LMFDB - Embedded newform 30.5.d.a.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [30,5,Mod(11,30)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(30, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("30.11");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	30.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:	$3.10109889252$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} + 9 $ x^4 - 4*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.2
Root			$-1.58114 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	30.11
Dual form			30.5.d.a.11.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82843i q^{2} +(4.32456 - 7.89292i) q^{3} -8.00000 q^{4} -11.1803i q^{5} +(-22.3246 - 12.2317i) q^{6} -8.05267 q^{7} +22.6274i q^{8} +(-43.5964 - 68.2668i) q^{9} +O(q^{10})$	\(q-2.82843i q^{2} +(4.32456 - 7.89292i) q^{3} -8.00000 q^{4} -11.1803i q^{5} +(-22.3246 - 12.2317i) q^{6} -8.05267 q^{7} +22.6274i q^{8} +(-43.5964 - 68.2668i) q^{9} -31.6228 q^{10} -51.7119i q^{11} +(-34.5964 + 63.1434i) q^{12} +269.737 q^{13} +22.7764i q^{14} +(-88.2456 - 48.3500i) q^{15} +64.0000 q^{16} +439.988i q^{17} +(-193.088 + 123.309i) q^{18} +529.684 q^{19} +89.4427i q^{20} +(-34.8242 + 63.5591i) q^{21} -146.263 q^{22} -230.833i q^{23} +(178.596 + 97.8535i) q^{24} -125.000 q^{25} -762.930i q^{26} +(-727.359 + 48.8800i) q^{27} +64.4213 q^{28} -183.829i q^{29} +(-136.754 + 249.596i) q^{30} -302.527 q^{31} -181.019i q^{32} +(-408.158 - 223.631i) q^{33} +1244.47 q^{34} +90.0316i q^{35} +(348.772 + 546.134i) q^{36} -2364.47 q^{37} -1498.17i q^{38} +(1166.49 - 2129.01i) q^{39} +252.982 q^{40} +883.176i q^{41} +(179.772 + 98.4977i) q^{42} +2357.10 q^{43} +413.695i q^{44} +(-763.246 + 487.423i) q^{45} -652.894 q^{46} +2468.27i q^{47} +(276.772 - 505.147i) q^{48} -2336.15 q^{49} +353.553i q^{50} +(3472.79 + 1902.75i) q^{51} -2157.89 q^{52} +4767.11i q^{53} +(138.253 + 2057.28i) q^{54} -578.157 q^{55} -182.211i q^{56} +(2290.65 - 4180.75i) q^{57} -519.946 q^{58} -3376.15i q^{59} +(705.964 + 386.800i) q^{60} -391.685 q^{61} +855.675i q^{62} +(351.068 + 549.730i) q^{63} -512.000 q^{64} -3015.75i q^{65} +(-632.524 + 1154.45i) q^{66} +4366.68 q^{67} -3519.90i q^{68} +(-1821.95 - 998.250i) q^{69} +254.648 q^{70} -8826.11i q^{71} +(1544.70 - 986.475i) q^{72} -2498.21 q^{73} +6687.74i q^{74} +(-540.569 + 986.615i) q^{75} -4237.47 q^{76} +416.419i q^{77} +(-6021.75 - 3299.34i) q^{78} -3054.95 q^{79} -715.542i q^{80} +(-2759.70 + 5952.38i) q^{81} +2498.00 q^{82} +1817.47i q^{83} +(278.594 - 508.473i) q^{84} +4919.21 q^{85} -6666.90i q^{86} +(-1450.95 - 794.977i) q^{87} +1170.11 q^{88} +7347.20i q^{89} +(1378.64 + 2158.78i) q^{90} -2172.10 q^{91} +1846.66i q^{92} +(-1308.29 + 2387.82i) q^{93} +6981.31 q^{94} -5922.05i q^{95} +(-1428.77 - 782.828i) q^{96} +16599.3 q^{97} +6607.64i q^{98} +(-3530.20 + 2254.45i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{3} - 32 q^{4} - 64 q^{6} - 184 q^{7} + 28 q^{9}+O(q^{10}) $ 4 * q - 8 * q^3 - 32 * q^4 - 64 * q^6 - 184 * q^7 + 28 * q^9	$ 4 q - 8 q^{3} - 32 q^{4} - 64 q^{6} - 184 q^{7} + 28 q^{9} + 64 q^{12} + 320 q^{13} - 100 q^{15} + 256 q^{16} - 64 q^{18} + 1208 q^{19} + 1328 q^{21} - 1344 q^{22} + 512 q^{24} - 500 q^{25} - 2024 q^{27} + 1472 q^{28} - 800 q^{30} - 2728 q^{31} - 2088 q^{33} + 576 q^{34} - 224 q^{36} - 5056 q^{37} + 4160 q^{39} + 1984 q^{42} + 6848 q^{43} - 2800 q^{45} + 576 q^{46} - 512 q^{48} + 4620 q^{49} + 4632 q^{51} - 2560 q^{52} - 3520 q^{54} + 3000 q^{55} + 3344 q^{57} + 3840 q^{58} + 800 q^{60} - 6424 q^{61} - 8968 q^{63} - 2048 q^{64} + 7488 q^{66} + 7904 q^{67} - 1368 q^{69} - 4800 q^{70} + 512 q^{72} - 10600 q^{73} + 1000 q^{75} - 9664 q^{76} - 9920 q^{78} - 26488 q^{79} - 5372 q^{81} + 4224 q^{82} - 10624 q^{84} + 17400 q^{85} + 3000 q^{87} + 10752 q^{88} + 6400 q^{90} + 14080 q^{91} + 15056 q^{93} + 2880 q^{94} - 4096 q^{96} + 35432 q^{97} + 14112 q^{99}+O(q^{100}) $ 4 * q - 8 * q^3 - 32 * q^4 - 64 * q^6 - 184 * q^7 + 28 * q^9 + 64 * q^12 + 320 * q^13 - 100 * q^15 + 256 * q^16 - 64 * q^18 + 1208 * q^19 + 1328 * q^21 - 1344 * q^22 + 512 * q^24 - 500 * q^25 - 2024 * q^27 + 1472 * q^28 - 800 * q^30 - 2728 * q^31 - 2088 * q^33 + 576 * q^34 - 224 * q^36 - 5056 * q^37 + 4160 * q^39 + 1984 * q^42 + 6848 * q^43 - 2800 * q^45 + 576 * q^46 - 512 * q^48 + 4620 * q^49 + 4632 * q^51 - 2560 * q^52 - 3520 * q^54 + 3000 * q^55 + 3344 * q^57 + 3840 * q^58 + 800 * q^60 - 6424 * q^61 - 8968 * q^63 - 2048 * q^64 + 7488 * q^66 + 7904 * q^67 - 1368 * q^69 - 4800 * q^70 + 512 * q^72 - 10600 * q^73 + 1000 * q^75 - 9664 * q^76 - 9920 * q^78 - 26488 * q^79 - 5372 * q^81 + 4224 * q^82 - 10624 * q^84 + 17400 * q^85 + 3000 * q^87 + 10752 * q^88 + 6400 * q^90 + 14080 * q^91 + 15056 * q^93 + 2880 * q^94 - 4096 * q^96 + 35432 * q^97 + 14112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	2.82843i		−	0.707107i
$2$		−	2.82843i		−	0.707107i
$3$	4.32456	−	7.89292i	0.480506	−	0.876991i
$3$	4.32456	−	7.89292i	0.480506	−	0.876991i
$4$	−8.00000			−0.500000
$5$		−	11.1803i		−	0.447214i
$5$		−	11.1803i		−	0.447214i
$6$	−22.3246	−	12.2317i	−0.620127	−	0.339769i
$7$	−8.05267			−0.164340			−0.0821701	−	0.996618i	$-0.526185\pi$
$7$	−8.05267			−0.164340			−0.0821701	+	0.996618i	$0.526185\pi$
$8$			22.6274i			0.353553i
$9$	−43.5964	−	68.2668i	−0.538228	−	0.842799i
$10$	−31.6228			−0.316228
$11$		−	51.7119i		−	0.427371i	−0.976902	−	0.213686i	$-0.931453\pi$
$11$		−	51.7119i		−	0.427371i	0.976902	−	0.213686i	$-0.0685468\pi$
$12$	−34.5964	+	63.1434i	−0.240253	+	0.438496i
$13$	269.737			1.59607			0.798037	−	0.602608i	$-0.205872\pi$
$13$	269.737			1.59607			0.798037	+	0.602608i	$0.205872\pi$
$14$			22.7764i			0.116206i
$15$	−88.2456	−	48.3500i	−0.392202	−	0.214889i
$16$	64.0000			0.250000
$17$			439.988i			1.52245i	0.648489	+	0.761224i	$0.275401\pi$
$17$			439.988i			1.52245i	−0.648489	+	0.761224i	$0.724599\pi$
$18$	−193.088	+	123.309i	−0.595949	+	0.380584i
$19$	529.684			1.46727			0.733634	−	0.679544i	$-0.237823\pi$
$19$	529.684			1.46727			0.733634	+	0.679544i	$0.237823\pi$
$20$			89.4427i			0.223607i
$21$	−34.8242	+	63.5591i	−0.0789665	+	0.144125i
$22$	−146.263			−0.302197
$23$		−	230.833i		−	0.436357i	−0.975909	−	0.218179i	$-0.929988\pi$
$23$		−	230.833i		−	0.436357i	0.975909	−	0.218179i	$-0.0700115\pi$
$24$	178.596	+	97.8535i	0.310063	+	0.169885i
$25$	−125.000			−0.200000
$26$		−	762.930i		−	1.12860i
$27$	−727.359	+	48.8800i	−0.997750	+	0.0670507i
$28$	64.4213			0.0821701
$29$		−	183.829i		−	0.218583i	−0.994010	−	0.109292i	$-0.965142\pi$
$29$		−	183.829i		−	0.218583i	0.994010	−	0.109292i	$-0.0348583\pi$
$30$	−136.754	+	249.596i	−0.151949	+	0.277329i
$31$	−302.527			−0.314804			−0.157402	−	0.987535i	$-0.550312\pi$
$31$	−302.527			−0.314804			−0.157402	+	0.987535i	$0.550312\pi$
$32$		−	181.019i		−	0.176777i
$33$	−408.158	−	223.631i	−0.374801	−	0.205354i
$34$	1244.47			1.07653
$35$			90.0316i			0.0734952i
$36$	348.772	+	546.134i	0.269114	+	0.421400i
$37$	−2364.47			−1.72715			−0.863577	−	0.504218i	$-0.831781\pi$
$37$	−2364.47			−1.72715			−0.863577	+	0.504218i	$0.831781\pi$
$38$		−	1498.17i		−	1.03752i
$39$	1166.49	−	2129.01i	0.766924	−	1.39974i
$40$	252.982			0.158114
$41$			883.176i			0.525387i	0.964879	+	0.262694i	$0.0846108\pi$
$41$			883.176i			0.525387i	−0.964879	+	0.262694i	$0.915389\pi$
$42$	179.772	+	98.4977i	0.101912	+	0.0558377i
$43$	2357.10			1.27480			0.637400	−	0.770533i	$-0.280010\pi$
$43$	2357.10			1.27480			0.637400	+	0.770533i	$0.280010\pi$
$44$			413.695i			0.213686i
$45$	−763.246	+	487.423i	−0.376911	+	0.240703i
$46$	−652.894			−0.308551
$47$			2468.27i			1.11737i	0.829381	+	0.558684i	$0.188694\pi$
$47$			2468.27i			1.11737i	−0.829381	+	0.558684i	$0.811306\pi$
$48$	276.772	−	505.147i	0.120127	−	0.219248i
$49$	−2336.15			−0.972992
$50$			353.553i			0.141421i
$51$	3472.79	+	1902.75i	1.33517	+	0.731546i
$52$	−2157.89			−0.798037
$53$			4767.11i			1.69708i	0.529129	+	0.848542i	$0.322519\pi$
$53$			4767.11i			1.69708i	−0.529129	+	0.848542i	$0.677481\pi$
$54$	138.253	+	2057.28i	0.0474120	+	0.705515i
$55$	−578.157			−0.191126
$56$		−	182.211i		−	0.0581030i
$57$	2290.65	−	4180.75i	0.705032	−	1.28678i
$58$	−519.946			−0.154562
$59$		−	3376.15i		−	0.969881i	−0.874547	−	0.484940i	$-0.838841\pi$
$59$		−	3376.15i		−	0.969881i	0.874547	−	0.484940i	$-0.161159\pi$
$60$	705.964	+	386.800i	0.196101	+	0.107444i
$61$	−391.685			−0.105263			−0.0526317	−	0.998614i	$-0.516761\pi$
$61$	−391.685			−0.105263			−0.0526317	+	0.998614i	$0.516761\pi$
$62$			855.675i			0.222600i
$63$	351.068	+	549.730i	0.0884524	+	0.138506i
$64$	−512.000			−0.125000
$65$		−	3015.75i		−	0.713786i
$66$	−632.524	+	1154.45i	−0.145208	+	0.265024i
$67$	4366.68			0.972752			0.486376	−	0.873750i	$-0.338319\pi$
$67$	4366.68			0.972752			0.486376	+	0.873750i	$0.338319\pi$
$68$		−	3519.90i		−	0.761224i
$69$	−1821.95	−	998.250i	−0.382681	−	0.209672i
$70$	254.648			0.0519689
$71$		−	8826.11i		−	1.75086i	−0.483341	−	0.875432i	$-0.660577\pi$
$71$		−	8826.11i		−	1.75086i	0.483341	−	0.875432i	$-0.339423\pi$
$72$	1544.70	−	986.475i	0.297975	−	0.190292i
$73$	−2498.21			−0.468795			−0.234398	−	0.972141i	$-0.575312\pi$
$73$	−2498.21			−0.468795			−0.234398	+	0.972141i	$0.575312\pi$
$74$			6687.74i			1.22128i
$75$	−540.569	+	986.615i	−0.0961012	+	0.175398i
$76$	−4237.47			−0.733634
$77$			416.419i			0.0702342i
$78$	−6021.75	−	3299.34i	−0.989768	−	0.542297i
$79$	−3054.95			−0.489497			−0.244749	−	0.969587i	$-0.578705\pi$
$79$	−3054.95			−0.489497			−0.244749	+	0.969587i	$0.578705\pi$
$80$		−	715.542i		−	0.111803i
$81$	−2759.70	+	5952.38i	−0.420622	+	0.907236i
$82$	2498.00			0.371505
$83$			1817.47i			0.263822i	0.991262	+	0.131911i	$0.0421114\pi$
$83$			1817.47i			0.263822i	−0.991262	+	0.131911i	$0.957889\pi$
$84$	278.594	−	508.473i	0.0394832	−	0.0720625i
$85$	4919.21			0.680860
$86$		−	6666.90i		−	0.901420i
$87$	−1450.95	−	794.977i	−0.191696	−	0.105031i
$88$	1170.11			0.151098
$89$			7347.20i			0.927560i	0.885950	+	0.463780i	$0.153507\pi$
$89$			7347.20i			0.927560i	−0.885950	+	0.463780i	$0.846493\pi$
$90$	1378.64	+	2158.78i	0.170203	+	0.266517i
$91$	−2172.10			−0.262299
$92$			1846.66i			0.218179i
$93$	−1308.29	+	2387.82i	−0.151265	+	0.276080i
$94$	6981.31			0.790098
$95$		−	5922.05i		−	0.656182i
$96$	−1428.77	−	782.828i	−0.155032	−	0.0849423i
$97$	16599.3			1.76419			0.882095	−	0.471072i	$-0.156133\pi$
$97$	16599.3			1.76419			0.882095	+	0.471072i	$0.156133\pi$
$98$			6607.64i			0.688009i
$99$	−3530.20	+	2254.45i	−0.360188	+	0.230023i
$100$	1000.00			0.100000
$101$			836.151i			0.0819675i	0.999160	+	0.0409838i	$0.0130492\pi$
$101$			836.151i			0.0819675i	−0.999160	+	0.0409838i	$0.986951\pi$
$102$	5381.79	−	9822.53i	0.517281	−	0.944111i
$103$	138.151			0.0130221			0.00651103	−	0.999979i	$-0.497927\pi$
$103$	138.151			0.0130221			0.00651103	+	0.999979i	$0.497927\pi$
$104$			6103.44i			0.564298i
$105$	710.612	+	389.346i	0.0644546	+	0.0353149i
$106$	13483.4			1.20002
$107$			9925.87i			0.866964i	0.901162	+	0.433482i	$0.142715\pi$
$107$			9925.87i			0.866964i	−0.901162	+	0.433482i	$0.857285\pi$
$108$	5818.88	−	391.040i	0.498875	−	0.0335254i
$109$	−15684.4			−1.32013			−0.660063	−	0.751211i	$-0.729470\pi$
$109$	−15684.4			−1.32013			−0.660063	+	0.751211i	$0.729470\pi$
$110$			1635.27i			0.135147i
$111$	−10225.3	+	18662.6i	−0.829908	+	1.51470i
$112$	−515.371			−0.0410850
$113$		−	4627.40i		−	0.362394i	−0.983447	−	0.181197i	$-0.942003\pi$
$113$		−	4627.40i		−	0.362394i	0.983447	−	0.181197i	$-0.0579971\pi$
$114$	−11825.0	−	6478.93i	−0.909892	−	0.498533i
$115$	−2580.79			−0.195145
$116$			1470.63i			0.109292i
$117$	−11759.6	−	18414.0i	−0.859052	−	1.34517i
$118$	−9549.21			−0.685809
$119$		−	3543.07i		−	0.250199i
$120$	1094.04	−	1996.77i	0.0759747	−	0.138665i
$121$	11966.9			0.817354
$122$			1107.85i			0.0744325i
$123$	6970.84	+	3819.34i	0.460760	+	0.252452i
$124$	2420.21			0.157402
$125$			1397.54i			0.0894427i
$126$	1554.87	−	992.969i	0.0979384	−	0.0625453i
$127$	−6066.04			−0.376095			−0.188048	−	0.982160i	$-0.560216\pi$
$127$	−6066.04			−0.376095			−0.188048	+	0.982160i	$0.560216\pi$
$128$			1448.15i			0.0883883i
$129$	10193.4	−	18604.4i	0.612549	−	1.11799i
$130$	−8529.82			−0.504723
$131$		−	22615.4i		−	1.31784i	−0.752215	−	0.658918i	$-0.771015\pi$
$131$		−	22615.4i		−	1.31784i	0.752215	−	0.658918i	$-0.228985\pi$
$132$	3265.26	+	1789.05i	0.187400	+	0.102677i
$133$	−4265.37			−0.241131
$134$		−	12350.8i		−	0.687839i
$135$	546.495	+	8132.13i	0.0299860	+	0.446207i
$136$	−9955.78			−0.538267
$137$		−	7721.45i		−	0.411394i	−0.978616	−	0.205697i	$-0.934054\pi$
$137$		−	7721.45i		−	0.411394i	0.978616	−	0.205697i	$-0.0659461\pi$
$138$	−2823.48	+	5153.24i	−0.148261	+	0.270597i
$139$	8922.30			0.461793			0.230897	−	0.972978i	$-0.425834\pi$
$139$	8922.30			0.461793			0.230897	+	0.972978i	$0.425834\pi$
$140$		−	720.253i		−	0.0367476i
$141$	19481.8	+	10674.2i	0.979922	+	0.536902i
$142$	−24964.0			−1.23805
$143$		−	13948.6i		−	0.682116i
$144$	−2790.17	−	4369.07i	−0.134557	−	0.210700i
$145$	−2055.27			−0.0977535
$146$			7066.01i			0.331488i
$147$	−10102.8	+	18439.1i	−0.467529	+	0.853306i
$148$	18915.8			0.863577
$149$			12527.5i			0.564278i	0.959374	+	0.282139i	$0.0910439\pi$
$149$			12527.5i			0.564278i	−0.959374	+	0.282139i	$0.908956\pi$
$150$	2790.57	+	1528.96i	0.124025	+	0.0679538i
$151$	−2937.56			−0.128835			−0.0644175	−	0.997923i	$-0.520519\pi$
$151$	−2937.56			−0.128835			−0.0644175	+	0.997923i	$0.520519\pi$
$152$			11985.4i			0.518758i
$153$	30036.5	−	19181.9i	1.28312	−	0.819424i
$154$	1177.81			0.0496631
$155$			3382.35i			0.140785i
$156$	−9331.93	+	17032.1i	−0.383462	+	0.699872i
$157$	−12343.5			−0.500771			−0.250386	−	0.968146i	$-0.580557\pi$
$157$	−12343.5			−0.500771			−0.250386	+	0.968146i	$0.580557\pi$
$158$			8640.71i			0.346127i
$159$	37626.4	+	20615.6i	1.48833	+	0.815459i
$160$	−2023.86			−0.0790569
$161$			1858.82i			0.0717110i
$162$	16835.9	+	7805.61i	0.641513	+	0.297425i
$163$	−43726.9			−1.64578			−0.822892	−	0.568197i	$-0.807641\pi$
$163$	−43726.9			−1.64578			−0.822892	+	0.568197i	$0.807641\pi$
$164$		−	7065.41i		−	0.262694i
$165$	−2500.27	+	4563.35i	−0.0918373	+	0.167616i
$166$	5140.59			0.186551
$167$			27799.8i			0.996801i	0.866947	+	0.498401i	$0.166079\pi$
$167$			27799.8i			0.996801i	−0.866947	+	0.498401i	$0.833921\pi$
$168$	−1438.18	−	787.982i	−0.0509558	−	0.0279189i
$169$	44196.9			1.54746
$170$		−	13913.6i		−	0.481440i
$171$	−23092.3	−	36159.8i	−0.789725	−	1.23661i
$172$	−18856.8			−0.637400
$173$			6355.98i			0.212369i	0.994346	+	0.106184i	$0.0338634\pi$
$173$			6355.98i			0.212369i	−0.994346	+	0.106184i	$0.966137\pi$
$174$	−2248.54	+	4103.89i	−0.0742679	+	0.135549i
$175$	1006.58			0.0328680
$176$		−	3309.56i		−	0.106843i
$177$	−26647.7	−	14600.4i	−0.850577	−	0.466034i
$178$	20781.0			0.655884
$179$			17762.2i			0.554359i	0.960818	+	0.277179i	$0.0893996\pi$
$179$			17762.2i			0.554359i	−0.960818	+	0.277179i	$0.910600\pi$
$180$	6105.96	−	3899.38i	0.188456	−	0.120351i
$181$	−17106.6			−0.522164			−0.261082	−	0.965317i	$-0.584079\pi$
$181$	−17106.6			−0.522164			−0.261082	+	0.965317i	$0.584079\pi$
$182$			6143.63i			0.185474i
$183$	−1693.87	+	3091.54i	−0.0505797	+	0.0923152i
$184$	5223.15			0.154276
$185$			26435.6i			0.772406i
$186$	6753.77	+	3700.41i	0.195218	+	0.106961i
$187$	22752.6			0.650650
$188$		−	19746.1i		−	0.558684i
$189$	5857.18	−	393.614i	0.163970	−	0.0110191i
$190$	−16750.1			−0.463991
$191$		−	28596.8i		−	0.783883i	−0.919990	−	0.391941i	$-0.871804\pi$
$191$		−	28596.8i		−	0.783883i	0.919990	−	0.391941i	$-0.128196\pi$
$192$	−2214.17	+	4041.18i	−0.0600633	+	0.109624i
$193$	9303.99			0.249778			0.124889	−	0.992171i	$-0.460142\pi$
$193$	9303.99			0.249778			0.124889	+	0.992171i	$0.460142\pi$
$194$		−	46949.8i		−	1.24747i
$195$	−23803.1	−	13041.8i	−0.625985	−	0.342979i
$196$	18689.2			0.486496
$197$			19956.2i			0.514216i	0.966383	+	0.257108i	$0.0827697\pi$
$197$			19956.2i			0.514216i	−0.966383	+	0.257108i	$0.917230\pi$
$198$	6376.56	+	9984.92i	0.162651	+	0.254691i
$199$	−42070.8			−1.06237			−0.531184	−	0.847256i	$-0.678253\pi$
$199$	−42070.8			−1.06237			−0.531184	+	0.847256i	$0.678253\pi$
$200$		−	2828.43i		−	0.0707107i
$201$	18884.0	−	34465.9i	0.467413	−	0.853095i
$202$	2364.99			0.0579598
$203$			1480.31i			0.0359220i
$204$	−27782.3	−	15222.0i	−0.667587	−	0.365773i
$205$	9874.21			0.234960
$206$		−	390.750i		−	0.00920799i
$207$	−15758.2	+	10063.5i	−0.367761	+	0.234859i
$208$	17263.1			0.399019
$209$		−	27391.0i		−	0.627068i
$210$	1101.24	−	2009.91i	0.0249714	−	0.0455763i
$211$	−6619.68			−0.148687			−0.0743433	−	0.997233i	$-0.523686\pi$
$211$	−6619.68			−0.148687			−0.0743433	+	0.997233i	$0.523686\pi$
$212$		−	38136.9i		−	0.848542i
$213$	−69663.8	−	38169.0i	−1.53549	−	0.841301i
$214$	28074.6			0.613036
$215$		−	26353.2i		−	0.570108i
$216$	−1106.03	−	16458.3i	−0.0237060	−	0.352758i
$217$	2436.15			0.0517349
$218$			44362.2i			0.933470i
$219$	−10803.7	+	19718.2i	−0.225259	+	0.411130i
$220$	4625.25			0.0955631
$221$			118681.i			2.42994i
$222$	52785.8	+	28921.5i	1.07105	+	0.586833i
$223$	60590.3			1.21841			0.609205	−	0.793013i	$-0.291489\pi$
$223$	60590.3			1.21841			0.609205	+	0.793013i	$0.291489\pi$
$224$			1457.69i			0.0290515i
$225$	5449.56	+	8533.34i	0.107646	+	0.168560i
$226$	−13088.3			−0.256251
$227$		−	76544.6i		−	1.48547i	−0.669587	−	0.742734i	$-0.733529\pi$
$227$		−	76544.6i		−	1.48547i	0.669587	−	0.742734i	$-0.266471\pi$
$228$	−18325.2	+	33446.0i	−0.352516	+	0.643391i
$229$	−65681.0			−1.25247			−0.626237	−	0.779632i	$-0.715406\pi$
$229$	−65681.0			−1.25247			−0.626237	+	0.779632i	$0.715406\pi$
$230$			7299.58i			0.137988i
$231$	3286.76	+	1800.83i	0.0615948	+	0.0337480i
$232$	4159.57			0.0772809
$233$			1273.59i			0.0234595i	0.999931	+	0.0117297i	$0.00373378\pi$
$233$			1273.59i			0.0234595i	−0.999931	+	0.0117297i	$0.996266\pi$
$234$	−52082.8	+	33261.1i	−0.951180	+	0.607441i
$235$	27596.0			0.499702
$236$			27009.2i			0.484940i
$237$	−13211.3	+	24112.5i	−0.235206	+	0.429285i
$238$	−10021.3			−0.176918
$239$			67328.9i			1.17871i	0.807876	+	0.589353i	$0.200617\pi$
$239$			67328.9i			1.17871i	−0.807876	+	0.589353i	$0.799383\pi$
$240$	−5647.72	−	3094.40i	−0.0980506	−	0.0537222i
$241$	27335.6			0.470646			0.235323	−	0.971917i	$-0.424385\pi$
$241$	27335.6			0.470646			0.235323	+	0.971917i	$0.424385\pi$
$242$		−	33847.4i		−	0.577957i
$243$	35047.2	+	47523.5i	0.593527	+	0.804814i
$244$	3133.48			0.0526317
$245$			26119.0i			0.435135i
$246$	10802.7	−	19716.5i	0.178510	−	0.325807i
$247$	142875.			2.34187
$248$		−	6845.40i		−	0.111300i
$249$	14345.2	+	7859.76i	0.231370	+	0.126768i
$250$	3952.85			0.0632456
$251$		−	3820.53i		−	0.0606424i	−0.999540	−	0.0303212i	$-0.990347\pi$
$251$		−	3820.53i		−	0.0606424i	0.999540	−	0.0303212i	$-0.00965301\pi$
$252$	−2808.54	−	4397.84i	−0.0442262	−	0.0692529i
$253$	−11936.8			−0.186486
$254$			17157.3i			0.265939i
$255$	21273.4	−	38826.9i	0.327157	−	0.597108i
$256$	4096.00			0.0625000
$257$		−	100977.i		−	1.52882i	−0.644733	−	0.764408i	$-0.723031\pi$
$257$		−	100977.i		−	1.52882i	0.644733	−	0.764408i	$-0.276969\pi$
$258$	−52621.3	−	28831.4i	−0.790537	−	0.433138i
$259$	19040.3			0.283841
$260$			24126.0i			0.356893i
$261$	−12549.4	+	8014.28i	−0.184222	+	0.117648i
$262$	−63965.9			−0.931850
$263$		−	69320.9i		−	1.00220i	−0.865390	−	0.501098i	$-0.832930\pi$
$263$		−	69320.9i		−	1.00220i	0.865390	−	0.501098i	$-0.167070\pi$
$264$	5060.19	−	9235.56i	0.0726038	−	0.132512i
$265$	53297.9			0.758959
$266$			12064.3i			0.170505i
$267$	57990.9	+	31773.4i	0.813462	+	0.445698i
$268$	−34933.5			−0.486376
$269$		−	76293.7i		−	1.05435i	−0.849757	−	0.527174i	$-0.823251\pi$
$269$		−	76293.7i		−	1.05435i	0.849757	−	0.527174i	$-0.176749\pi$
$270$	23001.1	−	1545.72i	0.315516	−	0.0212033i
$271$	−76598.1			−1.04299			−0.521494	−	0.853255i	$-0.674625\pi$
$271$	−76598.1			−1.04299			−0.521494	+	0.853255i	$0.674625\pi$
$272$			28159.2i			0.380612i
$273$	−9393.37	+	17144.2i	−0.126036	+	0.230034i
$274$	−21839.6			−0.290899
$275$			6463.99i			0.0854742i
$276$	14575.6	+	7986.00i	0.191341	+	0.104836i
$277$	−90489.2			−1.17934			−0.589668	−	0.807646i	$-0.700741\pi$
$277$	−90489.2			−1.17934			−0.589668	+	0.807646i	$0.700741\pi$
$278$		−	25236.1i		−	0.326537i
$279$	13189.1	+	20652.5i	0.169436	+	0.265317i
$280$	−2037.18			−0.0259845
$281$			84812.6i			1.07411i	0.843548	+	0.537054i	$0.180463\pi$
$281$			84812.6i			1.07411i	−0.843548	+	0.537054i	$0.819537\pi$
$282$	30191.1	−	55102.9i	0.379647	−	0.692909i
$283$	−84577.7			−1.05605			−0.528023	−	0.849230i	$-0.677067\pi$
$283$	−84577.7			−1.05605			−0.528023	+	0.849230i	$0.677067\pi$
$284$			70608.8i			0.875432i
$285$	−46742.3	−	25610.2i	−0.575466	−	0.315300i
$286$	−39452.6			−0.482329
$287$		−	7111.92i		−	0.0863422i
$288$	−12357.6	+	7891.80i	−0.148987	+	0.0951461i
$289$	−110068.			−1.31785
$290$			5813.17i			0.0691221i
$291$	71784.4	−	131017.i	0.847704	−	1.54718i
$292$	19985.7			0.234398
$293$			8186.37i			0.0953577i	0.998863	+	0.0476789i	$0.0151824\pi$
$293$			8186.37i			0.0953577i	−0.998863	+	0.0476789i	$0.984818\pi$
$294$	52153.6	+	28575.1i	0.603378	+	0.330593i
$295$	−37746.6			−0.433744
$296$		−	53501.9i		−	0.610641i
$297$	2527.68	+	37613.1i	0.0286555	+	0.426409i
$298$	35433.2			0.399005
$299$		−	62264.1i		−	0.696459i
$300$	4324.56	−	7892.92i	0.0480506	−	0.0876991i
$301$	−18981.0			−0.209501
$302$			8308.69i			0.0911000i
$303$	6599.67	+	3615.98i	0.0718848	+	0.0393859i
$304$	33899.8			0.366817
$305$			4379.18i			0.0470753i
$306$	−54254.6	−	84956.1i	−0.579420	−	0.907302i
$307$	67615.8			0.717417			0.358708	−	0.933450i	$-0.383217\pi$
$307$	67615.8			0.717417			0.358708	+	0.933450i	$0.383217\pi$
$308$		−	3331.35i		−	0.0351171i
$309$	597.442	−	1090.42i	0.00625718	−	0.0114202i
$310$	9566.73			0.0995498
$311$		−	44800.1i		−	0.463189i	−0.972812	−	0.231595i	$-0.925606\pi$
$311$		−	44800.1i		−	0.463189i	0.972812	−	0.231595i	$-0.0743943\pi$
$312$	48174.0	+	26394.7i	0.494884	+	0.271149i
$313$	30752.0			0.313895			0.156947	−	0.987607i	$-0.449835\pi$
$313$	30752.0			0.313895			0.156947	+	0.987607i	$0.449835\pi$
$314$			34912.7i			0.354099i
$315$	6146.16	−	3925.06i	0.0619417	−	0.0395571i
$316$	24439.6			0.244749
$317$		−	56148.0i		−	0.558747i	−0.960182	−	0.279374i	$-0.909873\pi$
$317$		−	56148.0i		−	0.558747i	0.960182	−	0.279374i	$-0.0901268\pi$
$318$	58309.8	−	106424.i	0.576617	−	1.05241i
$319$	−9506.13			−0.0934162
$320$			5724.33i			0.0559017i
$321$	78344.1	+	42925.0i	0.760320	+	0.416581i
$322$	5257.54			0.0507073
$323$			233054.i			2.23384i
$324$	22077.6	−	47619.0i	0.210311	−	0.453618i
$325$	−33717.1			−0.319215
$326$			123678.i			1.16375i
$327$	−67828.1	+	123796.i	−0.634328	+	1.15774i
$328$	−19984.0			−0.185752
$329$		−	19876.1i		−	0.183628i
$330$	12907.1	+	7071.83i	0.118522	+	0.0649388i
$331$	21677.4			0.197857			0.0989284	−	0.995095i	$-0.468459\pi$
$331$	21677.4			0.197857			0.0989284	+	0.995095i	$0.468459\pi$
$332$		−	14539.8i		−	0.131911i
$333$	103083.	+	161415.i	0.929602	+	1.45564i
$334$	78629.7			0.704845
$335$		−	48821.0i		−	0.435028i
$336$	−2228.75	+	4067.78i	−0.0197416	+	0.0360312i
$337$	−21432.6			−0.188719			−0.0943593	−	0.995538i	$-0.530080\pi$
$337$	−21432.6			−0.188719			−0.0943593	+	0.995538i	$0.530080\pi$
$338$		−	125008.i		−	1.09422i
$339$	−36523.7	−	20011.5i	−0.317816	−	0.174132i
$340$	−39353.7			−0.340430
$341$			15644.2i			0.134538i
$342$	−102275.	+	65315.0i	−0.874418	+	0.558420i
$343$	38146.7			0.324242
$344$			53335.2i			0.450710i
$345$	−11160.8	+	20370.0i	−0.0937683	+	0.171140i
$346$	17977.4			0.150167
$347$			194273.i			1.61344i	0.590933	+	0.806720i	$0.298760\pi$
$347$			194273.i			1.61344i	−0.590933	+	0.806720i	$0.701240\pi$
$348$	11607.6	+	6359.82i	0.0958479	+	0.0525153i
$349$	38807.4			0.318613			0.159307	−	0.987229i	$-0.449074\pi$
$349$	38807.4			0.318613			0.159307	+	0.987229i	$0.449074\pi$
$350$		−	2847.05i		−	0.0232412i
$351$	−196196.	+	13184.7i	−1.59248	+	0.107018i
$352$	−9360.85			−0.0755492
$353$		−	99488.2i		−	0.798403i	−0.916863	−	0.399202i	$-0.869287\pi$
$353$		−	99488.2i		−	0.798403i	0.916863	−	0.399202i	$-0.130713\pi$
$354$	−41296.1	+	75371.1i	−0.329536	+	0.601449i
$355$	−98678.9			−0.783010
$356$		−	58777.6i		−	0.463780i
$357$	−27965.2	−	15322.2i	−0.219423	−	0.120222i
$358$	50239.1			0.391991
$359$		−	168998.i		−	1.31127i	−0.755076	−	0.655637i	$-0.772400\pi$
$359$		−	168998.i		−	1.31127i	0.755076	−	0.655637i	$-0.227600\pi$
$360$	−11029.1	−	17270.3i	−0.0851013	−	0.133258i
$361$	150244.			1.15288
$362$			48384.8i			0.369226i
$363$	51751.4	−	94453.6i	0.392744	−	0.716812i
$364$	17376.8			0.131150
$365$			27930.8i			0.209652i
$366$	8744.20	+	4790.97i	0.0652767	+	0.0357653i
$367$	−225144.			−1.67158			−0.835792	−	0.549046i	$-0.814991\pi$
$367$	−225144.			−1.67158			−0.835792	+	0.549046i	$0.814991\pi$
$368$		−	14773.3i		−	0.109089i
$369$	60291.6	−	38503.3i	0.442796	−	0.282778i
$370$	74771.2			0.546174
$371$		−	38387.9i		−	0.278899i
$372$	10466.3	−	19102.6i	0.0756326	−	0.138040i
$373$	93217.4			0.670007			0.335004	−	0.942217i	$-0.391262\pi$
$373$	93217.4			0.670007			0.335004	+	0.942217i	$0.391262\pi$
$374$		−	64354.0i		−	0.460079i
$375$	11030.7	+	6043.75i	0.0784405	+	0.0429778i
$376$	−55850.5			−0.395049
$377$		−	49585.3i		−	0.348876i
$378$	−1113.31	−	16566.6i	−0.00779170	−	0.115945i
$379$	203532.			1.41695			0.708474	−	0.705737i	$-0.249384\pi$
$379$	203532.			1.41695			0.708474	+	0.705737i	$0.249384\pi$
$380$			47376.4i			0.328091i
$381$	−26232.9	+	47878.8i	−0.180716	+	0.329832i
$382$	−80884.0			−0.554289
$383$		−	95116.1i		−	0.648420i	−0.945985	−	0.324210i	$-0.894902\pi$
$383$		−	95116.1i		−	0.648420i	0.945985	−	0.324210i	$-0.105098\pi$
$384$	11430.2	+	6262.63i	0.0775158	+	0.0424711i
$385$	4655.70			0.0314097
$386$		−	26315.7i		−	0.176620i
$387$	−102761.	−	160912.i	−0.686132	−	1.07440i
$388$	−132794.			−0.882095
$389$		−	168755.i		−	1.11521i	−0.830106	−	0.557606i	$-0.811720\pi$
$389$		−	168755.i		−	1.11521i	0.830106	−	0.557606i	$-0.188280\pi$
$390$	−36887.7	+	67325.2i	−0.242523	+	0.442638i
$391$	101564.			0.664331
$392$		−	52861.1i		−	0.344005i
$393$	−178501.	−	97801.4i	−1.15573	−	0.633228i
$394$	56444.7			0.363606
$395$			34155.4i			0.218910i
$396$	28241.6	−	18035.6i	0.180094	−	0.115011i
$397$	111865.			0.709764			0.354882	−	0.934911i	$-0.384521\pi$
$397$	111865.			0.709764			0.354882	+	0.934911i	$0.384521\pi$
$398$			118994.i			0.751208i
$399$	−18445.8	+	33666.2i	−0.115865	+	0.211470i
$400$	−8000.00			−0.0500000
$401$		−	18794.2i		−	0.116879i	−0.998291	−	0.0584393i	$-0.981388\pi$
$401$		−	18794.2i		−	0.116879i	0.998291	−	0.0584393i	$-0.0186124\pi$
$402$	−97484.2	−	53411.9i	−0.603229	−	0.330511i
$403$	−81602.5			−0.502451
$404$		−	6689.20i		−	0.0409838i
$405$	66549.6	+	30854.4i	0.405728	+	0.188108i
$406$	4186.95			0.0254007
$407$			122271.i			0.738135i
$408$	−43054.3	+	78580.2i	−0.258640	+	0.472055i
$409$	121667.			0.727321			0.363661	−	0.931532i	$-0.381527\pi$
$409$	121667.			0.727321			0.363661	+	0.931532i	$0.381527\pi$
$410$		−	27928.5i		−	0.166142i
$411$	−60944.8	−	33391.8i	−0.360789	−	0.197677i
$412$	−1105.21			−0.00651103
$413$			27187.1i			0.159390i
$414$	28463.9	+	44571.0i	0.166071	+	0.260047i
$415$	20320.0			0.117985
$416$		−	48827.6i		−	0.282149i
$417$	38585.0	−	70423.1i	0.221894	−	0.404989i
$418$	−77473.3			−0.443404
$419$			338264.i			1.92676i	0.268139	+	0.963380i	$0.413591\pi$
$419$			338264.i			1.92676i	−0.268139	+	0.963380i	$0.586409\pi$
$420$	−5684.90	−	3114.77i	−0.0322273	−	0.0176574i
$421$	26726.9			0.150794			0.0753971	−	0.997154i	$-0.475978\pi$
$421$	26726.9			0.150794			0.0753971	+	0.997154i	$0.475978\pi$
$422$			18723.3i			0.105137i
$423$	168500.	−	107608.i	0.941717	−	0.601398i
$424$	−107867.			−0.600010
$425$		−	54998.4i		−	0.304490i
$426$	−107958.	+	197039.i	−0.594890	+	1.08576i
$427$	3154.11			0.0172990
$428$		−	79406.9i		−	0.433482i
$429$	−110095.	−	60321.5i	−0.598210	−	0.327761i
$430$	−74538.2			−0.403127
$431$			218641.i			1.17700i	0.808497	+	0.588501i	$0.200282\pi$
$431$			218641.i			1.17700i	−0.808497	+	0.588501i	$0.799718\pi$
$432$	−46551.0	+	3128.32i	−0.249437	+	0.0167627i
$433$	62283.0			0.332196			0.166098	−	0.986109i	$-0.446883\pi$
$433$	62283.0			0.332196			0.166098	+	0.986109i	$0.446883\pi$
$434$		−	6890.46i		−	0.0365821i
$435$	−8888.12	+	16222.1i	−0.0469711	+	0.0857290i
$436$	125475.			0.660063
$437$		−	122268.i		−	0.640253i
$438$	55771.4	+	30557.3i	0.290712	+	0.159282i
$439$	−91347.6			−0.473989			−0.236994	−	0.971511i	$-0.576162\pi$
$439$	−91347.6			−0.473989			−0.236994	+	0.971511i	$0.576162\pi$
$440$		−	13082.2i		−	0.0675733i
$441$	101848.	+	159482.i	0.523691	+	0.820037i
$442$	335680.			1.71823
$443$			147288.i			0.750514i	0.926921	+	0.375257i	$0.122446\pi$
$443$			147288.i			0.750514i	−0.926921	+	0.375257i	$0.877554\pi$
$444$	81802.3	−	149301.i	0.414954	−	0.757349i
$445$	82144.2			0.414817
$446$		−	171375.i		−	0.861546i
$447$	98878.8	+	54176.0i	0.494867	+	0.271139i
$448$	4122.97			0.0205425
$449$			287609.i			1.42662i	0.700847	+	0.713312i	$0.252806\pi$
$449$			287609.i			1.42662i	−0.700847	+	0.713312i	$0.747194\pi$
$450$	24135.9	−	15413.7i	0.119190	−	0.0761169i
$451$	45670.7			0.224535
$452$			37019.2i			0.181197i
$453$	−12703.7	+	23186.0i	−0.0619060	+	0.112987i
$454$	−216501.			−1.05038
$455$			24284.8i			0.117304i
$456$	94599.7	+	51831.4i	0.454946	+	0.249266i
$457$	−189229.			−0.906055			−0.453028	−	0.891496i	$-0.649656\pi$
$457$	−189229.			−0.906055			−0.453028	+	0.891496i	$0.649656\pi$
$458$			185774.i			0.885634i
$459$	−21506.6	−	320029.i	−0.102081	−	1.51902i
$460$	20646.3			0.0975724
$461$		−	246211.i		−	1.15852i	−0.815141	−	0.579262i	$-0.803341\pi$
$461$		−	246211.i		−	1.15852i	0.815141	−	0.579262i	$-0.196659\pi$
$462$	5093.51	−	9296.36i	0.0238634	−	0.0435541i
$463$	−202841.			−0.946225			−0.473113	−	0.881002i	$-0.656870\pi$
$463$	−202841.			−0.946225			−0.473113	+	0.881002i	$0.656870\pi$
$464$		−	11765.0i		−	0.0546459i
$465$	26696.6	+	14627.2i	0.123467	+	0.0676479i
$466$	3602.26			0.0165884
$467$			302984.i			1.38927i	0.719363	+	0.694634i	$0.244434\pi$
$467$			302984.i			1.38927i	−0.719363	+	0.694634i	$0.755566\pi$
$468$	94076.5	+	147312.i	0.429526	+	0.672586i
$469$	−35163.4			−0.159862
$470$		−	78053.4i		−	0.353343i
$471$	−53380.2	+	97426.4i	−0.240624	+	0.439172i
$472$	76393.7			0.342905
$473$		−	121890.i		−	0.544813i
$474$	68200.4	+	37367.2i	0.303550	+	0.166316i
$475$	−66210.5			−0.293454
$476$			28344.6i			0.125100i
$477$	325435.	−	207829.i	1.43030	−	0.913417i
$478$	190435.			0.833471
$479$			57893.7i			0.252325i	0.992010	+	0.126163i	$0.0402661\pi$
$479$			57893.7i			0.252325i	−0.992010	+	0.126163i	$0.959734\pi$
$480$	−8752.28	+	15974.2i	−0.0379873	+	0.0693323i
$481$	−637785.			−2.75667
$482$		−	77316.8i		−	0.332797i
$483$	14671.5	+	8038.57i	0.0628899	+	0.0344576i
$484$	−95735.0			−0.408677
$485$		−	185585.i		−	0.788969i
$486$	134417.	−	99128.3i	0.569090	−	0.419687i
$487$	118496.			0.499625			0.249813	−	0.968294i	$-0.419631\pi$
$487$	118496.			0.499625			0.249813	+	0.968294i	$0.419631\pi$
$488$		−	8862.83i		−	0.0372163i
$489$	−189099.	+	345133.i	−0.790810	+	1.44334i
$490$	73875.7			0.307687
$491$		−	421168.i		−	1.74700i	−0.486825	−	0.873499i	$-0.661845\pi$
$491$		−	421168.i		−	1.74700i	0.486825	−	0.873499i	$-0.338155\pi$
$492$	−55766.7	−	30554.7i	−0.230380	−	0.126226i
$493$	80882.3			0.332782
$494$		−	404112.i		−	1.65595i
$495$	25205.6	+	39468.9i	0.102869	+	0.161081i
$496$	−19361.7			−0.0787010
$497$			71073.7i			0.287737i
$498$	22230.7	−	40574.2i	0.0896387	−	0.163603i
$499$	−343588.			−1.37987			−0.689933	−	0.723873i	$-0.742360\pi$
$499$	−343588.			−1.37987			−0.689933	+	0.723873i	$0.742360\pi$
$500$		−	11180.3i		−	0.0447214i
$501$	219422.	+	120222.i	0.874186	+	0.478969i
$502$	−10806.1			−0.0428806
$503$		−	207798.i		−	0.821307i	−0.911791	−	0.410654i	$-0.865301\pi$
$503$		−	207798.i		−	0.821307i	0.911791	−	0.410654i	$-0.134699\pi$
$504$	−12439.0	+	7943.75i	−0.0489692	+	0.0312727i
$505$	9348.45			0.0366570
$506$			33762.4i			0.131866i
$507$	191132.	−	348842.i	0.743562	−	1.35710i
$508$	48528.3			0.188048
$509$			271700.i			1.04871i	0.851501	+	0.524354i	$0.175693\pi$
$509$			271700.i			1.04871i	−0.851501	+	0.524354i	$0.824307\pi$
$510$	−109819.	−	60170.2i	−0.422219	−	0.231335i
$511$	20117.3			0.0770419
$512$		−	11585.2i		−	0.0441942i
$513$	−385271.	+	25890.9i	−1.46397	+	0.0983814i
$514$	−285605.			−1.08104
$515$		−	1544.58i		−	0.00582364i
$516$	−81547.4	+	148836.i	−0.306275	+	0.558994i
$517$	127639.			0.477531
$518$		−	53854.1i		−	0.200706i
$519$	50167.3	+	27486.8i	0.186245	+	0.102044i
$520$	68238.6			0.252362
$521$		−	278019.i		−	1.02423i	−0.858916	−	0.512117i	$-0.828862\pi$
$521$		−	278019.i		−	1.02423i	0.858916	−	0.512117i	$-0.171138\pi$
$522$	22667.8	+	35495.0i	0.0831894	+	0.130265i
$523$	−133147.			−0.486773			−0.243386	−	0.969929i	$-0.578258\pi$
$523$	−133147.			−0.486773			−0.243386	+	0.969929i	$0.578258\pi$
$524$			180923.i			0.658918i
$525$	4353.03	−	7944.89i	0.0157933	−	0.0288250i
$526$	−196069.			−0.708660
$527$		−	133108.i		−	0.479273i
$528$	−26122.1	−	14312.4i	−0.0937002	−	0.0513386i
$529$	226557.			0.809593
$530$		−	150749.i		−	0.536665i
$531$	−230479.	+	147188.i	−0.817415	+	0.522017i
$532$	34123.0			0.120566
$533$			238225.i			0.838557i
$534$	89868.7	−	164023.i	0.315156	−	0.575205i
$535$	110975.			0.387718
$536$			98806.7i			0.343920i
$537$	140196.	+	76813.6i	0.486168	+	0.266373i
$538$	−215791.			−0.745537
$539$			120807.i			0.415829i
$540$	−4371.96	−	65057.0i	−0.0149930	−	0.223104i
$541$	240623.			0.822133			0.411067	−	0.911605i	$-0.365156\pi$
$541$	240623.			0.822133			0.411067	+	0.911605i	$0.365156\pi$
$542$			216652.i			0.737504i
$543$	−73978.5	+	135021.i	−0.250903	+	0.457933i
$544$	79646.2			0.269133
$545$			175357.i			0.590378i
$546$	48491.2	+	26568.5i	0.162659	+	0.0891212i
$547$	−195078.			−0.651981			−0.325990	−	0.945373i	$-0.605698\pi$
$547$	−195078.			−0.651981			−0.325990	+	0.945373i	$0.605698\pi$
$548$			61771.6i			0.205697i
$549$	17076.1	+	26739.1i	0.0566557	+	0.0887160i
$550$	18282.9			0.0604394
$551$		−	97371.1i		−	0.320721i
$552$	22587.8	−	41225.9i	0.0741303	−	0.135298i
$553$	24600.5			0.0804440
$554$			255942.i			0.833916i
$555$	208654.	+	114322.i	0.677394	+	0.371146i
$556$	−71378.4			−0.230897
$557$			86002.4i			0.277204i	0.990348	+	0.138602i	$0.0442609\pi$
$557$			86002.4i			0.277204i	−0.990348	+	0.138602i	$0.955739\pi$
$558$	58414.1	−	37304.4i	0.187607	−	0.119810i
$559$	635798.			2.03468
$560$			5762.02i			0.0183738i
$561$	98394.8	−	179584.i	0.312641	−	0.570615i
$562$	239886.			0.759509
$563$		−	171495.i		−	0.541047i	−0.962713	−	0.270524i	$-0.912803\pi$
$563$		−	171495.i		−	0.541047i	0.962713	−	0.270524i	$-0.0871968\pi$
$564$	−155855.	−	85393.2i	−0.489961	−	0.268451i
$565$	−51736.0			−0.162067
$566$			239222.i			0.746738i
$567$	22223.0	−	47932.5i	0.0691251	−	0.149095i
$568$	199712.			0.619024
$569$		−	9078.16i		−	0.0280397i	−0.999902	−	0.0140198i	$-0.995537\pi$
$569$		−	9078.16i		−	0.0280397i	0.999902	−	0.0140198i	$-0.00446280\pi$
$570$	−72436.6	+	132207.i	−0.222951	+	0.406916i
$571$	502472.			1.54113			0.770565	−	0.637361i	$-0.219974\pi$
$571$	502472.			1.54113			0.770565	+	0.637361i	$0.219974\pi$
$572$			111589.i			0.341058i
$573$	−225712.	−	123669.i	−0.687458	−	0.376660i
$574$	−20115.6			−0.0610532
$575$			28854.1i			0.0872714i
$576$	22321.4	+	34952.6i	0.0672785	+	0.105350i
$577$	−110356.			−0.331471			−0.165735	−	0.986170i	$-0.553000\pi$
$577$	−110356.			−0.331471			−0.165735	+	0.986170i	$0.553000\pi$
$578$			311319.i			0.931860i
$579$	40235.6	−	73435.7i	0.120020	−	0.219053i
$580$	16442.1			0.0488767
$581$		−	14635.5i		−	0.0433566i
$582$	−370571.	−	203037.i	−1.09402	−	0.599417i
$583$	246516.			0.725284
$584$		−	56528.1i		−	0.165744i
$585$	−205875.	+	131476.i	−0.601579	+	0.384180i
$586$	23154.5			0.0674281
$587$		−	383110.i		−	1.11185i	−0.831231	−	0.555927i	$-0.812364\pi$
$587$		−	383110.i		−	1.11185i	0.831231	−	0.555927i	$-0.187636\pi$
$588$	80822.6	−	147513.i	0.233764	−	0.426653i
$589$	−160244.			−0.461902
$590$			106763.i			0.306703i
$591$	157513.	+	86301.8i	0.450963	+	0.247084i
$592$	−151326.			−0.431788
$593$			15107.0i			0.0429604i	0.999769	+	0.0214802i	$0.00683789\pi$
$593$			15107.0i			0.0429604i	−0.999769	+	0.0214802i	$0.993162\pi$
$594$	106386.	−	7149.35i	0.301517	−	0.0202625i
$595$	−39612.8			−0.111893
$596$		−	100220.i		−	0.282139i
$597$	−181938.	+	332062.i	−0.510474	+	0.931688i
$598$	−176109.			−0.492471
$599$		−	52653.8i		−	0.146749i	−0.997304	−	0.0733747i	$-0.976623\pi$
$599$		−	52653.8i		−	0.146749i	0.997304	−	0.0733747i	$-0.0233769\pi$
$600$	−22324.6	−	12231.7i	−0.0620127	−	0.0339769i
$601$	−636606.			−1.76247			−0.881236	−	0.472677i	$-0.843288\pi$
$601$	−636606.			−1.76247			−0.881236	+	0.472677i	$0.843288\pi$
$602$			53686.3i			0.148139i
$603$	−190372.	−	298099.i	−0.523562	−	0.819835i
$604$	23500.5			0.0644175
$605$		−	133794.i		−	0.365532i
$606$	10227.5	−	18666.7i	0.0278500	−	0.0508302i
$607$	−130049.			−0.352963			−0.176481	−	0.984304i	$-0.556472\pi$
$607$	−130049.			−0.352963			−0.176481	+	0.984304i	$0.556472\pi$
$608$		−	95883.0i		−	0.259379i
$609$	11684.0	+	6401.69i	0.0315033	+	0.0172608i
$610$	12386.2			0.0332872
$611$			665782.i			1.78340i
$612$	−240292.	+	153455.i	−0.641559	+	0.409712i
$613$	604004.			1.60738			0.803690	−	0.595048i	$-0.202867\pi$
$613$	604004.			1.60738			0.803690	+	0.595048i	$0.202867\pi$
$614$		−	191246.i		−	0.507290i
$615$	42701.6	−	77936.3i	0.112900	−	0.206058i
$616$	−9422.48			−0.0248316
$617$			473832.i			1.24467i	0.782751	+	0.622335i	$0.213816\pi$
$617$			473832.i			1.24467i	−0.782751	+	0.622335i	$0.786184\pi$
$618$	−3084.16	−	1689.82i	−0.00807533	−	0.00442450i
$619$	416734.			1.08762			0.543811	−	0.839208i	$-0.316981\pi$
$619$	416734.			1.08762			0.543811	+	0.839208i	$0.316981\pi$
$620$		−	27058.8i		−	0.0703923i
$621$	11283.1	+	167898.i	0.0292580	+	0.435375i
$622$	−126714.			−0.327524
$623$		−	59164.6i		−	0.152435i
$624$	74655.4	−	136257.i	0.191731	−	0.349936i
$625$	15625.0			0.0400000
$626$		−	86979.7i		−	0.221957i
$627$	−216195.	−	118454.i	−0.549933	−	0.301310i
$628$	98748.1			0.250386
$629$		−	1.04034e6i		−	2.62950i
$630$	−11101.7	−	17384.0i	−0.0279711	−	0.0437994i
$631$	144231.			0.362243			0.181122	−	0.983461i	$-0.442027\pi$
$631$	144231.			0.362243			0.181122	+	0.983461i	$0.442027\pi$
$632$		−	69125.6i		−	0.173063i
$633$	−28627.2	+	52248.6i	−0.0714448	+	0.130397i
$634$	−158810.			−0.395094
$635$			67820.4i			0.168195i
$636$	−301011.	−	164925.i	−0.744164	−	0.407729i
$637$	−630147.			−1.55297
$638$			26887.4i			0.0660552i
$639$	−602530.	+	384787.i	−1.47563	+	0.942364i
$640$	16190.9			0.0395285
$641$		−	199624.i		−	0.485844i	−0.970046	−	0.242922i	$-0.921894\pi$
$641$		−	199624.i		−	0.485844i	0.970046	−	0.242922i	$-0.0781060\pi$
$642$	121410.	−	221591.i	0.294568	−	0.537627i
$643$	219848.			0.531742			0.265871	−	0.964009i	$-0.414340\pi$
$643$	219848.			0.531742			0.265871	+	0.964009i	$0.414340\pi$
$644$		−	14870.6i		−	0.0358555i
$645$	−208004.	−	113966.i	−0.499980	−	0.273940i
$646$	659177.			1.57956
$647$		−	591334.i		−	1.41262i	−0.707904	−	0.706308i	$-0.750359\pi$
$647$		−	591334.i		−	1.41262i	0.707904	−	0.706308i	$-0.249641\pi$
$648$	−134687.	−	62444.9i	−0.320756	−	0.148712i
$649$	−174587.			−0.414499
$650$			95366.3i			0.225719i
$651$	10535.3	−	19228.3i	0.0248590	−	0.0453711i
$652$	349815.			0.822892
$653$		−	346617.i		−	0.812875i	−0.913679	−	0.406438i	$-0.866771\pi$
$653$		−	346617.i		−	0.812875i	0.913679	−	0.406438i	$-0.133229\pi$
$654$	350147.	+	191847.i	0.818645	+	0.448538i
$655$	−252847.			−0.589354
$656$			56523.3i			0.131347i
$657$	108913.	+	170545.i	0.252319	+	0.395101i
$658$	−56218.2			−0.129845
$659$		−	497210.i		−	1.14490i	−0.819939	−	0.572452i	$-0.805992\pi$
$659$		−	497210.i		−	1.14490i	0.819939	−	0.572452i	$-0.194008\pi$
$660$	20002.2	−	36506.8i	0.0459186	−	0.0838080i
$661$	73561.3			0.168363			0.0841814	−	0.996450i	$-0.473172\pi$
$661$	73561.3			0.168363			0.0841814	+	0.996450i	$0.473172\pi$
$662$		−	61312.9i		−	0.139906i
$663$	936738.	+	513242.i	2.13104	+	1.16760i
$664$	−41124.7			−0.0932753
$665$			47688.3i			0.107837i
$666$	456550.	−	291562.i	1.02930	−	0.657328i
$667$	−42433.7			−0.0953804
$668$		−	222398.i		−	0.498401i
$669$	262026.	−	478235.i	0.585454	−	1.06854i
$670$	−138087.			−0.307611
$671$			20254.8i			0.0449866i
$672$	11505.4	+	6303.86i	0.0254779	+	0.0139594i
$673$	−110929.			−0.244914			−0.122457	−	0.992474i	$-0.539077\pi$
$673$	−110929.			−0.244914			−0.122457	+	0.992474i	$0.539077\pi$
$674$			60620.5i			0.133444i
$675$	90919.9	−	6110.00i	0.199550	−	0.0134101i
$676$	−353575.			−0.773728
$677$			797825.i			1.74073i	0.492411	+	0.870363i	$0.336116\pi$
$677$			797825.i			1.74073i	−0.492411	+	0.870363i	$0.663884\pi$
$678$	−56601.0	+	103305.i	−0.123130	+	0.224730i
$679$	−133668.			−0.289927
$680$			111309.i			0.240720i
$681$	−604161.	−	331022.i	−1.30274	−	0.713776i
$682$	44248.6			0.0951328
$683$			525269.i			1.12601i	0.826455	+	0.563003i	$0.190354\pi$
$683$			525269.i			1.12601i	−0.826455	+	0.563003i	$0.809646\pi$
$684$	184739.	+	289278.i	0.394862	+	0.618307i
$685$	−86328.5			−0.183981
$686$		−	107895.i		−	0.229274i
$687$	−284041.	+	518415.i	−0.601822	+	1.09841i
$688$	150855.			0.318700
$689$			1.28586e6i			2.70867i
$690$	57615.0	+	31567.4i	0.121014	+	0.0663042i
$691$	227686.			0.476849			0.238425	−	0.971161i	$-0.423369\pi$
$691$	227686.			0.476849			0.238425	+	0.971161i	$0.423369\pi$
$692$		−	50847.8i		−	0.106184i
$693$	28427.6	−	18154.4i	0.0591934	−	0.0378020i
$694$	549486.			1.14087
$695$		−	99754.4i		−	0.206520i
$696$	17988.3	−	32831.1i	0.0371340	−	0.0677747i
$697$	−388586.			−0.799875
$698$		−	109764.i		−	0.225294i
$699$	10052.4	+	5507.72i	0.0205738	+	0.0112724i
$700$	−8052.67			−0.0164340
$701$			170710.i			0.347394i	0.984799	+	0.173697i	$0.0555713\pi$
$701$			170710.i			0.347394i	−0.984799	+	0.173697i	$0.944429\pi$
$702$	37292.0	+	554925.i	0.0756731	+	1.12606i
$703$	−1.25242e6			−2.53420
$704$			26476.5i			0.0534214i
$705$	119341.	−	217813.i	0.240110	−	0.438234i
$706$	−281395.			−0.564556
$707$		−	6733.24i		−	0.0134706i
$708$	213182.	+	116803.i	0.425288	+	0.233017i
$709$	581208.			1.15622			0.578109	−	0.815960i	$-0.303791\pi$
$709$	581208.			1.15622			0.578109	+	0.815960i	$0.303791\pi$
$710$			279106.i			0.553672i
$711$	133185.	+	208552.i	0.263461	+	0.412548i
$712$	−166248.			−0.327942
$713$			69833.1i			0.137367i
$714$	−43337.8	+	79097.5i	−0.0850100	+	0.155155i
$715$	−155950.			−0.305052
$716$		−	142098.i		−	0.277179i
$717$	531421.	+	291167.i	1.03371	+	0.566375i
$718$	−478000.			−0.927211
$719$		−	805766.i		−	1.55866i	−0.626614	−	0.779330i	$-0.715560\pi$
$719$		−	805766.i		−	1.55866i	0.626614	−	0.779330i	$-0.284440\pi$
$720$	−48847.7	+	31195.1i	−0.0942278	+	0.0601757i
$721$	−1112.48			−0.00214005
$722$		−	424955.i		−	0.815207i
$723$	118214.	−	215758.i	0.226149	−	0.412753i
$724$	136853.			0.261082
$725$			22978.6i			0.0437167i
$726$	−267155.	−	146375.i	−0.506863	−	0.277712i
$727$	473619.			0.896108			0.448054	−	0.894006i	$-0.352117\pi$
$727$	473619.			0.896108			0.448054	+	0.894006i	$0.352117\pi$
$728$		−	49149.0i		−	0.0927368i
$729$	526662.	−	71106.6i	0.991008	−	0.133800i
$730$	79000.4			0.148246
$731$			1.03710e6i			1.94082i
$732$	13550.9	−	24732.3i	0.0252899	−	0.0461576i
$733$	502978.			0.936140			0.468070	−	0.883691i	$-0.344950\pi$
$733$	502978.			0.936140			0.468070	+	0.883691i	$0.344950\pi$
$734$			636803.i			1.18199i
$735$	206155.	+	112953.i	0.381610	+	0.209085i
$736$	−41785.2			−0.0771378
$737$		−	225809.i		−	0.415726i
$738$	−108904.	−	170530.i	−0.199954	−	0.313104i
$739$	−1.00807e6			−1.84588			−0.922938	−	0.384950i	$-0.874219\pi$
$739$	−1.00807e6			−1.84588			−0.922938	+	0.384950i	$0.874219\pi$
$740$		−	211485.i		−	0.386203i
$741$	617872.	−	1.12770e6i	1.12528	−	2.05380i
$742$	−108577.			−0.197211
$743$		−	424910.i		−	0.769696i	−0.922980	−	0.384848i	$-0.874254\pi$
$743$		−	424910.i		−	0.769696i	0.922980	−	0.384848i	$-0.125746\pi$
$744$	−54030.2	−	29603.3i	−0.0976092	−	0.0534804i
$745$	140062.			0.252353
$746$		−	263659.i		−	0.473767i
$747$	124073.	−	79235.3i	0.222349	−	0.141996i
$748$	−182021.			−0.325325
$749$		−	79929.7i		−	0.142477i
$750$	17094.3	−	31199.5i	0.0303899	−	0.0554658i
$751$	8095.16			0.0143531			0.00717655	−	0.999974i	$-0.497716\pi$
$751$	8095.16			0.0143531			0.00717655	+	0.999974i	$0.497716\pi$
$752$			157969.i			0.279342i
$753$	−30155.1	−	16522.1i	−0.0531828	−	0.0291390i
$754$	−140248.			−0.246692
$755$			32843.0i			0.0576167i
$756$	−46857.5	+	3148.91i	−0.0819852	+	0.00550956i
$757$	530937.			0.926512			0.463256	−	0.886224i	$-0.346681\pi$
$757$	530937.			0.926512			0.463256	+	0.886224i	$0.346681\pi$
$758$		−	575675.i		−	1.00193i
$759$	−51621.4	+	94216.3i	−0.0896079	+	0.163547i
$760$	134001.			0.231996
$761$		−	288951.i		−	0.498947i	−0.968382	−	0.249474i	$-0.919742\pi$
$761$		−	288951.i		−	0.498947i	0.968382	−	0.249474i	$-0.0802576\pi$
$762$	135422.	+	74197.9i	0.233227	+	0.127786i
$763$	126301.			0.216950
$764$			228775.i			0.391941i
$765$	−214460.	−	335819.i	−0.366457	−	0.573828i
$766$	−269029.			−0.458502
$767$		−	910673.i		−	1.54800i
$768$	17713.4	−	32329.4i	0.0300316	−	0.0548120i
$769$	436387.			0.737937			0.368969	−	0.929442i	$-0.379711\pi$
$769$	436387.			0.737937			0.368969	+	0.929442i	$0.379711\pi$
$770$		−	13168.3i		−	0.0222100i
$771$	−797002.	−	436680.i	−1.34076	−	0.734605i
$772$	−74431.9			−0.124889
$773$			1.12125e6i			1.87647i	0.345997	+	0.938236i	$0.387541\pi$
$773$			1.12125e6i			1.87647i	−0.345997	+	0.938236i	$0.612459\pi$
$774$	−455128.	+	290653.i	−0.759716	+	0.485169i
$775$	37815.8			0.0629608
$776$			375598.i			0.623735i
$777$	82340.9	−	150284.i	0.136387	−	0.248926i
$778$	−477312.			−0.788574
$779$			467804.i			0.770884i
$780$	190424.	+	104334.i	0.312992	+	0.171489i
$781$	−456415.			−0.748269
$782$		−	287265.i		−	0.469753i
$783$	8985.54	+	133710.i	0.0146562	+	0.218092i
$784$	−149514.			−0.243248
$785$			138005.i			0.223952i
$786$	−276624.	+	504878.i	−0.447760	+	0.817225i
$787$	349787.			0.564747			0.282373	−	0.959305i	$-0.408878\pi$
$787$	349787.			0.564747			0.282373	+	0.959305i	$0.408878\pi$
$788$		−	159650.i		−	0.257108i
$789$	−547145.	−	299782.i	−0.878917	−	0.481561i
$790$	96606.0			0.154793
$791$			37263.0i			0.0595558i
$792$	−51012.5	−	79879.4i	−0.0813254	−	0.127346i
$793$	−105652.			−0.168008
$794$		−	316403.i		−	0.501879i
$795$	230490.	−	420676.i	0.364684	−	0.665600i
$796$	336567.			0.531184
$797$		−	627937.i		−	0.988551i	−0.869305	−	0.494276i	$-0.835433\pi$
$797$		−	627937.i		−	0.988551i	0.869305	−	0.494276i	$-0.164567\pi$
$798$	95222.5	+	52172.7i	0.149532	+	0.0819289i
$799$	−1.08601e6			−1.70113
$800$			22627.4i			0.0353553i
$801$	501570.	−	320312.i	0.781747	−	0.499238i
$802$	−53158.0			−0.0826456
$803$			129187.i			0.200350i
$804$	−151072.	+	275727.i	−0.233707	+	0.426547i
$805$	20782.2			0.0320701
$806$			230807.i			0.355286i
$807$	−602181.	−	329936.i	−0.924655	−	0.506621i
$808$	−18919.9			−0.0289799
$809$		−	738097.i		−	1.12776i	−0.825857	−	0.563880i	$-0.809308\pi$
$809$		−	738097.i		−	1.12776i	0.825857	−	0.563880i	$-0.190692\pi$
$810$	87269.4	−	188231.i	0.133012	−	0.286893i
$811$	584442.			0.888587			0.444293	−	0.895881i	$-0.353455\pi$
$811$	584442.			0.888587			0.444293	+	0.895881i	$0.353455\pi$
$812$		−	11842.5i		−	0.0179610i
$813$	−331253.	+	604583.i	−0.501162	+	0.914692i
$814$	345836.			0.521940
$815$			488881.i			0.736017i
$816$	222258.	+	121776.i	0.333793	+	0.182886i
$817$	1.24852e6			1.87047
$818$		−	344126.i		−	0.514294i
$819$	94695.8	+	148282.i	0.141177	+	0.221066i
$820$	−78993.7			−0.117480
$821$			908911.i			1.34845i	0.738526	+	0.674225i	$0.235522\pi$
$821$			908911.i			1.34845i	−0.738526	+	0.674225i	$0.764478\pi$
$822$	−94446.4	+	172378.i	−0.139779	+	0.255116i
$823$	−713222.			−1.05299			−0.526496	−	0.850178i	$-0.676494\pi$
$823$	−713222.			−1.05299			−0.526496	+	0.850178i	$0.676494\pi$
$824$			3126.00i			0.00460399i
$825$	51019.8	+	27953.9i	0.0749601	+	0.0410709i
$826$	76896.6			0.112706
$827$		−	269914.i		−	0.394652i	−0.980338	−	0.197326i	$-0.936774\pi$
$827$		−	269914.i		−	0.394652i	0.980338	−	0.197326i	$-0.0632258\pi$
$828$	126066.	−	80507.9i	0.183881	−	0.117430i
$829$	−1.11355e6			−1.62032			−0.810161	−	0.586208i	$-0.800620\pi$
$829$	−1.11355e6			−1.62032			−0.810161	+	0.586208i	$0.800620\pi$
$830$		−	57473.5i		−	0.0834279i
$831$	−391326.	+	714225.i	−0.566678	+	1.03427i
$832$	−138105.			−0.199509
$833$		−	1.02788e6i		−	1.48133i
$834$	−199186.	−	109135.i	−0.286370	−	0.156903i
$835$	310811.			0.445783
$836$			219128.i			0.313534i
$837$	220046.	−	14787.5i	0.314096	−	0.0211078i
$838$	956755.			1.36243
$839$		−	112450.i		−	0.159748i	−0.996805	−	0.0798738i	$-0.974548\pi$
$839$		−	112450.i		−	0.159748i	0.996805	−	0.0798738i	$-0.0254517\pi$
$840$	−8809.91	+	16079.3i	−0.0124857	+	0.0227881i
$841$	673488.			0.952221
$842$		−	75595.1i		−	0.106628i
$843$	669419.	+	366777.i	0.941983	+	0.516115i
$844$	52957.4			0.0743433
$845$		−	494136.i		−	0.692043i
$846$	−304360.	−	476591.i	−0.425253	−	0.665895i
$847$	−96365.3			−0.134324
$848$			305095.i			0.424271i
$849$	−365761.	+	667566.i	−0.507437	+	0.926144i
$850$	−155559.			−0.215307
$851$			545798.i			0.753655i
$852$	557310.	+	305352.i	0.767746	+	0.420650i
$853$	1.05357e6			1.44799			0.723993	−	0.689807i	$-0.242305\pi$
$853$	1.05357e6			1.44799			0.723993	+	0.689807i	$0.242305\pi$
$854$		−	8921.18i		−	0.0122323i
$855$	−404279.	+	258180.i	−0.553030	+	0.353176i
$856$	−224597.			−0.306518
$857$			595969.i			0.811450i	0.913995	+	0.405725i	$0.132981\pi$
$857$			595969.i			0.811450i	−0.913995	+	0.405725i	$0.867019\pi$
$858$	−170615.	+	311396.i	−0.231762	+	0.422998i
$859$	681772.			0.923959			0.461980	−	0.886891i	$-0.347139\pi$
$859$	681772.			0.923959			0.461980	+	0.886891i	$0.347139\pi$
$860$			210826.i			0.285054i
$861$	−56133.8	−	30755.9i	−0.0757214	−	0.0414880i
$862$	618410.			0.832266
$863$			1.09609e6i			1.47172i	0.677133	+	0.735861i	$0.263222\pi$
$863$			1.09609e6i			1.47172i	−0.677133	+	0.735861i	$0.736778\pi$
$864$	8848.22	+	131666.i	0.0118530	+	0.176379i
$865$	71062.0			0.0949741
$866$		−	176163.i		−	0.234898i
$867$	−475995.	+	868758.i	−0.633234	+	1.15574i
$868$	−19489.2			−0.0258675
$869$			157977.i			0.209197i
$870$	45882.9	+	25139.4i	0.0606195	+	0.0332136i
$871$	1.17785e6			1.55258
$872$		−	354898.i		−	0.466735i
$873$	−723668.	−	1.13318e6i	−0.949535	−	1.48686i
$874$	−345827.			−0.452727
$875$		−	11253.9i		−	0.0146990i
$876$	86429.2	−	157745.i	0.112630	−	0.205565i
$877$	340016.			0.442080			0.221040	−	0.975265i	$-0.429055\pi$
$877$	340016.			0.442080			0.221040	+	0.975265i	$0.429055\pi$
$878$			258370.i			0.335161i
$879$	64614.4	+	35402.4i	0.0836279	+	0.0458200i
$880$	−37002.0			−0.0477815
$881$			11670.2i			0.0150358i	0.999972	+	0.00751792i	$0.00239305\pi$
$881$			11670.2i			0.0150358i	−0.999972	+	0.00751792i	$0.997607\pi$
$882$	451082.	−	288070.i	0.579854	−	0.370306i
$883$	−1.09214e6			−1.40074			−0.700371	−	0.713779i	$-0.746982\pi$
$883$	−1.09214e6			−1.40074			−0.700371	+	0.713779i	$0.746982\pi$
$884$		−	949446.i		−	1.21497i
$885$	−163237.	+	297931.i	−0.208417	+	0.380390i
$886$	416592.			0.530693
$887$		−	776611.i		−	0.987089i	−0.869721	−	0.493544i	$-0.835701\pi$
$887$		−	776611.i		−	0.987089i	0.869721	−	0.493544i	$-0.164299\pi$
$888$	−422286.	−	231372.i	−0.535527	−	0.293417i
$889$	48847.8			0.0618075
$890$		−	232339.i		−	0.293320i
$891$	307809.	+	142709.i	0.387726	+	0.179762i
$892$	−484723.			−0.609205
$893$			1.30740e6i			1.63948i
$894$	153233.	−	279671.i	0.191724	−	0.349924i
$895$	198587.			0.247917
$896$		−	11661.5i		−	0.0145258i
$897$	−491446.	−	269264.i	−0.610788	−	0.334653i
$898$	813481.			1.00878
$899$			55613.1i			0.0688109i
$900$	−43596.4	−	68266.8i	−0.0538228	−	0.0842799i
$901$	−2.09747e6			−2.58372
$902$		−	129176.i		−	0.158770i
$903$	−82084.3	+	149815.i	−0.100666	+	0.183730i
$904$	104706.			0.128125
$905$			191258.i			0.233519i
$906$	65579.8	+	35931.4i	0.0798939	+	0.0437741i
$907$	−240861.			−0.292787			−0.146393	−	0.989226i	$-0.546767\pi$
$907$	−240861.			−0.292787			−0.146393	+	0.989226i	$0.546767\pi$
$908$			612357.i			0.742734i
$909$	57081.3	−	36453.2i	0.0690822	−	0.0441172i
$910$	68687.8			0.0829463
$911$		−	963956.i		−	1.16150i	−0.814081	−	0.580751i	$-0.802759\pi$
$911$		−	963956.i		−	1.16150i	0.814081	−	0.580751i	$-0.197241\pi$
$912$	146601.	−	267568.i	0.176258	−	0.321695i
$913$	93984.9			0.112750
$914$			535220.i			0.640678i
$915$	34564.5	+	18938.0i	0.0412846	+	0.0226199i
$916$	525448.			0.626237
$917$			182114.i			0.216573i
$918$	−905179.	+	60829.8i	−1.07411	+	0.0721823i
$919$	1.18858e6			1.40734			0.703670	−	0.710527i	$-0.251543\pi$
$919$	1.18858e6			1.40734			0.703670	+	0.710527i	$0.251543\pi$
$920$		−	58396.6i		−	0.0689941i
$921$	292408.	−	533686.i	0.344723	−	0.629168i
$922$	−696390.			−0.819201
$923$		−	2.38072e6i		−	2.79451i
$924$	−26294.1	−	14406.6i	−0.0307974	−	0.0168740i
$925$	295559.			0.345431
$926$			573722.i			0.669082i
$927$	−6022.90	−	9431.13i	−0.00700883	−	0.0109750i
$928$	−33276.5			−0.0386405
$929$			1.19575e6i			1.38551i	0.721175	+	0.692753i	$0.243602\pi$
$929$			1.19575e6i			1.38551i	−0.721175	+	0.692753i	$0.756398\pi$
$930$	41371.9	−	75509.5i	0.0478343	−	0.0873043i
$931$	−1.23742e6			−1.42764
$932$		−	10188.7i		−	0.0117297i
$933$	−353604.	−	193741.i	−0.406213	−	0.222565i
$934$	856969.			0.982361
$935$		−	254382.i		−	0.290980i
$936$	416662.	−	266088.i	0.475590	−	0.303721i
$937$	−835878.			−0.952058			−0.476029	−	0.879430i	$-0.657924\pi$
$937$	−835878.			−0.952058			−0.476029	+	0.879430i	$0.657924\pi$
$938$			99457.2i			0.113040i
$939$	132989.	−	242723.i	0.150828	−	0.275283i
$940$	−220768.			−0.249851
$941$		−	952371.i		−	1.07554i	−0.843091	−	0.537770i	$-0.819267\pi$
$941$		−	952371.i		−	1.07554i	0.843091	−	0.537770i	$-0.180733\pi$
$942$	275563.	+	150982.i	0.310542	+	0.170147i
$943$	203866.			0.229256
$944$		−	216074.i		−	0.242470i
$945$	−4400.74	−	65485.3i	−0.00492790	−	0.0733298i
$946$	−344758.			−0.385241
$947$			993135.i			1.10741i	0.832713	+	0.553705i	$0.186786\pi$
$947$			993135.i			1.10741i	−0.832713	+	0.553705i	$0.813214\pi$
$948$	105690.	−	192900.i	0.117603	−	0.214642i
$949$	−673859.			−0.748233
$950$			187272.i			0.207503i
$951$	−443172.	−	242815.i	−0.490017	−	0.268482i
$952$	80170.6			0.0884588
$953$		−	1.44683e6i		−	1.59306i	−0.604597	−	0.796531i	$-0.706666\pi$
$953$		−	1.44683e6i		−	1.59306i	0.604597	−	0.796531i	$-0.293334\pi$
$954$	−587829.	−	920469.i	−0.645883	−	1.01138i
$955$	−319722.			−0.350563
$956$		−	538631.i		−	0.589353i
$957$	−41109.8	+	75031.1i	−0.0448871	+	0.0819252i
$958$	163748.			0.178421
$959$			62178.3i			0.0676085i
$960$	45181.7	+	24755.2i	0.0490253	+	0.0268611i
$961$	−831999.			−0.900898
$962$			1.80393e6i			1.94926i
$963$	677607.	−	432733.i	0.730677	−	0.466624i
$964$	−218685.			−0.235323
$965$		−	104022.i		−	0.111704i
$966$	22736.5	−	41497.3i	0.0243652	−	0.0444699i
$967$	−41957.3			−0.0448698			−0.0224349	−	0.999748i	$-0.507142\pi$
$967$	−41957.3			−0.0448698			−0.0224349	+	0.999748i	$0.507142\pi$
$968$			270780.i			0.288978i
$969$	1.83948e6	+	1.00786e6i	1.95906	+	1.07337i
$970$	−524915.			−0.557886
$971$		−	34137.0i		−	0.0362065i	−0.999836	−	0.0181032i	$-0.994237\pi$
$971$		−	34137.0i		−	0.0362065i	0.999836	−	0.0181032i	$-0.00576276\pi$
$972$	−280377.	−	380188.i	−0.296763	−	0.402407i
$973$	−71848.4			−0.0758912
$974$		−	335156.i		−	0.353289i
$975$	−145811.	+	266126.i	−0.153385	+	0.279949i
$976$	−25067.9			−0.0263159
$977$		−	278436.i		−	0.291700i	−0.989307	−	0.145850i	$-0.953408\pi$
$977$		−	278436.i		−	0.291700i	0.989307	−	0.145850i	$-0.0465917\pi$
$978$	976183.	+	534853.i	1.02059	+	0.559187i
$979$	379938.			0.396412
$980$		−	208952.i		−	0.217568i
$981$	683784.	+	1.07072e6i	0.710528	+	1.11260i
$982$	−1.19124e6			−1.23531
$983$		−	323632.i		−	0.334922i	−0.985879	−	0.167461i	$-0.946443\pi$
$983$		−	323632.i		−	0.334922i	0.985879	−	0.167461i	$-0.0535569\pi$
$984$	−86421.9	+	157732.i	−0.0892552	+	0.162903i
$985$	223117.			0.229965
$986$		−	228770.i		−	0.235312i
$987$	−156881.	−	85955.4i	−0.161041	−	0.0882346i
$988$	−1.14300e6			−1.17094
$989$		−	544097.i		−	0.556268i
$990$	111635.	−	71292.1i	0.113901	−	0.0727396i
$991$	928677.			0.945622			0.472811	−	0.881164i	$-0.343239\pi$
$991$	928677.			0.945622			0.472811	+	0.881164i	$0.343239\pi$
$992$			54763.2i			0.0556500i
$993$	93745.0	−	171098.i	0.0950714	−	0.173519i
$994$	201027.			0.203461
$995$			470366.i			0.475106i
$996$	−114761.	−	62878.1i	−0.115685	−	0.0633841i
$997$	−284841.			−0.286558			−0.143279	−	0.989682i	$-0.545765\pi$
$997$	−284841.			−0.286558			−0.143279	+	0.989682i	$0.545765\pi$
$998$			971814.i			0.975713i
$999$	1.71982e6	−	115575.i	1.72327	−	0.115807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	30.5.d.a.11.2	✓	4
3.2	odd	2	inner	30.5.d.a.11.4	yes	4
4.3	odd	2		240.5.l.b.161.2		4
5.2	odd	4		150.5.b.b.149.5		8
5.3	odd	4		150.5.b.b.149.4		8
5.4	even	2		150.5.d.b.101.3		4
12.11	even	2		240.5.l.b.161.1		4
15.2	even	4		150.5.b.b.149.3		8
15.8	even	4		150.5.b.b.149.6		8
15.14	odd	2		150.5.d.b.101.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.5.d.a.11.2	✓	4	1.1	even	1	trivial
30.5.d.a.11.4	yes	4	3.2	odd	2	inner
150.5.b.b.149.3		8	15.2	even	4
150.5.b.b.149.4		8	5.3	odd	4
150.5.b.b.149.5		8	5.2	odd	4
150.5.b.b.149.6		8	15.8	even	4
150.5.d.b.101.1		4	15.14	odd	2
150.5.d.b.101.3		4	5.4	even	2
240.5.l.b.161.1		4	12.11	even	2
240.5.l.b.161.2		4	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	30.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.82843i q^{2} +(4.32456 - 7.89292i) q^{3} -8.00000 q^{4} -11.1803i q^{5} +(-22.3246 - 12.2317i) q^{6} -8.05267 q^{7} +22.6274i q^{8} +(-43.5964 - 68.2668i) q^{9} +O(q^{10})\)	\(q-2.82843i q^{2} +(4.32456 - 7.89292i) q^{3} -8.00000 q^{4} -11.1803i q^{5} +(-22.3246 - 12.2317i) q^{6} -8.05267 q^{7} +22.6274i q^{8} +(-43.5964 - 68.2668i) q^{9} -31.6228 q^{10} -51.7119i q^{11} +(-34.5964 + 63.1434i) q^{12} +269.737 q^{13} +22.7764i q^{14} +(-88.2456 - 48.3500i) q^{15} +64.0000 q^{16} +439.988i q^{17} +(-193.088 + 123.309i) q^{18} +529.684 q^{19} +89.4427i q^{20} +(-34.8242 + 63.5591i) q^{21} -146.263 q^{22} -230.833i q^{23} +(178.596 + 97.8535i) q^{24} -125.000 q^{25} -762.930i q^{26} +(-727.359 + 48.8800i) q^{27} +64.4213 q^{28} -183.829i q^{29} +(-136.754 + 249.596i) q^{30} -302.527 q^{31} -181.019i q^{32} +(-408.158 - 223.631i) q^{33} +1244.47 q^{34} +90.0316i q^{35} +(348.772 + 546.134i) q^{36} -2364.47 q^{37} -1498.17i q^{38} +(1166.49 - 2129.01i) q^{39} +252.982 q^{40} +883.176i q^{41} +(179.772 + 98.4977i) q^{42} +2357.10 q^{43} +413.695i q^{44} +(-763.246 + 487.423i) q^{45} -652.894 q^{46} +2468.27i q^{47} +(276.772 - 505.147i) q^{48} -2336.15 q^{49} +353.553i q^{50} +(3472.79 + 1902.75i) q^{51} -2157.89 q^{52} +4767.11i q^{53} +(138.253 + 2057.28i) q^{54} -578.157 q^{55} -182.211i q^{56} +(2290.65 - 4180.75i) q^{57} -519.946 q^{58} -3376.15i q^{59} +(705.964 + 386.800i) q^{60} -391.685 q^{61} +855.675i q^{62} +(351.068 + 549.730i) q^{63} -512.000 q^{64} -3015.75i q^{65} +(-632.524 + 1154.45i) q^{66} +4366.68 q^{67} -3519.90i q^{68} +(-1821.95 - 998.250i) q^{69} +254.648 q^{70} -8826.11i q^{71} +(1544.70 - 986.475i) q^{72} -2498.21 q^{73} +6687.74i q^{74} +(-540.569 + 986.615i) q^{75} -4237.47 q^{76} +416.419i q^{77} +(-6021.75 - 3299.34i) q^{78} -3054.95 q^{79} -715.542i q^{80} +(-2759.70 + 5952.38i) q^{81} +2498.00 q^{82} +1817.47i q^{83} +(278.594 - 508.473i) q^{84} +4919.21 q^{85} -6666.90i q^{86} +(-1450.95 - 794.977i) q^{87} +1170.11 q^{88} +7347.20i q^{89} +(1378.64 + 2158.78i) q^{90} -2172.10 q^{91} +1846.66i q^{92} +(-1308.29 + 2387.82i) q^{93} +6981.31 q^{94} -5922.05i q^{95} +(-1428.77 - 782.828i) q^{96} +16599.3 q^{97} +6607.64i q^{98} +(-3530.20 + 2254.45i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{3} - 32 q^{4} - 64 q^{6} - 184 q^{7} + 28 q^{9}+O(q^{10}) \) 4 * q - 8 * q^3 - 32 * q^4 - 64 * q^6 - 184 * q^7 + 28 * q^9	\( 4 q - 8 q^{3} - 32 q^{4} - 64 q^{6} - 184 q^{7} + 28 q^{9} + 64 q^{12} + 320 q^{13} - 100 q^{15} + 256 q^{16} - 64 q^{18} + 1208 q^{19} + 1328 q^{21} - 1344 q^{22} + 512 q^{24} - 500 q^{25} - 2024 q^{27} + 1472 q^{28} - 800 q^{30} - 2728 q^{31} - 2088 q^{33} + 576 q^{34} - 224 q^{36} - 5056 q^{37} + 4160 q^{39} + 1984 q^{42} + 6848 q^{43} - 2800 q^{45} + 576 q^{46} - 512 q^{48} + 4620 q^{49} + 4632 q^{51} - 2560 q^{52} - 3520 q^{54} + 3000 q^{55} + 3344 q^{57} + 3840 q^{58} + 800 q^{60} - 6424 q^{61} - 8968 q^{63} - 2048 q^{64} + 7488 q^{66} + 7904 q^{67} - 1368 q^{69} - 4800 q^{70} + 512 q^{72} - 10600 q^{73} + 1000 q^{75} - 9664 q^{76} - 9920 q^{78} - 26488 q^{79} - 5372 q^{81} + 4224 q^{82} - 10624 q^{84} + 17400 q^{85} + 3000 q^{87} + 10752 q^{88} + 6400 q^{90} + 14080 q^{91} + 15056 q^{93} + 2880 q^{94} - 4096 q^{96} + 35432 q^{97} + 14112 q^{99}+O(q^{100}) \) 4 * q - 8 * q^3 - 32 * q^4 - 64 * q^6 - 184 * q^7 + 28 * q^9 + 64 * q^12 + 320 * q^13 - 100 * q^15 + 256 * q^16 - 64 * q^18 + 1208 * q^19 + 1328 * q^21 - 1344 * q^22 + 512 * q^24 - 500 * q^25 - 2024 * q^27 + 1472 * q^28 - 800 * q^30 - 2728 * q^31 - 2088 * q^33 + 576 * q^34 - 224 * q^36 - 5056 * q^37 + 4160 * q^39 + 1984 * q^42 + 6848 * q^43 - 2800 * q^45 + 576 * q^46 - 512 * q^48 + 4620 * q^49 + 4632 * q^51 - 2560 * q^52 - 3520 * q^54 + 3000 * q^55 + 3344 * q^57 + 3840 * q^58 + 800 * q^60 - 6424 * q^61 - 8968 * q^63 - 2048 * q^64 + 7488 * q^66 + 7904 * q^67 - 1368 * q^69 - 4800 * q^70 + 512 * q^72 - 10600 * q^73 + 1000 * q^75 - 9664 * q^76 - 9920 * q^78 - 26488 * q^79 - 5372 * q^81 + 4224 * q^82 - 10624 * q^84 + 17400 * q^85 + 3000 * q^87 + 10752 * q^88 + 6400 * q^90 + 14080 * q^91 + 15056 * q^93 + 2880 * q^94 - 4096 * q^96 + 35432 * q^97 + 14112 * q^99

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