LMFDB - Embedded newform 930.4.d.c.559.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,4,Mod(559,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("930.559");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	930.d (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:	$54.8717763053$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 2763 x^{18} + 2652899 x^{16} + 1161420105 x^{14} + 247831438280 x^{12} + 26461073949176 x^{10} + \cdots + 34\!\cdots\!00 $ x^20 + 2763x^18 + 2652899x^16 + 1161420105x^14 + 247831438280x^12 + 26461073949176x^10 + 1433368340491408x^8 + 37536884921183444x^6 + 414170668954972900x^4 + 1987578737873500000*x^2 + 3460065015625000000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			559.8
Root			$9.07744i$ of defining polynomial
Character	$\chi$	$=$	930.559
Dual form			930.4.d.c.559.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} +3.00000i q^{3} -4.00000 q^{4} +(4.77279 - 10.1104i) q^{5} +6.00000 q^{6} +9.07744i q^{7} +8.00000i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} +3.00000i q^{3} -4.00000 q^{4} +(4.77279 - 10.1104i) q^{5} +6.00000 q^{6} +9.07744i q^{7} +8.00000i q^{8} -9.00000 q^{9} +(-20.2208 - 9.54558i) q^{10} -32.1292 q^{11} -12.0000i q^{12} -7.13775i q^{13} +18.1549 q^{14} +(30.3312 + 14.3184i) q^{15} +16.0000 q^{16} -54.1508i q^{17} +18.0000i q^{18} +51.5597 q^{19} +(-19.0912 + 40.4417i) q^{20} -27.2323 q^{21} +64.2584i q^{22} +104.764i q^{23} -24.0000 q^{24} +(-79.4409 - 96.5098i) q^{25} -14.2755 q^{26} -27.0000i q^{27} -36.3098i q^{28} -75.8981 q^{29} +(28.6368 - 60.6625i) q^{30} -31.0000 q^{31} -32.0000i q^{32} -96.3876i q^{33} -108.302 q^{34} +(91.7767 + 43.3247i) q^{35} +36.0000 q^{36} +315.458i q^{37} -103.119i q^{38} +21.4133 q^{39} +(80.8833 + 38.1823i) q^{40} +157.366 q^{41} +54.4646i q^{42} +235.193i q^{43} +128.517 q^{44} +(-42.9551 + 90.9937i) q^{45} +209.529 q^{46} +482.605i q^{47} +48.0000i q^{48} +260.600 q^{49} +(-193.020 + 158.882i) q^{50} +162.452 q^{51} +28.5510i q^{52} -644.559i q^{53} -54.0000 q^{54} +(-153.346 + 324.839i) q^{55} -72.6195 q^{56} +154.679i q^{57} +151.796i q^{58} -833.942 q^{59} +(-121.325 - 57.2735i) q^{60} +113.206 q^{61} +62.0000i q^{62} -81.6969i q^{63} -64.0000 q^{64} +(-72.1656 - 34.0670i) q^{65} -192.775 q^{66} +45.7825i q^{67} +216.603i q^{68} -314.293 q^{69} +(86.6494 - 183.553i) q^{70} -874.495 q^{71} -72.0000i q^{72} +249.978i q^{73} +630.916 q^{74} +(289.529 - 238.323i) q^{75} -206.239 q^{76} -291.651i q^{77} -42.8265i q^{78} +1108.39 q^{79} +(76.3647 - 161.767i) q^{80} +81.0000 q^{81} -314.731i q^{82} +794.792i q^{83} +108.929 q^{84} +(-547.487 - 258.450i) q^{85} +470.387 q^{86} -227.694i q^{87} -257.033i q^{88} -1035.00 q^{89} +(181.987 + 85.9103i) q^{90} +64.7925 q^{91} -419.057i q^{92} -93.0000i q^{93} +965.211 q^{94} +(246.083 - 521.289i) q^{95} +96.0000 q^{96} +904.411i q^{97} -521.200i q^{98} +289.163 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 80 q^{4} - 2 q^{5} + 120 q^{6} - 180 q^{9}+O(q^{10}) $ 20 * q - 80 * q^4 - 2 * q^5 + 120 * q^6 - 180 * q^9	$ 20 q - 80 q^{4} - 2 q^{5} + 120 q^{6} - 180 q^{9} + 8 q^{10} - 114 q^{11} + 52 q^{14} - 12 q^{15} + 320 q^{16} + 370 q^{19} + 8 q^{20} - 78 q^{21} - 480 q^{24} - 90 q^{25} - 368 q^{26} + 368 q^{29} - 12 q^{30} - 620 q^{31} + 712 q^{34} + 374 q^{35} + 720 q^{36} + 552 q^{39} - 32 q^{40} - 872 q^{41} + 456 q^{44} + 18 q^{45} - 1236 q^{46} + 1334 q^{49} + 416 q^{50} - 1068 q^{51} - 1080 q^{54} - 1290 q^{55} - 208 q^{56} + 3228 q^{59} + 48 q^{60} - 2604 q^{61} - 1280 q^{64} + 44 q^{65} - 684 q^{66} + 1854 q^{69} - 852 q^{70} - 2290 q^{71} + 2008 q^{74} - 624 q^{75} - 1480 q^{76} + 4342 q^{79} - 32 q^{80} + 1620 q^{81} + 312 q^{84} + 500 q^{85} - 4 q^{86} + 1390 q^{89} - 72 q^{90} - 5744 q^{91} + 2608 q^{94} - 1136 q^{95} + 1920 q^{96} + 1026 q^{99}+O(q^{100}) $ 20 * q - 80 * q^4 - 2 * q^5 + 120 * q^6 - 180 * q^9 + 8 * q^10 - 114 * q^11 + 52 * q^14 - 12 * q^15 + 320 * q^16 + 370 * q^19 + 8 * q^20 - 78 * q^21 - 480 * q^24 - 90 * q^25 - 368 * q^26 + 368 * q^29 - 12 * q^30 - 620 * q^31 + 712 * q^34 + 374 * q^35 + 720 * q^36 + 552 * q^39 - 32 * q^40 - 872 * q^41 + 456 * q^44 + 18 * q^45 - 1236 * q^46 + 1334 * q^49 + 416 * q^50 - 1068 * q^51 - 1080 * q^54 - 1290 * q^55 - 208 * q^56 + 3228 * q^59 + 48 * q^60 - 2604 * q^61 - 1280 * q^64 + 44 * q^65 - 684 * q^66 + 1854 * q^69 - 852 * q^70 - 2290 * q^71 + 2008 * q^74 - 624 * q^75 - 1480 * q^76 + 4342 * q^79 - 32 * q^80 + 1620 * q^81 + 312 * q^84 + 500 * q^85 - 4 * q^86 + 1390 * q^89 - 72 * q^90 - 5744 * q^91 + 2608 * q^94 - 1136 * q^95 + 1920 * q^96 + 1026 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		−	2.00000i		−	0.707107i
$2$		−	2.00000i		−	0.707107i
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	−4.00000			−0.500000
$5$	4.77279	−	10.1104i	0.426891	−	0.904303i
$5$	4.77279	−	10.1104i	0.426891	−	0.904303i
$6$	6.00000			0.408248
$7$			9.07744i			0.490136i	0.969506	+	0.245068i	$0.0788102\pi$
$7$			9.07744i			0.490136i	−0.969506	+	0.245068i	$0.921190\pi$
$8$			8.00000i			0.353553i
$9$	−9.00000			−0.333333
$10$	−20.2208	−	9.54558i	−0.639439	−	0.301858i
$11$	−32.1292			−0.880665			−0.440332	−	0.897835i	$-0.645139\pi$
$11$	−32.1292			−0.880665			−0.440332	+	0.897835i	$0.645139\pi$
$12$		−	12.0000i		−	0.288675i
$13$		−	7.13775i		−	0.152281i	−0.997097	−	0.0761406i	$-0.975740\pi$
$13$		−	7.13775i		−	0.152281i	0.997097	−	0.0761406i	$-0.0242598\pi$
$14$	18.1549			0.346578
$15$	30.3312	+	14.3184i	0.522099	+	0.246466i
$16$	16.0000			0.250000
$17$		−	54.1508i		−	0.772559i	−0.922382	−	0.386279i	$-0.873760\pi$
$17$		−	54.1508i		−	0.772559i	0.922382	−	0.386279i	$-0.126240\pi$
$18$			18.0000i			0.235702i
$19$	51.5597			0.622558			0.311279	−	0.950319i	$-0.399243\pi$
$19$	51.5597			0.622558			0.311279	+	0.950319i	$0.399243\pi$
$20$	−19.0912	+	40.4417i	−0.213446	+	0.452151i
$21$	−27.2323			−0.282980
$22$			64.2584i			0.622724i
$23$			104.764i			0.949777i	0.880046	+	0.474889i	$0.157512\pi$
$23$			104.764i			0.949777i	−0.880046	+	0.474889i	$0.842488\pi$
$24$	−24.0000			−0.204124
$25$	−79.4409	−	96.5098i	−0.635527	−	0.772078i
$26$	−14.2755			−0.107679
$27$		−	27.0000i		−	0.192450i
$28$		−	36.3098i		−	0.245068i
$29$	−75.8981			−0.485997			−0.242999	−	0.970027i	$-0.578131\pi$
$29$	−75.8981			−0.485997			−0.242999	+	0.970027i	$0.578131\pi$
$30$	28.6368	−	60.6625i	0.174278	−	0.369180i
$31$	−31.0000			−0.179605
$31$	−31.0000			−0.179605
$32$		−	32.0000i		−	0.176777i
$33$		−	96.3876i		−	0.508452i
$34$	−108.302			−0.546281
$35$	91.7767	+	43.3247i	0.443231	+	0.209235i
$36$	36.0000			0.166667
$37$			315.458i			1.40165i	0.713335	+	0.700823i	$0.247184\pi$
$37$			315.458i			1.40165i	−0.713335	+	0.700823i	$0.752816\pi$
$38$		−	103.119i		−	0.440215i
$39$	21.4133			0.0879196
$40$	80.8833	+	38.1823i	0.319719	+	0.150929i
$41$	157.366			0.599424			0.299712	−	0.954030i	$-0.403109\pi$
$41$	157.366			0.599424			0.299712	+	0.954030i	$0.403109\pi$
$42$			54.4646i			0.200097i
$43$			235.193i			0.834108i	0.908882	+	0.417054i	$0.136937\pi$
$43$			235.193i			0.834108i	−0.908882	+	0.417054i	$0.863063\pi$
$44$	128.517			0.440332
$45$	−42.9551	+	90.9937i	−0.142297	+	0.301434i
$46$	209.529			0.671594
$47$			482.605i			1.49777i	0.662699	+	0.748885i	$0.269411\pi$
$47$			482.605i			1.49777i	−0.662699	+	0.748885i	$0.730589\pi$
$48$			48.0000i			0.144338i
$49$	260.600			0.759767
$50$	−193.020	+	158.882i	−0.545942	+	0.449386i
$51$	162.452			0.446037
$52$			28.5510i			0.0761406i
$53$		−	644.559i		−	1.67051i	−0.549864	−	0.835254i	$-0.685320\pi$
$53$		−	644.559i		−	1.67051i	0.549864	−	0.835254i	$-0.314680\pi$
$54$	−54.0000			−0.136083
$55$	−153.346	+	324.839i	−0.375948	+	0.796388i
$56$	−72.6195			−0.173289
$57$			154.679i			0.359434i
$58$			151.796i			0.343652i
$59$	−833.942			−1.84017			−0.920085	−	0.391720i	$-0.871880\pi$
$59$	−833.942			−1.84017			−0.920085	+	0.391720i	$0.871880\pi$
$60$	−121.325	−	57.2735i	−0.261050	−	0.123233i
$61$	113.206			0.237616			0.118808	−	0.992917i	$-0.462093\pi$
$61$	113.206			0.237616			0.118808	+	0.992917i	$0.462093\pi$
$62$			62.0000i			0.127000i
$63$		−	81.6969i		−	0.163379i
$64$	−64.0000			−0.125000
$65$	−72.1656	−	34.0670i	−0.137708	−	0.0650076i
$66$	−192.775			−0.359530
$67$			45.7825i			0.0834809i	0.999128	+	0.0417405i	$0.0132903\pi$
$67$			45.7825i			0.0834809i	−0.999128	+	0.0417405i	$0.986710\pi$
$68$			216.603i			0.386279i
$69$	−314.293			−0.548354
$70$	86.6494	−	183.553i	0.147951	−	0.313412i
$71$	−874.495			−1.46174			−0.730870	−	0.682517i	$-0.760885\pi$
$71$	−874.495			−1.46174			−0.730870	+	0.682517i	$0.760885\pi$
$72$		−	72.0000i		−	0.117851i
$73$			249.978i			0.400791i	0.979715	+	0.200395i	$0.0642227\pi$
$73$			249.978i			0.400791i	−0.979715	+	0.200395i	$0.935777\pi$
$74$	630.916			0.991114
$75$	289.529	−	238.323i	0.445760	−	0.366922i
$76$	−206.239			−0.311279
$77$		−	291.651i		−	0.431645i
$78$		−	42.8265i		−	0.0621686i
$79$	1108.39			1.57852			0.789261	−	0.614057i	$-0.210464\pi$
$79$	1108.39			1.57852			0.789261	+	0.614057i	$0.210464\pi$
$80$	76.3647	−	161.767i	0.106723	−	0.226076i
$81$	81.0000			0.111111
$82$		−	314.731i		−	0.423857i
$83$			794.792i			1.05108i	0.850768	+	0.525541i	$0.176137\pi$
$83$			794.792i			1.05108i	−0.850768	+	0.525541i	$0.823863\pi$
$84$	108.929			0.141490
$85$	−547.487	−	258.450i	−0.698627	−	0.329799i
$86$	470.387			0.589803
$87$		−	227.694i		−	0.280591i
$88$		−	257.033i		−	0.311362i
$89$	−1035.00			−1.23270			−0.616349	−	0.787473i	$-0.711389\pi$
$89$	−1035.00			−1.23270			−0.616349	+	0.787473i	$0.711389\pi$
$90$	181.987	+	85.9103i	0.213146	+	0.100619i
$91$	64.7925			0.0746385
$92$		−	419.057i		−	0.474889i
$93$		−	93.0000i		−	0.103695i
$94$	965.211			1.05908
$95$	246.083	−	521.289i	0.265765	−	0.562981i
$96$	96.0000			0.102062
$97$			904.411i			0.946691i	0.880877	+	0.473346i	$0.156954\pi$
$97$			904.411i			0.946691i	−0.880877	+	0.473346i	$0.843046\pi$
$98$		−	521.200i		−	0.537236i
$99$	289.163			0.293555
$100$	317.764	+	386.039i	0.317764	+	0.386039i
$101$	692.124			0.681870			0.340935	−	0.940087i	$-0.389256\pi$
$101$	692.124			0.681870			0.340935	+	0.940087i	$0.389256\pi$
$102$		−	324.905i		−	0.315396i
$103$			935.763i			0.895179i	0.894239	+	0.447590i	$0.147717\pi$
$103$			935.763i			0.895179i	−0.894239	+	0.447590i	$0.852283\pi$
$104$	57.1020			0.0538395
$105$	−129.974	+	275.330i	−0.120802	+	0.255900i
$106$	−1289.12			−1.18123
$107$			1793.57i			1.62047i	0.586103	+	0.810237i	$0.300662\pi$
$107$			1793.57i			1.62047i	−0.586103	+	0.810237i	$0.699338\pi$
$108$			108.000i			0.0962250i
$109$	540.065			0.474577			0.237288	−	0.971439i	$-0.423741\pi$
$109$	540.065			0.474577			0.237288	+	0.971439i	$0.423741\pi$
$110$	649.679	+	306.692i	0.563131	+	0.265836i
$111$	−946.373			−0.809241
$112$			145.239i			0.122534i
$113$			654.637i			0.544983i	0.962158	+	0.272492i	$0.0878477\pi$
$113$			654.637i			0.544983i	−0.962158	+	0.272492i	$0.912152\pi$
$114$	309.358			0.254158
$115$	1059.21	+	500.018i	0.858886	+	0.405452i
$116$	303.592			0.242999
$117$			64.2398i			0.0507604i
$118$			1667.88i			1.30120i
$119$	491.550			0.378658
$120$	−114.547	+	242.650i	−0.0871389	+	0.184590i
$121$	−298.716			−0.224429
$122$		−	226.413i		−	0.168020i
$123$			472.097i			0.346078i
$124$	124.000			0.0898027
$125$	−1354.91	+	342.559i	−0.969494	+	0.245115i
$126$	−163.394			−0.115526
$127$			1501.47i			1.04909i	0.851383	+	0.524544i	$0.175764\pi$
$127$			1501.47i			1.04909i	−0.851383	+	0.524544i	$0.824236\pi$
$128$			128.000i			0.0883883i
$129$	−705.580			−0.481572
$130$	−68.1340	+	144.331i	−0.0459673	+	0.0973745i
$131$	2083.43			1.38954			0.694772	−	0.719230i	$-0.255505\pi$
$131$	2083.43			1.38954			0.694772	+	0.719230i	$0.255505\pi$
$132$			385.550i			0.254226i
$133$			468.030i			0.305138i
$134$	91.5650			0.0590299
$135$	−272.981	−	128.865i	−0.174033	−	0.0821553i
$136$	433.206			0.273141
$137$			1170.09i			0.729689i	0.931068	+	0.364845i	$0.118878\pi$
$137$			1170.09i			0.729689i	−0.931068	+	0.364845i	$0.881122\pi$
$138$			628.586i			0.387745i
$139$	2871.67			1.75232			0.876158	−	0.482024i	$-0.160098\pi$
$139$	2871.67			1.75232			0.876158	+	0.482024i	$0.160098\pi$
$140$	−367.107	−	173.299i	−0.221616	−	0.104617i
$141$	−1447.82			−0.864738
$142$			1748.99i			1.03361i
$143$			229.330i			0.134109i
$144$	−144.000			−0.0833333
$145$	−362.246	+	767.361i	−0.207468	+	0.439489i
$146$	499.956			0.283402
$147$			781.800i			0.438652i
$148$		−	1261.83i		−	0.700823i
$149$	530.321			0.291581			0.145790	−	0.989315i	$-0.453427\pi$
$149$	530.321			0.291581			0.145790	+	0.989315i	$0.453427\pi$
$150$	−476.645	−	579.059i	−0.259453	−	0.315200i
$151$	−1197.55			−0.645399			−0.322699	−	0.946502i	$-0.604590\pi$
$151$	−1197.55			−0.645399			−0.322699	+	0.946502i	$0.604590\pi$
$152$			412.477i			0.220107i
$153$			487.357i			0.257520i
$154$	−583.301			−0.305219
$155$	−147.957	+	313.423i	−0.0766720	+	0.162418i
$156$	−85.6530			−0.0439598
$157$			2582.53i			1.31279i	0.754417	+	0.656396i	$0.227920\pi$
$157$			2582.53i			1.31279i	−0.754417	+	0.656396i	$0.772080\pi$
$158$		−	2216.77i		−	1.11618i
$159$	1933.68			0.964469
$160$	−323.533	−	152.729i	−0.159860	−	0.0754645i
$161$	−950.992			−0.465520
$162$		−	162.000i		−	0.0785674i
$163$			1936.78i			0.930677i	0.885133	+	0.465338i	$0.154067\pi$
$163$			1936.78i			0.930677i	−0.885133	+	0.465338i	$0.845933\pi$
$164$	−629.463			−0.299712
$165$	−974.518	−	460.038i	−0.459795	−	0.217054i
$166$	1589.58			0.743227
$167$		−	265.120i		−	0.122848i	−0.998112	−	0.0614239i	$-0.980436\pi$
$167$		−	265.120i		−	0.122848i	0.998112	−	0.0614239i	$-0.0195641\pi$
$168$		−	217.859i		−	0.100049i
$169$	2146.05			0.976810
$170$	−516.901	+	1094.97i	−0.233203	+	0.494004i
$171$	−464.037			−0.207519
$172$		−	940.773i		−	0.417054i
$173$		−	1779.61i		−	0.782090i	−0.920372	−	0.391045i	$-0.872114\pi$
$173$		−	1779.61i		−	0.782090i	0.920372	−	0.391045i	$-0.127886\pi$
$174$	−455.388			−0.198408
$175$	876.062	−	721.120i	0.378423	−	0.311495i
$176$	−514.067			−0.220166
$177$		−	2501.83i		−	1.06242i
$178$			2070.01i			0.871649i
$179$	93.5598			0.0390670			0.0195335	−	0.999809i	$-0.493782\pi$
$179$	93.5598			0.0390670			0.0195335	+	0.999809i	$0.493782\pi$
$180$	171.821	−	363.975i	0.0711486	−	0.150717i
$181$	−2161.15			−0.887497			−0.443749	−	0.896151i	$-0.646352\pi$
$181$	−2161.15			−0.887497			−0.443749	+	0.896151i	$0.646352\pi$
$182$		−	129.585i		−	0.0527774i
$183$			339.619i			0.137188i
$184$	−838.115			−0.335797
$185$	3189.41	+	1505.61i	1.26751	+	0.598351i
$186$	−186.000			−0.0733236
$187$			1739.82i			0.680365i
$188$		−	1930.42i		−	0.748885i
$189$	245.091			0.0943266
$190$	−1042.58	−	492.167i	−0.398087	−	0.187924i
$191$	−2736.56			−1.03670			−0.518352	−	0.855167i	$-0.673454\pi$
$191$	−2736.56			−1.03670			−0.518352	+	0.855167i	$0.673454\pi$
$192$		−	192.000i		−	0.0721688i
$193$			3267.77i			1.21875i	0.792881	+	0.609376i	$0.208580\pi$
$193$			3267.77i			1.21875i	−0.792881	+	0.609376i	$0.791420\pi$
$194$	1808.82			0.669412
$195$	102.201	−	216.497i	0.0375321	−	0.0795060i
$196$	−1042.40			−0.379884
$197$			1633.13i			0.590637i	0.955399	+	0.295318i	$0.0954257\pi$
$197$			1633.13i			0.590637i	−0.955399	+	0.295318i	$0.904574\pi$
$198$		−	578.325i		−	0.207575i
$199$	−3770.25			−1.34304			−0.671522	−	0.740985i	$-0.734359\pi$
$199$	−3770.25			−1.34304			−0.671522	+	0.740985i	$0.734359\pi$
$200$	772.078	−	635.527i	0.272971	−	0.224693i
$201$	−137.347			−0.0481977
$202$		−	1384.25i		−	0.482155i
$203$		−	688.960i		−	0.238204i
$204$	−649.810			−0.223018
$205$	751.074	−	1591.03i	0.255889	−	0.542061i
$206$	1871.53			0.632987
$207$		−	942.879i		−	0.316592i
$208$		−	114.204i		−	0.0380703i
$209$	−1656.57			−0.548265
$210$	550.660	+	259.948i	0.180948	+	0.0854197i
$211$	−5086.36			−1.65952			−0.829761	−	0.558119i	$-0.811523\pi$
$211$	−5086.36			−1.65952			−0.829761	+	0.558119i	$0.811523\pi$
$212$			2578.23i			0.835254i
$213$		−	2623.49i		−	0.843936i
$214$	3587.13			1.14585
$215$	2377.90	+	1122.53i	0.754286	+	0.356074i
$216$	216.000			0.0680414
$217$		−	281.401i		−	0.0880309i
$218$		−	1080.13i		−	0.335576i
$219$	−749.934			−0.231397
$220$	613.384	−	1299.36i	0.187974	−	0.398194i
$221$	−386.515			−0.117646
$222$			1892.75i			0.572220i
$223$		−	6492.52i		−	1.94965i	−0.222977	−	0.974824i	$-0.571578\pi$
$223$		−	6492.52i		−	1.94965i	0.222977	−	0.974824i	$-0.428422\pi$
$224$	290.478			0.0866445
$225$	714.968	+	868.588i	0.211842	+	0.257359i
$226$	1309.27			0.385361
$227$			4071.75i			1.19053i	0.803528	+	0.595267i	$0.202954\pi$
$227$			4071.75i			1.19053i	−0.803528	+	0.595267i	$0.797046\pi$
$228$		−	618.716i		−	0.179717i
$229$	−3683.38			−1.06290			−0.531451	−	0.847089i	$-0.678353\pi$
$229$	−3683.38			−1.06290			−0.531451	+	0.847089i	$0.678353\pi$
$230$	1000.04	−	2118.42i	0.286698	−	0.607324i
$231$	874.952			0.249210
$232$		−	607.185i		−	0.171826i
$233$		−	538.595i		−	0.151436i	−0.997129	−	0.0757179i	$-0.975875\pi$
$233$		−	538.595i		−	0.151436i	0.997129	−	0.0757179i	$-0.0241248\pi$
$234$	128.480			0.0358930
$235$	4879.34	+	2303.38i	1.35444	+	0.639386i
$236$	3335.77			0.920085
$237$			3325.16i			0.911361i
$238$		−	983.101i		−	0.267752i
$239$	7126.82			1.92885			0.964426	−	0.264354i	$-0.0851589\pi$
$239$	7126.82			1.92885			0.964426	+	0.264354i	$0.0851589\pi$
$240$	485.300	+	229.094i	0.130525	+	0.0616165i
$241$	2463.81			0.658538			0.329269	−	0.944236i	$-0.393198\pi$
$241$	2463.81			0.658538			0.329269	+	0.944236i	$0.393198\pi$
$242$			597.431i			0.158696i
$243$			243.000i			0.0641500i
$244$	−452.826			−0.118808
$245$	1243.79	−	2634.77i	0.324338	−	0.687060i
$246$	944.194			0.244714
$247$		−	368.020i		−	0.0948038i
$248$		−	248.000i		−	0.0635001i
$249$	−2384.38			−0.606842
$250$	685.119	+	2709.82i	0.173323	+	0.685536i
$251$	2016.68			0.507139			0.253570	−	0.967317i	$-0.418395\pi$
$251$	2016.68			0.507139			0.253570	+	0.967317i	$0.418395\pi$
$252$			326.788i			0.0816893i
$253$		−	3365.99i		−	0.836435i
$254$	3002.95			0.741818
$255$	775.351	−	1642.46i	0.190409	−	0.403352i
$256$	256.000			0.0625000
$257$		−	6756.77i		−	1.63998i	−0.572376	−	0.819991i	$-0.693978\pi$
$257$		−	6756.77i		−	1.63998i	0.572376	−	0.819991i	$-0.306022\pi$
$258$			1411.16i			0.340523i
$259$	−2863.55			−0.686997
$260$	288.662	+	136.268i	0.0688542	+	0.0325038i
$261$	683.083			0.161999
$262$		−	4166.87i		−	0.982557i
$263$			641.080i			0.150307i	0.997172	+	0.0751533i	$0.0239446\pi$
$263$			641.080i			0.150307i	−0.997172	+	0.0751533i	$0.976055\pi$
$264$	771.100			0.179765
$265$	−6516.76	−	3076.34i	−1.51065	−	0.713126i
$266$	936.059			0.215765
$267$		−	3105.01i		−	0.711699i
$268$		−	183.130i		−	0.0417405i
$269$	3925.57			0.889763			0.444881	−	0.895590i	$-0.353246\pi$
$269$	3925.57			0.889763			0.444881	+	0.895590i	$0.353246\pi$
$270$	−257.731	+	545.962i	−0.0580926	+	0.123060i
$271$	6670.56			1.49523			0.747615	−	0.664132i	$-0.231199\pi$
$271$	6670.56			1.49523			0.747615	+	0.664132i	$0.231199\pi$
$272$		−	866.413i		−	0.193140i
$273$			194.377i			0.0430925i
$274$	2340.18			0.515968
$275$	2552.37	+	3100.78i	0.559687	+	0.679942i
$276$	1257.17			0.274177
$277$			6727.49i			1.45926i	0.683841	+	0.729631i	$0.260308\pi$
$277$			6727.49i			1.45926i	−0.683841	+	0.729631i	$0.739692\pi$
$278$		−	5743.34i		−	1.23907i
$279$	279.000			0.0598684
$280$	−346.598	+	734.213i	−0.0739756	+	0.156706i
$281$	−6188.49			−1.31379			−0.656894	−	0.753983i	$-0.728130\pi$
$281$	−6188.49			−1.31379			−0.656894	+	0.753983i	$0.728130\pi$
$282$			2895.63i			0.611462i
$283$			3752.48i			0.788204i	0.919067	+	0.394102i	$0.128944\pi$
$283$			3752.48i			0.788204i	−0.919067	+	0.394102i	$0.871056\pi$
$284$	3497.98			0.730870
$285$	1563.87	+	738.250i	0.325037	+	0.153439i
$286$	458.660			0.0948292
$287$			1428.48i			0.293799i
$288$			288.000i			0.0589256i
$289$	1980.69			0.403153
$290$	1534.72	+	724.491i	0.310765	+	0.146702i
$291$	−2713.23			−0.546572
$292$		−	999.912i		−	0.200395i
$293$		−	7291.33i		−	1.45380i	−0.686743	−	0.726901i	$-0.740960\pi$
$293$		−	7291.33i		−	1.45380i	0.686743	−	0.726901i	$-0.259040\pi$
$294$	1563.60			0.310174
$295$	−3980.23	+	8431.50i	−0.785553	+	1.66407i
$296$	−2523.66			−0.495557
$297$			867.488i			0.169484i
$298$		−	1060.64i		−	0.206179i
$299$	747.782			0.144633
$300$	−1158.12	+	953.291i	−0.222880	+	0.183461i
$301$	−2134.95			−0.408826
$302$			2395.10i			0.456366i
$303$			2076.37i			0.393678i
$304$	824.954			0.155639
$305$	540.311	−	1144.56i	0.101436	−	0.214877i
$306$	974.714			0.182094
$307$		−	10518.7i		−	1.95549i	−0.209808	−	0.977743i	$-0.567284\pi$
$307$		−	10518.7i		−	1.95549i	0.209808	−	0.977743i	$-0.432716\pi$
$308$			1166.60i			0.215823i
$309$	−2807.29			−0.516832
$310$	626.846	+	295.913i	0.114847	+	0.0542153i
$311$	−33.0861			−0.00603261			−0.00301631	−	0.999995i	$-0.500960\pi$
$311$	−33.0861			−0.00603261			−0.00301631	+	0.999995i	$0.500960\pi$
$312$			171.306i			0.0310843i
$313$		−	4050.50i		−	0.731462i	−0.930721	−	0.365731i	$-0.880819\pi$
$313$		−	4050.50i		−	0.731462i	0.930721	−	0.365731i	$-0.119181\pi$
$314$	5165.06			0.928284
$315$	−825.990	−	389.923i	−0.147744	−	0.0697449i
$316$	−4433.55			−0.789261
$317$		−	8367.18i		−	1.48248i	−0.671238	−	0.741242i	$-0.734237\pi$
$317$		−	8367.18i		−	1.48248i	0.671238	−	0.741242i	$-0.265763\pi$
$318$		−	3867.35i		−	0.681982i
$319$	2438.54			0.428001
$320$	−305.459	+	647.066i	−0.0533614	+	0.113038i
$321$	−5380.70			−0.935581
$322$			1901.98i			0.329172i
$323$		−	2792.00i		−	0.480962i
$324$	−324.000			−0.0555556
$325$	−688.863	+	567.029i	−0.117573	+	0.0967789i
$326$	3873.56			0.658088
$327$			1620.20i			0.273997i
$328$			1258.93i			0.211928i
$329$	−4380.82			−0.734111
$330$	−920.075	+	1949.04i	−0.153480	+	0.325124i
$331$	−9192.18			−1.52643			−0.763215	−	0.646145i	$-0.776380\pi$
$331$	−9192.18			−1.52643			−0.763215	+	0.646145i	$0.776380\pi$
$332$		−	3179.17i		−	0.525541i
$333$		−	2839.12i		−	0.467216i
$334$	−530.239			−0.0868665
$335$	462.880	+	218.510i	0.0754920	+	0.0356373i
$336$	−435.717			−0.0707450
$337$			4870.87i			0.787340i	0.919252	+	0.393670i	$0.128795\pi$
$337$			4870.87i			0.787340i	−0.919252	+	0.393670i	$0.871205\pi$
$338$		−	4292.11i		−	0.690709i
$339$	−1963.91			−0.314646
$340$	2189.95	+	1033.80i	0.349313	+	0.164899i
$341$	996.005			0.158172
$342$			928.074i			0.146738i
$343$			5479.14i			0.862524i
$344$	−1881.55			−0.294902
$345$	−1500.06	+	3177.63i	−0.234088	+	0.495878i
$346$	−3559.23			−0.553021
$347$			3257.95i			0.504023i	0.967724	+	0.252011i	$0.0810920\pi$
$347$			3257.95i			0.504023i	−0.967724	+	0.252011i	$0.918908\pi$
$348$			910.777i			0.140295i
$349$	1232.22			0.188995			0.0944974	−	0.995525i	$-0.469876\pi$
$349$	1232.22			0.188995			0.0944974	+	0.995525i	$0.469876\pi$
$350$	−1442.24	−	1752.12i	−0.220260	−	0.267586i
$351$	−192.719			−0.0293065
$352$			1028.13i			0.155681i
$353$		−	8874.19i		−	1.33803i	−0.743248	−	0.669016i	$-0.766716\pi$
$353$		−	8874.19i		−	1.33803i	0.743248	−	0.669016i	$-0.233284\pi$
$354$	−5003.65			−0.751246
$355$	−4173.78	+	8841.51i	−0.624004	+	1.32186i
$356$	4140.01			0.616349
$357$			1474.65i			0.218619i
$358$		−	187.120i		−	0.0276245i
$359$	−12377.8			−1.81970			−0.909851	−	0.414935i	$-0.863804\pi$
$359$	−12377.8			−1.81970			−0.909851	+	0.414935i	$0.863804\pi$
$360$	−727.950	−	343.641i	−0.106573	−	0.0503096i
$361$	−4200.60			−0.612422
$362$			4322.30i			0.627555i
$363$		−	896.147i		−	0.129574i
$364$	−259.170			−0.0373192
$365$	2527.38	+	1193.09i	0.362436	+	0.171094i
$366$	679.239			0.0970065
$367$		−	533.425i		−	0.0758707i	−0.999280	−	0.0379353i	$-0.987922\pi$
$367$		−	533.425i		−	0.0758707i	0.999280	−	0.0379353i	$-0.0120781\pi$
$368$			1676.23i			0.237444i
$369$	−1416.29			−0.199808
$370$	3011.23	−	6378.82i	0.423098	−	0.896267i
$371$	5850.94			0.818776
$372$			372.000i			0.0518476i
$373$		−	8560.38i		−	1.18831i	−0.804350	−	0.594155i	$-0.797487\pi$
$373$		−	8560.38i		−	1.18831i	0.804350	−	0.594155i	$-0.202513\pi$
$374$	3479.64			0.481091
$375$	−1027.68	−	4064.73i	−0.141517	−	0.559738i
$376$	−3860.84			−0.529542
$377$			541.742i			0.0740082i
$378$		−	490.182i		−	0.0666990i
$379$	−9910.39			−1.34317			−0.671587	−	0.740926i	$-0.734387\pi$
$379$	−9910.39			−1.34317			−0.671587	+	0.740926i	$0.734387\pi$
$380$	−984.334	+	2085.16i	−0.132882	+	0.281490i
$381$	−4504.42			−0.605692
$382$			5473.12i			0.733061i
$383$			6029.91i			0.804475i	0.915535	+	0.402237i	$0.131767\pi$
$383$			6029.91i			0.804475i	−0.915535	+	0.402237i	$0.868233\pi$
$384$	−384.000			−0.0510310
$385$	−2948.71	−	1391.99i	−0.390338	−	0.184266i
$386$	6535.54			0.861788
$387$		−	2116.74i		−	0.278036i
$388$		−	3617.64i		−	0.473346i
$389$	−1588.87			−0.207093			−0.103546	−	0.994625i	$-0.533019\pi$
$389$	−1588.87			−0.207093			−0.103546	+	0.994625i	$0.533019\pi$
$390$	−432.994	−	204.402i	−0.0562192	−	0.0265392i
$391$	5673.07			0.733758
$392$			2084.80i			0.268618i
$393$			6250.30i			0.802254i
$394$	3266.25			0.417643
$395$	5290.10	−	11206.3i	0.673858	−	1.42746i
$396$	−1156.65			−0.146777
$397$		−	2434.72i		−	0.307796i	−0.988087	−	0.153898i	$-0.950817\pi$
$397$		−	2434.72i		−	0.307796i	0.988087	−	0.153898i	$-0.0491827\pi$
$398$			7540.50i			0.949676i
$399$	−1404.09			−0.176171
$400$	−1271.05	−	1544.16i	−0.158882	−	0.193020i
$401$	3333.61			0.415144			0.207572	−	0.978220i	$-0.433444\pi$
$401$	3333.61			0.415144			0.207572	+	0.978220i	$0.433444\pi$
$402$			274.695i			0.0340809i
$403$			221.270i			0.0273505i
$404$	−2768.50			−0.340935
$405$	386.596	−	818.943i	0.0474324	−	0.100478i
$406$	−1377.92			−0.168436
$407$		−	10135.4i		−	1.23438i
$408$			1299.62i			0.157698i
$409$	−6085.01			−0.735659			−0.367830	−	0.929893i	$-0.619899\pi$
$409$	−6085.01			−0.735659			−0.367830	+	0.929893i	$0.619899\pi$
$410$	−3182.06	−	1502.15i	−0.383295	−	0.180941i
$411$	−3510.27			−0.421286
$412$		−	3743.05i		−	0.447590i
$413$		−	7570.06i		−	0.901932i
$414$	−1885.76			−0.223865
$415$	8035.68	+	3793.38i	0.950496	+	0.448698i
$416$	−228.408			−0.0269198
$417$			8615.01i			1.01170i
$418$			3313.14i			0.387682i
$419$	−2064.15			−0.240669			−0.120335	−	0.992733i	$-0.538397\pi$
$419$	−2064.15			−0.240669			−0.120335	+	0.992733i	$0.538397\pi$
$420$	519.897	−	1101.32i	0.0604009	−	0.127950i
$421$	−13289.5			−1.53846			−0.769231	−	0.638970i	$-0.779361\pi$
$421$	−13289.5			−1.53846			−0.769231	+	0.638970i	$0.779361\pi$
$422$			10172.7i			1.17346i
$423$		−	4343.45i		−	0.499257i
$424$	5156.47			0.590614
$425$	−5226.08	+	4301.79i	−0.596476	+	0.490982i
$426$	−5246.97			−0.596753
$427$			1027.62i			0.116464i
$428$		−	7174.27i		−	0.810237i
$429$	−687.990			−0.0774277
$430$	2245.06	−	4755.80i	0.251782	−	0.533361i
$431$	−7677.53			−0.858037			−0.429018	−	0.903296i	$-0.641140\pi$
$431$	−7677.53			−0.858037			−0.429018	+	0.903296i	$0.641140\pi$
$432$		−	432.000i		−	0.0481125i
$433$			12132.1i			1.34649i	0.739420	+	0.673245i	$0.235100\pi$
$433$			12132.1i			1.34649i	−0.739420	+	0.673245i	$0.764900\pi$
$434$	−562.801			−0.0622473
$435$	−2302.08	−	1086.74i	−0.253739	−	0.119782i
$436$	−2160.26			−0.237288
$437$			5401.61i			0.591291i
$438$			1499.87i			0.163622i
$439$	253.995			0.0276140			0.0138070	−	0.999905i	$-0.495605\pi$
$439$	253.995			0.0276140			0.0138070	+	0.999905i	$0.495605\pi$
$440$	−2598.71	−	1226.77i	−0.281566	−	0.132918i
$441$	−2345.40			−0.253256
$442$			773.030i			0.0831884i
$443$		−	16277.7i		−	1.74577i	−0.487922	−	0.872887i	$-0.662245\pi$
$443$		−	16277.7i		−	1.74577i	0.487922	−	0.872887i	$-0.337755\pi$
$444$	3785.49			0.404621
$445$	−4939.86	+	10464.3i	−0.526228	+	1.11473i
$446$	−12985.0			−1.37861
$447$			1590.96i			0.168344i
$448$		−	580.956i		−	0.0612669i
$449$	−8319.12			−0.874395			−0.437198	−	0.899365i	$-0.644029\pi$
$449$	−8319.12			−0.874395			−0.437198	+	0.899365i	$0.644029\pi$
$450$	1737.18	−	1429.94i	0.181981	−	0.149795i
$451$	−5056.03			−0.527892
$452$		−	2618.55i		−	0.272492i
$453$		−	3592.65i		−	0.372621i
$454$	8143.49			0.841835
$455$	309.241	−	655.079i	0.0318625	−	0.0674958i
$456$	−1237.43			−0.127079
$457$			3468.18i			0.354999i	0.984121	+	0.177500i	$0.0568008\pi$
$457$			3468.18i			0.354999i	−0.984121	+	0.177500i	$0.943199\pi$
$458$			7366.76i			0.751586i
$459$	−1462.07			−0.148679
$460$	−4236.84	−	2000.07i	−0.429443	−	0.202726i
$461$	−3537.74			−0.357416			−0.178708	−	0.983902i	$-0.557192\pi$
$461$	−3537.74			−0.357416			−0.178708	+	0.983902i	$0.557192\pi$
$462$		−	1749.90i		−	0.176218i
$463$			4192.53i			0.420828i	0.977612	+	0.210414i	$0.0674812\pi$
$463$			4192.53i			0.420828i	−0.977612	+	0.210414i	$0.932519\pi$
$464$	−1214.37			−0.121499
$465$	−940.268	−	443.870i	−0.0937718	−	0.0442666i
$466$	−1077.19			−0.107081
$467$		−	8432.51i		−	0.835567i	−0.908547	−	0.417784i	$-0.862807\pi$
$467$		−	8432.51i		−	0.835567i	0.908547	−	0.417784i	$-0.137193\pi$
$468$		−	256.959i		−	0.0253802i
$469$	−415.588			−0.0409170
$470$	4606.75	−	9758.68i	0.452114	−	0.957733i
$471$	−7747.59			−0.757941
$472$		−	6671.54i		−	0.650598i
$473$		−	7556.57i		−	0.734570i
$474$	6650.32			0.644429
$475$	−4095.95	−	4976.01i	−0.395652	−	0.480663i
$476$	−1966.20			−0.189329
$477$			5801.03i			0.556836i
$478$		−	14253.6i		−	1.36390i
$479$	10314.7			0.983909			0.491954	−	0.870621i	$-0.336283\pi$
$479$	10314.7			0.983909			0.491954	+	0.870621i	$0.336283\pi$
$480$	458.188	−	970.600i	0.0435694	−	0.0922950i
$481$	2251.66			0.213445
$482$		−	4927.61i		−	0.465657i
$483$		−	2852.98i		−	0.268768i
$484$	1194.86			0.112215
$485$	9143.97	+	4316.57i	0.856096	+	0.404134i
$486$	486.000			0.0453609
$487$		−	4486.46i		−	0.417455i	−0.977974	−	0.208728i	$-0.933068\pi$
$487$		−	4486.46i		−	0.417455i	0.977974	−	0.208728i	$-0.0669322\pi$
$488$			905.652i			0.0840101i
$489$	−5810.34			−0.537326
$490$	−5269.55	−	2487.58i	−0.485824	−	0.229342i
$491$	6928.79			0.636847			0.318424	−	0.947948i	$-0.396847\pi$
$491$	6928.79			0.636847			0.318424	+	0.947948i	$0.396847\pi$
$492$		−	1888.39i		−	0.173039i
$493$			4109.94i			0.375461i
$494$	−736.040			−0.0670364
$495$	1380.11	−	2923.55i	0.125316	−	0.265463i
$496$	−496.000			−0.0449013
$497$		−	7938.18i		−	0.716451i
$498$			4768.75i			0.429102i
$499$	−5327.70			−0.477957			−0.238978	−	0.971025i	$-0.576813\pi$
$499$	−5327.70			−0.477957			−0.238978	+	0.971025i	$0.576813\pi$
$500$	5419.64	−	1370.24i	0.484747	−	0.122558i
$501$	795.359			0.0709262
$502$		−	4033.37i		−	0.358602i
$503$			7174.60i			0.635984i	0.948093	+	0.317992i	$0.103008\pi$
$503$			7174.60i			0.635984i	−0.948093	+	0.317992i	$0.896992\pi$
$504$	653.576			0.0577630
$505$	3303.36	−	6997.66i	0.291085	−	0.616617i
$506$	−6731.99			−0.591449
$507$			6438.16i			0.563962i
$508$		−	6005.90i		−	0.524544i
$509$	15739.7			1.37063			0.685316	−	0.728246i	$-0.259664\pi$
$509$	15739.7			1.37063			0.685316	+	0.728246i	$0.259664\pi$
$510$	−3284.92	−	1550.70i	−0.285213	−	0.134640i
$511$	−2269.16			−0.196442
$512$		−	512.000i		−	0.0441942i
$513$		−	1392.11i		−	0.119811i
$514$	−13513.5			−1.15964
$515$	9460.95	+	4466.20i	0.809513	+	0.382144i
$516$	2822.32			0.240786
$517$		−	15505.7i		−	1.31903i
$518$			5727.10i			0.485780i
$519$	5338.84			0.451540
$520$	272.536	−	577.325i	0.0229836	−	0.0486873i
$521$	7744.64			0.651246			0.325623	−	0.945500i	$-0.394426\pi$
$521$	7744.64			0.651246			0.325623	+	0.945500i	$0.394426\pi$
$522$		−	1366.17i		−	0.114551i
$523$		−	12806.6i		−	1.07073i	−0.844621	−	0.535365i	$-0.820174\pi$
$523$		−	12806.6i		−	1.07073i	0.844621	−	0.535365i	$-0.179826\pi$
$524$	−8333.73			−0.694772
$525$	2163.36	+	2628.19i	0.179841	+	0.218483i
$526$	1282.16			0.106283
$527$			1678.67i			0.138756i
$528$		−	1542.20i		−	0.127113i
$529$	1191.43			0.0979234
$530$	−6152.69	+	13033.5i	−0.504256	+	1.06819i
$531$	7505.48			0.613390
$532$		−	1872.12i		−	0.152569i
$533$		−	1123.24i		−	0.0912811i
$534$	−6210.02			−0.503247
$535$	18133.7	+	8560.32i	1.46540	+	0.691766i
$536$	−366.260			−0.0295150
$537$			280.679i			0.0225553i
$538$		−	7851.14i		−	0.629157i
$539$	−8372.87			−0.669100
$540$	1091.92	+	515.462i	0.0870166	+	0.0410777i
$541$	−18940.8			−1.50523			−0.752614	−	0.658462i	$-0.771207\pi$
$541$	−18940.8			−1.50523			−0.752614	+	0.658462i	$0.771207\pi$
$542$		−	13341.1i		−	1.05729i
$543$		−	6483.45i		−	0.512397i
$544$	−1732.83			−0.136570
$545$	2577.62	−	5460.28i	0.202593	−	0.429161i
$546$	388.755			0.0304710
$547$		−	4898.05i		−	0.382862i	−0.981506	−	0.191431i	$-0.938687\pi$
$547$		−	4898.05i		−	0.382862i	0.981506	−	0.191431i	$-0.0613128\pi$
$548$		−	4680.35i		−	0.364845i
$549$	−1018.86			−0.0792055
$550$	6201.56	−	5104.74i	0.480792	−	0.395758i
$551$	−3913.28			−0.302561
$552$		−	2514.34i		−	0.193872i
$553$			10061.3i			0.773690i
$554$	13455.0			1.03185
$555$	−4516.84	+	9568.23i	−0.345458	+	0.731799i
$556$	−11486.7			−0.876158
$557$		−	5582.19i		−	0.424641i	−0.977200	−	0.212320i	$-0.931898\pi$
$557$		−	5582.19i		−	0.424641i	0.977200	−	0.212320i	$-0.0681020\pi$
$558$		−	558.000i		−	0.0423334i
$559$	1678.75			0.127019
$560$	1468.43	+	693.196i	0.110808	+	0.0523087i
$561$	−5219.46			−0.392809
$562$			12377.0i			0.928988i
$563$			3904.14i			0.292256i	0.989266	+	0.146128i	$0.0466811\pi$
$563$			3904.14i			0.292256i	−0.989266	+	0.146128i	$0.953319\pi$
$564$	5791.26			0.432369
$565$	6618.66	+	3124.45i	0.492830	+	0.232649i
$566$	7504.96			0.557344
$567$			735.272i			0.0544595i
$568$		−	6995.96i		−	0.516803i
$569$	155.186			0.0114336			0.00571680	−	0.999984i	$-0.498180\pi$
$569$	155.186			0.0114336			0.00571680	+	0.999984i	$0.498180\pi$
$570$	1476.50	−	3127.74i	0.108498	−	0.229836i
$571$	10366.4			0.759756			0.379878	−	0.925037i	$-0.375966\pi$
$571$	10366.4			0.759756			0.379878	+	0.925037i	$0.375966\pi$
$572$		−	917.321i		−	0.0670544i
$573$		−	8209.68i		−	0.598542i
$574$	2856.95			0.207747
$575$	10110.8	−	8322.57i	0.733302	−	0.603609i
$576$	576.000			0.0416667
$577$			2423.08i			0.174826i	0.996172	+	0.0874128i	$0.0278599\pi$
$577$			2423.08i			0.174826i	−0.996172	+	0.0874128i	$0.972140\pi$
$578$		−	3961.38i		−	0.285072i
$579$	−9803.31			−0.703647
$580$	1448.98	−	3069.44i	0.103734	−	0.219744i
$581$	−7214.68			−0.515172
$582$			5426.47i			0.386485i
$583$			20709.1i			1.47116i
$584$	−1999.82			−0.141701
$585$	649.491	+	306.603i	0.0459028	+	0.0216692i
$586$	−14582.7			−1.02799
$587$		−	22277.5i		−	1.56642i	−0.621755	−	0.783212i	$-0.713580\pi$
$587$		−	22277.5i		−	1.56642i	0.621755	−	0.783212i	$-0.286420\pi$
$588$		−	3127.20i		−	0.219326i
$589$	−1598.35			−0.111815
$590$	16863.0	+	7960.46i	1.17668	+	0.555470i
$591$	−4899.38			−0.341004
$592$			5047.32i			0.350412i
$593$			17117.8i			1.18540i	0.805422	+	0.592702i	$0.201939\pi$
$593$			17117.8i			1.18540i	−0.805422	+	0.592702i	$0.798061\pi$
$594$	1734.98			0.119843
$595$	2346.07	−	4969.78i	0.161646	−	0.342422i
$596$	−2121.28			−0.145790
$597$		−	11310.7i		−	0.775407i
$598$		−	1495.56i		−	0.102271i
$599$	21075.8			1.43762			0.718811	−	0.695205i	$-0.244687\pi$
$599$	21075.8			1.43762			0.718811	+	0.695205i	$0.244687\pi$
$600$	1906.58	+	2316.24i	0.129726	+	0.157600i
$601$	−2470.28			−0.167662			−0.0838309	−	0.996480i	$-0.526716\pi$
$601$	−2470.28			−0.167662			−0.0838309	+	0.996480i	$0.526716\pi$
$602$			4269.91i			0.289084i
$603$		−	412.042i		−	0.0278270i
$604$	4790.20			0.322699
$605$	−1425.71	+	3020.14i	−0.0958070	+	0.202952i
$606$	4152.74			0.278372
$607$			15838.7i			1.05910i	0.848279	+	0.529550i	$0.177639\pi$
$607$			15838.7i			1.05910i	−0.848279	+	0.529550i	$0.822361\pi$
$608$		−	1649.91i		−	0.110054i
$609$	2066.88			0.137527
$610$	−2289.13	−	1080.62i	−0.151941	−	0.0717264i
$611$	3444.72			0.228082
$612$		−	1949.43i		−	0.128760i
$613$			14180.0i			0.934301i	0.884178	+	0.467150i	$0.154719\pi$
$613$			14180.0i			0.934301i	−0.884178	+	0.467150i	$0.845281\pi$
$614$	−21037.4			−1.38274
$615$	4773.10	+	2253.22i	0.312959	+	0.147738i
$616$	2333.21			0.152610
$617$		−	779.036i		−	0.0508311i	−0.999677	−	0.0254156i	$-0.991909\pi$
$617$		−	779.036i		−	0.0508311i	0.999677	−	0.0254156i	$-0.00809090\pi$
$618$			5614.58i			0.365455i
$619$	27567.3			1.79002			0.895012	−	0.446043i	$-0.147167\pi$
$619$	27567.3			1.79002			0.895012	+	0.446043i	$0.147167\pi$
$620$	591.826	−	1253.69i	0.0383360	−	0.0812088i
$621$	2828.64			0.182785
$622$			66.1723i			0.00426570i
$623$		−	9395.18i		−	0.604189i
$624$	342.612			0.0219799
$625$	−3003.28	+	15333.7i	−0.192210	+	0.981354i
$626$	−8101.00			−0.517222
$627$		−	4969.71i		−	0.316541i
$628$		−	10330.1i		−	0.656396i
$629$	17082.3			1.08285
$630$	−779.845	+	1651.98i	−0.0493171	+	0.104471i
$631$	871.245			0.0549663			0.0274831	−	0.999622i	$-0.491251\pi$
$631$	871.245			0.0549663			0.0274831	+	0.999622i	$0.491251\pi$
$632$			8867.10i			0.558092i
$633$		−	15259.1i		−	0.958126i
$634$	−16734.4			−1.04827
$635$	15180.5	+	7166.22i	0.948694	+	0.447847i
$636$	−7734.70			−0.482234
$637$		−	1860.10i		−	0.115698i
$638$		−	4877.09i		−	0.302642i
$639$	7870.46			0.487246
$640$	1294.13	+	610.917i	0.0799298	+	0.0377322i
$641$	−15804.5			−0.973853			−0.486927	−	0.873443i	$-0.661882\pi$
$641$	−15804.5			−0.973853			−0.486927	+	0.873443i	$0.661882\pi$
$642$			10761.4i			0.661556i
$643$		−	14704.9i		−	0.901872i	−0.892556	−	0.450936i	$-0.851090\pi$
$643$		−	14704.9i		−	0.901872i	0.892556	−	0.450936i	$-0.148910\pi$
$644$	3803.97			0.232760
$645$	−3367.59	+	7133.70i	−0.205579	+	0.435487i
$646$	−5583.99			−0.340092
$647$			19126.1i			1.16217i	0.813842	+	0.581087i	$0.197372\pi$
$647$			19126.1i			1.16217i	−0.813842	+	0.581087i	$0.802628\pi$
$648$			648.000i			0.0392837i
$649$	26793.9			1.62057
$650$	1134.06	+	1377.73i	0.0684330	+	0.0831367i
$651$	844.202			0.0508247
$652$		−	7747.12i		−	0.465338i
$653$			20752.6i			1.24366i	0.783152	+	0.621830i	$0.213611\pi$
$653$			20752.6i			1.24366i	−0.783152	+	0.621830i	$0.786389\pi$
$654$	3240.39			0.193745
$655$	9943.79	−	21064.4i	0.593185	−	1.25657i
$656$	2517.85			0.149856
$657$		−	2249.80i		−	0.133597i
$658$			8761.64i			0.519095i
$659$	−20921.8			−1.23672			−0.618359	−	0.785896i	$-0.712202\pi$
$659$	−20921.8			−1.23672			−0.618359	+	0.785896i	$0.712202\pi$
$660$	3898.07	+	1840.15i	0.229897	+	0.108527i
$661$	11116.4			0.654128			0.327064	−	0.945002i	$-0.393941\pi$
$661$	11116.4			0.654128			0.327064	+	0.945002i	$0.393941\pi$
$662$			18384.4i			1.07935i
$663$		−	1159.54i		−	0.0679231i
$664$	−6358.34			−0.371613
$665$	4731.97	+	2233.81i	0.275937	+	0.130261i
$666$	−5678.24			−0.330371
$667$		−	7951.41i		−	0.461589i
$668$			1060.48i			0.0614239i
$669$	19477.6			1.12563
$670$	437.021	−	925.760i	0.0251994	−	0.0533809i
$671$	−3637.23			−0.209260
$672$			871.434i			0.0500243i
$673$		−	10118.1i		−	0.579532i	−0.957098	−	0.289766i	$-0.906423\pi$
$673$		−	10118.1i		−	0.579532i	0.957098	−	0.289766i	$-0.0935774\pi$
$674$	9741.75			0.556733
$675$	−2605.76	+	2144.90i	−0.148587	+	0.122307i
$676$	−8584.21			−0.488405
$677$			10739.9i			0.609699i	0.952401	+	0.304849i	$0.0986061\pi$
$677$			10739.9i			0.609699i	−0.952401	+	0.304849i	$0.901394\pi$
$678$			3927.82i			0.222488i
$679$	−8209.74			−0.464007
$680$	2067.60	−	4379.90i	0.116601	−	0.247002i
$681$	−12215.2			−0.687355
$682$		−	1992.01i		−	0.111845i
$683$			18165.9i			1.01772i	0.860851	+	0.508858i	$0.169932\pi$
$683$			18165.9i			1.01772i	−0.860851	+	0.508858i	$0.830068\pi$
$684$	1856.15			0.103760
$685$	11830.1	+	5584.59i	0.659860	+	0.311498i
$686$	10958.3			0.609897
$687$		−	11050.1i		−	0.613667i
$688$			3763.09i			0.208527i
$689$	−4600.70			−0.254387
$690$	6355.26	+	3000.11i	0.350639	+	0.165525i
$691$	234.999			0.0129375			0.00646874	−	0.999979i	$-0.497941\pi$
$691$	234.999			0.0129375			0.00646874	+	0.999979i	$0.497941\pi$
$692$			7118.46i			0.391045i
$693$			2624.86i			0.143882i
$694$	6515.90			0.356398
$695$	13705.9	−	29033.8i	0.748049	−	1.58462i
$696$	1821.55			0.0992038
$697$		−	8521.48i		−	0.463090i
$698$		−	2464.44i		−	0.133639i
$699$	1615.78			0.0874315
$700$	−3504.25	+	2884.48i	−0.189212	+	0.155747i
$701$	−5392.01			−0.290518			−0.145259	−	0.989394i	$-0.546402\pi$
$701$	−5392.01			−0.290518			−0.145259	+	0.989394i	$0.546402\pi$
$702$			385.439i			0.0207229i
$703$			16264.9i			0.872606i
$704$	2056.27			0.110083
$705$	−6910.13	+	14638.0i	−0.369149	+	0.781985i
$706$	−17748.4			−0.946132
$707$			6282.71i			0.334209i
$708$			10007.3i			0.531211i
$709$	3949.69			0.209215			0.104608	−	0.994514i	$-0.466641\pi$
$709$	3949.69			0.209215			0.104608	+	0.994514i	$0.466641\pi$
$710$	17683.0	+	8347.57i	0.934693	+	0.441238i
$711$	−9975.49			−0.526174
$712$		−	8280.03i		−	0.435825i
$713$		−	3247.69i		−	0.170585i
$714$	2949.30			0.154587
$715$	2318.62	+	1094.55i	0.121275	+	0.0572499i
$716$	−374.239			−0.0195335
$717$			21380.4i			1.11362i
$718$			24755.5i			1.28672i
$719$	8981.09			0.465839			0.232919	−	0.972496i	$-0.425172\pi$
$719$	8981.09			0.465839			0.232919	+	0.972496i	$0.425172\pi$
$720$	−687.282	+	1455.90i	−0.0355743	+	0.0753586i
$721$	−8494.33			−0.438759
$722$			8401.20i			0.433048i
$723$			7391.42i			0.380207i
$724$	8644.60			0.443749
$725$	6029.41	+	7324.91i	0.308864	+	0.375228i
$726$	−1792.29			−0.0916229
$727$		−	29389.4i		−	1.49930i	−0.661832	−	0.749652i	$-0.730221\pi$
$727$		−	29389.4i		−	1.49930i	0.661832	−	0.749652i	$-0.269779\pi$
$728$			518.340i			0.0263887i
$729$	−729.000			−0.0370370
$730$	2386.19	−	5054.76i	0.120982	−	0.256281i
$731$	12735.9			0.644397
$732$		−	1358.48i		−	0.0685939i
$733$			3408.89i			0.171774i	0.996305	+	0.0858869i	$0.0273724\pi$
$733$			3408.89i			0.171774i	−0.996305	+	0.0858869i	$0.972628\pi$
$734$	−1066.85			−0.0536487
$735$	7904.32	+	3731.37i	0.396674	+	0.187257i
$736$	3352.46			0.167898
$737$		−	1470.95i		−	0.0735187i
$738$			2832.58i			0.141286i
$739$	−3307.73			−0.164651			−0.0823253	−	0.996606i	$-0.526235\pi$
$739$	−3307.73			−0.164651			−0.0823253	+	0.996606i	$0.526235\pi$
$740$	−12757.6	−	6022.46i	−0.633757	−	0.299176i
$741$	1104.06			0.0547350
$742$		−	11701.9i		−	0.578962i
$743$		−	20436.5i		−	1.00908i	−0.863389	−	0.504538i	$-0.831663\pi$
$743$		−	20436.5i		−	1.00908i	0.863389	−	0.504538i	$-0.168337\pi$
$744$	744.000			0.0366618
$745$	2531.11	−	5361.76i	0.124473	−	0.263677i
$746$	−17120.8			−0.840262
$747$		−	7153.13i		−	0.350361i
$748$		−	6959.28i		−	0.340183i
$749$	−16281.0			−0.794252
$750$	−8129.45	+	2055.36i	−0.395794	+	0.100068i
$751$	−15687.2			−0.762230			−0.381115	−	0.924528i	$-0.624460\pi$
$751$	−15687.2			−0.762230			−0.381115	+	0.924528i	$0.624460\pi$
$752$			7721.69i			0.374443i
$753$			6050.05i			0.292797i
$754$	1083.48			0.0523317
$755$	−5715.66	+	12107.7i	−0.275515	+	0.583636i
$756$	−980.363			−0.0471633
$757$		−	4574.89i		−	0.219653i	−0.993951	−	0.109826i	$-0.964971\pi$
$757$		−	4574.89i		−	0.219653i	0.993951	−	0.109826i	$-0.0350295\pi$
$758$			19820.8i			0.949767i
$759$	10098.0			0.482916
$760$	4170.32	+	1968.67i	0.199044	+	0.0939620i
$761$	7036.05			0.335160			0.167580	−	0.985858i	$-0.446405\pi$
$761$	7036.05			0.335160			0.167580	+	0.985858i	$0.446405\pi$
$762$			9008.85i			0.428289i
$763$			4902.41i			0.232607i
$764$	10946.2			0.518352
$765$	4927.38	+	2326.05i	0.232876	+	0.109933i
$766$	12059.8			0.568849
$767$			5952.47i			0.280223i
$768$			768.000i			0.0360844i
$769$	−13120.5			−0.615265			−0.307633	−	0.951505i	$-0.599537\pi$
$769$	−13120.5			−0.615265			−0.307633	+	0.951505i	$0.599537\pi$
$770$	−2783.98	+	5897.42i	−0.130295	+	0.276011i
$771$	20270.3			0.946844
$772$		−	13071.1i		−	0.609376i
$773$			27282.1i			1.26943i	0.772747	+	0.634715i	$0.218882\pi$
$773$			27282.1i			1.26943i	−0.772747	+	0.634715i	$0.781118\pi$
$774$	−4233.48			−0.196601
$775$	2462.67	+	2991.80i	0.114144	+	0.138669i
$776$	−7235.29			−0.334706
$777$		−	8590.64i		−	0.396638i
$778$			3177.74i			0.146437i
$779$	8113.72			0.373176
$780$	−408.804	+	865.987i	−0.0187661	+	0.0397530i
$781$	28096.8			1.28730
$782$		−	11346.1i		−	0.518846i
$783$			2049.25i			0.0935302i
$784$	4169.60			0.189942
$785$	26110.4	+	12325.9i	1.18716	+	0.560420i
$786$	12500.6			0.567279
$787$		−	13449.8i		−	0.609191i	−0.952482	−	0.304595i	$-0.901479\pi$
$787$		−	13449.8i		−	0.609191i	0.952482	−	0.304595i	$-0.0985212\pi$
$788$		−	6532.51i		−	0.295318i
$789$	−1923.24			−0.0867796
$790$	−22412.5	−	10580.2i	−1.00937	−	0.476490i
$791$	−5942.43			−0.267116
$792$			2313.30i			0.103787i
$793$		−	808.039i		−	0.0361845i
$794$	−4869.43			−0.217644
$795$	9229.03	−	19550.3i	0.411723	−	0.872172i
$796$	15081.0			0.671522
$797$		−	24264.9i		−	1.07843i	−0.842169	−	0.539213i	$-0.818722\pi$
$797$		−	24264.9i		−	1.07843i	0.842169	−	0.539213i	$-0.181278\pi$
$798$			2808.18i			0.124572i
$799$	26133.5			1.15712
$800$	−3088.31	+	2542.11i	−0.136485	+	0.112346i
$801$	9315.03			0.410899
$802$		−	6667.23i		−	0.293551i
$803$		−	8031.59i		−	0.352962i
$804$	549.390			0.0240989
$805$	−4538.89	+	9614.92i	−0.198726	+	0.420971i
$806$	442.541			0.0193397
$807$			11776.7i			0.513705i
$808$			5536.99i			0.241078i
$809$	14313.7			0.622057			0.311028	−	0.950401i	$-0.399327\pi$
$809$	14313.7			0.622057			0.311028	+	0.950401i	$0.399327\pi$
$810$	−1637.89	−	773.192i	−0.0710487	−	0.0335398i
$811$	−1662.74			−0.0719933			−0.0359966	−	0.999352i	$-0.511461\pi$
$811$	−1662.74			−0.0719933			−0.0359966	+	0.999352i	$0.511461\pi$
$812$			2755.84i			0.119102i
$813$			20011.7i			0.863272i
$814$	−20270.8			−0.872839
$815$	19581.6	+	9243.85i	0.841613	+	0.397298i
$816$	2599.24			0.111509
$817$			12126.5i			0.519280i
$818$			12170.0i			0.520190i
$819$	−583.132			−0.0248795
$820$	−3004.29	+	6364.13i	−0.127945	+	0.271031i
$821$	−10518.9			−0.447154			−0.223577	−	0.974686i	$-0.571773\pi$
$821$	−10518.9			−0.447154			−0.223577	+	0.974686i	$0.571773\pi$
$822$			7020.53i			0.297894i
$823$			20979.5i			0.888579i	0.895883	+	0.444289i	$0.146544\pi$
$823$			20979.5i			0.888579i	−0.895883	+	0.444289i	$0.853456\pi$
$824$	−7486.10			−0.316494
$825$	−9302.34	+	7657.12i	−0.392565	+	0.323135i
$826$	−15140.1			−0.637763
$827$			2472.33i			0.103956i	0.998648	+	0.0519778i	$0.0165525\pi$
$827$			2472.33i			0.103956i	−0.998648	+	0.0519778i	$0.983447\pi$
$828$			3771.52i			0.158296i
$829$	−4742.28			−0.198681			−0.0993404	−	0.995054i	$-0.531673\pi$
$829$	−4742.28			−0.198681			−0.0993404	+	0.995054i	$0.531673\pi$
$830$	7586.75	−	16071.4i	0.317277	−	0.672102i
$831$	−20182.5			−0.842506
$832$			456.816i			0.0190352i
$833$		−	14111.7i		−	0.586965i
$834$	17230.0			0.715380
$835$	−2680.47	−	1265.36i	−0.111092	−	0.0524427i
$836$	6626.28			0.274132
$837$			837.000i			0.0345651i
$838$			4128.30i			0.170179i
$839$	−25105.8			−1.03307			−0.516537	−	0.856265i	$-0.672779\pi$
$839$	−25105.8			−1.03307			−0.516537	+	0.856265i	$0.672779\pi$
$840$	−2202.64	−	1039.79i	−0.0904742	−	0.0427099i
$841$	−18628.5			−0.763807
$842$			26579.1i			1.08786i
$843$		−	18565.5i		−	0.758515i
$844$	20345.4			0.829761
$845$	10242.7	−	21697.5i	0.416992	−	0.883332i
$846$	−8686.90			−0.353028
$847$		−	2711.57i		−	0.110001i
$848$		−	10312.9i		−	0.417627i
$849$	−11257.4			−0.455070
$850$	8603.58	+	10452.2i	0.347177	+	0.421772i
$851$	−33048.7			−1.33125
$852$			10493.9i			0.421968i
$853$			20550.6i			0.824899i	0.910980	+	0.412449i	$0.135327\pi$
$853$			20550.6i			0.824899i	−0.910980	+	0.412449i	$0.864673\pi$
$854$	2055.25			0.0823527
$855$	−2214.75	+	4691.60i	−0.0885882	+	0.187660i
$856$	−14348.5			−0.572924
$857$		−	21952.5i		−	0.875009i	−0.899216	−	0.437505i	$-0.855862\pi$
$857$		−	21952.5i		−	0.875009i	0.899216	−	0.437505i	$-0.144138\pi$
$858$			1375.98i			0.0547497i
$859$	11738.4			0.466249			0.233125	−	0.972447i	$-0.425105\pi$
$859$	11738.4			0.466249			0.233125	+	0.972447i	$0.425105\pi$
$860$	−9511.61	−	4490.11i	−0.377143	−	0.178037i
$861$	−4285.43			−0.169625
$862$			15355.1i			0.606724i
$863$			21287.1i			0.839653i	0.907604	+	0.419826i	$0.137909\pi$
$863$			21287.1i			0.839653i	−0.907604	+	0.419826i	$0.862091\pi$
$864$	−864.000			−0.0340207
$865$	−17992.6	−	8493.73i	−0.707246	−	0.333868i
$866$	24264.1			0.952112
$867$			5942.08i			0.232761i
$868$			1125.60i			0.0440155i
$869$	−35611.6			−1.39015
$870$	−2173.47	+	4604.16i	−0.0846985	+	0.179420i
$871$	326.784			0.0127126
$872$			4320.52i			0.167788i
$873$		−	8139.70i		−	0.315564i
$874$	10803.2			0.418106
$875$	−3109.56	−	12299.1i	−0.120140	−	0.475183i
$876$	2999.74			0.115698
$877$		−	37315.9i		−	1.43679i	−0.695633	−	0.718397i	$-0.744876\pi$
$877$		−	37315.9i		−	1.43679i	0.695633	−	0.718397i	$-0.255124\pi$
$878$		−	507.991i		−	0.0195260i
$879$	21874.0			0.839353
$880$	−2453.53	+	5197.43i	−0.0939871	+	0.199097i
$881$	33967.3			1.29897			0.649483	−	0.760376i	$-0.274985\pi$
$881$	33967.3			1.29897			0.649483	+	0.760376i	$0.274985\pi$
$882$			4690.80i			0.179079i
$883$			27657.1i			1.05406i	0.849846	+	0.527031i	$0.176695\pi$
$883$			27657.1i			1.05406i	−0.849846	+	0.527031i	$0.823305\pi$
$884$	1546.06			0.0588231
$885$	−25294.5	−	11940.7i	−0.960751	−	0.453539i
$886$	−32555.5			−1.23445
$887$		−	26934.0i		−	1.01956i	−0.860303	−	0.509782i	$-0.829726\pi$
$887$		−	26934.0i		−	1.01956i	0.860303	−	0.509782i	$-0.170274\pi$
$888$		−	7570.99i		−	0.286110i
$889$	−13629.5			−0.514196
$890$	20928.6	+	9879.71i	0.788235	+	0.372100i
$891$	−2602.46			−0.0978517
$892$			25970.1i			0.974824i
$893$			24883.0i			0.932449i
$894$	3181.92			0.119037
$895$	446.542	−	945.928i	0.0166774	−	0.0353284i
$896$	−1161.91			−0.0433223
$897$			2243.35i			0.0835040i
$898$			16638.2i			0.618291i
$899$	2352.84			0.0872877
$900$	−2859.87	−	3474.35i	−0.105921	−	0.128680i
$901$	−34903.4			−1.29057
$902$			10112.1i			0.373276i
$903$		−	6404.86i		−	0.236036i
$904$	−5237.10			−0.192681
$905$	−10314.7	+	21850.1i	−0.378865	+	0.802566i
$906$	−7185.30			−0.263483
$907$		−	26490.5i		−	0.969794i	−0.874571	−	0.484897i	$-0.838857\pi$
$907$		−	26490.5i		−	0.969794i	0.874571	−	0.484897i	$-0.161143\pi$
$908$		−	16287.0i		−	0.595267i
$909$	−6229.12			−0.227290
$910$	−1310.16	−	618.482i	−0.0477267	−	0.0225302i
$911$	−9643.78			−0.350727			−0.175364	−	0.984504i	$-0.556110\pi$
$911$	−9643.78			−0.350727			−0.175364	+	0.984504i	$0.556110\pi$
$912$			2474.86i			0.0898585i
$913$		−	25536.0i		−	0.925651i
$914$	6936.36			0.251022
$915$	3433.69	+	1620.93i	0.124059	+	0.0585643i
$916$	14733.5			0.531451
$917$			18912.2i			0.681065i
$918$			2924.14i			0.105132i
$919$	−12477.8			−0.447884			−0.223942	−	0.974602i	$-0.571893\pi$
$919$	−12477.8			−0.447884			−0.223942	+	0.974602i	$0.571893\pi$
$920$	−4000.15	+	8473.69i	−0.143349	+	0.303662i
$921$	31556.1			1.12900
$922$			7075.47i			0.252731i
$923$			6241.93i			0.222595i
$924$	−3499.81			−0.124605
$925$	30444.8	−	25060.3i	1.08218	−	0.890785i
$926$	8385.06			0.297570
$927$		−	8421.86i		−	0.298393i
$928$			2428.74i			0.0859130i
$929$	44343.8			1.56606			0.783032	−	0.621982i	$-0.213672\pi$
$929$	44343.8			1.56606			0.783032	+	0.621982i	$0.213672\pi$
$930$	−887.739	+	1880.54i	−0.0313012	+	0.0663067i
$931$	13436.5			0.472999
$932$			2154.38i			0.0757179i
$933$		−	99.2584i		−	0.00348293i
$934$	−16865.0			−0.590835
$935$	17590.3	+	8303.80i	0.615256	+	0.290442i
$936$	−513.918			−0.0179465
$937$			51152.4i			1.78343i	0.452595	+	0.891716i	$0.350498\pi$
$937$			51152.4i			1.78343i	−0.452595	+	0.891716i	$0.649502\pi$
$938$			831.175i			0.0289327i
$939$	12151.5			0.422310
$940$	−19517.4	−	9213.50i	−0.677219	−	0.319693i
$941$	−23068.9			−0.799178			−0.399589	−	0.916694i	$-0.630847\pi$
$941$	−23068.9			−0.799178			−0.399589	+	0.916694i	$0.630847\pi$
$942$			15495.2i			0.535945i
$943$			16486.3i			0.569319i
$944$	−13343.1			−0.460042
$945$	1169.77	−	2477.97i	0.0402672	−	0.0852998i
$946$	−15113.1			−0.519419
$947$		−	23900.2i		−	0.820118i	−0.912059	−	0.410059i	$-0.865508\pi$
$947$		−	23900.2i		−	0.820118i	0.912059	−	0.410059i	$-0.134492\pi$
$948$		−	13300.6i		−	0.455680i
$949$	1784.28			0.0610329
$950$	−9952.02	+	8191.89i	−0.339880	+	0.279768i
$951$	25101.5			0.855913
$952$			3932.40i			0.133876i
$953$		−	27745.8i		−	0.943099i	−0.881839	−	0.471550i	$-0.843695\pi$
$953$		−	27745.8i		−	0.943099i	0.881839	−	0.471550i	$-0.156305\pi$
$954$	11602.1			0.393743
$955$	−13061.0	+	27667.8i	−0.442560	+	0.937495i
$956$	−28507.3			−0.964426
$957$			7315.63i			0.247106i
$958$		−	20629.5i		−	0.695729i
$959$	−10621.4			−0.357647
$960$	−1941.20	−	916.376i	−0.0652624	−	0.0308082i
$961$	961.000			0.0322581
$962$		−	4503.32i		−	0.150928i
$963$		−	16142.1i		−	0.540158i
$964$	−9855.23			−0.329269
$965$	33038.5	+	15596.4i	1.10212	+	0.520275i
$966$	−5705.95			−0.190048
$967$		−	6528.20i		−	0.217097i	−0.994091	−	0.108548i	$-0.965380\pi$
$967$		−	6528.20i		−	0.217097i	0.994091	−	0.108548i	$-0.0346203\pi$
$968$		−	2389.72i		−	0.0793478i
$969$	8375.99			0.277684
$970$	8633.13	−	18287.9i	0.285766	−	0.605351i
$971$	−44795.4			−1.48049			−0.740243	−	0.672339i	$-0.765290\pi$
$971$	−44795.4			−1.48049			−0.740243	+	0.672339i	$0.765290\pi$
$972$		−	972.000i		−	0.0320750i
$973$			26067.4i			0.858873i
$974$	−8972.91			−0.295185
$975$	−1701.09	−	2066.59i	−0.0558753	−	0.0678808i
$976$	1811.30			0.0594041
$977$			46848.8i			1.53411i	0.641581	+	0.767055i	$0.278279\pi$
$977$			46848.8i			1.53411i	−0.641581	+	0.767055i	$0.721721\pi$
$978$			11620.7i			0.379947i
$979$	33253.8			1.08559
$980$	−4975.16	+	10539.1i	−0.162169	+	0.343530i
$981$	−4860.59			−0.158192
$982$		−	13857.6i		−	0.450319i
$983$			6665.21i			0.216264i	0.994137	+	0.108132i	$0.0344869\pi$
$983$			6665.21i			0.216264i	−0.994137	+	0.108132i	$0.965513\pi$
$984$	−3776.78			−0.122357
$985$	16511.6	+	7794.57i	0.534115	+	0.252138i
$986$	8219.88			0.265491
$987$		−	13142.5i		−	0.423839i
$988$			1472.08i			0.0474019i
$989$	−24639.9			−0.792217
$990$	−5847.11	−	2760.23i	−0.187710	−	0.0886119i
$991$	25004.9			0.801521			0.400760	−	0.916183i	$-0.368746\pi$
$991$	25004.9			0.801521			0.400760	+	0.916183i	$0.368746\pi$
$992$			992.000i			0.0317500i
$993$		−	27576.6i		−	0.881284i
$994$	−15876.4			−0.506607
$995$	−17994.6	+	38118.8i	−0.573334	+	1.21452i
$996$	9537.51			0.303421
$997$			37530.1i			1.19217i	0.802923	+	0.596083i	$0.203277\pi$
$997$			37530.1i			1.19217i	−0.802923	+	0.596083i	$0.796723\pi$
$998$			10655.4i			0.337966i
$999$	8517.36			0.269747

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.4.d.c.559.8	✓	20
5.4	even	2	inner	930.4.d.c.559.18	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.4.d.c.559.8	✓	20	1.1	even	1	trivial
930.4.d.c.559.18	yes	20	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	930.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} +3.00000i q^{3} -4.00000 q^{4} +(4.77279 - 10.1104i) q^{5} +6.00000 q^{6} +9.07744i q^{7} +8.00000i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} +3.00000i q^{3} -4.00000 q^{4} +(4.77279 - 10.1104i) q^{5} +6.00000 q^{6} +9.07744i q^{7} +8.00000i q^{8} -9.00000 q^{9} +(-20.2208 - 9.54558i) q^{10} -32.1292 q^{11} -12.0000i q^{12} -7.13775i q^{13} +18.1549 q^{14} +(30.3312 + 14.3184i) q^{15} +16.0000 q^{16} -54.1508i q^{17} +18.0000i q^{18} +51.5597 q^{19} +(-19.0912 + 40.4417i) q^{20} -27.2323 q^{21} +64.2584i q^{22} +104.764i q^{23} -24.0000 q^{24} +(-79.4409 - 96.5098i) q^{25} -14.2755 q^{26} -27.0000i q^{27} -36.3098i q^{28} -75.8981 q^{29} +(28.6368 - 60.6625i) q^{30} -31.0000 q^{31} -32.0000i q^{32} -96.3876i q^{33} -108.302 q^{34} +(91.7767 + 43.3247i) q^{35} +36.0000 q^{36} +315.458i q^{37} -103.119i q^{38} +21.4133 q^{39} +(80.8833 + 38.1823i) q^{40} +157.366 q^{41} +54.4646i q^{42} +235.193i q^{43} +128.517 q^{44} +(-42.9551 + 90.9937i) q^{45} +209.529 q^{46} +482.605i q^{47} +48.0000i q^{48} +260.600 q^{49} +(-193.020 + 158.882i) q^{50} +162.452 q^{51} +28.5510i q^{52} -644.559i q^{53} -54.0000 q^{54} +(-153.346 + 324.839i) q^{55} -72.6195 q^{56} +154.679i q^{57} +151.796i q^{58} -833.942 q^{59} +(-121.325 - 57.2735i) q^{60} +113.206 q^{61} +62.0000i q^{62} -81.6969i q^{63} -64.0000 q^{64} +(-72.1656 - 34.0670i) q^{65} -192.775 q^{66} +45.7825i q^{67} +216.603i q^{68} -314.293 q^{69} +(86.6494 - 183.553i) q^{70} -874.495 q^{71} -72.0000i q^{72} +249.978i q^{73} +630.916 q^{74} +(289.529 - 238.323i) q^{75} -206.239 q^{76} -291.651i q^{77} -42.8265i q^{78} +1108.39 q^{79} +(76.3647 - 161.767i) q^{80} +81.0000 q^{81} -314.731i q^{82} +794.792i q^{83} +108.929 q^{84} +(-547.487 - 258.450i) q^{85} +470.387 q^{86} -227.694i q^{87} -257.033i q^{88} -1035.00 q^{89} +(181.987 + 85.9103i) q^{90} +64.7925 q^{91} -419.057i q^{92} -93.0000i q^{93} +965.211 q^{94} +(246.083 - 521.289i) q^{95} +96.0000 q^{96} +904.411i q^{97} -521.200i q^{98} +289.163 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 80 q^{4} - 2 q^{5} + 120 q^{6} - 180 q^{9}+O(q^{10}) \) 20 * q - 80 * q^4 - 2 * q^5 + 120 * q^6 - 180 * q^9	\( 20 q - 80 q^{4} - 2 q^{5} + 120 q^{6} - 180 q^{9} + 8 q^{10} - 114 q^{11} + 52 q^{14} - 12 q^{15} + 320 q^{16} + 370 q^{19} + 8 q^{20} - 78 q^{21} - 480 q^{24} - 90 q^{25} - 368 q^{26} + 368 q^{29} - 12 q^{30} - 620 q^{31} + 712 q^{34} + 374 q^{35} + 720 q^{36} + 552 q^{39} - 32 q^{40} - 872 q^{41} + 456 q^{44} + 18 q^{45} - 1236 q^{46} + 1334 q^{49} + 416 q^{50} - 1068 q^{51} - 1080 q^{54} - 1290 q^{55} - 208 q^{56} + 3228 q^{59} + 48 q^{60} - 2604 q^{61} - 1280 q^{64} + 44 q^{65} - 684 q^{66} + 1854 q^{69} - 852 q^{70} - 2290 q^{71} + 2008 q^{74} - 624 q^{75} - 1480 q^{76} + 4342 q^{79} - 32 q^{80} + 1620 q^{81} + 312 q^{84} + 500 q^{85} - 4 q^{86} + 1390 q^{89} - 72 q^{90} - 5744 q^{91} + 2608 q^{94} - 1136 q^{95} + 1920 q^{96} + 1026 q^{99}+O(q^{100}) \) 20 * q - 80 * q^4 - 2 * q^5 + 120 * q^6 - 180 * q^9 + 8 * q^10 - 114 * q^11 + 52 * q^14 - 12 * q^15 + 320 * q^16 + 370 * q^19 + 8 * q^20 - 78 * q^21 - 480 * q^24 - 90 * q^25 - 368 * q^26 + 368 * q^29 - 12 * q^30 - 620 * q^31 + 712 * q^34 + 374 * q^35 + 720 * q^36 + 552 * q^39 - 32 * q^40 - 872 * q^41 + 456 * q^44 + 18 * q^45 - 1236 * q^46 + 1334 * q^49 + 416 * q^50 - 1068 * q^51 - 1080 * q^54 - 1290 * q^55 - 208 * q^56 + 3228 * q^59 + 48 * q^60 - 2604 * q^61 - 1280 * q^64 + 44 * q^65 - 684 * q^66 + 1854 * q^69 - 852 * q^70 - 2290 * q^71 + 2008 * q^74 - 624 * q^75 - 1480 * q^76 + 4342 * q^79 - 32 * q^80 + 1620 * q^81 + 312 * q^84 + 500 * q^85 - 4 * q^86 + 1390 * q^89 - 72 * q^90 - 5744 * q^91 + 2608 * q^94 - 1136 * q^95 + 1920 * q^96 + 1026 * q^99

Introduction

L-functions

Modular forms

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