i	0.750768	−	0.545465i
$26$	25.8885	+	18.8091i	0.195275	+	0.141876i
$27$	−16.3779	−	50.4060i	−0.116738	−	0.359283i
$28$	−12.3607	−	38.0423i	−0.0834267	−	0.256761i
$29$	97.0820	+	70.5342i	0.621644	+	0.451651i	0.853495	−	0.521100i	$-0.174478\pi$
$29$	97.0820	+	70.5342i	0.621644	+	0.451651i	−0.231851	+	0.972751i	$0.574478\pi$
$30$	4.85410	−	3.52671i	0.0295411	−	0.0214629i
$31$	−50.3698	+	155.022i	−0.291828	+	0.898155i	0.692440	+	0.721475i	$0.256536\pi$
$31$	−50.3698	+	155.022i	−0.291828	+	0.898155i	−0.984268	+	0.176680i	$0.943464\pi$
$32$	32.0000			0.176777
$33$		0			0
$34$	84.0000			0.423702
$35$	9.27051	−	28.5317i	0.0447715	−	0.137792i
$36$	84.1378	−	61.1297i	0.389527	−	0.283008i
$37$	330.888	+	240.404i	1.47021	+	1.06817i	0.980554	+	0.196250i	$0.0628764\pi$
$37$	330.888	+	240.404i	1.47021	+	1.06817i	0.489653	+	0.871918i	$0.337124\pi$
$38$	71.6919	+	220.645i	0.306052	+	0.941931i
$39$	−4.94427	−	15.2169i	−0.0203004	−	0.0624783i
$40$	19.4164	+	14.1068i	0.0767501	+	0.0557622i
$41$	−378.620	+	275.083i	−1.44221	+	1.04782i	−0.454632	+	0.890679i	$0.650229\pi$
$41$	−378.620	+	275.083i	−1.44221	+	1.04782i	−0.987575	+	0.157146i	$0.949771\pi$
$42$	−6.18034	+	19.0211i	−0.0227059	+	0.0698815i
$43$	110.000			0.390113			0.195056	−	0.980792i	$-0.437511\pi$
$43$	110.000			0.390113			0.195056	+	0.980792i	$0.437511\pi$
$44$		0			0
$45$	78.0000			0.258390
$46$	116.808	−	359.499i	0.374401	−	1.15229i
$47$	−116.498	+	84.6411i	−0.361554	+	0.262684i	−0.753700	−	0.657219i	$-0.771733\pi$
$47$	−116.498	+	84.6411i	−0.361554	+	0.262684i	0.392146	+	0.919903i	$0.371733\pi$
$48$	−12.9443	−	9.40456i	−0.0389238	−	0.0282798i
$49$	−75.0911	−	231.107i	−0.218925	−	0.673781i
$50$	−71.6919	−	220.645i	−0.202775	−	0.624079i
$51$	−33.9787	−	24.6870i	−0.0932936	−	0.0677817i
$52$	51.7771	−	37.6183i	0.138081	−	0.100321i
$53$	27.8115	−	85.5951i	0.0720794	−	0.221838i	−0.908527	−	0.417827i	$-0.862792\pi$
$53$	27.8115	−	85.5951i	0.0720794	−	0.221838i	0.980606	+	0.195989i	$0.0627918\pi$
$54$	−106.000			−0.267125
$55$		0			0
$56$	−80.0000			−0.190901
$57$	35.8460	−	110.323i	0.0832968	−	0.256361i
$58$	194.164	−	141.068i	0.439569	−	0.319365i
$59$	366.485	+	266.267i	0.808682	+	0.587542i	0.913448	−	0.406955i	$-0.133409\pi$
$59$	366.485	+	266.267i	0.808682	+	0.587542i	−0.104766	+	0.994497i	$0.533409\pi$
$60$	−3.70820	−	11.4127i	−0.00797878	−	0.0245562i
$61$	6.18034	+	19.0211i	0.0129723	+	0.0399247i	0.957333	−	0.288987i	$-0.0933183\pi$
$61$	6.18034	+	19.0211i	0.0129723	+	0.0399247i	−0.944361	+	0.328911i	$0.893318\pi$
$62$	263.740	+	191.618i	0.540241	+	0.392508i
$63$	−210.344	+	152.824i	−0.420649	+	0.305620i
$64$	19.7771	−	60.8676i	0.0386271	−	0.118882i
$65$	48.0000			0.0915949
$66$		0			0
$67$	−97.0000			−0.176872			−0.0884361	−	0.996082i	$-0.528187\pi$
$67$	−97.0000			−0.176872			−0.0884361	+	0.996082i	$0.528187\pi$
$68$	51.9149	−	159.777i	0.0925824	−	0.284939i
$69$	−152.904	+	111.091i	−0.266775	+	0.193824i
$70$	−48.5410	−	35.2671i	−0.0828823	−	0.0602175i
$71$	−143.693	−	442.241i	−0.240186	−	0.739217i	−0.996391	−	0.0848819i	$-0.972949\pi$
$71$	−143.693	−	442.241i	−0.240186	−	0.739217i	0.756205	−	0.654335i	$-0.227051\pi$
$72$	−64.2755	−	197.820i	−0.105208	−	0.323796i
$73$	−686.046	−	498.442i	−1.09994	−	0.799154i	−0.118890	−	0.992907i	$-0.537934\pi$
$73$	−686.046	−	498.442i	−1.09994	−	0.799154i	−0.981050	+	0.193754i	$0.937934\pi$
$74$	661.776	−	480.808i	1.03959	−	0.755309i
$75$	−35.8460	+	110.323i	−0.0551885	+	0.169853i
$76$	464.000			0.700322
$77$		0			0
$78$	−32.0000			−0.0464524
$79$	−229.291	+	705.684i	−0.326547	+	1.00501i	0.644191	+	0.764865i	$0.277194\pi$
$79$	−229.291	+	705.684i	−0.326547	+	1.00501i	−0.970737	+	0.240143i	$0.922806\pi$
$80$	38.8328	−	28.2137i	0.0542705	−	0.0394298i
$81$	−525.052	−	381.473i	−0.720236	−	0.523282i
$82$	289.240	+	890.189i	0.389527	+	1.19884i
$83$	135.349	+	416.563i	0.178994	+	0.550888i	0.999793	−	0.0203292i	$-0.00647142\pi$
$83$	135.349	+	416.563i	0.178994	+	0.550888i	−0.820799	+	0.571217i	$0.806471\pi$
$84$	32.3607	+	23.5114i	0.0420338	+	0.0305393i
$85$	101.936	−	74.0609i	0.130077	−	0.0945063i
$86$	67.9837	−	209.232i	0.0852427	−	0.262350i
$87$	−120.000			−0.147878
$88$		0			0
$89$	−273.000			−0.325145			−0.162573	−	0.986697i	$-0.551979\pi$
$89$	−273.000			−0.325145			−0.162573	+	0.986697i	$0.551979\pi$
$90$	48.2067	−	148.365i	0.0564603	−	0.173767i
$91$	−129.443	+	94.0456i	−0.149113	+	0.108337i
$92$	−611.617	−	444.366i	−0.693103	−	0.503569i
$93$	−50.3698	−	155.022i	−0.0561624	−	0.172850i
$94$	88.9969	+	273.904i	0.0976524	+	0.300543i
$95$	281.538	+	204.549i	0.304055	+	0.220909i
$96$	−25.8885	+	18.8091i	−0.0275233	+	0.0199969i
$97$	235.162	−	723.754i	0.246155	−	0.757589i	−0.749289	−	0.662243i	$-0.769605\pi$
$97$	235.162	−	723.754i	0.246155	−	0.757589i	0.995444	−	0.0953452i	$-0.0303955\pi$
$98$	−486.000			−0.500953
$99$		0			0
$100$	−464.000			−0.464000
$101$	−487.629	+	1500.77i	−0.480405	+	1.47853i	0.358123	+	0.933675i	$0.383417\pi$
$101$	−487.629	+	1500.77i	−0.480405	+	1.47853i	−0.838527	+	0.544859i	$0.816583\pi$
$102$	−67.9574	+	49.3740i	−0.0659685	+	0.0479289i
$103$	−977.293	−	710.045i	−0.934908	−	0.679250i	0.0122818	−	0.999925i	$-0.496090\pi$
$103$	−977.293	−	710.045i	−0.934908	−	0.679250i	−0.947190	+	0.320674i	$0.896090\pi$
$104$	−39.5542	−	121.735i	−0.0372943	−	0.114780i
$105$	9.27051	+	28.5317i	0.00861628	+	0.0265182i
$106$	−145.623	−	105.801i	−0.133435	−	0.0969466i
$107$	1169.84	−	849.937i	1.05694	−	0.767912i	0.0834200	−	0.996514i	$-0.473416\pi$
$107$	1169.84	−	849.937i	1.05694	−	0.767912i	0.973520	+	0.228603i	$0.0734157\pi$
$108$	−65.5116	+	201.624i	−0.0583690	+	0.179641i
$109$	−1342.00			−1.17927			−0.589634	−	0.807670i	$-0.700728\pi$
$109$	−1342.00			−1.17927			−0.589634	+	0.807670i	$0.700728\pi$
$110$		0			0
$111$	−409.000			−0.349735
$112$	−49.4427	+	152.169i	−0.0417134	+	0.128381i
$113$	−1424.68	+	1035.09i	−1.18604	+	0.861708i	−0.992840	−	0.119451i	$-0.961887\pi$
$113$	−1424.68	+	1035.09i	−1.18604	+	0.861708i	−0.193200	+	0.981159i	$0.561887\pi$
$114$	−187.692	−	136.366i	−0.154201	−	0.112034i
$115$	−175.213	−	539.249i	−0.142075	−	0.437263i
$116$	−148.328	−	456.507i	−0.118723	−	0.365393i
$117$	−336.551	−	244.519i	−0.265933	−	0.193212i
$118$	732.969	−	532.533i	0.571825	−	0.415455i
$119$	−129.787	+	399.444i	−0.0999796	+	0.307705i
$120$	−24.0000			−0.0182574
$121$		0			0
$122$	40.0000			0.0296839
$123$	144.620	−	445.094i	0.106016	−	0.326283i
$124$	527.479	−	383.236i	0.382008	−	0.277545i
$125$	−584.919	−	424.969i	−0.418534	−	0.304083i
$126$	160.689	+	494.549i	0.113613	+	0.349666i
$127$	658.824	+	2027.65i	0.460324	+	1.41673i	0.864769	+	0.502170i	$0.167465\pi$
$127$	658.824	+	2027.65i	0.460324	+	1.41673i	−0.404444	+	0.914563i	$0.632535\pi$
$128$	−103.554	−	75.2365i	−0.0715077	−	0.0519534i
$129$	−88.9919	+	64.6564i	−0.0607387	+	0.0441293i
$130$	29.6656	−	91.3014i	0.0200142	−	0.0615974i
$131$	1782.00			1.18850			0.594252	−	0.804279i	$-0.297448\pi$
$131$	1782.00			1.18850			0.594252	+	0.804279i	$0.297448\pi$
$132$		0			0
$133$	−1160.00			−0.756276
$134$	−59.9493	+	184.505i	−0.0386480	+	0.118946i
$135$	−128.634	+	93.4579i	−0.0820076	+	0.0595820i
$136$	−271.830	−	197.496i	−0.171391	−	0.124523i
$137$	284.605	+	875.923i	0.177485	+	0.546242i	0.999738	−	0.0228795i	$-0.00728340\pi$
$137$	284.605	+	875.923i	0.177485	+	0.546242i	−0.822253	+	0.569121i	$0.807283\pi$
$138$	116.808	+	359.499i	0.0720536	+	0.221758i
$139$	−1166.60	−	847.586i	−0.711870	−	0.517204i	0.171906	−	0.985113i	$-0.445007\pi$
$139$	−1166.60	−	847.586i	−0.711870	−	0.517204i	−0.883776	+	0.467909i	$0.845007\pi$
$140$	−97.0820	+	70.5342i	−0.0586066	+	0.0425802i
$141$	44.4984	−	136.952i	0.0265776	−	0.0817975i
$142$	−930.000			−0.549605
$143$		0			0
$144$	−416.000			−0.240741
$145$	111.246	−	342.380i	0.0637137	−	0.196091i
$146$	−1372.09	+	996.884i	−0.777775	+	0.565087i
$147$	196.591	+	142.832i	0.110303	+	0.0801399i
$148$	−505.552	−	1555.93i	−0.280784	−	0.864166i
$149$	−558.085	−	1717.61i	−0.306846	−	0.944375i	−0.978982	−	0.203947i	$-0.934623\pi$
$149$	−558.085	−	1717.61i	−0.306846	−	0.944375i	0.672136	−	0.740428i	$-0.265377\pi$
$150$	187.692	+	136.366i	0.102167	+	0.0742283i
$151$	1134.24	−	824.075i	0.611280	−	0.444121i	−0.238585	−	0.971122i	$-0.576683\pi$
$151$	1134.24	−	824.075i	0.611280	−	0.444121i	0.849865	+	0.527001i	$0.176683\pi$
$152$	286.768	−	882.580i	0.153026	−	0.470965i
$153$	−1092.00			−0.577013
$154$		0			0
$155$	489.000			0.253403
$156$	−19.7771	+	60.8676i	−0.0101502	+	0.0312392i
$157$	2384.17	−	1732.20i	1.21196	−	0.880541i	0.216553	−	0.976271i	$-0.430519\pi$
$157$	2384.17	−	1732.20i	1.21196	−	0.880541i	0.995407	+	0.0957304i	$0.0305187\pi$
$158$	1200.58	+	872.273i	0.604513	+	0.439205i
$159$	27.8115	+	85.5951i	0.0138717	+	0.0426927i
$160$	−29.6656	−	91.3014i	−0.0146580	−	0.0451126i
$161$	1529.04	+	1110.91i	0.748481	+	0.543803i
$162$	−1050.10	+	762.945i	−0.509284	+	0.370016i
$163$	102.594	−	315.751i	0.0492991	−	0.151727i	−0.923376	−	0.383896i	$-0.874582\pi$
$163$	102.594	−	315.751i	0.0492991	−	0.151727i	0.972676	+	0.232169i	$0.0745822\pi$
$164$	1872.00			0.891333
$165$		0			0
$166$	876.000			0.409583
$167$	593.313	−	1826.03i	0.274922	−	0.846122i	−0.714319	−	0.699821i	$-0.753263\pi$
$167$	593.313	−	1826.03i	0.274922	−	0.846122i	0.989240	−	0.146301i	$-0.0467368\pi$
$168$	64.7214	−	47.0228i	0.0297224	−	0.0215946i
$169$	1570.30	+	1140.89i	0.714748	+	0.519295i
$170$	−77.8723	−	239.666i	−0.0351325	−	0.108127i
$171$	−931.995	−	2868.39i	−0.416792	−	1.28275i
$172$	−355.967	−	258.626i	−0.157804	−	0.114651i
$173$	−1606.71	+	1167.34i	−0.706102	+	0.513013i	−0.881914	−	0.471410i	$-0.843745\pi$
$173$	−1606.71	+	1167.34i	−0.706102	+	0.513013i	0.175812	+	0.984424i	$0.443745\pi$
$174$	−74.1641	+	228.254i	−0.0323124	+	0.0994475i
$175$	1160.00			0.501073
$176$		0			0
$177$	−453.000			−0.192370
$178$	−168.723	+	519.277i	−0.0710469	+	0.218660i
$179$	−89.8009	+	65.2442i	−0.0374974	+	0.0272435i	−0.606376	−	0.795178i	$-0.707377\pi$
$179$	−89.8009	+	65.2442i	−0.0374974	+	0.0272435i	0.568879	+	0.822421i	$0.307377\pi$
$180$	−252.413	−	183.389i	−0.104521	−	0.0759389i
$181$	277.806	+	855.000i	0.114084	+	0.351114i	0.991755	−	0.128150i	$-0.0409038\pi$
$181$	277.806	+	855.000i	0.114084	+	0.351114i	−0.877671	+	0.479264i	$0.840904\pi$
$182$	98.8854	+	304.338i	0.0402740	+	0.123951i
$183$	−16.1803	−	11.7557i	−0.00653598	−	0.00474867i
$184$	−1223.23	+	888.731i	−0.490098	+	0.356077i
$185$	379.164	−	1166.95i	0.150685	−	0.463760i
$186$	−326.000			−0.128513
$187$		0			0
$188$	576.000			0.223453
$189$	163.779	−	504.060i	0.0630326	−	0.193995i
$190$	563.076	−	409.099i	0.214999	−	0.156206i
$191$	1220.81	+	886.968i	0.462484	+	0.336014i	0.794505	−	0.607258i	$-0.207730\pi$
$191$	1220.81	+	886.968i	0.462484	+	0.336014i	−0.332021	+	0.943272i	$0.607730\pi$
$192$	19.7771	+	60.8676i	0.00743379	+	0.0228789i
$193$	6.18034	+	19.0211i	0.00230503	+	0.00709415i	0.952202	−	0.305468i	$-0.0988128\pi$
$193$	6.18034	+	19.0211i	0.00230503	+	0.00709415i	−0.949897	+	0.312562i	$0.898813\pi$
$194$	−1231.32	−	894.609i	−0.455690	−	0.331078i
$195$	−38.8328	+	28.2137i	−0.0142609	+	0.0103612i
$196$	−300.365	+	924.427i	−0.109462	+	0.336890i
$197$	1254.00			0.453522			0.226761	−	0.973950i	$-0.427186\pi$
$197$	1254.00			0.453522			0.226761	+	0.973950i	$0.427186\pi$
$198$		0			0
$199$	4688.00			1.66997			0.834984	−	0.550275i	$-0.185477\pi$
$199$	4688.00			1.66997			0.834984	+	0.550275i	$0.185477\pi$
$200$	−286.768	+	882.580i	−0.101388	+	0.312039i
$201$	78.4746	−	57.0152i	0.0275382	−	0.0200077i
$202$	2553.26	+	1855.05i	0.889340	+	0.646143i
$203$	370.820	+	1141.27i	0.128209	+	0.394588i
$204$	51.9149	+	159.777i	0.0178175	+	0.0548366i
$205$	1135.86	+	825.250i	0.386985	+	0.281161i
$206$	−1954.59	+	1420.09i	−0.661080	+	0.480302i
$207$	−1518.51	+	4673.49i	−0.509873	+	1.56923i
$208$	−256.000			−0.0853385
$209$		0			0
$210$	60.0000			0.0197162
$211$	1504.29	−	4629.74i	0.490805	−	1.51054i	−0.332588	−	0.943072i	$-0.607922\pi$
$211$	1504.29	−	4629.74i	0.490805	−	1.51054i	0.823393	−	0.567471i	$-0.192078\pi$
$212$	−291.246	+	211.603i	−0.0943531	+	0.0685516i
$213$	376.193	+	273.320i	0.121016	+	0.0879229i
$214$	−893.677	−	2750.46i	−0.285470	−	0.878585i
$215$	−101.976	−	313.849i	−0.0323473	−	0.0995549i
$216$	343.023	+	249.221i	0.108055	+	0.0785062i
$217$	−1318.70	+	958.090i	−0.412530	+	0.299721i
$218$	−829.402	+	2552.64i	−0.257680	+	0.793056i
$219$	848.000			0.261655
$220$		0			0
$221$	−672.000			−0.204541
$222$	−252.776	+	777.964i	−0.0764199	+	0.235196i
$223$	3772.45	−	2740.84i	1.13283	−	0.823051i	0.146728	−	0.989177i	$-0.453126\pi$
$223$	3772.45	−	2740.84i	1.13283	−	0.823051i	0.986105	+	0.166126i	$0.0531258\pi$
$224$	258.885	+	188.091i	0.0772210	+	0.0561044i
$225$	931.995	+	2868.39i	0.276147	+	0.849892i
$226$	1088.36	+	3349.62i	0.320338	+	0.985900i
$227$	4742.46	+	3445.60i	1.38664	+	1.00746i	0.996224	+	0.0868178i	$0.0276698\pi$
$227$	4742.46	+	3445.60i	1.38664	+	1.00746i	0.390419	+	0.920637i	$0.372330\pi$
$228$	−375.384	+	272.732i	−0.109037	+	0.0792199i
$229$	1560.84	−	4803.79i	0.450408	−	1.38621i	−0.426034	−	0.904707i	$-0.640089\pi$
$229$	1560.84	−	4803.79i	0.450408	−	1.38621i	0.876442	−	0.481507i	$-0.159911\pi$
$230$	−1134.00			−0.325103
$231$		0			0
$232$	−960.000			−0.271668
$233$	−222.492	+	684.761i	−0.0625577	+	0.192533i	−0.977451	−	0.211163i	$-0.932275\pi$
$233$	−222.492	+	684.761i	−0.0625577	+	0.192533i	0.914893	+	0.403696i	$0.132275\pi$
$234$	−673.102	+	489.037i	−0.188043	+	0.136621i
$235$	349.495	+	253.923i	0.0970152	+	0.0704856i
$236$	−559.939	−	1723.31i	−0.154445	−	0.475331i
$237$	−229.291	−	705.684i	−0.0628440	−	0.193414i
$238$	679.574	+	493.740i	0.185085	+	0.134472i
$239$	422.307	−	306.824i	0.114296	−	0.0830410i	−0.529169	−	0.848517i	$-0.677496\pi$
$239$	422.307	−	306.824i	0.114296	−	0.0830410i	0.643465	+	0.765476i	$0.277496\pi$
$240$	−14.8328	+	45.6507i	−0.00398939	+	0.0122781i
$241$	−5632.00			−1.50535			−0.752674	−	0.658393i	$-0.771236\pi$
$241$	−5632.00			−1.50535			−0.752674	+	0.658393i	$0.771236\pi$
$242$		0			0
$243$	2080.00			0.549103
$244$	24.7214	−	76.0845i	0.00648616	−	0.0199623i
$245$	−589.773	+	428.495i	−0.153793	+	0.111737i
$246$	−757.240	−	550.167i	−0.196260	−	0.142591i
$247$	−573.536	−	1765.16i	−0.147746	−	0.454715i
$248$	−402.958	−	1240.18i	−0.103177	−	0.317546i
$249$	−354.349	−	257.450i	−0.0901847	−	0.0655230i
$250$	−1169.84	+	849.937i	−0.295948	+	0.215019i
$251$	−1960.71	+	6034.45i	−0.493064	+	1.51750i	0.326888	+	0.945063i	$0.394000\pi$
$251$	−1960.71	+	6034.45i	−0.493064	+	1.51750i	−0.819952	+	0.572432i	$0.806000\pi$
$252$	1040.00			0.259976
$253$		0			0
$254$	4264.00			1.05334
$255$	−38.9361	+	119.833i	−0.00956187	+	0.0294284i
$256$	−207.108	+	150.473i	−0.0505636	+	0.0367366i
$257$	−1208.67	−	878.151i	−0.293365	−	0.213142i	0.431361	−	0.902180i	$-0.358034\pi$
$257$	−1208.67	−	878.151i	−0.293365	−	0.213142i	−0.724726	+	0.689037i	$0.758034\pi$
$258$	67.9837	+	209.232i	0.0164050	+	0.0504893i
$259$	1263.88	+	3889.82i	0.303219	+	0.933211i
$260$	−155.331	−	112.855i	−0.0370509	−	0.0269191i
$261$	−2524.13	+	1833.89i	−0.598620	+	0.434923i
$262$	1101.34	−	3389.57i	0.259698	−	0.799267i
$263$	1254.00			0.294011			0.147006	−	0.989136i	$-0.453036\pi$
$263$	1254.00			0.294011			0.147006	+	0.989136i	$0.453036\pi$
$264$		0			0
$265$	−270.000			−0.0625886
$266$	−716.919	+	2206.45i	−0.165252	+	0.508595i
$267$	220.862	−	160.465i	0.0506236	−	0.0367802i
$268$	313.899	+	228.061i	0.0715463	+	0.0519814i
$269$	1681.67	+	5175.65i	0.381165	+	1.17310i	0.939225	+	0.343303i	$0.111546\pi$
$269$	1681.67	+	5175.65i	0.381165	+	1.17310i	−0.558060	+	0.829801i	$0.688454\pi$
$270$	98.2674	+	302.436i	0.0221495	+	0.0681691i
$271$	−1967.53	−	1429.49i	−0.441029	−	0.320426i	0.345015	−	0.938597i	$-0.387874\pi$
$271$	−1967.53	−	1429.49i	−0.441029	−	0.320426i	−0.786044	+	0.618171i	$0.787874\pi$
$272$	−543.659	+	394.992i	−0.121192	+	0.0880511i
$273$	49.4427	−	152.169i	0.0109612	−	0.0337351i
$274$	1842.00			0.406129
$275$		0			0
$276$	756.000			0.164876
$277$	−514.822	+	1584.46i	−0.111670	+	0.343686i	−0.991238	−	0.132088i	$-0.957832\pi$
$277$	−514.822	+	1584.46i	−0.111670	+	0.343686i	0.879568	+	0.475774i	$0.157832\pi$
$278$	−2333.21	+	1695.17i	−0.503368	+	0.365718i
$279$	−3428.61	−	2491.03i	−0.735720	−	0.534532i
$280$	74.1641	+	228.254i	0.0158291	+	0.0487170i
$281$	−1006.78	−	3098.54i	−0.213734	−	0.657806i	−0.999241	−	0.0389532i	$-0.987598\pi$
$281$	−1006.78	−	3098.54i	−0.213734	−	0.657806i	0.785507	−	0.618853i	$-0.212402\pi$
$282$	−232.997	−	169.282i	−0.0492013	−	0.0357468i
$283$	6313.57	−	4587.08i	1.32616	−	0.963510i	0.326325	−	0.945258i	$-0.394190\pi$
$283$	6313.57	−	4587.08i	1.32616	−	0.963510i	0.999833	−	0.0182524i	$-0.00581023\pi$
$284$	−574.772	+	1768.97i	−0.120093	+	0.369608i
$285$	−348.000			−0.0723289
$286$		0			0
$287$	−4680.00			−0.962549
$288$	−257.102	+	791.279i	−0.0526038	+	0.161898i
$289$	2547.59	−	1850.94i	0.518542	−	0.376742i
$290$	−582.492	−	423.205i	−0.117949	−	0.0856947i
$291$	235.162	+	723.754i	0.0473726	+	0.145798i
$292$	1048.19	+	3225.98i	0.210070	+	0.646529i
$293$	−9.70820	−	7.05342i	−0.00193570	−	0.00140637i	0.586817	−	0.809720i	$-0.300381\pi$
$293$	−9.70820	−	7.05342i	−0.00193570	−	0.00140637i	−0.588753	+	0.808313i	$0.700381\pi$
$294$	393.182	−	285.664i	0.0779961	−	0.0566675i
$295$	419.954	−	1292.49i	0.0828836	−	0.255090i
$296$	−3272.00			−0.642504
$297$		0			0
$298$	−3612.00			−0.702139
$299$	−934.467	+	2875.99i	−0.180741	+	0.556264i
$300$	375.384	−	272.732i	0.0722427	−	0.0524874i
$301$	889.919	+	646.564i	0.170412	+	0.123812i
$302$	−866.484	−	2666.76i	−0.165101	−	0.508129i
$303$	−487.629	−	1500.77i	−0.0924539	−	0.284544i
$304$	−1501.54	−	1090.93i	−0.283286	−	0.205819i
$305$	48.5410	−	35.2671i	0.00911295	−	0.00662095i
$306$	−674.893	+	2077.11i	−0.126082	+	0.388040i
$307$	5852.00			1.08792			0.543960	−	0.839111i	$-0.316924\pi$
$307$	5852.00			1.08792			0.543960	+	0.839111i	$0.316924\pi$
$308$		0			0
$309$	1208.00			0.222397
$310$	302.219	−	930.133i	0.0553705	−	0.170413i
$311$	−2145.51	+	1558.81i	−0.391193	+	0.284218i	−0.765944	−	0.642907i	$-0.777728\pi$
$311$	−2145.51	+	1558.81i	−0.391193	+	0.284218i	0.374751	+	0.927125i	$0.377728\pi$
$312$	103.554	+	75.2365i	0.0187904	+	0.0136520i
$313$	−2210.40	−	6802.91i	−0.399166	−	1.22851i	−0.925669	−	0.378335i	$-0.876497\pi$
$313$	−2210.40	−	6802.91i	−0.399166	−	1.22851i	0.526502	−	0.850174i	$-0.323503\pi$
$314$	−1821.35	−	5605.53i	−0.327339	−	1.00745i
$315$	631.033	+	458.472i	0.112872	+	0.0820063i
$316$	2401.16	−	1744.55i	0.427456	−	0.310565i
$317$	1893.97	−	5829.03i	0.335570	−	1.03278i	−0.630871	−	0.775888i	$-0.717302\pi$
$317$	1893.97	−	5829.03i	0.335570	−	1.03278i	0.966441	−	0.256890i	$-0.0826979\pi$
$318$	180.000			0.0317418
$319$		0			0
$320$	−192.000			−0.0335410
$321$	−446.839	+	1375.23i	−0.0776950	+	0.239121i
$322$	3058.08	−	2221.83i	0.529256	−	0.384527i
$323$	−3941.53	−	2863.69i	−0.678987	−	0.493313i
$324$	802.208	+	2468.94i	0.137553	+	0.423344i
$325$	573.536	+	1765.16i	0.0978893	+	0.301272i
$326$	−537.187	−	390.289i	−0.0912640	−	0.0663072i
$327$	1085.70	−	788.808i	0.183607	−	0.133398i
$328$	1156.96	−	3560.76i	0.194763	−	0.599420i
$329$	−1440.00			−0.241306
$330$		0			0
$331$	−823.000			−0.136665			−0.0683326	−	0.997663i	$-0.521768\pi$
$331$	−823.000			−0.136665			−0.0683326	+	0.997663i	$0.521768\pi$
$332$	541.398	−	1666.25i	0.0894972	−	0.275444i
$333$	−8603.09	+	6250.51i	−1.41575	+	1.02861i
$334$	−3106.63	−	2257.10i	−0.508943	−	0.369769i
$335$	89.9239	+	276.757i	0.0146659	+	0.0451369i
$336$	−49.4427	−	152.169i	−0.00802774	−	0.0247069i
$337$	−4263.52	−	3097.63i	−0.689165	−	0.500708i	0.187220	−	0.982318i	$-0.440052\pi$
$337$	−4263.52	−	3097.63i	−0.689165	−	0.500708i	−0.876386	+	0.481610i	$0.840052\pi$
$338$	3140.60	−	2281.78i	0.505403	−	0.367197i
$339$	544.179	−	1674.81i	0.0871851	−	0.268328i
$340$	−504.000			−0.0803919
$341$		0			0
$342$	−6032.00			−0.953723
$343$	1810.84	−	5573.19i	0.285062	−	0.877330i
$344$	−711.935	+	517.251i	−0.111584	+	0.0810707i
$345$	458.713	+	333.274i	0.0715834	+	0.0520084i
$346$	1227.42	+	3777.60i	0.190712	+	0.586950i
$347$	2032.10	+	6254.15i	0.314376	+	0.967551i	0.976010	+	0.217724i	$0.0698633\pi$
$347$	2032.10	+	6254.15i	0.314376	+	0.967551i	−0.661634	+	0.749827i	$0.730137\pi$
$348$	388.328	+	282.137i	0.0598177	+	0.0434601i
$349$	5085.48	−	3694.82i	0.779999	−	0.566702i	−0.124980	−	0.992159i	$-0.539887\pi$
$349$	5085.48	−	3694.82i	0.779999	−	0.566702i	0.904979	+	0.425457i	$0.139887\pi$
$350$	716.919	−	2206.45i	0.109488	−	0.336971i
$351$	848.000			0.128954
$352$		0			0
$353$	−10701.0			−1.61348			−0.806738	−	0.590910i	$-0.798769\pi$
$353$	−10701.0			−1.61348			−0.806738	+	0.590910i	$0.798769\pi$
$354$	−279.969	+	861.657i	−0.0420345	+	0.129369i
$355$	−1128.58	+	819.960i	−0.168729	+	0.122589i
$356$	883.447	+	641.861i	0.131524	+	0.0955578i
$357$	−129.787	−	399.444i	−0.0192411	−	0.0592179i
$358$	68.6018	+	211.135i	0.0101277	+	0.0311699i
$359$	−6737.49	−	4895.08i	−0.990505	−	0.719644i	−0.0304734	−	0.999536i	$-0.509701\pi$
$359$	−6737.49	−	4895.08i	−0.990505	−	0.719644i	−0.960032	+	0.279892i	$0.909701\pi$
$360$	−504.827	+	366.778i	−0.0739075	+	0.0536969i
$361$	2038.59	−	6274.12i	0.297213	−	0.914728i
$362$	1798.00			0.261052
$363$		0			0
$364$	640.000			0.0921569
$365$	−786.139	+	2419.49i	−0.112735	+	0.346964i
$366$	−32.3607	+	23.5114i	−0.00462164	+	0.00335782i
$367$	2947.25	+	2141.30i	0.419197	+	0.304564i	0.777314	−	0.629112i	$-0.216581\pi$
$367$	2947.25	+	2141.30i	0.419197	+	0.304564i	−0.358118	+	0.933676i	$0.616581\pi$
$368$	934.467	+	2875.99i	0.132371	+	0.407396i
$369$	−3760.12	−	11572.5i	−0.530471	−	1.63262i
$370$	−1985.33	−	1442.43i	−0.278952	−	0.202671i
$371$	728.115	−	529.007i	0.101892	−	0.0740287i
$372$	−201.479	+	620.089i	−0.0280812	+	0.0864250i
$373$	−7942.00			−1.10247			−0.551235	−	0.834350i	$-0.685843\pi$
$373$	−7942.00			−1.10247			−0.551235	+	0.834350i	$0.685843\pi$
$374$		0			0
$375$	723.000			0.0995615
$376$	355.988	−	1095.62i	0.0488262	−	0.150272i
$377$	−1553.31	+	1128.55i	−0.212201	+	0.154173i
$378$	−857.558	−	623.052i	−0.116688	−	0.0847787i
$379$	−2883.44	−	8874.31i	−0.390797	−	1.20275i	−0.932186	−	0.361979i	$-0.882101\pi$
$379$	−2883.44	−	8874.31i	−0.390797	−	1.20275i	0.541389	−	0.840772i	$-0.317899\pi$
$380$	−430.152	−	1323.87i	−0.0580692	−	0.178719i
$381$	−1724.82	−	1253.16i	−0.231930	−	0.168507i
$382$	2441.61	−	1773.94i	0.327026	−	0.237598i
$383$	−2389.01	+	7352.62i	−0.318728	+	0.980943i	0.655465	+	0.755226i	$0.272473\pi$
$383$	−2389.01	+	7352.62i	−0.318728	+	0.980943i	−0.974193	+	0.225718i	$0.927527\pi$
$384$	128.000			0.0170103
$385$		0			0
$386$	40.0000			0.00527447
$387$	−883.789	+	2720.02i	−0.116087	+	0.357278i
$388$	−2462.65	+	1789.22i	−0.322222	+	0.234108i
$389$	−1181.97	−	858.754i	−0.154058	−	0.111929i	0.508086	−	0.861306i	$-0.330353\pi$
$389$	−1181.97	−	858.754i	−0.154058	−	0.111929i	−0.662144	+	0.749377i	$0.730353\pi$
$390$	29.6656	+	91.3014i	0.00385174	+	0.0118544i
$391$	2452.98	+	7549.49i	0.317269	+	0.976455i
$392$	1572.73	+	1142.65i	0.202640	+	0.147226i
$393$	−1441.67	+	1047.43i	−0.185045	+	0.134443i
$394$	775.015	−	2385.25i	0.0990982	−	0.304993i
$395$	2226.00			0.283550
$396$		0			0
$397$	−6466.00			−0.817429			−0.408714	−	0.912662i	$-0.634023\pi$
$397$	−6466.00			−0.817429			−0.408714	+	0.912662i	$0.634023\pi$
$398$	2897.34	−	8917.11i	0.364901	−	1.12305i
$399$	938.460	−	681.831i	0.117749	−	0.0855495i
$400$	1501.54	+	1090.93i	0.187692	+	0.136366i
$401$	621.124	+	1911.62i	0.0773503	+	0.238060i	0.982254	−	0.187557i	$-0.0600571\pi$
$401$	621.124	+	1911.62i	0.0773503	+	0.238060i	−0.904903	+	0.425617i	$0.860057\pi$
$402$	−59.9493	−	184.505i	−0.00743781	−	0.0228912i
$403$	−2109.92	−	1532.94i	−0.260800	−	0.189482i
$404$	5106.52	−	3710.10i	0.628858	−	0.456892i
$405$	−601.656	+	1851.71i	−0.0738186	+	0.227190i
$406$	2400.00			0.293374
$407$		0			0
$408$	336.000			0.0407708
$409$	−3900.41	+	12004.2i	−0.471548	+	1.45127i	0.379010	+	0.925393i	$0.376265\pi$
$409$	−3900.41	+	12004.2i	−0.471548	+	1.45127i	−0.850558	+	0.525882i	$0.823735\pi$
$410$	2271.72	−	1650.50i	0.273640	−	0.198811i
$411$	−745.105	−	541.350i	−0.0894241	−	0.0649704i
$412$	1493.17	+	4595.51i	0.178551	+	0.549525i
$413$	1399.85	+	4308.29i	0.166784	+	0.513310i
$414$	7951.02	+	5776.75i	0.943892	+	0.685778i
$415$	1063.05	−	772.350i	0.125742	−	0.0913570i
$416$	−158.217	+	486.941i	−0.0186471	+	0.0573900i
$417$	1442.00			0.169341
$418$		0			0
$419$	10980.0			1.28021			0.640105	−	0.768287i	$-0.278891\pi$
$419$	10980.0			1.28021			0.640105	+	0.768287i	$0.278891\pi$
$420$	37.0820	−	114.127i	0.00430814	−	0.0132591i
$421$	435.251	−	316.228i	0.0503868	−	0.0366082i	−0.562307	−	0.826929i	$-0.690086\pi$
$421$	435.251	−	316.228i	0.0503868	−	0.0366082i	0.612694	+	0.790321i	$0.290086\pi$
$422$	−7876.59	−	5722.68i	−0.908593	−	0.660132i
$423$	−1156.96	−	3560.76i	−0.132987	−	0.409290i
$424$	222.492	+	684.761i	0.0254839	+	0.0784314i
$425$	3941.53	+	2863.69i	0.449864	+	0.326846i
$426$	752.386	−	546.640i	0.0855709	−	0.0621709i
$427$	−61.8034	+	190.211i	−0.00700439	+	0.0215573i
$428$	−5784.00			−0.653225
$429$		0			0
$430$	−660.000			−0.0740187
$431$	1551.88	−	4776.21i	0.173438	−	0.533786i	−0.826121	−	0.563493i	$-0.809457\pi$
$431$	1551.88	−	4776.21i	0.173438	−	0.533786i	0.999559	+	0.0297067i	$0.00945732\pi$
$432$	686.046	−	498.442i	0.0764061	−	0.0555123i
$433$	2092.93	+	1520.60i	0.232286	+	0.168765i	0.697839	−	0.716254i	$-0.254145\pi$
$433$	2092.93	+	1520.60i	0.232286	+	0.168765i	−0.465554	+	0.885020i	$0.654145\pi$
$434$	1007.40	+	3100.44i	0.111421	+	0.342917i
$435$	111.246	+	342.380i	0.0122617	+	0.0377377i
$436$	4342.80	+	3155.23i	0.477024	+	0.346578i
$437$	−17736.9	+	12886.6i	−1.94158	+	1.41064i
$438$	524.093	−	1612.99i	0.0571738	−	0.175963i
$439$	704.000			0.0765378			0.0382689	−	0.999267i	$-0.487816\pi$
$439$	704.000			0.0765378			0.0382689	+	0.999267i	$0.487816\pi$
$440$		0			0
$441$	6318.00			0.682216
$442$	−415.319	+	1278.22i	−0.0446939	+	0.137554i
$443$	−3400.30	+	2470.46i	−0.364680	+	0.264955i	−0.755001	−	0.655723i	$-0.772364\pi$
$443$	−3400.30	+	2470.46i	−0.364680	+	0.264955i	0.390322	+	0.920679i	$0.372364\pi$
$444$	1323.55	+	961.617i	0.141471	+	0.102784i
$445$	253.085	+	778.915i	0.0269604	+	0.0829756i
$446$	−2881.89	−	8869.55i	−0.305968	−	0.941672i
$447$	1461.08	+	1061.54i	0.154602	+	0.112325i
$448$	517.771	−	376.183i	0.0546035	−	0.0396718i
$449$	−288.313	+	887.336i	−0.0303036	+	0.0932649i	−0.965064	−	0.262013i	$-0.915614\pi$
$449$	−288.313	+	887.336i	−0.0303036	+	0.0932649i	0.934761	+	0.355278i	$0.115614\pi$
$450$	6032.00			0.631892
$451$		0			0
$452$	7044.00			0.733013
$453$	−433.242	+	1333.38i	−0.0449348	+	0.138295i
$454$	9484.92	−	6891.19i	0.980505	−	0.712378i
$455$	388.328	+	282.137i	0.0400112	+	0.0290699i
$456$	286.768	+	882.580i	0.0294498	+	0.0906373i
$457$	3187.82	+	9811.10i	0.326302	+	1.00425i	0.970850	+	0.239690i	$0.0770457\pi$
$457$	3187.82	+	9811.10i	0.326302	+	1.00425i	−0.644548	+	0.764564i	$0.722954\pi$
$458$	−8172.69	−	5937.81i	−0.833809	−	0.605798i
$459$	1800.87	−	1308.41i	0.183132	−	0.133053i
$460$	−700.851	+	2157.00i	−0.0710377	+	0.218631i
$461$	132.000			0.0133359			0.00666795	−	0.999978i	$-0.497878\pi$
$461$	132.000			0.0133359			0.00666795	+	0.999978i	$0.497878\pi$
$462$		0			0
$463$	7823.00			0.785239			0.392619	−	0.919701i	$-0.371569\pi$
$463$	7823.00			0.785239			0.392619	+	0.919701i	$0.371569\pi$
$464$	−593.313	+	1826.03i	−0.0593617	+	0.182697i
$465$	−395.609	+	287.427i	−0.0394536	+	0.0286647i
$466$	1164.98	+	846.411i	0.115809	+	0.0841400i
$467$	223.419	+	687.614i	0.0221384	+	0.0681348i	0.961515	−	0.274751i	$-0.0885955\pi$
$467$	223.419	+	687.614i	0.0221384	+	0.0681348i	−0.939377	+	0.342886i	$0.888596\pi$
$468$	514.204	+	1582.56i	0.0507887	+	0.156311i
$469$	−784.746	−	570.152i	−0.0772627	−	0.0561347i
$470$	698.991	−	507.846i	0.0686001	−	0.0498409i
$471$	−910.673	+	2802.76i	−0.0890904	+	0.274192i
$472$	−3624.00			−0.353407
$473$		0			0
$474$	−1484.00			−0.143802
$475$	−4158.13	+	12797.4i	−0.401659	+	1.23618i
$476$	1359.15	−	987.479i	0.130875	−	0.0950862i
$477$	1893.10	+	1375.42i	0.181717	+	0.132025i
$478$	−322.614	−	992.903i	−0.0308703	−	0.0950091i
$479$	−2291.67	−	7053.04i	−0.218599	−	0.672780i	−0.998878	−	0.0473481i	$-0.984923\pi$
$479$	−2291.67	−	7053.04i	−0.218599	−	0.672780i	0.780279	−	0.625431i	$-0.215077\pi$
$480$	77.6656	+	56.4274i	0.00738528	+	0.00536572i
$481$	−5294.21	+	3846.47i	−0.501861	+	0.364623i
$482$	−3480.77	+	10712.7i	−0.328931	+	1.01234i
$483$	−1890.00			−0.178050
$484$		0			0
$485$	−2283.00			−0.213744
$486$	1285.51	−	3956.40i	0.119983	−	0.369271i
$487$	5801.46	−	4215.01i	0.539814	−	0.392198i	−0.284202	−	0.958764i	$-0.591729\pi$
$487$	5801.46	−	4215.01i	0.539814	−	0.392198i	0.824016	+	0.566567i	$0.191729\pi$
$488$	−129.443	−	94.0456i	−0.0120074	−	0.00872386i
$489$	102.594	+	315.751i	0.00948762	+	0.0291999i
$490$	450.547	+	1386.64i	0.0415380	+	0.127841i
$491$	9921.78	+	7208.60i	0.911943	+	0.662565i	0.941505	−	0.336998i	$-0.109411\pi$
$491$	9921.78	+	7208.60i	0.911943	+	0.662565i	−0.0295627	+	0.999563i	$0.509411\pi$
$492$	−1514.48	+	1100.33i	−0.138776	+	0.100827i
$493$	−1557.45	+	4793.32i	−0.142280	+	0.437891i
$494$	−3712.00			−0.338078
$495$		0			0
$496$	−2608.00			−0.236094
$497$	1436.93	−	4422.41i	0.129688	−	0.399139i
$498$	−708.699	+	514.900i	−0.0637702	+	0.0463318i
$499$	9594.94	+	6971.13i	0.860779	+	0.625392i	0.928097	−	0.372339i	$-0.121444\pi$
$499$	9594.94	+	6971.13i	0.860779	+	0.625392i	−0.0673180	+	0.997732i	$0.521444\pi$
$500$	893.677	+	2750.46i	0.0799329	+	0.246008i
$501$	593.313	+	1826.03i	0.0529087	+	0.162836i
$502$	10266.4	+	7458.99i	0.912775	+	0.663170i
$503$	−12499.3	+	9081.28i	−1.10799	+	0.804999i	−0.982345	−	0.187077i	$-0.940099\pi$
$503$	−12499.3	+	9081.28i	−1.10799	+	0.804999i	−0.125640	+	0.992076i	$0.540099\pi$
$504$	642.755	−	1978.20i	0.0568067	−	0.174833i
$505$	4734.00			0.417149
$506$		0			0
$507$	−1941.00			−0.170025
$508$	2635.30	−	8110.61i	0.230162	−	0.708366i
$509$	13899.7	−	10098.7i	1.21040	−	0.879408i	0.215134	−	0.976584i	$-0.430981\pi$
$509$	13899.7	−	10098.7i	1.21040	−	0.879408i	0.995267	+	0.0971764i	$0.0309811\pi$
$510$	203.872	+	148.122i	0.0177012	+	0.0128607i
$511$	−2620.46	−	8064.96i	−0.226854	−	0.698186i
$512$	158.217	+	486.941i	0.0136568	+	0.0420312i
$513$	4973.84	+	3613.70i	0.428071	+	0.311012i
$514$	−2417.34	+	1756.30i	−0.207441	+	0.150714i
$515$	−1119.88	+	3446.63i	−0.0958208	+	0.294906i
$516$	440.000			0.0375386
$517$		0			0
$518$	8180.00			0.693839
$519$	613.708	−	1888.80i	0.0519052	−	0.159748i
$520$	−310.663	+	225.710i	−0.0261989	+	0.0190346i
$521$	2235.31	+	1624.05i	0.187967	+	0.136566i	0.677789	−	0.735256i	$-0.262938\pi$
$521$	2235.31	+	1624.05i	0.187967	+	0.136566i	−0.489822	+	0.871822i	$0.662938\pi$
$522$	1928.27	+	5934.59i	0.161682	+	0.497605i
$523$	−238.561	−	734.216i	−0.0199456	−	0.0613862i	0.940588	−	0.339549i	$-0.110274\pi$
$523$	−238.561	−	734.216i	−0.0199456	−	0.0613862i	−0.960534	+	0.278163i	$0.910274\pi$
$524$	−5766.67	−	4189.73i	−0.480760	−	0.349293i
$525$	−938.460	+	681.831i	−0.0780147	+	0.0566810i
$526$	775.015	−	2385.25i	0.0642438	−	0.197722i
$527$	−6846.00			−0.565876
$528$		0			0
$529$	23554.0			1.93589
$530$	−166.869	+	513.571i	−0.0136761	+	0.0420907i
$531$	−9528.60	+	6922.93i	−0.778731	+	0.565781i
$532$	3753.84	+	2727.32i	0.305920	+	0.222264i
$533$	−2313.92	−	7121.51i	−0.188043	−	0.578737i
$534$	−168.723	−	519.277i	−0.0136730	−	0.0420811i
$535$	−3509.52	−	2549.81i	−0.283607	−	0.206052i
$536$	627.797	−	456.121i	0.0505909	−	0.0367564i
$537$	34.3009	−	105.567i	0.00275641	−	0.00848336i
$538$	10884.0			0.872198
$539$		0			0
$540$	636.000			0.0506835
$541$	5991.22	−	18439.1i	0.476123	−	1.46536i	−0.368313	−	0.929702i	$-0.620065\pi$
$541$	5991.22	−	18439.1i	0.476123	−	1.46536i	0.844437	−	0.535655i	$-0.179935\pi$
$542$	−3935.06	+	2858.99i	−0.311855	+	0.226576i
$543$	−727.306	−	528.419i	−0.0574801	−	0.0417617i
$544$	415.319	+	1278.22i	0.0327328	+	0.100741i
$545$	1244.10	+	3828.95i	0.0977826	+	0.300944i
$546$	−258.885	−	188.091i	−0.0202917	−	0.0147428i
$547$	−1268.54	+	921.647i	−0.0991568	+	0.0720417i	−0.636259	−	0.771476i	$-0.719519\pi$
$547$	−1268.54	+	921.647i	−0.0991568	+	0.0720417i	0.537102	+	0.843517i	$0.319519\pi$
$548$	1138.42	−	3503.69i	0.0887424	−	0.273121i
$549$	−520.000			−0.0404245
$550$		0			0
$551$	−13920.0			−1.07625
$552$	467.234	−	1438.00i	0.0360268	−	0.110879i
$553$	−6002.91	+	4361.37i	−0.461609	+	0.335378i
$554$	2695.64	+	1958.50i	0.206727	+	0.150196i
$555$	379.164	+	1166.95i	0.0289993	+	0.0892507i
$556$	1782.41	+	5485.69i	0.135955	+	0.418427i
$557$	3888.14	+	2824.90i	0.295773	+	0.214892i	0.725768	−	0.687940i	$-0.241485\pi$
$557$	3888.14	+	2824.90i	0.295773	+	0.214892i	−0.429995	+	0.902831i	$0.641485\pi$
$558$	−6857.23	+	4982.07i	−0.520232	+	0.377971i
$559$	−543.870	+	1673.86i	−0.0411507	+	0.126649i
$560$	480.000			0.0362209
$561$		0			0
$562$	−6516.00			−0.489076
$563$	3081.52	−	9483.94i	0.230676	−	0.709947i	−0.766990	−	0.641659i	$-0.778246\pi$
$563$	3081.52	−	9483.94i	0.230676	−	0.709947i	0.997666	−	0.0682879i	$-0.0217536\pi$
$564$	−465.994	+	338.564i	−0.0347906	+	0.0252768i
$565$	4274.04	+	3105.27i	0.318248	+	0.231221i
$566$	−4823.14	−	14844.1i	−0.358183	−	1.10237i
$567$	−2005.52	−	6172.36i	−0.148543	−	0.457169i
$568$	3009.54	+	2186.56i	0.222320	+	0.161525i
$569$	368.912	−	268.030i	0.0271803	−	0.0197476i	−0.574112	−	0.818777i	$-0.694653\pi$
$569$	368.912	−	268.030i	0.0271803	−	0.0197476i	0.601292	+	0.799029i	$0.294653\pi$
$570$	−215.076	+	661.935i	−0.0158044	+	0.0486411i
$571$	11132.0			0.815866			0.407933	−	0.913012i	$-0.366250\pi$
$571$	11132.0			0.815866			0.407933	+	0.913012i	$0.366250\pi$
$572$		0			0
$573$	−1509.00			−0.110016
$574$	−2892.40	+	8901.89i	−0.210325	+	0.647313i
$575$	17736.9	−	12886.6i	1.28640	−	0.934624i
$576$	1346.20	+	978.075i	0.0973817	+	0.0707519i
$577$	3602.21	+	11086.5i	0.259899	+	0.799888i	0.992825	+	0.119579i	$0.0381545\pi$
$577$	3602.21	+	11086.5i	0.259899	+	0.799888i	−0.732925	+	0.680309i	$0.761845\pi$
$578$	−1946.19	−	5989.75i	−0.140053	−	0.431040i
$579$	−16.1803	−	11.7557i	−0.00116137	−	0.000843783i
$580$	−1164.98	+	846.411i	−0.0834023	+	0.0605953i
$581$	−1353.49	+	4165.63i	−0.0966479	+	0.297452i
$582$	1522.00			0.108400
$583$		0			0
$584$	6784.00			0.480692
$585$	−385.653	+	1186.92i	−0.0272561	+	0.0838855i
$586$	−19.4164	+	14.1068i	−0.00136874	+	0.000994451i
$587$	12300.3	+	8936.69i	0.864885	+	0.628376i	0.929210	−	0.369553i	$-0.120489\pi$
$587$	12300.3	+	8936.69i	0.864885	+	0.628376i	−0.0643246	+	0.997929i	$0.520489\pi$
$588$	−300.365	−	924.427i	−0.0210660	−	0.0648346i
$589$	−5842.89	−	17982.6i	−0.408747	−	1.25800i
$590$	−2198.91	−	1597.60i	−0.153437	−	0.111478i
$591$	−1014.51	+	737.083i	−0.0706113	+	0.0513021i
$592$	−2022.21	+	6223.71i	−0.140392	+	0.432083i
$593$	−4884.00			−0.338216			−0.169108	−	0.985598i	$-0.554089\pi$
$593$	−4884.00			−0.338216			−0.169108	+	0.985598i	$0.554089\pi$
$594$		0			0
$595$	1260.00			0.0868151
$596$	−2232.34	+	6870.43i	−0.153423	+	0.472188i
$597$	−3792.67	+	2755.54i	−0.260006	+	0.188906i
$598$	4892.93	+	3554.93i	0.334594	+	0.243096i
$599$	6800.85	+	20930.9i	0.463898	+	1.42773i	0.860363	+	0.509682i	$0.170237\pi$
$599$	6800.85	+	20930.9i	0.463898	+	1.42773i	−0.396465	+	0.918050i	$0.629763\pi$
$600$	−286.768	−	882.580i	−0.0195121	−	0.0600520i
$601$	−15796.9	−	11477.1i	−1.07216	−	0.778969i	−0.0958600	−	0.995395i	$-0.530560\pi$
$601$	−15796.9	−	11477.1i	−1.07216	−	0.778969i	−0.976299	+	0.216426i	$0.930560\pi$
$602$	1779.84	−	1293.13i	0.120500	−	0.0875481i
$603$	779.341	−	2398.56i	0.0526322	−	0.161985i
$604$	−5608.00			−0.377792
$605$		0			0
$606$	−3156.00			−0.211557
$607$	1524.69	−	4692.51i	0.101953	−	0.313778i	−0.887051	−	0.461672i	$-0.847250\pi$
$607$	1524.69	−	4692.51i	0.101953	−	0.313778i	0.989003	+	0.147894i	$0.0472496\pi$
$608$	−3003.07	+	2181.86i	−0.200314	+	0.145536i
$609$	−970.820	−	705.342i	−0.0645971	−	0.0469325i
$610$	−37.0820	−	114.127i	−0.00246132	−	0.00757518i
$611$	−711.975	−	2191.23i	−0.0471415	−	0.145086i
$612$	3533.79	+	2567.45i	0.233407	+	0.169580i
$613$	16672.2	−	12113.1i	1.09851	−	0.798112i	0.117691	−	0.993050i	$-0.462451\pi$
$613$	16672.2	−	12113.1i	1.09851	−	0.798112i	0.980816	+	0.194938i	$0.0624507\pi$
$614$	3616.73	−	11131.2i	0.237719	−	0.731624i
$615$	−1404.00			−0.0920565
$616$		0			0
$617$	−7038.00			−0.459221			−0.229610	−	0.973283i	$-0.573745\pi$
$617$	−7038.00			−0.459221			−0.229610	+	0.973283i	$0.573745\pi$
$618$	746.585	−	2297.75i	0.0485956	−	0.149562i
$619$	−11818.9	+	8586.95i	−0.767436	+	0.557575i	−0.901182	−	0.433441i	$-0.857299\pi$
$619$	−11818.9	+	8586.95i	−0.767436	+	0.557575i	0.133746	+	0.991016i	$0.457299\pi$
$620$	−1582.44	−	1149.71i	−0.102504	−	0.0744732i
$621$	−3095.42	−	9526.73i	−0.200024	−	0.615611i
$622$	1639.03	+	5044.40i	0.105657	+	0.325180i
$623$	−2208.62	−	1604.65i	−0.142033	−	0.103193i
$624$	207.108	−	150.473i	0.0132868	−	0.00965343i
$625$	3810.49	−	11727.5i	0.243871	−	0.750559i
$626$	−14306.0			−0.913391
$627$		0			0
$628$	−11788.0			−0.749032
$629$	−5308.29	+	16337.2i	−0.336495	+	1.03563i
$630$	1262.07	−	916.945i	0.0798126	−	0.0579872i
$631$	−12430.5	−	9031.32i	−0.784235	−	0.569780i	0.122012	−	0.992529i	$-0.461065\pi$
$631$	−12430.5	−	9031.32i	−0.784235	−	0.569780i	−0.906247	+	0.422749i	$0.861065\pi$
$632$	−1834.32	−	5645.47i	−0.115452	−	0.355324i
$633$	1504.29	+	4629.74i	0.0944555	+	0.290704i
$634$	−9916.93	−	7205.07i	−0.621217	−	0.451341i
$635$	5174.47	−	3759.47i	0.323374	−	0.234945i
$636$	111.246	−	342.380i	0.00693584	−	0.0213463i
$637$	3888.00			0.241834
$638$		0			0
$639$	12090.0			0.748471
$640$	−118.663	+	365.206i	−0.00732898	+	0.0225563i
$641$	5463.29	−	3969.31i	0.336641	−	0.244584i	−0.406602	−	0.913605i	$-0.633286\pi$
$641$	5463.29	−	3969.31i	0.336641	−	0.244584i	0.743243	+	0.669021i	$0.233286\pi$
$642$	2339.68	+	1699.87i	0.143831	+	0.104500i
$643$	1583.09	+	4872.26i	0.0970935	+	0.298823i	0.987794	−	0.155768i	$-0.0497853\pi$
$643$	1583.09	+	4872.26i	0.0970935	+	0.298823i	−0.890700	+	0.454591i	$0.849785\pi$
$644$	−2336.17	−	7189.99i	−0.142947	−	0.439946i
$645$	266.976	+	193.969i	0.0162979	+	0.0118411i
$646$	−7883.06	+	5727.38i	−0.480116	+	0.348825i
$647$	5585.48	−	17190.3i	0.339394	−	1.04455i	−0.625123	−	0.780526i	$-0.714951\pi$
$647$	5585.48	−	17190.3i	0.339394	−	1.04455i	0.964517	−	0.264021i	$-0.0850489\pi$
$648$	5192.00			0.314755
$649$		0			0
$650$	3712.00			0.223995
$651$	503.698	−	1550.22i	0.0303248	−	0.0933303i
$652$	−1074.37	+	780.579i	−0.0645334	+	0.0468862i
$653$	−12448.3	−	9044.25i	−0.746005	−	0.542004i	0.148581	−	0.988900i	$-0.452529\pi$
$653$	−12448.3	−	9044.25i	−0.746005	−	0.542004i	−0.894586	+	0.446896i	$0.852529\pi$
$654$	−829.402	−	2552.64i	−0.0495905	−	0.152624i
$655$	−1652.00	−	5084.35i	−0.0985484	−	0.303301i
$656$	−6057.92	−	4401.34i	−0.360552	−	0.261956i
$657$	17837.2	−	12959.5i	1.05920	−	0.769555i
$658$	−889.969	+	2739.04i	−0.0527274	+	0.162278i
$659$	24222.0			1.43180			0.715899	−	0.698204i	$-0.246017\pi$
$659$	24222.0			1.43180			0.715899	+	0.698204i	$0.246017\pi$
$660$		0			0
$661$	−12967.0			−0.763022			−0.381511	−	0.924364i	$-0.624596\pi$
$661$	−12967.0			−0.763022			−0.381511	+	0.924364i	$0.624596\pi$
$662$	−508.642	+	1565.44i	−0.0298624	+	0.0919071i
$663$	543.659	−	394.992i	0.0318461	−	0.0231376i
$664$	−2834.80	−	2059.60i	−0.165680	−	0.120373i
$665$	1075.38	+	3309.68i	0.0627089	+	0.192998i
$666$	6572.17	+	20227.1i	0.382382	+	1.17685i
$667$	18348.5	+	13331.0i	1.06515	+	0.773879i
$668$	−6213.25	+	4514.19i	−0.359877	+	0.261466i
$669$	−1440.95	+	4434.78i	−0.0832738	+	0.256291i
$670$	582.000			0.0335591
$671$		0			0
$672$	−320.000			−0.0183694
$673$	5522.13	−	16995.4i	0.316289	−	0.973438i	−0.658931	−	0.752203i	$-0.728991\pi$
$673$	5522.13	−	16995.4i	0.316289	−	0.973438i	0.975221	−	0.221235i	$-0.0710088\pi$
$674$	−8527.04	+	6195.26i	−0.487313	+	0.354054i
$675$	−4973.84	−	3613.70i	−0.283619	−	0.206062i
$676$	−2399.21	−	7384.00i	−0.136505	−	0.420119i
$677$	4010.42	+	12342.8i	0.227671	+	0.700698i	0.998010	+	0.0630636i	$0.0200871\pi$
$677$	4010.42	+	12342.8i	0.227671	+	0.700698i	−0.770339	+	0.637635i	$0.779913\pi$
$678$	−2849.36	−	2070.18i	−0.161400	−	0.117264i
$679$	6156.62	−	4473.05i	0.347967	−	0.252813i
$680$	−311.489	+	958.665i	−0.0175663	+	0.0540634i
$681$	−5862.00			−0.329857
$682$		0			0
$683$	−28488.0			−1.59599			−0.797996	−	0.602662i	$-0.794107\pi$
$683$	−28488.0			−1.59599			−0.797996	+	0.602662i	$0.794107\pi$
$684$	−3727.98	+	11473.5i	−0.208396	+	0.641377i
$685$	2235.31	−	1624.05i	0.124682	−	0.0905865i
$686$	−9481.68	−	6888.84i	−0.527715	−	0.383407i
$687$	1560.84	+	4803.79i	0.0866811	+	0.266777i
$688$	543.870	+	1673.86i	0.0301379	+	0.0927548i
$689$	1164.98	+	846.411i	0.0644156	+	0.0468007i
$690$	917.425	−	666.548i	0.0506171	−	0.0367755i
$691$	5517.50	−	16981.1i	0.303756	−	0.934865i	−0.676382	−	0.736551i	$-0.736453\pi$
$691$	5517.50	−	16981.1i	0.303756	−	0.934865i	0.980138	−	0.198315i	$-0.0635468\pi$
$692$	7944.00			0.436395
$693$		0			0
$694$	13152.0			0.719370
$695$	−1336.81	+	4114.27i	−0.0729612	+	0.224551i
$696$	776.656	−	564.274i	0.0422975	−	0.0307310i
$697$	−15902.0	−	11553.5i	−0.864179	−	0.627863i
$698$	−3884.96	−	11956.7i	−0.210670	−	0.648377i
$699$	−222.492	−	684.761i	−0.0120392	−	0.0370530i
$700$	−3753.84	−	2727.32i	−0.202688	−	0.147262i
$701$	25624.8	−	18617.5i	1.38065	−	1.00310i	0.383831	−	0.923403i	$-0.374605\pi$
$701$	25624.8	−	18617.5i	1.38065	−	1.00310i	0.996819	−	0.0796973i	$-0.0253954\pi$
$702$	524.093	−	1612.99i	0.0281775	−	0.0867214i
$703$	−47444.0			−2.54535
$704$		0			0
$705$	−432.000			−0.0230781
$706$	−6613.58	+	20354.5i	−0.352557	+	1.08506i
$707$	−12766.3	+	9275.25i	−0.679103	+	0.493397i
$708$	1465.94	+	1065.07i	0.0778155	+	0.0565362i
$709$	114.645	+	352.842i	0.00607277	+	0.0186901i	0.954047	−	0.299657i	$-0.0968723\pi$
$709$	114.645	+	352.842i	0.00607277	+	0.0186901i	−0.947974	+	0.318347i	$0.896872\pi$
$710$	862.157	+	2653.45i	0.0455721	+	0.140257i
$711$	−15607.6	−	11339.6i	−0.823248	−	0.598124i
$712$	1766.89	−	1283.72i	0.0930016	−	0.0675696i
$713$	−9519.89	+	29299.2i	−0.500032	+	1.53894i
$714$	−840.000			−0.0440283
$715$		0			0
$716$	444.000			0.0231747
$717$	−161.307	+	496.452i	−0.00840183	+	0.0258582i
$718$	−13475.0	+	9790.15i	−0.700393	+	0.508865i
$719$	−21899.3	−	15910.8i	−1.13589	−	0.825273i	−0.149349	−	0.988785i	$-0.547718\pi$
$719$	−21899.3	−	15910.8i	−1.13589	−	0.825273i	−0.986541	+	0.163512i	$0.947718\pi$
$720$	385.653	+	1186.92i	0.0199617	+	0.0614359i
$721$	−3732.93	−	11488.8i	−0.192817	−	0.593431i
$722$	−10674.2	−	7755.24i	−0.550210	−	0.399751i
$723$	4556.38	−	3310.41i	0.234376	−	0.170284i
$724$	1111.23	−	3420.00i	0.0570419	−	0.175557i
$725$	13920.0			0.713070
$726$		0			0
$727$	−20095.0			−1.02515			−0.512574	−	0.858643i	$-0.671308\pi$
$727$	−20095.0			−1.02515			−0.512574	+	0.858643i	$0.671308\pi$
$728$	395.542	−	1217.35i	0.0201370	−	0.0619754i
$729$	12493.6	−	9077.17i	0.634743	−	0.461168i
$730$	4116.28	+	2990.65i	0.208699	+	0.151629i
$731$	1427.66	+	4393.88i	0.0722351	+	0.222317i
$732$	24.7214	+	76.0845i	0.00124826	+	0.00384176i
$733$	9886.19	+	7182.74i	0.498165	+	0.361938i	0.808316	−	0.588750i	$-0.200380\pi$
$733$	9886.19	+	7182.74i	0.498165	+	0.361938i	−0.310151	+	0.950687i	$0.600380\pi$
$734$	5894.50	−	4282.60i	0.296417	−	0.215359i
$735$	225.273	−	693.320i	0.0113052	−	0.0347939i
$736$	6048.00			0.302897
$737$		0			0
$738$	−24336.0			−1.21385
$739$	−10141.3	+	31211.8i	−0.504810	+	1.55364i	0.296280	+	0.955101i	$0.404254\pi$
$739$	−10141.3	+	31211.8i	−0.504810	+	1.55364i	−0.801090	+	0.598544i	$0.795746\pi$
$740$	−3970.66	+	2884.85i	−0.197249	+	0.143310i
$741$	1501.54	+	1090.93i	0.0744403	+	0.0540841i
$742$	−556.231	−	1711.90i	−0.0275200	−	0.0846980i
$743$	7538.78	+	23202.0i	0.372235	+	1.14562i	0.945325	+	0.326130i	$0.105745\pi$
$743$	7538.78	+	23202.0i	0.372235	+	1.14562i	−0.573089	+	0.819493i	$0.694255\pi$
$744$	1054.96	+	766.472i	0.0519847	+	0.0377691i
$745$	−4383.25	+	3184.62i	−0.215557	+	0.156611i
$746$	−4908.43	+	15106.6i	−0.240898	+	0.741409i
$747$	−11388.0			−0.557785
$748$		0			0
$749$	14460.0			0.705416
$750$	446.839	−	1375.23i	0.0217550	−	0.0669550i
$751$	2010.41	−	1460.65i	0.0976842	−	0.0709717i	−0.537871	−	0.843027i	$-0.680771\pi$
$751$	2010.41	−	1460.65i	0.0976842	−	0.0709717i	0.635555	+	0.772055i	$0.280771\pi$
$752$	−1863.98	−	1354.26i	−0.0903885	−	0.0656711i
$753$	−1960.71	−	6034.45i	−0.0948902	−	0.292042i
$754$	1186.63	+	3652.06i	0.0573135	+	0.176393i
$755$	−3402.73	−	2472.22i	−0.164024	−	0.119170i
$756$	−1715.12	+	1246.10i	−0.0825108	+	0.0599476i
$757$	−4404.73	+	13556.4i	−0.211483	+	0.650878i	0.787902	+	0.615801i	$0.211167\pi$
$757$	−4404.73	+	13556.4i	−0.211483	+	0.650878i	−0.999385	+	0.0350765i	$0.988833\pi$
$758$	−18662.0			−0.894241
$759$		0			0
$760$	−2784.00			−0.132877
$761$	5324.98	−	16388.6i	0.253654	−	0.780666i	−0.740438	−	0.672124i	$-0.765382\pi$
$761$	5324.98	−	16388.6i	0.253654	−	0.780666i	0.994092	−	0.108541i	$-0.0346180\pi$
$762$	−3449.65	+	2506.32i	−0.163999	+	0.119153i
$763$	−10857.0	−	7888.08i	−0.515138	−	0.374269i
$764$	−1865.23	−	5740.58i	−0.0883266	−	0.271841i
$765$	1012.34	+	3115.66i	0.0478447	+	0.147251i
$766$	12509.0	+	9088.34i	0.590038	+	0.428688i
$767$	−5863.76	+	4260.27i	−0.276047	+	0.200560i
$768$	79.1084	−	243.470i	0.00371690	−	0.0114394i
$769$	25520.0			1.19672			0.598358	−	0.801229i	$-0.295820\pi$
$769$	25520.0			1.19672			0.598358	+	0.801229i	$0.295820\pi$
$770$		0			0
$771$	1494.00			0.0697861
$772$	24.7214	−	76.0845i	0.00115251	−	0.00354707i
$773$	−12130.4	+	8813.25i	−0.564425	+	0.410078i	−0.833076	−	0.553159i	$-0.813422\pi$
$773$	−12130.4	+	8813.25i	−0.564425	+	0.410078i	0.268651	+	0.963238i	$0.413422\pi$
$774$	4627.58	+	3362.13i	0.214903	+	0.156136i
$775$	5842.89	+	17982.6i	0.270817	+	0.833488i
$776$	1881.30	+	5790.03i	0.0870291	+	0.267848i
$777$	−3308.88	−	2404.04i	−0.152774	−	0.110997i
$778$	−2363.95	+	1717.51i	−0.108935	+	0.0791461i
$779$	16775.9	−	51631.0i	0.771578	−	2.37467i
$780$	192.000			0.00881372
$781$		0			0
$782$	15876.0			0.725991
$783$	1965.35	−	6048.72i	0.0897009	−	0.276071i
$784$	3145.46	−	2285.31i	0.143288	−	0.104105i
$785$	−7152.52	−	5196.61i	−0.325203	−	0.236274i
$786$	1101.34	+	3389.57i	0.0499788	+	0.153819i
$787$	−10884.8	−	33500.0i	−0.493014	−	1.51734i	−0.820030	−	0.572321i	$-0.806043\pi$
$787$	−10884.8	−	33500.0i	−0.493014	−	1.51734i	0.327016	−	0.945019i	$-0.393957\pi$
$788$	−4058.03	−	2948.33i	−0.183453	−	0.133287i
$789$	−1014.51	+	737.083i	−0.0457762	+	0.0332584i
$790$	1375.74	−	4234.10i	0.0619579	−	0.190687i
$791$	−17610.0			−0.791580
$792$		0			0
$793$	−320.000			−0.0143298
$794$	−3996.21	+	12299.1i	−0.178615	+	0.549720i
$795$	218.435	−	158.702i	0.00974475	−	0.00707998i
$796$	−15170.7	−	11022.1i	−0.675516	−	0.490791i
$797$	5750.50	+	17698.2i	0.255575	+	0.786578i	0.993716	+	0.111932i	$0.0357038\pi$
$797$	5750.50	+	17698.2i	0.255575	+	0.786578i	−0.738141	+	0.674646i	$0.764296\pi$
$798$	−716.919	−	2206.45i	−0.0318028	−	0.0978791i
$799$	−4892.93	−	3554.93i	−0.216645	−	0.157402i
$800$	3003.07	−	2181.86i	0.132718	−	0.0964254i
$801$	2193.40	−	6750.60i	0.0967541	−	0.297779i
$802$	4020.00			0.176996
$803$		0			0
$804$	−388.000			−0.0170195
$805$	1752.13	−	5392.49i	0.0767135	−	0.236100i
$806$	−4219.83	+	3065.89i	−0.184413	+	0.133984i
$807$	−4402.67	−	3198.73i	−0.192046	−	0.139530i
$808$	−3901.03	−	12006.1i	−0.169849	−	0.522741i
$809$	5091.36	+	15669.6i	0.221264	+	0.680982i	0.998649	+	0.0519565i	$0.0165457\pi$
$809$	5091.36	+	15669.6i	0.221264	+	0.680982i	−0.777385	+	0.629025i	$0.783454\pi$
$810$	3150.31	+	2288.84i	0.136655	+	0.0992858i
$811$	2202.14	−	1599.95i	0.0953486	−	0.0692748i	−0.539089	−	0.842248i	$-0.681232\pi$
$811$	2202.14	−	1599.95i	0.0953486	−	0.0692748i	0.634438	+	0.772974i	$0.281232\pi$
$812$	1483.28	−	4565.07i	0.0641047	−	0.197294i
$813$	2432.00			0.104913
$814$		0			0
$815$	−996.000			−0.0428078
$816$	207.659	−	639.110i	0.00890874	−	0.0274183i
$817$	−10323.1	+	7500.14i	−0.442054	+	0.321171i
$818$	20422.8	+	14838.1i	0.872943	+	0.634230i
$819$	−1285.51	−	3956.40i	−0.0548466	−	0.168801i
$820$	−1735.44	−	5341.13i	−0.0739075	−	0.227464i
$821$	14887.5	+	10816.4i	0.632860	+	0.459800i	0.857390	−	0.514667i	$-0.172085\pi$
$821$	14887.5	+	10816.4i	0.632860	+	0.459800i	−0.224530	+	0.974467i	$0.572085\pi$
$822$	−1490.21	+	1082.70i	−0.0632324	+	0.0459410i
$823$	−12287.4	+	37816.9i	−0.520429	+	1.60172i	0.252752	+	0.967531i	$0.418664\pi$
$823$	−12287.4	+	37816.9i	−0.520429	+	1.60172i	−0.773181	+	0.634186i	$0.781336\pi$
$824$	9664.00			0.408570
$825$		0			0
$826$	9060.00			0.381644
$827$	−385.653	+	1186.92i	−0.0162158	+	0.0499071i	−0.958837	−	0.283957i	$-0.908353\pi$
$827$	−385.653	+	1186.92i	−0.0162158	+	0.0499071i	0.942621	+	0.333864i	$0.108353\pi$
$828$	15902.0	−	11553.5i	0.667432	−	0.484918i
$829$	7005.28	+	5089.63i	0.293490	+	0.213233i	0.724780	−	0.688980i	$-0.241941\pi$
$829$	7005.28	+	5089.63i	0.293490	+	0.213233i	−0.431290	+	0.902213i	$0.641941\pi$
$830$	−812.097	−	2499.38i	−0.0339618	−	0.104524i
$831$	−514.822	−	1584.46i	−0.0214910	−	0.0661424i
$832$	828.433	+	601.892i	0.0345201	+	0.0250804i
$833$	8256.83	−	5998.94i	0.343436	−	0.249521i
$834$	891.205	−	2742.85i	0.0370023	−	0.113881i
$835$	−5760.00			−0.238722
$836$		0			0
$837$	8639.00			0.356759
$838$	6786.01	−	20885.2i	0.279736	−	0.860939i
$839$	33388.9	−	24258.5i	1.37391	−	0.998207i	0.376495	−	0.926419i	$-0.377129\pi$
$839$	33388.9	−	24258.5i	1.37391	−	0.998207i	0.997420	−	0.0717885i	$-0.0228707\pi$
$840$	−194.164	−	141.068i	−0.00797535	−	0.00579443i
$841$	−3086.77	−	9500.10i	−0.126564	−	0.389524i
$842$	−332.502	−	1023.34i	−0.0136090	−	0.0418842i
$843$	2635.78	+	1915.00i	0.107688	+	0.0782399i
$844$	−15753.2	+	11445.4i	−0.642472	+	0.466784i
$845$	1799.41	−	5538.00i	0.0732562	−	0.225459i
$846$	−7488.00			−0.304306
$847$		0			0
$848$	1440.00			0.0583134
$849$	−2411.57	+	7422.05i	−0.0974851	+	0.300028i
$850$	7883.06	−	5727.38i	0.318102	−	0.231115i
$851$	62537.8	+	45436.4i	2.51912	+	1.83025i
$852$	−574.772	−	1768.97i	−0.0231119	−	0.0711312i
$853$	679.219	+	2090.42i	0.0272638	+	0.0839094i	0.963763	−	0.266761i	$-0.0859536\pi$
$853$	679.219	+	2090.42i	0.0272638	+	0.0839094i	−0.936499	+	0.350671i	$0.885954\pi$
$854$	323.607	+	235.114i	0.0129667	+	0.00942089i
$855$	−7319.99	+	5318.28i	−0.292793	+	0.212727i
$856$	−3574.71	+	11001.8i	−0.142735	+	0.439293i
$857$	27192.0			1.08385			0.541926	−	0.840426i	$-0.317695\pi$
$857$	27192.0			1.08385			0.541926	+	0.840426i	$0.317695\pi$
$858$		0			0
$859$	27095.0			1.07622			0.538108	−	0.842876i	$-0.319139\pi$
$859$	27095.0			1.07622			0.538108	+	0.842876i	$0.319139\pi$
$860$	−407.902	+	1255.39i	−0.0161737	+	0.0497774i
$861$	3786.20	−	2750.83i	0.149865	−	0.108883i
$862$	−8125.77	−	5903.72i	−0.321073	−	0.233273i
$863$	−4946.74	−	15224.5i	−0.195121	−	0.600520i	−0.999975	−	0.00704746i	$-0.997757\pi$
$863$	−4946.74	−	15224.5i	−0.195121	−	0.600520i	0.804855	−	0.593472i	$-0.202243\pi$
$864$	−524.093	−	1612.99i	−0.0206366	−	0.0635128i
$865$	4820.12	+	3502.02i	0.189467	+	0.137656i
$866$	4185.85	−	3041.20i	0.164251	−	0.119335i
$867$	−973.095	+	2994.88i	−0.0381177	+	0.117314i
$868$	6520.00			0.254958
$869$		0			0
$870$	720.000			0.0280578
$871$	479.594	−	1476.04i	0.0186572	−	0.0574210i
$872$	8685.61	−	6310.46i	0.337307	−	0.245068i
$873$	16007.2	+	11629.9i	0.620575	+	0.450874i
$874$	13549.8	+	41701.9i	0.524403	+	1.61395i
$875$	−2234.19	−	6876.14i	−0.0863194	−	0.265664i
$876$	−2744.19	−	1993.77i	−0.105842	−	0.0768986i
$877$	−18141.4	+	13180.5i	−0.698508	+	0.507496i	−0.879446	−	0.475999i	$-0.842087\pi$
$877$	−18141.4	+	13180.5i	−0.698508	+	0.507496i	0.180938	+	0.983495i	$0.442087\pi$
$878$	435.096	−	1339.09i	0.0167241	−	0.0514715i
$879$	12.0000			0.000460466
$880$		0			0
$881$	−11427.0			−0.436987			−0.218493	−	0.975838i	$-0.570114\pi$
$881$	−11427.0			−0.436987			−0.218493	+	0.975838i	$0.570114\pi$
$882$	3904.74	−	12017.6i	0.149070	−	0.458789i
$883$	−24286.7	+	17645.3i	−0.925608	+	0.672494i	−0.944914	−	0.327320i	$-0.893855\pi$
$883$	−24286.7	+	17645.3i	−0.925608	+	0.672494i	0.0193052	+	0.999814i	$0.493855\pi$
$884$	2174.64	+	1579.97i	0.0827387	+	0.0601132i
$885$	419.954	+	1292.49i	0.0159510	+	0.0490920i
$886$	2597.60	+	7994.58i	0.0984966	+	0.303141i
$887$	−9674.23	−	7028.74i	−0.366210	−	0.266067i	0.389427	−	0.921057i	$-0.372673\pi$
$887$	−9674.23	−	7028.74i	−0.366210	−	0.266067i	−0.755638	+	0.654990i	$0.772673\pi$
$888$	2647.10	−	1923.23i	0.100035	−	0.0726796i
$889$	−6588.24	+	20276.5i	−0.248552	+	0.764964i
$890$	1638.00			0.0616920
$891$		0			0
$892$	−18652.0			−0.700129
$893$	5161.82	−	15886.4i	0.193431	−	0.595319i
$894$	2922.17	−	2123.08i	0.109320	−	0.0794255i
$895$	269.403	+	195.732i	0.0100616	+	0.00731018i
$896$	−395.542	−	1217.35i	−0.0147479	−	0.0453894i
$897$	−934.467	−	2875.99i	−0.0347837	−	0.107053i
$898$	1509.63	+	1096.81i	0.0560990	+	0.0407583i
$899$	−15824.4	+	11497.1i	−0.587066	+	0.426528i
$900$	3727.98	−	11473.5i	0.138073	−	0.424946i
$901$	3780.00			0.139767
$902$		0			0
$903$	−1100.00			−0.0405379
$904$	4353.43	−	13398.5i	0.160169	−	0.492950i
$905$	2181.92	−	1585.26i	0.0801430	−	0.0582273i
$906$	2268.48	+	1648.15i	0.0831847	+	0.0604372i
$907$	−4035.76	−	12420.8i	−0.147746	−	0.454714i	0.849608	−	0.527414i	$-0.176838\pi$
$907$	−4035.76	−	12420.8i	−0.147746	−	0.454714i	−0.997354	+	0.0727001i	$0.976838\pi$
$908$	−7245.83	−	22300.4i	−0.264825	−	0.815048i
$909$	−33192.3	−	24115.7i	−1.21113	−	0.879940i
$910$	776.656	−	564.274i	0.0282922	−	0.0205555i
$911$	3148.27	−	9689.36i	0.114497	−	0.352385i	−0.877345	−	0.479860i	$-0.840687\pi$
$911$	3148.27	−	9689.36i	0.114497	−	0.352385i	0.991842	+	0.127475i	$0.0406873\pi$
$912$	1856.00			0.0673885
$913$		0			0
$914$	20632.0			0.746659
$915$	−18.5410	+	57.0634i	−0.000669888	+	0.00206170i
$916$	−16345.4	+	11875.6i	−0.589592	+	0.428364i
$917$	14416.7	+	10474.3i	0.519172	+	0.377201i
$918$	−1375.74	−	4234.10i	−0.0494622	−	0.152229i
$919$	−13515.8	−	41597.3i	−0.485141	−	1.49311i	−0.831776	−	0.555111i	$-0.812676\pi$
$919$	−13515.8	−	41597.3i	−0.485141	−	1.49311i	0.346635	−	0.938000i	$-0.387324\pi$
$920$	3669.70	+	2666.19i	0.131507	+	0.0955454i
$921$	−4734.37	+	3439.72i	−0.169384	+	0.123065i
$922$	81.5805	−	251.079i	0.00291400	−	0.00896838i
$923$	7440.00			0.265320
$924$		0			0
$925$	47444.0			1.68643
$926$	4834.88	−	14880.2i	0.171581	−	0.528072i
$927$	25409.6	−	18461.2i	0.900281	−	0.654093i
$928$	3106.63	+	2257.10i	0.109892	+	0.0798414i
$929$	−5089.51	−	15663.9i	−0.179743	−	0.553193i	0.820075	−	0.572256i	$-0.193932\pi$
$929$	−5089.51	−	15663.9i	−0.179743	−	0.553193i	−0.999818	+	0.0190633i	$0.993932\pi$
$930$	302.219	+	930.133i	0.0106561	+	0.0327960i
$931$	22804.6	+	16568.5i	0.802782	+	0.583255i
$932$	2329.97	−	1692.82i	0.0818891	−	0.0594959i
$933$	819.513	−	2522.20i	0.0287563	−	0.0885029i
$934$	1446.00			0.0506580
$935$		0			0
$936$	3328.00			0.116217
$937$	7378.09	−	22707.4i	0.257238	−	0.791696i	−0.736143	−	0.676826i	$-0.763355\pi$
$937$	7378.09	−	22707.4i	0.257238	−	0.791696i	0.993381	−	0.114870i	$-0.0366451\pi$
$938$	−1569.49	+	1140.30i	−0.0546330	+	0.0396932i
$939$	5786.90	+	4204.43i	0.201116	+	0.146120i
$940$	−533.981	−	1643.43i	−0.0185282	−	0.0570241i
$941$	6865.74	+	21130.6i	0.237850	+	0.732027i	0.996731	+	0.0807969i	$0.0257465\pi$
$941$	6865.74	+	21130.6i	0.237850	+	0.732027i	−0.758881	+	0.651230i	$0.774253\pi$
$942$	4768.35	+	3464.41i	0.164927	+	0.119826i
$943$	−71559.2	+	51990.8i	−2.47114	+	1.79539i
$944$	−2239.76	+	6893.26i	−0.0772223	+	0.237666i
$945$	−1590.00			−0.0547330
$946$		0			0
$947$	−9909.00			−0.340020			−0.170010	−	0.985442i	$-0.554380\pi$
$947$	−9909.00			−0.340020			−0.170010	+	0.985442i	$0.554380\pi$
$948$	−917.162	+	2822.74i	−0.0314220	+	0.0967070i
$949$	10976.7	−	7975.07i	0.375469	−	0.272794i
$950$	21772.3	+	15818.5i	0.743564	+	0.540231i
$951$	1893.97	+	5829.03i	0.0645805	+	0.198758i
$952$	−1038.30	−	3195.55i	−0.0353481	−	0.108790i
$953$	37099.9	+	26954.7i	1.26105	+	0.916209i	0.998809	−	0.0487928i	$-0.0155374\pi$
$953$	37099.9	+	26954.7i	1.26105	+	0.916209i	0.262244	+	0.965002i	$0.415537\pi$
$954$	3786.20	−	2750.83i	0.128493	−	0.0933559i
$955$	1398.92	−	4305.43i	0.0474010	−	0.145885i
$956$	−2088.00			−0.0706389
$957$		0			0
$958$	−14832.0			−0.500209
$959$	−2846.05	+	8759.23i	−0.0958328	+	0.294943i
$960$	155.331	−	112.855i	0.00522218	−	0.00379414i
$961$	2606.65	+	1893.84i	0.0874980	+	0.0635710i
$962$	4044.41	+	12447.4i	0.135548	+	0.417174i
$963$	11617.8	+	35755.9i	0.388763	+	1.19649i
$964$	18225.5	+	13241.6i	0.608926	+	0.442411i
$965$	48.5410	−	35.2671i	0.00161926	−	0.00117646i
$966$	−1168.08	+	3594.99i	−0.0389053	+	0.119738i
$967$	−33352.0			−1.10913			−0.554565	−	0.832141i	$-0.687115\pi$
$967$	−33352.0			−1.10913			−0.554565	+	0.832141i	$0.687115\pi$
$968$		0			0
$969$	4872.00			0.161518
$970$	−1410.97	+	4342.52i	−0.0467047	+	0.143742i
$971$	−30471.6	+	22138.9i	−1.00709	+	0.731691i	−0.963596	−	0.267363i	$-0.913848\pi$
$971$	−30471.6	+	22138.9i	−1.00709	+	0.731691i	−0.0434905	+	0.999054i	$0.513848\pi$
$972$	−6731.02	−	4890.37i	−0.222117	−	0.161377i
$973$	−4456.03	−	13714.2i	−0.146818	−	0.451858i
$974$	−4431.92	−	13640.1i	−0.145799	−	0.448722i
$975$	−1501.54	−	1090.93i	−0.0493206	−	0.0358335i
$976$	−258.885	+	188.091i	−0.00849049	+	0.00616870i
$977$	−11036.5	+	33967.0i	−0.361403	+	1.11228i	0.590801	+	0.806817i	$0.298812\pi$
$977$	−11036.5	+	33967.0i	−0.361403	+	1.11228i	−0.952203	+	0.305465i	$0.901188\pi$
$978$	664.000			0.0217100
$979$		0			0
$980$	2916.00			0.0950492
$981$	10782.2	−	33184.3i	0.350917	−	1.08001i
$982$	19843.6	−	14417.2i	0.644841	−	0.468504i
$983$	−4812.84	−	3496.73i	−0.156161	−	0.113457i	0.506961	−	0.861969i	$-0.330769\pi$
$983$	−4812.84	−	3496.73i	−0.156161	−	0.113457i	−0.663122	+	0.748512i	$0.730769\pi$
$984$	1156.96	+	3560.76i	0.0374822	+	0.115358i
$985$	−1162.52	−	3577.87i	−0.0376051	−	0.115737i
$986$	8154.89	+	5924.88i	0.263392	+	0.191366i
$987$	1164.98	−	846.411i	0.0375703	−	0.0272964i
$988$	−2294.14	+	7060.64i	−0.0738729	+	0.227357i
$989$	20790.0			0.668436
$990$		0			0
$991$	−23560.0			−0.755205			−0.377602	−	0.925968i	$-0.623251\pi$
$991$	−23560.0			−0.755205			−0.377602	+	0.925968i	$0.623251\pi$
$992$	−1611.83	+	4960.71i	−0.0515884	+	0.158773i
$993$	665.821	−	483.747i	0.0212781	−	0.0154595i
$994$	−7523.86	−	5466.40i	−0.240083	−	0.174430i
$995$	−4346.02	−	13375.7i	−0.138470	−	0.426168i
$996$	541.398	+	1666.25i	0.0172237	+	0.0530092i
$997$	−21670.3	−	15744.4i	−0.688371	−	0.500131i	0.187753	−	0.982216i	$-0.439880\pi$
$997$	−21670.3	−	15744.4i	−0.688371	−	0.500131i	−0.876124	+	0.482085i	$0.839880\pi$
$998$	19189.9	−	13942.3i	0.608662	−	0.442219i
$999$	6698.56	−	20616.1i	0.212145	−	0.652916i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	242.4.c.d.9.1		4
11.2	odd	10		242.4.c.k.3.1		4
11.3	even	5	inner	242.4.c.d.81.1		4
11.4	even	5		22.4.a.c.1.1	✓	1
11.5	even	5	inner	242.4.c.d.27.1		4
11.6	odd	10		242.4.c.k.27.1		4
11.7	odd	10		242.4.a.a.1.1		1
11.8	odd	10		242.4.c.k.81.1		4
11.9	even	5	inner	242.4.c.d.3.1		4
11.10	odd	2		242.4.c.k.9.1		4
33.26	odd	10		198.4.a.b.1.1		1
33.29	even	10		2178.4.a.r.1.1		1
44.7	even	10		1936.4.a.h.1.1		1
44.15	odd	10		176.4.a.c.1.1		1
55.4	even	10		550.4.a.e.1.1		1
55.37	odd	20		550.4.b.g.199.2		2
55.48	odd	20		550.4.b.g.199.1		2
77.48	odd	10		1078.4.a.f.1.1		1
88.37	even	10		704.4.a.e.1.1		1
88.59	odd	10		704.4.a.g.1.1		1
132.59	even	10		1584.4.a.k.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.4.a.c.1.1	✓	1	11.4	even	5
176.4.a.c.1.1		1	44.15	odd	10
198.4.a.b.1.1		1	33.26	odd	10
242.4.a.a.1.1		1	11.7	odd	10
242.4.c.d.3.1		4	11.9	even	5	inner
242.4.c.d.9.1		4	1.1	even	1	trivial
242.4.c.d.27.1		4	11.5	even	5	inner
242.4.c.d.81.1		4	11.3	even	5	inner
242.4.c.k.3.1		4	11.2	odd	10
242.4.c.k.9.1		4	11.10	odd	2
242.4.c.k.27.1		4	11.6	odd	10
242.4.c.k.81.1		4	11.8	odd	10
550.4.a.e.1.1		1	55.4	even	10
550.4.b.g.199.1		2	55.48	odd	20
550.4.b.g.199.2		2	55.37	odd	20
704.4.a.e.1.1		1	88.37	even	10
704.4.a.g.1.1		1	88.59	odd	10
1078.4.a.f.1.1		1	77.48	odd	10
1584.4.a.k.1.1		1	132.59	even	10
1936.4.a.h.1.1		1	44.7	even	10
2178.4.a.r.1.1		1	33.29	even	10

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:	\( N \)	\(=\)	\( 242 = 2 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	242.c (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.618034 - 1.90211i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-3.23607 - 2.35114i) q^{4} +(-0.927051 - 2.85317i) q^{5} +(0.618034 + 1.90211i) q^{6} +(8.09017 + 5.87785i) q^{7} +(-6.47214 + 4.70228i) q^{8} +(-8.03444 + 24.7275i) q^{9} +O(q^{10})\)	\(q+(0.618034 - 1.90211i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-3.23607 - 2.35114i) q^{4} +(-0.927051 - 2.85317i) q^{5} +(0.618034 + 1.90211i) q^{6} +(8.09017 + 5.87785i) q^{7} +(-6.47214 + 4.70228i) q^{8} +(-8.03444 + 24.7275i) q^{9} -6.00000 q^{10} +4.00000 q^{12} +(-4.94427 + 15.2169i) q^{13} +(16.1803 - 11.7557i) q^{14} +(2.42705 + 1.76336i) q^{15} +(4.94427 + 15.2169i) q^{16} +(12.9787 + 39.9444i) q^{17} +(42.0689 + 30.5648i) q^{18} +(-93.8460 + 68.1831i) q^{19} +(-3.70820 + 11.4127i) q^{20} -10.0000 q^{21} +189.000 q^{23} +(2.47214 - 7.60845i) q^{24} +(93.8460 - 68.1831i) q^{25} +(25.8885 + 18.8091i) q^{26} +(-16.3779 - 50.4060i) q^{27} +(-12.3607 - 38.0423i) q^{28} +(97.0820 + 70.5342i) q^{29} +(4.85410 - 3.52671i) q^{30} +(-50.3698 + 155.022i) q^{31} +32.0000 q^{32} +84.0000 q^{34} +(9.27051 - 28.5317i) q^{35} +(84.1378 - 61.1297i) q^{36} +(330.888 + 240.404i) q^{37} +(71.6919 + 220.645i) q^{38} +(-4.94427 - 15.2169i) q^{39} +(19.4164 + 14.1068i) q^{40} +(-378.620 + 275.083i) q^{41} +(-6.18034 + 19.0211i) q^{42} +110.000 q^{43} +78.0000 q^{45} +(116.808 - 359.499i) q^{46} +(-116.498 + 84.6411i) q^{47} +(-12.9443 - 9.40456i) q^{48} +(-75.0911 - 231.107i) q^{49} +(-71.6919 - 220.645i) q^{50} +(-33.9787 - 24.6870i) q^{51} +(51.7771 - 37.6183i) q^{52} +(27.8115 - 85.5951i) q^{53} -106.000 q^{54} -80.0000 q^{56} +(35.8460 - 110.323i) q^{57} +(194.164 - 141.068i) q^{58} +(366.485 + 266.267i) q^{59} +(-3.70820 - 11.4127i) q^{60} +(6.18034 + 19.0211i) q^{61} +(263.740 + 191.618i) q^{62} +(-210.344 + 152.824i) q^{63} +(19.7771 - 60.8676i) q^{64} +48.0000 q^{65} -97.0000 q^{67} +(51.9149 - 159.777i) q^{68} +(-152.904 + 111.091i) q^{69} +(-48.5410 - 35.2671i) q^{70} +(-143.693 - 442.241i) q^{71} +(-64.2755 - 197.820i) q^{72} +(-686.046 - 498.442i) q^{73} +(661.776 - 480.808i) q^{74} +(-35.8460 + 110.323i) q^{75} +464.000 q^{76} -32.0000 q^{78} +(-229.291 + 705.684i) q^{79} +(38.8328 - 28.2137i) q^{80} +(-525.052 - 381.473i) q^{81} +(289.240 + 890.189i) q^{82} +(135.349 + 416.563i) q^{83} +(32.3607 + 23.5114i) q^{84} +(101.936 - 74.0609i) q^{85} +(67.9837 - 209.232i) q^{86} -120.000 q^{87} -273.000 q^{89} +(48.2067 - 148.365i) q^{90} +(-129.443 + 94.0456i) q^{91} +(-611.617 - 444.366i) q^{92} +(-50.3698 - 155.022i) q^{93} +(88.9969 + 273.904i) q^{94} +(281.538 + 204.549i) q^{95} +(-25.8885 + 18.8091i) q^{96} +(235.162 - 723.754i) q^{97} -486.000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - q^{3} - 4 q^{4} + 3 q^{5} - 2 q^{6} + 10 q^{7} - 8 q^{8} + 26 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - q^3 - 4 * q^4 + 3 * q^5 - 2 * q^6 + 10 * q^7 - 8 * q^8 + 26 * q^9	\( 4 q - 2 q^{2} - q^{3} - 4 q^{4} + 3 q^{5} - 2 q^{6} + 10 q^{7} - 8 q^{8} + 26 q^{9} - 24 q^{10} + 16 q^{12} + 16 q^{13} + 20 q^{14} + 3 q^{15} - 16 q^{16} - 42 q^{17} + 52 q^{18} - 116 q^{19} + 12 q^{20} - 40 q^{21} + 756 q^{23} - 8 q^{24} + 116 q^{25} + 32 q^{26} + 53 q^{27} + 40 q^{28} + 120 q^{29} + 6 q^{30} + 163 q^{31} + 128 q^{32} + 336 q^{34} - 30 q^{35} + 104 q^{36} + 409 q^{37} - 232 q^{38} + 16 q^{39} + 24 q^{40} - 468 q^{41} + 20 q^{42} + 440 q^{43} + 312 q^{45} - 378 q^{46} - 144 q^{47} - 16 q^{48} + 243 q^{49} + 232 q^{50} - 42 q^{51} + 64 q^{52} - 90 q^{53} - 424 q^{54} - 320 q^{56} - 116 q^{57} + 240 q^{58} + 453 q^{59} + 12 q^{60} - 20 q^{61} + 326 q^{62} - 260 q^{63} - 64 q^{64} + 192 q^{65} - 388 q^{67} - 168 q^{68} - 189 q^{69} - 60 q^{70} + 465 q^{71} + 208 q^{72} - 848 q^{73} + 818 q^{74} + 116 q^{75} + 1856 q^{76} - 128 q^{78} + 742 q^{79} + 48 q^{80} - 649 q^{81} - 936 q^{82} - 438 q^{83} + 40 q^{84} + 126 q^{85} - 220 q^{86} - 480 q^{87} - 1092 q^{89} - 156 q^{90} - 160 q^{91} - 756 q^{92} + 163 q^{93} - 288 q^{94} + 348 q^{95} - 32 q^{96} - 761 q^{97} - 1944 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - q^3 - 4 * q^4 + 3 * q^5 - 2 * q^6 + 10 * q^7 - 8 * q^8 + 26 * q^9 - 24 * q^10 + 16 * q^12 + 16 * q^13 + 20 * q^14 + 3 * q^15 - 16 * q^16 - 42 * q^17 + 52 * q^18 - 116 * q^19 + 12 * q^20 - 40 * q^21 + 756 * q^23 - 8 * q^24 + 116 * q^25 + 32 * q^26 + 53 * q^27 + 40 * q^28 + 120 * q^29 + 6 * q^30 + 163 * q^31 + 128 * q^32 + 336 * q^34 - 30 * q^35 + 104 * q^36 + 409 * q^37 - 232 * q^38 + 16 * q^39 + 24 * q^40 - 468 * q^41 + 20 * q^42 + 440 * q^43 + 312 * q^45 - 378 * q^46 - 144 * q^47 - 16 * q^48 + 243 * q^49 + 232 * q^50 - 42 * q^51 + 64 * q^52 - 90 * q^53 - 424 * q^54 - 320 * q^56 - 116 * q^57 + 240 * q^58 + 453 * q^59 + 12 * q^60 - 20 * q^61 + 326 * q^62 - 260 * q^63 - 64 * q^64 + 192 * q^65 - 388 * q^67 - 168 * q^68 - 189 * q^69 - 60 * q^70 + 465 * q^71 + 208 * q^72 - 848 * q^73 + 818 * q^74 + 116 * q^75 + 1856 * q^76 - 128 * q^78 + 742 * q^79 + 48 * q^80 - 649 * q^81 - 936 * q^82 - 438 * q^83 + 40 * q^84 + 126 * q^85 - 220 * q^86 - 480 * q^87 - 1092 * q^89 - 156 * q^90 - 160 * q^91 - 756 * q^92 + 163 * q^93 - 288 * q^94 + 348 * q^95 - 32 * q^96 - 761 * q^97 - 1944 * q^98

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