LMFDB - Embedded newform 75.3.f.c.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,3,Mod(7,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("75.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	75.f (of order $4$, degree $2$, 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:	$2.04360198270$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.1
Root			$-1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	75.43
Dual form			75.3.f.c.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.224745 + 0.224745i) q^{2} +(1.22474 + 1.22474i) q^{3} +3.89898i q^{4} -0.550510 q^{6} +(-3.44949 + 3.44949i) q^{7} +(-1.77526 - 1.77526i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-0.224745 + 0.224745i) q^{2} +(1.22474 + 1.22474i) q^{3} +3.89898i q^{4} -0.550510 q^{6} +(-3.44949 + 3.44949i) q^{7} +(-1.77526 - 1.77526i) q^{8} +3.00000i q^{9} +11.3485 q^{11} +(-4.77526 + 4.77526i) q^{12} +(5.55051 + 5.55051i) q^{13} -1.55051i q^{14} -14.7980 q^{16} +(17.3485 - 17.3485i) q^{17} +(-0.674235 - 0.674235i) q^{18} -8.69694i q^{19} -8.44949 q^{21} +(-2.55051 + 2.55051i) q^{22} +(-11.5505 - 11.5505i) q^{23} -4.34847i q^{24} -2.49490 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-13.4495 - 13.4495i) q^{28} -35.1464i q^{29} +10.6969 q^{31} +(10.4268 - 10.4268i) q^{32} +(13.8990 + 13.8990i) q^{33} +7.79796i q^{34} -11.6969 q^{36} +(6.04541 - 6.04541i) q^{37} +(1.95459 + 1.95459i) q^{38} +13.5959i q^{39} +0.696938 q^{41} +(1.89898 - 1.89898i) q^{42} +(26.4949 + 26.4949i) q^{43} +44.2474i q^{44} +5.19184 q^{46} +(-44.2474 + 44.2474i) q^{47} +(-18.1237 - 18.1237i) q^{48} +25.2020i q^{49} +42.4949 q^{51} +(-21.6413 + 21.6413i) q^{52} +(0.696938 + 0.696938i) q^{53} -1.65153i q^{54} +12.2474 q^{56} +(10.6515 - 10.6515i) q^{57} +(7.89898 + 7.89898i) q^{58} +39.9342i q^{59} +5.90918 q^{61} +(-2.40408 + 2.40408i) q^{62} +(-10.3485 - 10.3485i) q^{63} -54.5051i q^{64} -6.24745 q^{66} +(45.1010 - 45.1010i) q^{67} +(67.6413 + 67.6413i) q^{68} -28.2929i q^{69} -68.0000 q^{71} +(5.32577 - 5.32577i) q^{72} +(-77.7878 - 77.7878i) q^{73} +2.71735i q^{74} +33.9092 q^{76} +(-39.1464 + 39.1464i) q^{77} +(-3.05561 - 3.05561i) q^{78} +24.4949i q^{79} -9.00000 q^{81} +(-0.156633 + 0.156633i) q^{82} +(-13.1464 - 13.1464i) q^{83} -32.9444i q^{84} -11.9092 q^{86} +(43.0454 - 43.0454i) q^{87} +(-20.1464 - 20.1464i) q^{88} -82.1816i q^{89} -38.2929 q^{91} +(45.0352 - 45.0352i) q^{92} +(13.1010 + 13.1010i) q^{93} -19.8888i q^{94} +25.5403 q^{96} +(24.5959 - 24.5959i) q^{97} +(-5.66403 - 5.66403i) q^{98} +34.0454i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 12 q^{6} - 4 q^{7} - 12 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 12 * q^6 - 4 * q^7 - 12 * q^8	$ 4 q + 4 q^{2} - 12 q^{6} - 4 q^{7} - 12 q^{8} + 16 q^{11} - 24 q^{12} + 32 q^{13} - 20 q^{16} + 40 q^{17} + 12 q^{18} - 24 q^{21} - 20 q^{22} - 56 q^{23} + 88 q^{26} - 44 q^{28} - 16 q^{31} + 76 q^{32} + 36 q^{33} + 12 q^{36} - 64 q^{37} + 96 q^{38} - 56 q^{41} - 12 q^{42} + 8 q^{43} - 136 q^{46} - 128 q^{47} - 48 q^{48} + 72 q^{51} + 80 q^{52} - 56 q^{53} + 72 q^{57} + 12 q^{58} + 200 q^{61} - 88 q^{62} - 12 q^{63} + 24 q^{66} + 200 q^{67} + 104 q^{68} - 272 q^{71} + 36 q^{72} - 76 q^{73} + 312 q^{76} - 88 q^{77} - 120 q^{78} - 36 q^{81} - 128 q^{82} + 16 q^{83} - 224 q^{86} + 84 q^{87} - 12 q^{88} - 16 q^{91} - 104 q^{92} + 72 q^{93} - 84 q^{96} + 20 q^{97} + 188 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 12 * q^6 - 4 * q^7 - 12 * q^8 + 16 * q^11 - 24 * q^12 + 32 * q^13 - 20 * q^16 + 40 * q^17 + 12 * q^18 - 24 * q^21 - 20 * q^22 - 56 * q^23 + 88 * q^26 - 44 * q^28 - 16 * q^31 + 76 * q^32 + 36 * q^33 + 12 * q^36 - 64 * q^37 + 96 * q^38 - 56 * q^41 - 12 * q^42 + 8 * q^43 - 136 * q^46 - 128 * q^47 - 48 * q^48 + 72 * q^51 + 80 * q^52 - 56 * q^53 + 72 * q^57 + 12 * q^58 + 200 * q^61 - 88 * q^62 - 12 * q^63 + 24 * q^66 + 200 * q^67 + 104 * q^68 - 272 * q^71 + 36 * q^72 - 76 * q^73 + 312 * q^76 - 88 * q^77 - 120 * q^78 - 36 * q^81 - 128 * q^82 + 16 * q^83 - 224 * q^86 + 84 * q^87 - 12 * q^88 - 16 * q^91 - 104 * q^92 + 72 * q^93 - 84 * q^96 + 20 * q^97 + 188 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.224745	+	0.224745i	−0.112372	+	0.112372i	−0.761057	−	0.648685i	$-0.775319\pi$
$2$	−0.224745	+	0.224745i	−0.112372	+	0.112372i	0.648685	+	0.761057i	$0.275319\pi$
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$4$			3.89898i			0.974745i
$5$		0			0
$5$		0			0
$6$	−0.550510			−0.0917517
$7$	−3.44949	+	3.44949i	−0.492784	+	0.492784i	−0.909182	−	0.416398i	$-0.863292\pi$
$7$	−3.44949	+	3.44949i	−0.492784	+	0.492784i	0.416398	+	0.909182i	$0.363292\pi$
$8$	−1.77526	−	1.77526i	−0.221907	−	0.221907i
$9$			3.00000i			0.333333i
$10$		0			0
$11$	11.3485			1.03168			0.515840	−	0.856685i	$-0.327480\pi$
$11$	11.3485			1.03168			0.515840	+	0.856685i	$0.327480\pi$
$12$	−4.77526	+	4.77526i	−0.397938	+	0.397938i
$13$	5.55051	+	5.55051i	0.426962	+	0.426962i	0.887592	−	0.460630i	$-0.152376\pi$
$13$	5.55051	+	5.55051i	0.426962	+	0.426962i	−0.460630	+	0.887592i	$0.652376\pi$
$14$		−	1.55051i		−	0.110751i
$15$		0			0
$16$	−14.7980			−0.924872
$17$	17.3485	−	17.3485i	1.02050	−	1.02050i	0.0207127	−	0.999785i	$-0.493406\pi$
$17$	17.3485	−	17.3485i	1.02050	−	1.02050i	0.999785	−	0.0207127i	$-0.00659354\pi$
$18$	−0.674235	−	0.674235i	−0.0374575	−	0.0374575i
$19$		−	8.69694i		−	0.457734i	−0.973458	−	0.228867i	$-0.926498\pi$
$19$		−	8.69694i		−	0.457734i	0.973458	−	0.228867i	$-0.0735020\pi$
$20$		0			0
$21$	−8.44949			−0.402357
$22$	−2.55051	+	2.55051i	−0.115932	+	0.115932i
$23$	−11.5505	−	11.5505i	−0.502196	−	0.502196i	0.409924	−	0.912120i	$-0.365555\pi$
$23$	−11.5505	−	11.5505i	−0.502196	−	0.502196i	−0.912120	+	0.409924i	$0.865555\pi$
$24$		−	4.34847i		−	0.181186i
$25$		0			0
$26$	−2.49490			−0.0959576
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	−13.4495	−	13.4495i	−0.480339	−	0.480339i
$29$		−	35.1464i		−	1.21195i	−0.795485	−	0.605973i	$-0.792784\pi$
$29$		−	35.1464i		−	1.21195i	0.795485	−	0.605973i	$-0.207216\pi$
$30$		0			0
$31$	10.6969			0.345063			0.172531	−	0.985004i	$-0.444805\pi$
$31$	10.6969			0.345063			0.172531	+	0.985004i	$0.444805\pi$
$32$	10.4268	−	10.4268i	0.325837	−	0.325837i
$33$	13.8990	+	13.8990i	0.421181	+	0.421181i
$34$			7.79796i			0.229352i
$35$		0			0
$36$	−11.6969			−0.324915
$37$	6.04541	−	6.04541i	0.163389	−	0.163389i	−0.620677	−	0.784066i	$-0.713142\pi$
$37$	6.04541	−	6.04541i	0.163389	−	0.163389i	0.784066	+	0.620677i	$0.213142\pi$
$38$	1.95459	+	1.95459i	0.0514366	+	0.0514366i
$39$			13.5959i			0.348613i
$40$		0			0
$41$	0.696938			0.0169985			0.00849925	−	0.999964i	$-0.497295\pi$
$41$	0.696938			0.0169985			0.00849925	+	0.999964i	$0.497295\pi$
$42$	1.89898	−	1.89898i	0.0452138	−	0.0452138i
$43$	26.4949	+	26.4949i	0.616160	+	0.616160i	0.944544	−	0.328384i	$-0.106504\pi$
$43$	26.4949	+	26.4949i	0.616160	+	0.616160i	−0.328384	+	0.944544i	$0.606504\pi$
$44$			44.2474i			1.00562i
$45$		0			0
$46$	5.19184			0.112866
$47$	−44.2474	+	44.2474i	−0.941435	+	0.941435i	−0.998377	−	0.0569424i	$-0.981865\pi$
$47$	−44.2474	+	44.2474i	−0.941435	+	0.941435i	0.0569424	+	0.998377i	$0.481865\pi$
$48$	−18.1237	−	18.1237i	−0.377578	−	0.377578i
$49$			25.2020i			0.514327i
$50$		0			0
$51$	42.4949			0.833233
$52$	−21.6413	+	21.6413i	−0.416179	+	0.416179i
$53$	0.696938	+	0.696938i	0.0131498	+	0.0131498i	0.713651	−	0.700501i	$-0.247040\pi$
$53$	0.696938	+	0.696938i	0.0131498	+	0.0131498i	−0.700501	+	0.713651i	$0.747040\pi$
$54$		−	1.65153i		−	0.0305839i
$55$		0			0
$56$	12.2474			0.218704
$57$	10.6515	−	10.6515i	0.186869	−	0.186869i
$58$	7.89898	+	7.89898i	0.136189	+	0.136189i
$59$			39.9342i			0.676851i	0.940993	+	0.338425i	$0.109894\pi$
$59$			39.9342i			0.676851i	−0.940993	+	0.338425i	$0.890106\pi$
$60$		0			0
$61$	5.90918			0.0968719			0.0484359	−	0.998826i	$-0.484576\pi$
$61$	5.90918			0.0968719			0.0484359	+	0.998826i	$0.484576\pi$
$62$	−2.40408	+	2.40408i	−0.0387755	+	0.0387755i
$63$	−10.3485	−	10.3485i	−0.164261	−	0.164261i
$64$		−	54.5051i		−	0.851642i
$65$		0			0
$66$	−6.24745			−0.0946583
$67$	45.1010	−	45.1010i	0.673150	−	0.673150i	−0.285291	−	0.958441i	$-0.592090\pi$
$67$	45.1010	−	45.1010i	0.673150	−	0.673150i	0.958441	+	0.285291i	$0.0920903\pi$
$68$	67.6413	+	67.6413i	0.994725	+	0.994725i
$69$		−	28.2929i		−	0.410041i
$70$		0			0
$71$	−68.0000			−0.957746			−0.478873	−	0.877884i	$-0.658955\pi$
$71$	−68.0000			−0.957746			−0.478873	+	0.877884i	$0.658955\pi$
$72$	5.32577	−	5.32577i	0.0739690	−	0.0739690i
$73$	−77.7878	−	77.7878i	−1.06559	−	1.06559i	−0.997693	−	0.0678931i	$-0.978372\pi$
$73$	−77.7878	−	77.7878i	−1.06559	−	1.06559i	−0.0678931	−	0.997693i	$-0.521628\pi$
$74$			2.71735i			0.0367209i
$75$		0			0
$76$	33.9092			0.446173
$77$	−39.1464	+	39.1464i	−0.508395	+	0.508395i
$78$	−3.05561	−	3.05561i	−0.0391745	−	0.0391745i
$79$			24.4949i			0.310062i	0.987910	+	0.155031i	$0.0495477\pi$
$79$			24.4949i			0.310062i	−0.987910	+	0.155031i	$0.950452\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	−0.156633	+	0.156633i	−0.00191016	+	0.00191016i
$83$	−13.1464	−	13.1464i	−0.158391	−	0.158391i	0.623463	−	0.781853i	$-0.285725\pi$
$83$	−13.1464	−	13.1464i	−0.158391	−	0.158391i	−0.781853	+	0.623463i	$0.785725\pi$
$84$		−	32.9444i		−	0.392195i
$85$		0			0
$86$	−11.9092			−0.138479
$87$	43.0454	−	43.0454i	0.494775	−	0.494775i
$88$	−20.1464	−	20.1464i	−0.228937	−	0.228937i
$89$		−	82.1816i		−	0.923389i	−0.887039	−	0.461695i	$-0.847242\pi$
$89$		−	82.1816i		−	0.923389i	0.887039	−	0.461695i	$-0.152758\pi$
$90$		0			0
$91$	−38.2929			−0.420801
$92$	45.0352	−	45.0352i	0.489513	−	0.489513i
$93$	13.1010	+	13.1010i	0.140871	+	0.140871i
$94$		−	19.8888i		−	0.211583i
$95$		0			0
$96$	25.5403			0.266045
$97$	24.5959	−	24.5959i	0.253566	−	0.253566i	−0.568865	−	0.822431i	$-0.692617\pi$
$97$	24.5959	−	24.5959i	0.253566	−	0.253566i	0.822431	+	0.568865i	$0.192617\pi$
$98$	−5.66403	−	5.66403i	−0.0577962	−	0.0577962i
$99$			34.0454i			0.343893i
$100$		0			0
$101$	−105.621			−1.04575			−0.522876	−	0.852409i	$-0.675141\pi$
$101$	−105.621			−1.04575			−0.522876	+	0.852409i	$0.675141\pi$
$102$	−9.55051	+	9.55051i	−0.0936325	+	0.0936325i
$103$	89.2474	+	89.2474i	0.866480	+	0.866480i	0.992081	−	0.125601i	$-0.0400858\pi$
$103$	89.2474	+	89.2474i	0.866480	+	0.866480i	−0.125601	+	0.992081i	$0.540086\pi$
$104$		−	19.7071i		−	0.189492i
$105$		0			0
$106$	−0.313267			−0.00295535
$107$	−68.7423	+	68.7423i	−0.642452	+	0.642452i	−0.951158	−	0.308706i	$-0.900104\pi$
$107$	−68.7423	+	68.7423i	−0.642452	+	0.642452i	0.308706	+	0.951158i	$0.400104\pi$
$108$	−14.3258	−	14.3258i	−0.132646	−	0.132646i
$109$		−	68.6969i		−	0.630247i	−0.949051	−	0.315124i	$-0.897954\pi$
$109$		−	68.6969i		−	0.630247i	0.949051	−	0.315124i	$-0.102046\pi$
$110$		0			0
$111$	14.8082			0.133407
$112$	51.0454	−	51.0454i	0.455763	−	0.455763i
$113$	−97.6413	−	97.6413i	−0.864083	−	0.864083i	0.127727	−	0.991809i	$-0.459232\pi$
$113$	−97.6413	−	97.6413i	−0.864083	−	0.864083i	−0.991809	+	0.127727i	$0.959232\pi$
$114$			4.78775i			0.0419978i
$115$		0			0
$116$	137.035			1.18134
$117$	−16.6515	+	16.6515i	−0.142321	+	0.142321i
$118$	−8.97500	−	8.97500i	−0.0760593	−	0.0760593i
$119$			119.687i			1.00577i
$120$		0			0
$121$	7.78775			0.0643616
$122$	−1.32806	+	1.32806i	−0.0108857	+	0.0108857i
$123$	0.853572	+	0.853572i	0.00693961	+	0.00693961i
$124$			41.7071i			0.336348i
$125$		0			0
$126$	4.65153			0.0369169
$127$	−164.621	+	164.621i	−1.29623	+	1.29623i	−0.365362	+	0.930865i	$0.619055\pi$
$127$	−164.621	+	164.621i	−1.29623	+	1.29623i	−0.930865	+	0.365362i	$0.880945\pi$
$128$	53.9569	+	53.9569i	0.421538	+	0.421538i
$129$			64.8990i			0.503093i
$130$		0			0
$131$	106.136			0.810200			0.405100	−	0.914272i	$-0.367237\pi$
$131$	106.136			0.810200			0.405100	+	0.914272i	$0.367237\pi$
$132$	−54.1918	+	54.1918i	−0.410544	+	0.410544i
$133$	30.0000	+	30.0000i	0.225564	+	0.225564i
$134$			20.2724i			0.151287i
$135$		0			0
$136$	−61.5959			−0.452911
$137$	166.631	−	166.631i	1.21629	−	1.21629i	0.247363	−	0.968923i	$-0.420436\pi$
$137$	166.631	−	166.631i	1.21629	−	1.21629i	0.968923	−	0.247363i	$-0.0795639\pi$
$138$	6.35867	+	6.35867i	0.0460774	+	0.0460774i
$139$			191.171i			1.37533i	0.726026	+	0.687667i	$0.241365\pi$
$139$			191.171i			1.37533i	−0.726026	+	0.687667i	$0.758635\pi$
$140$		0			0
$141$	−108.384			−0.768679
$142$	15.2827	−	15.2827i	0.107624	−	0.107624i
$143$	62.9898	+	62.9898i	0.440488	+	0.440488i
$144$		−	44.3939i		−	0.308291i
$145$		0			0
$146$	34.9648			0.239485
$147$	−30.8661	+	30.8661i	−0.209973	+	0.209973i
$148$	23.5709	+	23.5709i	0.159263	+	0.159263i
$149$		−	84.8536i		−	0.569487i	−0.958604	−	0.284744i	$-0.908092\pi$
$149$		−	84.8536i		−	0.569487i	0.958604	−	0.284744i	$-0.0919084\pi$
$150$		0			0
$151$	148.969			0.986552			0.493276	−	0.869873i	$-0.335799\pi$
$151$	148.969			0.986552			0.493276	+	0.869873i	$0.335799\pi$
$152$	−15.4393	+	15.4393i	−0.101574	+	0.101574i
$153$	52.0454	+	52.0454i	0.340166	+	0.340166i
$154$		−	17.5959i		−	0.114259i
$155$		0			0
$156$	−53.0102			−0.339809
$157$	−16.8536	+	16.8536i	−0.107348	+	0.107348i	−0.758741	−	0.651393i	$-0.774185\pi$
$157$	−16.8536	+	16.8536i	−0.107348	+	0.107348i	0.651393	+	0.758741i	$0.274185\pi$
$158$	−5.50510	−	5.50510i	−0.0348424	−	0.0348424i
$159$			1.70714i			0.0107368i
$160$		0			0
$161$	79.6867			0.494949
$162$	2.02270	−	2.02270i	0.0124858	−	0.0124858i
$163$	−130.606	−	130.606i	−0.801265	−	0.801265i	0.182029	−	0.983293i	$-0.441734\pi$
$163$	−130.606	−	130.606i	−0.801265	−	0.801265i	−0.983293	+	0.182029i	$0.941734\pi$
$164$			2.71735i			0.0165692i
$165$		0			0
$166$	5.90918			0.0355975
$167$	45.0352	−	45.0352i	0.269672	−	0.269672i	−0.559296	−	0.828968i	$-0.688929\pi$
$167$	45.0352	−	45.0352i	0.269672	−	0.269672i	0.828968	+	0.559296i	$0.188929\pi$
$168$	15.0000	+	15.0000i	0.0892857	+	0.0892857i
$169$		−	107.384i		−	0.635406i
$170$		0			0
$171$	26.0908			0.152578
$172$	−103.303	+	103.303i	−0.600599	+	0.600599i
$173$	−146.631	−	146.631i	−0.847579	−	0.847579i	0.142252	−	0.989831i	$-0.454566\pi$
$173$	−146.631	−	146.631i	−0.847579	−	0.847579i	−0.989831	+	0.142252i	$0.954566\pi$
$174$			19.3485i			0.111198i
$175$		0			0
$176$	−167.934			−0.954171
$177$	−48.9092	+	48.9092i	−0.276323	+	0.276323i
$178$	18.4699	+	18.4699i	0.103763	+	0.103763i
$179$		−	183.712i		−	1.02632i	−0.858292	−	0.513161i	$-0.828474\pi$
$179$		−	183.712i		−	1.02632i	0.858292	−	0.513161i	$-0.171526\pi$
$180$		0			0
$181$	−286.272			−1.58162			−0.790808	−	0.612064i	$-0.790339\pi$
$181$	−286.272			−1.58162			−0.790808	+	0.612064i	$0.790339\pi$
$182$	8.60612	−	8.60612i	0.0472864	−	0.0472864i
$183$	7.23724	+	7.23724i	0.0395478	+	0.0395478i
$184$			41.0102i			0.222882i
$185$		0			0
$186$	−5.88877			−0.0316601
$187$	196.879	−	196.879i	1.05283	−	1.05283i
$188$	−172.520	−	172.520i	−0.917659	−	0.917659i
$189$		−	25.3485i		−	0.134119i
$190$		0			0
$191$	48.0908			0.251784			0.125892	−	0.992044i	$-0.459821\pi$
$191$	48.0908			0.251784			0.125892	+	0.992044i	$0.459821\pi$
$192$	66.7548	−	66.7548i	0.347681	−	0.347681i
$193$	255.565	+	255.565i	1.32417	+	1.32417i	0.910364	+	0.413809i	$0.135802\pi$
$193$	255.565	+	255.565i	1.32417	+	1.32417i	0.413809	+	0.910364i	$0.364198\pi$
$194$			11.0556i			0.0569877i
$195$		0			0
$196$	−98.2622			−0.501338
$197$	96.6969	−	96.6969i	0.490847	−	0.490847i	−0.417726	−	0.908573i	$-0.637173\pi$
$197$	96.6969	−	96.6969i	0.490847	−	0.490847i	0.908573	+	0.417726i	$0.137173\pi$
$198$	−7.65153	−	7.65153i	−0.0386441	−	0.0386441i
$199$		−	192.606i		−	0.967870i	−0.875104	−	0.483935i	$-0.839207\pi$
$199$		−	192.606i		−	0.967870i	0.875104	−	0.483935i	$-0.160793\pi$
$200$		0			0
$201$	110.474			0.549624
$202$	23.7378	−	23.7378i	0.117514	−	0.117514i
$203$	121.237	+	121.237i	0.597228	+	0.597228i
$204$			165.687i			0.812190i
$205$		0			0
$206$	−40.1158			−0.194737
$207$	34.6515	−	34.6515i	0.167399	−	0.167399i
$208$	−82.1362	−	82.1362i	−0.394886	−	0.394886i
$209$		−	98.6969i		−	0.472234i
$210$		0			0
$211$	147.212			0.697688			0.348844	−	0.937181i	$-0.386574\pi$
$211$	147.212			0.697688			0.348844	+	0.937181i	$0.386574\pi$
$212$	−2.71735	+	2.71735i	−0.0128177	+	0.0128177i
$213$	−83.2827	−	83.2827i	−0.390998	−	0.390998i
$214$		−	30.8990i		−	0.144388i
$215$		0			0
$216$	13.0454			0.0603954
$217$	−36.8990	+	36.8990i	−0.170041	+	0.170041i
$218$	15.4393	+	15.4393i	0.0708224	+	0.0708224i
$219$		−	190.540i		−	0.870047i
$220$		0			0
$221$	192.586			0.871429
$222$	−3.32806	+	3.32806i	−0.0149913	+	0.0149913i
$223$	−167.429	−	167.429i	−0.750803	−	0.750803i	0.223826	−	0.974629i	$-0.428145\pi$
$223$	−167.429	−	167.429i	−0.750803	−	0.750803i	−0.974629	+	0.223826i	$0.928145\pi$
$224$			71.9342i			0.321135i
$225$		0			0
$226$	43.8888			0.194198
$227$	−253.171	+	253.171i	−1.11529	+	1.11529i	−0.122870	+	0.992423i	$0.539210\pi$
$227$	−253.171	+	253.171i	−1.11529	+	1.11529i	−0.992423	+	0.122870i	$0.960790\pi$
$228$	41.5301	+	41.5301i	0.182150	+	0.182150i
$229$			224.202i			0.979048i	0.871990	+	0.489524i	$0.162829\pi$
$229$			224.202i			0.979048i	−0.871990	+	0.489524i	$0.837171\pi$
$230$		0			0
$231$	−95.8888			−0.415103
$232$	−62.3939	+	62.3939i	−0.268939	+	0.268939i
$233$	205.712	+	205.712i	0.882883	+	0.882883i	0.993827	−	0.110944i	$-0.0353873\pi$
$233$	205.712	+	205.712i	0.882883	+	0.882883i	−0.110944	+	0.993827i	$0.535387\pi$
$234$		−	7.48469i		−	0.0319859i
$235$		0			0
$236$	−155.703			−0.659757
$237$	−30.0000	+	30.0000i	−0.126582	+	0.126582i
$238$	−26.8990	−	26.8990i	−0.113021	−	0.113021i
$239$			345.798i			1.44685i	0.690401	+	0.723427i	$0.257434\pi$
$239$			345.798i			1.44685i	−0.690401	+	0.723427i	$0.742566\pi$
$240$		0			0
$241$	101.576			0.421475			0.210738	−	0.977543i	$-0.432413\pi$
$241$	101.576			0.421475			0.210738	+	0.977543i	$0.432413\pi$
$242$	−1.75026	+	1.75026i	−0.00723247	+	0.00723247i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$			23.0398i			0.0944254i
$245$		0			0
$246$	−0.383672			−0.00155964
$247$	48.2724	−	48.2724i	0.195435	−	0.195435i
$248$	−18.9898	−	18.9898i	−0.0765718	−	0.0765718i
$249$		−	32.2020i		−	0.129325i
$250$		0			0
$251$	−331.258			−1.31975			−0.659876	−	0.751375i	$-0.729391\pi$
$251$	−331.258			−1.31975			−0.659876	+	0.751375i	$0.729391\pi$
$252$	40.3485	−	40.3485i	0.160113	−	0.160113i
$253$	−131.081	−	131.081i	−0.518105	−	0.518105i
$254$		−	73.9954i		−	0.291321i
$255$		0			0
$256$	193.767			0.756904
$257$	−33.2372	+	33.2372i	−0.129328	+	0.129328i	−0.768808	−	0.639480i	$-0.779150\pi$
$257$	−33.2372	+	33.2372i	−0.129328	+	0.129328i	0.639480	+	0.768808i	$0.279150\pi$
$258$	−14.5857	−	14.5857i	−0.0565338	−	0.0565338i
$259$			41.7071i			0.161031i
$260$		0			0
$261$	105.439			0.403982
$262$	−23.8536	+	23.8536i	−0.0910442	+	0.0910442i
$263$	278.157	+	278.157i	1.05763	+	1.05763i	0.998235	+	0.0593952i	$0.0189172\pi$
$263$	278.157	+	278.157i	1.05763	+	1.05763i	0.0593952	+	0.998235i	$0.481083\pi$
$264$		−	49.3485i		−	0.186926i
$265$		0			0
$266$	−13.4847			−0.0506943
$267$	100.652	−	100.652i	0.376972	−	0.376972i
$268$	175.848	+	175.848i	0.656149	+	0.656149i
$269$			488.499i			1.81598i	0.418988	+	0.907992i	$0.362385\pi$
$269$			488.499i			1.81598i	−0.418988	+	0.907992i	$0.637615\pi$
$270$		0			0
$271$	131.576			0.485518			0.242759	−	0.970087i	$-0.421947\pi$
$271$	131.576			0.485518			0.242759	+	0.970087i	$0.421947\pi$
$272$	−256.722	+	256.722i	−0.943831	+	0.943831i
$273$	−46.8990	−	46.8990i	−0.171791	−	0.171791i
$274$			74.8990i			0.273354i
$275$		0			0
$276$	110.313			0.399686
$277$	−101.510	+	101.510i	−0.366461	+	0.366461i	−0.866185	−	0.499724i	$-0.833435\pi$
$277$	−101.510	+	101.510i	−0.366461	+	0.366461i	0.499724	+	0.866185i	$0.333435\pi$
$278$	−42.9648	−	42.9648i	−0.154550	−	0.154550i
$279$			32.0908i			0.115021i
$280$		0			0
$281$	343.303			1.22172			0.610860	−	0.791739i	$-0.290824\pi$
$281$	343.303			1.22172			0.610860	+	0.791739i	$0.290824\pi$
$282$	24.3587	−	24.3587i	0.0863783	−	0.0863783i
$283$	−1.19184	−	1.19184i	−0.00421143	−	0.00421143i	0.704998	−	0.709209i	$-0.250948\pi$
$283$	−1.19184	−	1.19184i	−0.00421143	−	0.00421143i	−0.709209	+	0.704998i	$0.750948\pi$
$284$		−	265.131i		−	0.933558i
$285$		0			0
$286$	−28.3133			−0.0989974
$287$	−2.40408	+	2.40408i	−0.00837659	+	0.00837659i
$288$	31.2804	+	31.2804i	0.108612	+	0.108612i
$289$		−	312.939i		−	1.08283i
$290$		0			0
$291$	60.2474			0.207036
$292$	303.293	−	303.293i	1.03867	−	1.03867i
$293$	−96.5653	−	96.5653i	−0.329574	−	0.329574i	0.522850	−	0.852425i	$-0.324869\pi$
$293$	−96.5653	−	96.5653i	−0.329574	−	0.329574i	−0.852425	+	0.522850i	$0.824869\pi$
$294$		−	13.8740i		−	0.0471904i
$295$		0			0
$296$	−21.4643			−0.0725145
$297$	−41.6969	+	41.6969i	−0.140394	+	0.140394i
$298$	19.0704	+	19.0704i	0.0639946	+	0.0639946i
$299$		−	128.222i		−	0.428838i
$300$		0			0
$301$	−182.788			−0.607268
$302$	−33.4801	+	33.4801i	−0.110861	+	0.110861i
$303$	−129.359	−	129.359i	−0.426926	−	0.426926i
$304$			128.697i			0.423345i
$305$		0			0
$306$	−23.3939			−0.0764506
$307$	124.969	−	124.969i	0.407066	−	0.407066i	−0.473648	−	0.880714i	$-0.657063\pi$
$307$	124.969	−	124.969i	0.407066	−	0.407066i	0.880714	+	0.473648i	$0.157063\pi$
$308$	−152.631	−	152.631i	−0.495556	−	0.495556i
$309$			218.611i			0.707478i
$310$		0			0
$311$	−586.302			−1.88522			−0.942608	−	0.333902i	$-0.891635\pi$
$311$	−586.302			−1.88522			−0.942608	+	0.333902i	$0.891635\pi$
$312$	24.1362	−	24.1362i	0.0773597	−	0.0773597i
$313$	102.373	+	102.373i	0.327072	+	0.327072i	0.851472	−	0.524400i	$-0.175710\pi$
$313$	102.373	+	102.373i	0.327072	+	0.327072i	−0.524400	+	0.851472i	$0.675710\pi$
$314$		−	7.57551i		−	0.0241258i
$315$		0			0
$316$	−95.5051			−0.302231
$317$	108.783	−	108.783i	0.343165	−	0.343165i	−0.514391	−	0.857556i	$-0.671982\pi$
$317$	108.783	−	108.783i	0.343165	−	0.343165i	0.857556	+	0.514391i	$0.171982\pi$
$318$	−0.383672	−	0.383672i	−0.00120651	−	0.00120651i
$319$		−	398.858i		−	1.25034i
$320$		0			0
$321$	−168.384			−0.524560
$322$	−17.9092	+	17.9092i	−0.0556186	+	0.0556186i
$323$	−150.879	−	150.879i	−0.467116	−	0.467116i
$324$		−	35.0908i		−	0.108305i
$325$		0			0
$326$	58.7061			0.180080
$327$	84.1362	−	84.1362i	0.257297	−	0.257297i
$328$	−1.23724	−	1.23724i	−0.00377208	−	0.00377208i
$329$		−	305.262i		−	0.927849i
$330$		0			0
$331$	−245.423			−0.741461			−0.370730	−	0.928741i	$-0.620893\pi$
$331$	−245.423			−0.741461			−0.370730	+	0.928741i	$0.620893\pi$
$332$	51.2577	−	51.2577i	0.154391	−	0.154391i
$333$	18.1362	+	18.1362i	0.0544631	+	0.0544631i
$334$			20.2429i			0.0606074i
$335$		0			0
$336$	125.035			0.372129
$337$	−213.808	+	213.808i	−0.634446	+	0.634446i	−0.949180	−	0.314734i	$-0.898085\pi$
$337$	−213.808	+	213.808i	−0.634446	+	0.634446i	0.314734	+	0.949180i	$0.398085\pi$
$338$	24.1339	+	24.1339i	0.0714022	+	0.0714022i
$339$		−	239.171i		−	0.705520i
$340$		0			0
$341$	121.394			0.355994
$342$	−5.86378	+	5.86378i	−0.0171455	+	0.0171455i
$343$	−255.959	−	255.959i	−0.746237	−	0.746237i
$344$		−	94.0704i		−	0.273460i
$345$		0			0
$346$	65.9092			0.190489
$347$	160.050	−	160.050i	0.461239	−	0.461239i	−0.437822	−	0.899062i	$-0.644250\pi$
$347$	160.050	−	160.050i	0.461239	−	0.461239i	0.899062	+	0.437822i	$0.144250\pi$
$348$	167.833	+	167.833i	0.482279	+	0.482279i
$349$			298.009i			0.853894i	0.904277	+	0.426947i	$0.140411\pi$
$349$			298.009i			0.853894i	−0.904277	+	0.426947i	$0.859589\pi$
$350$		0			0
$351$	−40.7878			−0.116204
$352$	118.328	−	118.328i	0.336159	−	0.336159i
$353$	22.5199	+	22.5199i	0.0637957	+	0.0637957i	0.738285	−	0.674489i	$-0.235636\pi$
$353$	22.5199	+	22.5199i	0.0637957	+	0.0637957i	−0.674489	+	0.738285i	$0.735636\pi$
$354$		−	21.9842i		−	0.0621022i
$355$		0			0
$356$	320.424			0.900069
$357$	−146.586	+	146.586i	−0.410604	+	0.410604i
$358$	41.2883	+	41.2883i	0.115330	+	0.115330i
$359$		−	48.2724i		−	0.134464i	−0.997737	−	0.0672318i	$-0.978583\pi$
$359$		−	48.2724i		−	0.134464i	0.997737	−	0.0672318i	$-0.0214167\pi$
$360$		0			0
$361$	285.363			0.790480
$362$	64.3383	−	64.3383i	0.177730	−	0.177730i
$363$	9.53801	+	9.53801i	0.0262755	+	0.0262755i
$364$		−	149.303i		−	0.410173i
$365$		0			0
$366$	−3.25307			−0.00888816
$367$	−146.510	+	146.510i	−0.399209	+	0.399209i	−0.877954	−	0.478745i	$-0.841092\pi$
$367$	−146.510	+	146.510i	−0.399209	+	0.399209i	0.478745	+	0.877954i	$0.341092\pi$
$368$	170.924	+	170.924i	0.464467	+	0.464467i
$369$			2.09082i			0.00566617i
$370$		0			0
$371$	−4.80816			−0.0129600
$372$	−51.0806	+	51.0806i	−0.137313	+	0.137313i
$373$	−86.2066	−	86.2066i	−0.231117	−	0.231117i	0.582042	−	0.813159i	$-0.302254\pi$
$373$	−86.2066	−	86.2066i	−0.231117	−	0.231117i	−0.813159	+	0.582042i	$0.802254\pi$
$374$			88.4949i			0.236617i
$375$		0			0
$376$	157.101			0.417822
$377$	195.081	−	195.081i	0.517455	−	0.517455i
$378$	5.69694	+	5.69694i	0.0150713	+	0.0150713i
$379$			210.000i			0.554090i	0.960857	+	0.277045i	$0.0893551\pi$
$379$			210.000i			0.554090i	−0.960857	+	0.277045i	$0.910645\pi$
$380$		0			0
$381$	−403.237			−1.05837
$382$	−10.8082	+	10.8082i	−0.0282936	+	0.0282936i
$383$	10.6311	+	10.6311i	0.0277575	+	0.0277575i	0.720849	−	0.693092i	$-0.243752\pi$
$383$	10.6311	+	10.6311i	0.0277575	+	0.0277575i	−0.693092	+	0.720849i	$0.743752\pi$
$384$			132.167i			0.344184i
$385$		0			0
$386$	−114.874			−0.297601
$387$	−79.4847	+	79.4847i	−0.205387	+	0.205387i
$388$	95.8990	+	95.8990i	0.247162	+	0.247162i
$389$			535.337i			1.37619i	0.725621	+	0.688094i	$0.241552\pi$
$389$			535.337i			1.37619i	−0.725621	+	0.688094i	$0.758448\pi$
$390$		0			0
$391$	−400.767			−1.02498
$392$	44.7401	−	44.7401i	0.114133	−	0.114133i
$393$	129.990	+	129.990i	0.330763	+	0.330763i
$394$			43.4643i			0.110315i
$395$		0			0
$396$	−132.742			−0.335208
$397$	−118.742	+	118.742i	−0.299099	+	0.299099i	−0.840661	−	0.541562i	$-0.817833\pi$
$397$	−118.742	+	118.742i	−0.299099	+	0.299099i	0.541562	+	0.840661i	$0.317833\pi$
$398$	43.2872	+	43.2872i	0.108762	+	0.108762i
$399$			73.4847i			0.184172i
$400$		0			0
$401$	420.302			1.04813			0.524067	−	0.851677i	$-0.324414\pi$
$401$	420.302			1.04813			0.524067	+	0.851677i	$0.324414\pi$
$402$	−24.8286	+	24.8286i	−0.0617626	+	0.0617626i
$403$	59.3735	+	59.3735i	0.147329	+	0.147329i
$404$		−	411.814i		−	1.01934i
$405$		0			0
$406$	−54.4949			−0.134224
$407$	68.6061	−	68.6061i	0.168565	−	0.168565i
$408$	−75.4393	−	75.4393i	−0.184900	−	0.184900i
$409$			515.110i			1.25944i	0.776823	+	0.629719i	$0.216830\pi$
$409$			515.110i			1.25944i	−0.776823	+	0.629719i	$0.783170\pi$
$410$		0			0
$411$	408.161			0.993093
$412$	−347.974	+	347.974i	−0.844597	+	0.844597i
$413$	−137.753	−	137.753i	−0.333541	−	0.333541i
$414$			15.5755i			0.0376220i
$415$		0			0
$416$	115.748			0.278240
$417$	−234.136	+	234.136i	−0.561478	+	0.561478i
$418$	22.1816	+	22.1816i	0.0530661	+	0.0530661i
$419$			88.6015i			0.211460i	0.994395	+	0.105730i	$0.0337178\pi$
$419$			88.6015i			0.211460i	−0.994395	+	0.105730i	$0.966282\pi$
$420$		0			0
$421$	−257.151			−0.610810			−0.305405	−	0.952223i	$-0.598792\pi$
$421$	−257.151			−0.610810			−0.305405	+	0.952223i	$0.598792\pi$
$422$	−33.0852	+	33.0852i	−0.0784009	+	0.0784009i
$423$	−132.742	−	132.742i	−0.313812	−	0.313812i
$424$		−	2.47449i		−	0.00583605i
$425$		0			0
$426$	37.4347			0.0878749
$427$	−20.3837	+	20.3837i	−0.0477369	+	0.0477369i
$428$	−268.025	−	268.025i	−0.626227	−	0.626227i
$429$			154.293i			0.359657i
$430$		0			0
$431$	804.636			1.86690			0.933452	−	0.358702i	$-0.116781\pi$
$431$	804.636			1.86690			0.933452	+	0.358702i	$0.116781\pi$
$432$	54.3712	−	54.3712i	0.125859	−	0.125859i
$433$	344.848	+	344.848i	0.796416	+	0.796416i	0.982528	−	0.186113i	$-0.0595890\pi$
$433$	344.848	+	344.848i	0.796416	+	0.796416i	−0.186113	+	0.982528i	$0.559589\pi$
$434$		−	16.5857i		−	0.0382159i
$435$		0			0
$436$	267.848			0.614330
$437$	−100.454	+	100.454i	−0.229872	+	0.229872i
$438$	42.8230	+	42.8230i	0.0977693	+	0.0977693i
$439$		−	432.929i		−	0.986170i	−0.869981	−	0.493085i	$-0.835869\pi$
$439$		−	432.929i		−	0.986170i	0.869981	−	0.493085i	$-0.164131\pi$
$440$		0			0
$441$	−75.6061			−0.171442
$442$	−43.2827	+	43.2827i	−0.0979246	+	0.0979246i
$443$	−245.131	−	245.131i	−0.553342	−	0.553342i	0.374062	−	0.927404i	$-0.377965\pi$
$443$	−245.131	−	245.131i	−0.553342	−	0.553342i	−0.927404	+	0.374062i	$0.877965\pi$
$444$			57.7367i			0.130038i
$445$		0			0
$446$	75.2577			0.168739
$447$	103.924	−	103.924i	0.232492	−	0.232492i
$448$	188.015	+	188.015i	0.419676	+	0.419676i
$449$		−	386.091i		−	0.859890i	−0.902855	−	0.429945i	$-0.858533\pi$
$449$		−	386.091i		−	0.859890i	0.902855	−	0.429945i	$-0.141467\pi$
$450$		0			0
$451$	7.90918			0.0175370
$452$	380.702	−	380.702i	0.842260	−	0.842260i
$453$	182.449	+	182.449i	0.402758	+	0.402758i
$454$		−	113.798i		−	0.250656i
$455$		0			0
$456$	−37.8184			−0.0829350
$457$	223.747	−	223.747i	0.489599	−	0.489599i	−0.418580	−	0.908180i	$-0.637472\pi$
$457$	223.747	−	223.747i	0.489599	−	0.489599i	0.908180	+	0.418580i	$0.137472\pi$
$458$	−50.3883	−	50.3883i	−0.110018	−	0.110018i
$459$			127.485i			0.277744i
$460$		0			0
$461$	−722.620			−1.56751			−0.783753	−	0.621073i	$-0.786697\pi$
$461$	−722.620			−1.56751			−0.783753	+	0.621073i	$0.786697\pi$
$462$	21.5505	−	21.5505i	0.0466461	−	0.0466461i
$463$	129.702	+	129.702i	0.280133	+	0.280133i	0.833162	−	0.553029i	$-0.186528\pi$
$463$	129.702	+	129.702i	0.280133	+	0.280133i	−0.553029	+	0.833162i	$0.686528\pi$
$464$			520.095i			1.12090i
$465$		0			0
$466$	−92.4653			−0.198423
$467$	−415.258	+	415.258i	−0.889203	+	0.889203i	−0.994446	−	0.105244i	$-0.966438\pi$
$467$	−415.258	+	415.258i	−0.889203	+	0.889203i	0.105244	+	0.994446i	$0.466438\pi$
$468$	−64.9240	−	64.9240i	−0.138726	−	0.138726i
$469$			311.151i			0.663435i
$470$		0			0
$471$	−41.2827			−0.0876489
$472$	70.8934	−	70.8934i	0.150198	−	0.150198i
$473$	300.677	+	300.677i	0.635680	+	0.635680i
$474$		−	13.4847i		−	0.0284487i
$475$		0			0
$476$	−466.656			−0.980370
$477$	−2.09082	+	2.09082i	−0.00438326	+	0.00438326i
$478$	−77.7163	−	77.7163i	−0.162586	−	0.162586i
$479$		−	304.949i		−	0.636637i	−0.947984	−	0.318318i	$-0.896882\pi$
$479$		−	304.949i		−	0.636637i	0.947984	−	0.318318i	$-0.103118\pi$
$480$		0			0
$481$	67.1102			0.139522
$482$	−22.8286	+	22.8286i	−0.0473622	+	0.0473622i
$483$	97.5959	+	97.5959i	0.202062	+	0.202062i
$484$			30.3643i			0.0627361i
$485$		0			0
$486$	4.95459			0.0101946
$487$	429.318	−	429.318i	0.881556	−	0.881556i	−0.112137	−	0.993693i	$-0.535769\pi$
$487$	429.318	−	429.318i	0.881556	−	0.881556i	0.993693	+	0.112137i	$0.0357694\pi$
$488$	−10.4903	−	10.4903i	−0.0214965	−	0.0214965i
$489$		−	319.918i		−	0.654230i
$490$		0			0
$491$	−414.318			−0.843825			−0.421912	−	0.906637i	$-0.638641\pi$
$491$	−414.318			−0.843825			−0.421912	+	0.906637i	$0.638641\pi$
$492$	−3.32806	+	3.32806i	−0.00676435	+	0.00676435i
$493$	−609.737	−	609.737i	−1.23679	−	1.23679i
$494$			21.6980i			0.0439230i
$495$		0			0
$496$	−158.293			−0.319139
$497$	234.565	−	234.565i	0.471962	−	0.471962i
$498$	7.23724	+	7.23724i	0.0145326	+	0.0145326i
$499$		−	367.585i		−	0.736643i	−0.929699	−	0.368321i	$-0.879933\pi$
$499$		−	367.585i		−	0.736643i	0.929699	−	0.368321i	$-0.120067\pi$
$500$		0			0
$501$	110.313			0.220186
$502$	74.4485	−	74.4485i	0.148304	−	0.148304i
$503$	9.59133	+	9.59133i	0.0190683	+	0.0190683i	0.716577	−	0.697508i	$-0.245708\pi$
$503$	9.59133	+	9.59133i	0.0190683	+	0.0190683i	−0.697508	+	0.716577i	$0.745708\pi$
$504$			36.7423i			0.0729015i
$505$		0			0
$506$	58.9194			0.116441
$507$	131.518	−	131.518i	0.259404	−	0.259404i
$508$	−641.854	−	641.854i	−1.26349	−	1.26349i
$509$		−	777.489i		−	1.52748i	−0.645522	−	0.763742i	$-0.723360\pi$
$509$		−	777.489i		−	1.52748i	0.645522	−	0.763742i	$-0.276640\pi$
$510$		0			0
$511$	536.656			1.05021
$512$	−259.376	+	259.376i	−0.506593	+	0.506593i
$513$	31.9546	+	31.9546i	0.0622897	+	0.0622897i
$514$		−	14.9398i		−	0.0290658i
$515$		0			0
$516$	−253.040			−0.490387
$517$	−502.141	+	502.141i	−0.971259	+	0.971259i
$518$	−9.37347	−	9.37347i	−0.0180955	−	0.0180955i
$519$		−	359.171i		−	0.692045i
$520$		0			0
$521$	321.605			0.617284			0.308642	−	0.951178i	$-0.400125\pi$
$521$	321.605			0.617284			0.308642	+	0.951178i	$0.400125\pi$
$522$	−23.6969	+	23.6969i	−0.0453964	+	0.0453964i
$523$	582.454	+	582.454i	1.11368	+	1.11368i	0.992649	+	0.121030i	$0.0386198\pi$
$523$	582.454	+	582.454i	1.11368	+	1.11368i	0.121030	+	0.992649i	$0.461380\pi$
$524$			413.823i			0.789738i
$525$		0			0
$526$	−125.029			−0.237697
$527$	185.576	−	185.576i	0.352136	−	0.352136i
$528$	−205.677	−	205.677i	−0.389539	−	0.389539i
$529$		−	262.171i		−	0.495598i
$530$		0			0
$531$	−119.803			−0.225617
$532$	−116.969	+	116.969i	−0.219867	+	0.219867i
$533$	3.86836	+	3.86836i	0.00725772	+	0.00725772i
$534$			45.2418i			0.0847225i
$535$		0			0
$536$	−160.132			−0.298753
$537$	225.000	−	225.000i	0.418994	−	0.418994i
$538$	−109.788	−	109.788i	−0.204066	−	0.204066i
$539$			286.005i			0.530621i
$540$		0			0
$541$	460.697			0.851566			0.425783	−	0.904825i	$-0.359999\pi$
$541$	460.697			0.851566			0.425783	+	0.904825i	$0.359999\pi$
$542$	−29.5709	+	29.5709i	−0.0545589	+	0.0545589i
$543$	−350.611	−	350.611i	−0.645692	−	0.645692i
$544$		−	361.778i		−	0.665032i
$545$		0			0
$546$	21.0806			0.0386092
$547$	661.778	−	661.778i	1.20983	−	1.20983i	0.238750	−	0.971081i	$-0.423262\pi$
$547$	661.778	−	661.778i	1.20983	−	1.20983i	0.971081	−	0.238750i	$-0.0767376\pi$
$548$	649.691	+	649.691i	1.18557	+	1.18557i
$549$			17.7276i			0.0322906i
$550$		0			0
$551$	−305.666			−0.554748
$552$	−50.2270	+	50.2270i	−0.0909910	+	0.0909910i
$553$	−84.4949	−	84.4949i	−0.152794	−	0.152794i
$554$		−	45.6276i		−	0.0823602i
$555$		0			0
$556$	−745.373			−1.34060
$557$	−125.909	+	125.909i	−0.226049	+	0.226049i	−0.811040	−	0.584991i	$-0.801098\pi$
$557$	−125.909	+	125.909i	−0.226049	+	0.226049i	0.584991	+	0.811040i	$0.301098\pi$
$558$	−7.21225	−	7.21225i	−0.0129252	−	0.0129252i
$559$			294.120i			0.526155i
$560$		0			0
$561$	482.252			0.859629
$562$	−77.1556	+	77.1556i	−0.137288	+	0.137288i
$563$	200.009	+	200.009i	0.355256	+	0.355256i	0.862061	−	0.506805i	$-0.169174\pi$
$563$	200.009	+	200.009i	0.355256	+	0.355256i	−0.506805	+	0.862061i	$0.669174\pi$
$564$		−	422.586i		−	0.749265i
$565$		0			0
$566$	0.535718			0.000946498
$567$	31.0454	−	31.0454i	0.0547538	−	0.0547538i
$568$	120.717	+	120.717i	0.212531	+	0.212531i
$569$			599.839i			1.05420i	0.849804	+	0.527099i	$0.176720\pi$
$569$			599.839i			1.05420i	−0.849804	+	0.527099i	$0.823280\pi$
$570$		0			0
$571$	−247.970			−0.434274			−0.217137	−	0.976141i	$-0.569672\pi$
$571$	−247.970			−0.434274			−0.217137	+	0.976141i	$0.569672\pi$
$572$	−245.596	+	245.596i	−0.429363	+	0.429363i
$573$	58.8990	+	58.8990i	0.102791	+	0.102791i
$574$		−	1.08061i		−	0.00188260i
$575$		0			0
$576$	163.515			0.283881
$577$	292.121	−	292.121i	0.506276	−	0.506276i	−0.407105	−	0.913381i	$-0.633462\pi$
$577$	292.121	−	292.121i	0.506276	−	0.506276i	0.913381	+	0.407105i	$0.133462\pi$
$578$	70.3314	+	70.3314i	0.121681	+	0.121681i
$579$			626.005i			1.08118i
$580$		0			0
$581$	90.6969			0.156105
$582$	−13.5403	+	13.5403i	−0.0232651	+	0.0232651i
$583$	7.90918	+	7.90918i	0.0135664	+	0.0135664i
$584$			276.186i			0.472922i
$585$		0			0
$586$	43.4051			0.0740702
$587$	−611.217	+	611.217i	−1.04126	+	1.04126i	−0.0421437	+	0.999112i	$0.513419\pi$
$587$	−611.217	+	611.217i	−1.04126	+	1.04126i	−0.999112	+	0.0421437i	$0.986581\pi$
$588$	−120.346	−	120.346i	−0.204670	−	0.204670i
$589$		−	93.0306i		−	0.157947i
$590$		0			0
$591$	236.858			0.400775
$592$	−89.4597	+	89.4597i	−0.151114	+	0.151114i
$593$	−524.742	−	524.742i	−0.884894	−	0.884894i	0.109133	−	0.994027i	$-0.465193\pi$
$593$	−524.742	−	524.742i	−0.884894	−	0.884894i	−0.994027	+	0.109133i	$0.965193\pi$
$594$		−	18.7423i		−	0.0315528i
$595$		0			0
$596$	330.842			0.555105
$597$	235.893	−	235.893i	0.395131	−	0.395131i
$598$	28.8173	+	28.8173i	0.0481895	+	0.0481895i
$599$			368.858i			0.615790i	0.951420	+	0.307895i	$0.0996245\pi$
$599$			368.858i			0.615790i	−0.951420	+	0.307895i	$0.900375\pi$
$600$		0			0
$601$	932.484			1.55155			0.775777	−	0.631007i	$-0.217358\pi$
$601$	932.484			1.55155			0.775777	+	0.631007i	$0.217358\pi$
$602$	41.0806	−	41.0806i	0.0682402	−	0.0682402i
$603$	135.303	+	135.303i	0.224383	+	0.224383i
$604$			580.829i			0.961637i
$605$		0			0
$606$	58.1454			0.0959495
$607$	−513.611	+	513.611i	−0.846146	+	0.846146i	−0.989650	−	0.143504i	$-0.954163\pi$
$607$	−513.611	+	513.611i	−0.846146	+	0.846146i	0.143504	+	0.989650i	$0.454163\pi$
$608$	−90.6811	−	90.6811i	−0.149147	−	0.149147i
$609$			296.969i			0.487634i
$610$		0			0
$611$	−491.192			−0.803915
$612$	−202.924	+	202.924i	−0.331575	+	0.331575i
$613$	615.287	+	615.287i	1.00373	+	1.00373i	0.999993	+	0.00373821i	$0.00118991\pi$
$613$	615.287	+	615.287i	1.00373	+	1.00373i	0.00373821	+	0.999993i	$0.498810\pi$
$614$			56.1725i			0.0914861i
$615$		0			0
$616$	138.990			0.225633
$617$	−546.752	+	546.752i	−0.886145	+	0.886145i	−0.994150	−	0.108005i	$-0.965554\pi$
$617$	−546.752	+	546.752i	−0.886145	+	0.886145i	0.108005	+	0.994150i	$0.465554\pi$
$618$	−49.1316	−	49.1316i	−0.0795010	−	0.0795010i
$619$		−	152.869i		−	0.246962i	−0.992347	−	0.123481i	$-0.960594\pi$
$619$		−	152.869i		−	0.246962i	0.992347	−	0.123481i	$-0.0394058\pi$
$620$		0			0
$621$	84.8786			0.136680
$622$	131.768	−	131.768i	0.211846	−	0.211846i
$623$	283.485	+	283.485i	0.455032	+	0.455032i
$624$		−	201.192i		−	0.322423i
$625$		0			0
$626$	−46.0158			−0.0735077
$627$	120.879	−	120.879i	0.192789	−	0.192789i
$628$	−65.7117	−	65.7117i	−0.104637	−	0.104637i
$629$		−	209.757i		−	0.333477i
$630$		0			0
$631$	−41.4847			−0.0657444			−0.0328722	−	0.999460i	$-0.510465\pi$
$631$	−41.4847			−0.0657444			−0.0328722	+	0.999460i	$0.510465\pi$
$632$	43.4847	−	43.4847i	0.0688049	−	0.0688049i
$633$	180.297	+	180.297i	0.284830	+	0.284830i
$634$			48.8969i			0.0771245i
$635$		0			0
$636$	−6.65612			−0.0104656
$637$	−139.884	+	139.884i	−0.219598	+	0.219598i
$638$	89.6413	+	89.6413i	0.140504	+	0.140504i
$639$		−	204.000i		−	0.319249i
$640$		0			0
$641$	47.2122			0.0736541			0.0368270	−	0.999322i	$-0.488275\pi$
$641$	47.2122			0.0736541			0.0368270	+	0.999322i	$0.488275\pi$
$642$	37.8434	−	37.8434i	0.0589461	−	0.0589461i
$643$	−460.372	−	460.372i	−0.715976	−	0.715976i	0.251803	−	0.967779i	$-0.418977\pi$
$643$	−460.372	−	460.372i	−0.715976	−	0.715976i	−0.967779	+	0.251803i	$0.918977\pi$
$644$			310.697i			0.482449i
$645$		0			0
$646$	67.8184			0.104982
$647$	281.287	−	281.287i	0.434756	−	0.434756i	−0.455487	−	0.890243i	$-0.650535\pi$
$647$	281.287	−	281.287i	0.434756	−	0.434756i	0.890243	+	0.455487i	$0.150535\pi$
$648$	15.9773	+	15.9773i	0.0246563	+	0.0246563i
$649$			453.192i			0.698293i
$650$		0			0
$651$	−90.3837			−0.138838
$652$	509.231	−	509.231i	0.781029	−	0.781029i
$653$	−89.8230	−	89.8230i	−0.137554	−	0.137554i	0.634977	−	0.772531i	$-0.281010\pi$
$653$	−89.8230	−	89.8230i	−0.137554	−	0.137554i	−0.772531	+	0.634977i	$0.781010\pi$
$654$			37.8184i			0.0578263i
$655$		0			0
$656$	−10.3133			−0.0157214
$657$	233.363	−	233.363i	0.355195	−	0.355195i
$658$	68.6061	+	68.6061i	0.104265	+	0.104265i
$659$		−	1081.24i		−	1.64072i	−0.571844	−	0.820362i	$-0.693772\pi$
$659$		−	1081.24i		−	1.64072i	0.571844	−	0.820362i	$-0.306228\pi$
$660$		0			0
$661$	−632.393			−0.956721			−0.478361	−	0.878163i	$-0.658769\pi$
$661$	−632.393			−0.956721			−0.478361	+	0.878163i	$0.658769\pi$
$662$	55.1577	−	55.1577i	0.0833197	−	0.0833197i
$663$	235.868	+	235.868i	0.355759	+	0.355759i
$664$			46.6765i			0.0702960i
$665$		0			0
$666$	−8.15205			−0.0122403
$667$	−405.959	+	405.959i	−0.608634	+	0.608634i
$668$	175.591	+	175.591i	0.262861	+	0.262861i
$669$		−	410.116i		−	0.613028i
$670$		0			0
$671$	67.0602			0.0999407
$672$	−88.1010	+	88.1010i	−0.131103	+	0.131103i
$673$	−233.293	−	233.293i	−0.346646	−	0.346646i	0.512213	−	0.858859i	$-0.328826\pi$
$673$	−233.293	−	233.293i	−0.346646	−	0.346646i	−0.858859	+	0.512213i	$0.828826\pi$
$674$		−	96.1046i		−	0.142588i
$675$		0			0
$676$	418.687			0.619359
$677$	48.3883	−	48.3883i	0.0714745	−	0.0714745i	−0.670466	−	0.741940i	$-0.733906\pi$
$677$	48.3883	−	48.3883i	0.0714745	−	0.0714745i	0.741940	+	0.670466i	$0.233906\pi$
$678$	53.7526	+	53.7526i	0.0792810	+	0.0792810i
$679$			169.687i			0.249907i
$680$		0			0
$681$	−620.141			−0.910633
$682$	−27.2827	+	27.2827i	−0.0400039	+	0.0400039i
$683$	−213.410	−	213.410i	−0.312459	−	0.312459i	0.533402	−	0.845862i	$-0.320913\pi$
$683$	−213.410	−	213.410i	−0.312459	−	0.312459i	−0.845862	+	0.533402i	$0.820913\pi$
$684$			101.728i			0.148724i
$685$		0			0
$686$	115.051			0.167713
$687$	−274.590	+	274.590i	−0.399695	+	0.399695i
$688$	−392.070	−	392.070i	−0.569870	−	0.569870i
$689$			7.73673i			0.0112289i
$690$		0			0
$691$	151.121			0.218700			0.109350	−	0.994003i	$-0.465123\pi$
$691$	151.121			0.218700			0.109350	+	0.994003i	$0.465123\pi$
$692$	571.712	−	571.712i	0.826173	−	0.826173i
$693$	−117.439	−	117.439i	−0.169465	−	0.169465i
$694$			71.9408i			0.103661i
$695$		0			0
$696$	−152.833			−0.219588
$697$	12.0908	−	12.0908i	0.0173469	−	0.0173469i
$698$	−66.9760	−	66.9760i	−0.0959542	−	0.0959542i
$699$			503.889i			0.720871i
$700$		0			0
$701$	−745.680			−1.06374			−0.531869	−	0.846827i	$-0.678510\pi$
$701$	−745.680			−1.06374			−0.531869	+	0.846827i	$0.678510\pi$
$702$	9.16684	−	9.16684i	0.0130582	−	0.0130582i
$703$	−52.5765	−	52.5765i	−0.0747888	−	0.0747888i
$704$		−	618.549i		−	0.878621i
$705$		0			0
$706$	−10.1225			−0.0143378
$707$	364.338	−	364.338i	0.515330	−	0.515330i
$708$	−190.696	−	190.696i	−0.269345	−	0.269345i
$709$		−	719.049i		−	1.01417i	−0.861895	−	0.507087i	$-0.830722\pi$
$709$		−	719.049i		−	1.01417i	0.861895	−	0.507087i	$-0.169278\pi$
$710$		0			0
$711$	−73.4847			−0.103354
$712$	−145.893	+	145.893i	−0.204906	+	0.204906i
$713$	−123.555	−	123.555i	−0.173289	−	0.173289i
$714$		−	65.8888i		−	0.0922812i
$715$		0			0
$716$	716.288			1.00040
$717$	−423.514	+	423.514i	−0.590675	+	0.590675i
$718$	10.8490	+	10.8490i	0.0151100	+	0.0151100i
$719$			605.271i			0.841824i	0.907101	+	0.420912i	$0.138290\pi$
$719$			605.271i			0.841824i	−0.907101	+	0.420912i	$0.861710\pi$
$720$		0			0
$721$	−615.716			−0.853975
$722$	−64.1339	+	64.1339i	−0.0888282	+	0.0888282i
$723$	124.404	+	124.404i	0.172067	+	0.172067i
$724$		−	1116.17i		−	1.54167i
$725$		0			0
$726$	−4.28724			−0.00590529
$727$	246.126	−	246.126i	0.338550	−	0.338550i	−0.517271	−	0.855821i	$-0.673052\pi$
$727$	246.126	−	246.126i	0.338550	−	0.338550i	0.855821	+	0.517271i	$0.173052\pi$
$728$	67.9796	+	67.9796i	0.0933786	+	0.0933786i
$729$		−	27.0000i		−	0.0370370i
$730$		0			0
$731$	919.292			1.25758
$732$	−28.2179	+	28.2179i	−0.0385490	+	0.0385490i
$733$	270.763	+	270.763i	0.369390	+	0.369390i	0.867255	−	0.497865i	$-0.165882\pi$
$733$	270.763	+	270.763i	0.369390	+	0.369390i	−0.497865	+	0.867255i	$0.665882\pi$
$734$		−	65.8546i		−	0.0897202i
$735$		0			0
$736$	−240.869			−0.327268
$737$	511.828	−	511.828i	0.694474	−	0.694474i
$738$	−0.469900	−	0.469900i	−0.000636721	−	0.000636721i
$739$			515.666i			0.697789i	0.937162	+	0.348895i	$0.113443\pi$
$739$			515.666i			0.697789i	−0.937162	+	0.348895i	$0.886557\pi$
$740$		0			0
$741$	118.243			0.159572
$742$	1.08061	−	1.08061i	0.00145635	−	0.00145635i
$743$	−420.702	−	420.702i	−0.566220	−	0.566220i	0.364847	−	0.931067i	$-0.381121\pi$
$743$	−420.702	−	420.702i	−0.566220	−	0.566220i	−0.931067	+	0.364847i	$0.881121\pi$
$744$		−	46.5153i		−	0.0625206i
$745$		0			0
$746$	38.7490			0.0519424
$747$	39.4393	−	39.4393i	0.0527969	−	0.0527969i
$748$	767.626	+	767.626i	1.02624	+	1.02624i
$749$		−	474.252i		−	0.633180i
$750$		0			0
$751$	−859.787			−1.14486			−0.572428	−	0.819955i	$-0.693998\pi$
$751$	−859.787			−1.14486			−0.572428	+	0.819955i	$0.693998\pi$
$752$	654.772	−	654.772i	0.870707	−	0.870707i
$753$	−405.706	−	405.706i	−0.538786	−	0.538786i
$754$			87.6867i			0.116295i
$755$		0			0
$756$	98.8332			0.130732
$757$	956.075	−	956.075i	1.26298	−	1.26298i	0.313337	−	0.949642i	$-0.398553\pi$
$757$	956.075	−	956.075i	1.26298	−	1.26298i	0.949642	−	0.313337i	$-0.101447\pi$
$758$	−47.1964	−	47.1964i	−0.0622644	−	0.0622644i
$759$		−	321.081i		−	0.423031i
$760$		0			0
$761$	−322.758			−0.424124			−0.212062	−	0.977256i	$-0.568018\pi$
$761$	−322.758			−0.424124			−0.212062	+	0.977256i	$0.568018\pi$
$762$	90.6255	−	90.6255i	0.118931	−	0.118931i
$763$	236.969	+	236.969i	0.310576	+	0.310576i
$764$			187.505i			0.245426i
$765$		0			0
$766$	−4.77858			−0.00623835
$767$	−221.655	+	221.655i	−0.288990	+	0.288990i
$768$	237.316	+	237.316i	0.309005	+	0.309005i
$769$		−	692.402i		−	0.900393i	−0.892930	−	0.450196i	$-0.851354\pi$
$769$		−	692.402i		−	0.900393i	0.892930	−	0.450196i	$-0.148646\pi$
$770$		0			0
$771$	−81.4143			−0.105596
$772$	−996.444	+	996.444i	−1.29073	+	1.29073i
$773$	−375.226	−	375.226i	−0.485415	−	0.485415i	0.421441	−	0.906856i	$-0.361525\pi$
$773$	−375.226	−	375.226i	−0.485415	−	0.485415i	−0.906856	+	0.421441i	$0.861525\pi$
$774$		−	35.7276i		−	0.0461596i
$775$		0			0
$776$	−87.3281			−0.112536
$777$	−51.0806	+	51.0806i	−0.0657408	+	0.0657408i
$778$	−120.314	−	120.314i	−0.154646	−	0.154646i
$779$		−	6.06123i		−	0.00778078i
$780$		0			0
$781$	−771.696			−0.988087
$782$	90.0704	−	90.0704i	0.115180	−	0.115180i
$783$	129.136	+	129.136i	0.164925	+	0.164925i
$784$		−	372.939i		−	0.475687i
$785$		0			0
$786$	−58.4291			−0.0743373
$787$	−910.990	+	910.990i	−1.15755	+	1.15755i	−0.172546	+	0.985001i	$0.555199\pi$
$787$	−910.990	+	910.990i	−1.15755	+	1.15755i	−0.985001	+	0.172546i	$0.944801\pi$
$788$	377.019	+	377.019i	0.478451	+	0.478451i
$789$			681.342i			0.863551i
$790$		0			0
$791$	673.626			0.851613
$792$	60.4393	−	60.4393i	0.0763122	−	0.0763122i
$793$	32.7990	+	32.7990i	0.0413606	+	0.0413606i
$794$		−	53.3735i		−	0.0672210i
$795$		0			0
$796$	750.967			0.943426
$797$	7.21683	−	7.21683i	0.00905500	−	0.00905500i	−0.702565	−	0.711620i	$-0.747962\pi$
$797$	7.21683	−	7.21683i	0.00905500	−	0.00905500i	0.711620	+	0.702565i	$0.247962\pi$
$798$	−16.5153	−	16.5153i	−0.0206959	−	0.0206959i
$799$			1535.25i			1.92147i
$800$		0			0
$801$	246.545			0.307796
$802$	−94.4607	+	94.4607i	−0.117781	+	0.117781i
$803$	−882.772	−	882.772i	−1.09934	−	1.09934i
$804$			430.738i			0.535743i
$805$		0			0
$806$	−26.6878			−0.0331114
$807$	−598.287	+	598.287i	−0.741372	+	0.741372i
$808$	187.504	+	187.504i	0.232059	+	0.232059i
$809$			150.000i			0.185414i	0.995693	+	0.0927070i	$0.0295520\pi$
$809$			150.000i			0.185414i	−0.995693	+	0.0927070i	$0.970448\pi$
$810$		0			0
$811$	1336.85			1.64839			0.824197	−	0.566304i	$-0.191627\pi$
$811$	1336.85			1.64839			0.824197	+	0.566304i	$0.191627\pi$
$812$	−472.702	+	472.702i	−0.582145	+	0.582145i
$813$	161.146	+	161.146i	0.198212	+	0.198212i
$814$			30.8377i			0.0378842i
$815$		0			0
$816$	−628.838			−0.770634
$817$	230.424	−	230.424i	0.282037	−	0.282037i
$818$	−115.768	−	115.768i	−0.141526	−	0.141526i
$819$		−	114.879i		−	0.140267i
$820$		0			0
$821$	−33.8934			−0.0412830			−0.0206415	−	0.999787i	$-0.506571\pi$
$821$	−33.8934			−0.0412830			−0.0206415	+	0.999787i	$0.506571\pi$
$822$	−91.7321	+	91.7321i	−0.111596	+	0.111596i
$823$	−481.631	−	481.631i	−0.585214	−	0.585214i	0.351117	−	0.936331i	$-0.385802\pi$
$823$	−481.631	−	481.631i	−0.585214	−	0.585214i	−0.936331	+	0.351117i	$0.885802\pi$
$824$		−	316.874i		−	0.384556i
$825$		0			0
$826$	61.9184			0.0749617
$827$	−350.756	+	350.756i	−0.424131	+	0.424131i	−0.886623	−	0.462492i	$-0.846955\pi$
$827$	−350.756	+	350.756i	−0.424131	+	0.424131i	0.462492	+	0.886623i	$0.346955\pi$
$828$	135.106	+	135.106i	0.163171	+	0.163171i
$829$			697.423i			0.841283i	0.907227	+	0.420641i	$0.138195\pi$
$829$			697.423i			0.841283i	−0.907227	+	0.420641i	$0.861805\pi$
$830$		0			0
$831$	−248.647			−0.299214
$832$	302.531	−	302.531i	0.363619	−	0.363619i
$833$	437.217	+	437.217i	0.524870	+	0.524870i
$834$		−	105.242i		−	0.126189i
$835$		0			0
$836$	384.817			0.460308
$837$	−39.3031	+	39.3031i	−0.0469571	+	0.0469571i
$838$	−19.9127	−	19.9127i	−0.0237622	−	0.0237622i
$839$		−	72.3724i		−	0.0862604i	−0.999069	−	0.0431302i	$-0.986267\pi$
$839$		−	72.3724i		−	0.0862604i	0.999069	−	0.0431302i	$-0.0137330\pi$
$840$		0			0
$841$	−394.271			−0.468813
$842$	57.7934	−	57.7934i	0.0686382	−	0.0686382i
$843$	420.459	+	420.459i	0.498765	+	0.498765i
$844$			573.978i			0.680068i
$845$		0			0
$846$	59.6663			0.0705276
$847$	−26.8638	+	26.8638i	−0.0317164	+	0.0317164i
$848$	−10.3133	−	10.3133i	−0.0121619	−	0.0121619i
$849$		−	2.91939i		−	0.00343862i
$850$		0			0
$851$	−139.655			−0.164107
$852$	324.717	−	324.717i	0.381124	−	0.381124i
$853$	74.5699	+	74.5699i	0.0874207	+	0.0874207i	0.749465	−	0.662044i	$-0.230311\pi$
$853$	74.5699	+	74.5699i	0.0874207	+	0.0874207i	−0.662044	+	0.749465i	$0.730311\pi$
$854$		−	9.16225i		−	0.0107286i
$855$		0			0
$856$	244.070			0.285129
$857$	293.176	−	293.176i	0.342096	−	0.342096i	−0.515059	−	0.857155i	$-0.672230\pi$
$857$	293.176	−	293.176i	0.342096	−	0.342096i	0.857155	+	0.515059i	$0.172230\pi$
$858$	−34.6765	−	34.6765i	−0.0404155	−	0.0404155i
$859$			786.867i			0.916027i	0.888945	+	0.458014i	$0.151439\pi$
$859$			786.867i			0.916027i	−0.888945	+	0.458014i	$0.848561\pi$
$860$		0			0
$861$	−5.88877			−0.00683946
$862$	−180.838	+	180.838i	−0.209789	+	0.209789i
$863$	1072.68	+	1072.68i	1.24297	+	1.24297i	0.958764	+	0.284204i	$0.0917292\pi$
$863$	1072.68	+	1072.68i	1.24297	+	1.24297i	0.284204	+	0.958764i	$0.408271\pi$
$864$			76.6209i			0.0886816i
$865$		0			0
$866$	−155.006			−0.178990
$867$	383.270	−	383.270i	0.442065	−	0.442065i
$868$	−143.868	−	143.868i	−0.165747	−	0.165747i
$869$			277.980i			0.319884i
$870$		0			0
$871$	500.667			0.574819
$872$	−121.955	+	121.955i	−0.139856	+	0.139856i
$873$	73.7878	+	73.7878i	0.0845221	+	0.0845221i
$874$		−	45.1531i		−	0.0516626i
$875$		0			0
$876$	742.913			0.848074
$877$	−239.460	+	239.460i	−0.273044	+	0.273044i	−0.830324	−	0.557280i	$-0.811845\pi$
$877$	−239.460	+	239.460i	−0.273044	+	0.273044i	0.557280	+	0.830324i	$0.311845\pi$
$878$	97.2985	+	97.2985i	0.110818	+	0.110818i
$879$		−	236.536i		−	0.269096i
$880$		0			0
$881$	62.8490			0.0713382			0.0356691	−	0.999364i	$-0.488644\pi$
$881$	62.8490			0.0713382			0.0356691	+	0.999364i	$0.488644\pi$
$882$	16.9921	−	16.9921i	0.0192654	−	0.0192654i
$883$	158.061	+	158.061i	0.179005	+	0.179005i	0.790922	−	0.611917i	$-0.209601\pi$
$883$	158.061	+	158.061i	0.179005	+	0.179005i	−0.611917	+	0.790922i	$0.709601\pi$
$884$			750.888i			0.849421i
$885$		0			0
$886$	110.184			0.124361
$887$	−30.2066	+	30.2066i	−0.0340548	+	0.0340548i	−0.723929	−	0.689874i	$-0.757666\pi$
$887$	−30.2066	+	30.2066i	−0.0340548	+	0.0340548i	0.689874	+	0.723929i	$0.257666\pi$
$888$	−26.2883	−	26.2883i	−0.0296039	−	0.0296039i
$889$		−	1135.72i		−	1.27752i
$890$		0			0
$891$	−102.136			−0.114631
$892$	652.803	−	652.803i	0.731841	−	0.731841i
$893$	384.817	+	384.817i	0.430926	+	0.430926i
$894$			46.7128i			0.0522514i
$895$		0			0
$896$	−372.247			−0.415455
$897$	157.040	−	157.040i	0.175072	−	0.175072i
$898$	86.7719	+	86.7719i	0.0966280	+	0.0966280i
$899$		−	375.959i		−	0.418197i
$900$		0			0
$901$	24.1816			0.0268387
$902$	−1.77755	+	1.77755i	−0.00197067	+	0.00197067i
$903$	−223.868	−	223.868i	−0.247916	−	0.247916i
$904$			346.677i			0.383492i
$905$		0			0
$906$	−82.0092			−0.0905179
$907$	−571.342	+	571.342i	−0.629925	+	0.629925i	−0.948049	−	0.318124i	$-0.896947\pi$
$907$	−571.342	+	571.342i	−0.629925	+	0.629925i	0.318124	+	0.948049i	$0.396947\pi$
$908$	−987.110	−	987.110i	−1.08713	−	1.08713i
$909$		−	316.863i		−	0.348584i
$910$		0			0
$911$	173.362			0.190299			0.0951494	−	0.995463i	$-0.469667\pi$
$911$	173.362			0.190299			0.0951494	+	0.995463i	$0.469667\pi$
$912$	−157.621	+	157.621i	−0.172830	+	0.172830i
$913$	−149.192	−	149.192i	−0.163408	−	0.163408i
$914$			100.572i			0.110035i
$915$		0			0
$916$	−874.159			−0.954322
$917$	−366.116	+	366.116i	−0.399254	+	0.399254i
$918$	−28.6515	−	28.6515i	−0.0312108	−	0.0312108i
$919$		−	1147.42i		−	1.24856i	−0.781202	−	0.624278i	$-0.785393\pi$
$919$		−	1147.42i		−	1.24856i	0.781202	−	0.624278i	$-0.214607\pi$
$920$		0			0
$921$	306.111			0.332368
$922$	162.405	−	162.405i	0.176144	−	0.176144i
$923$	−377.435	−	377.435i	−0.408922	−	0.408922i
$924$		−	373.868i		−	0.404619i
$925$		0			0
$926$	−58.2995			−0.0629584
$927$	−267.742	+	267.742i	−0.288827	+	0.288827i
$928$	−366.464	−	366.464i	−0.394897	−	0.394897i
$929$			220.293i			0.237129i	0.992946	+	0.118565i	$0.0378292\pi$
$929$			220.293i			0.237129i	−0.992946	+	0.118565i	$0.962171\pi$
$930$		0			0
$931$	219.181			0.235425
$932$	−802.066	+	802.066i	−0.860586	+	0.860586i
$933$	−718.070	−	718.070i	−0.769636	−	0.769636i
$934$		−	186.654i		−	0.199844i
$935$		0			0
$936$	59.1214			0.0631639
$937$	396.090	−	396.090i	0.422721	−	0.422721i	−0.463418	−	0.886140i	$-0.653377\pi$
$937$	396.090	−	396.090i	0.422721	−	0.422721i	0.886140	+	0.463418i	$0.153377\pi$
$938$	−69.9296	−	69.9296i	−0.0745518	−	0.0745518i
$939$			250.763i			0.267053i
$940$		0			0
$941$	185.771			0.197419			0.0987093	−	0.995116i	$-0.468529\pi$
$941$	185.771			0.197419			0.0987093	+	0.995116i	$0.468529\pi$
$942$	9.27806	−	9.27806i	0.00984932	−	0.00984932i
$943$	−8.04999	−	8.04999i	−0.00853658	−	0.00853658i
$944$		−	590.944i		−	0.626000i
$945$		0			0
$946$	−135.151			−0.142866
$947$	845.190	−	845.190i	0.892492	−	0.892492i	−0.102265	−	0.994757i	$-0.532609\pi$
$947$	845.190	−	845.190i	0.892492	−	0.892492i	0.994757	+	0.102265i	$0.0326091\pi$
$948$	−116.969	−	116.969i	−0.123385	−	0.123385i
$949$		−	863.523i		−	0.909930i
$950$		0			0
$951$	266.463			0.280193
$952$	212.474	−	212.474i	0.223187	−	0.223187i
$953$	630.499	+	630.499i	0.661594	+	0.661594i	0.955756	−	0.294161i	$-0.0950403\pi$
$953$	630.499	+	630.499i	0.661594	+	0.661594i	−0.294161	+	0.955756i	$0.595040\pi$
$954$		−	0.939800i		−	0.000985115i
$955$		0			0
$956$	−1348.26			−1.41031
$957$	488.499	−	488.499i	0.510449	−	0.510449i
$958$	68.5357	+	68.5357i	0.0715404	+	0.0715404i
$959$			1149.58i			1.19873i
$960$		0			0
$961$	−846.576			−0.880932
$962$	−15.0827	+	15.0827i	−0.0156785	+	0.0156785i
$963$	−206.227	−	206.227i	−0.214151	−	0.214151i
$964$			396.041i			0.410831i
$965$		0			0
$966$	−43.8684			−0.0454124
$967$	381.690	−	381.690i	0.394716	−	0.394716i	−0.481649	−	0.876364i	$-0.659962\pi$
$967$	381.690	−	381.690i	0.394716	−	0.394716i	0.876364	+	0.481649i	$0.159962\pi$
$968$	−13.8252	−	13.8252i	−0.0142823	−	0.0142823i
$969$		−	369.576i		−	0.381399i
$970$		0			0
$971$	−1000.44			−1.03032			−0.515159	−	0.857095i	$-0.672267\pi$
$971$	−1000.44			−1.03032			−0.515159	+	0.857095i	$0.672267\pi$
$972$	42.9773	−	42.9773i	0.0442153	−	0.0442153i
$973$	−659.444	−	659.444i	−0.677743	−	0.677743i
$974$			192.974i			0.198125i
$975$		0			0
$976$	−87.4439			−0.0895941
$977$	−593.662	+	593.662i	−0.607637	+	0.607637i	−0.942328	−	0.334691i	$-0.891368\pi$
$977$	−593.662	+	593.662i	−0.607637	+	0.607637i	0.334691	+	0.942328i	$0.391368\pi$
$978$	71.9000	+	71.9000i	0.0735174	+	0.0735174i
$979$		−	932.636i		−	0.952641i
$980$		0			0
$981$	206.091			0.210082
$982$	93.1158	−	93.1158i	0.0948226	−	0.0948226i
$983$	1217.34	+	1217.34i	1.23839	+	1.23839i	0.960659	+	0.277731i	$0.0895824\pi$
$983$	1217.34	+	1217.34i	1.23839	+	1.23839i	0.277731	+	0.960659i	$0.410418\pi$
$984$		−	3.03062i		−	0.00307989i
$985$		0			0
$986$	274.070			0.277962
$987$	373.868	−	373.868i	0.378793	−	0.378793i
$988$	188.213	+	188.213i	0.190499	+	0.190499i
$989$		−	612.059i		−	0.618867i
$990$		0			0
$991$	−544.061			−0.549002			−0.274501	−	0.961587i	$-0.588513\pi$
$991$	−544.061			−0.549002			−0.274501	+	0.961587i	$0.588513\pi$
$992$	111.535	−	111.535i	0.112434	−	0.112434i
$993$	−300.581	−	300.581i	−0.302700	−	0.302700i
$994$			105.435i			0.106071i
$995$		0			0
$996$	125.555			0.126059
$997$	316.733	−	316.733i	0.317686	−	0.317686i	−0.530192	−	0.847878i	$-0.677880\pi$
$997$	316.733	−	316.733i	0.317686	−	0.317686i	0.847878	+	0.530192i	$0.177880\pi$
$998$	82.6128	+	82.6128i	0.0827783	+	0.0827783i
$999$			44.4245i			0.0444690i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.f.c.43.1		4
3.2	odd	2		225.3.g.a.118.2		4
4.3	odd	2		1200.3.bg.k.193.1		4
5.2	odd	4	inner	75.3.f.c.7.1		4
5.3	odd	4		15.3.f.a.7.2	✓	4
5.4	even	2		15.3.f.a.13.2	yes	4
15.2	even	4		225.3.g.a.82.2		4
15.8	even	4		45.3.g.b.37.1		4
15.14	odd	2		45.3.g.b.28.1		4
20.3	even	4		240.3.bg.a.97.2		4
20.7	even	4		1200.3.bg.k.1057.1		4
20.19	odd	2		240.3.bg.a.193.2		4
40.3	even	4		960.3.bg.h.577.1		4
40.13	odd	4		960.3.bg.i.577.2		4
40.19	odd	2		960.3.bg.h.193.1		4
40.29	even	2		960.3.bg.i.193.2		4
45.4	even	6		405.3.l.h.298.2		8
45.13	odd	12		405.3.l.h.217.1		8
45.14	odd	6		405.3.l.f.298.1		8
45.23	even	12		405.3.l.f.217.2		8
45.29	odd	6		405.3.l.f.28.2		8
45.34	even	6		405.3.l.h.28.1		8
45.38	even	12		405.3.l.f.352.1		8
45.43	odd	12		405.3.l.h.352.2		8
60.23	odd	4		720.3.bh.k.577.2		4
60.59	even	2		720.3.bh.k.433.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.3.f.a.7.2	✓	4	5.3	odd	4
15.3.f.a.13.2	yes	4	5.4	even	2
45.3.g.b.28.1		4	15.14	odd	2
45.3.g.b.37.1		4	15.8	even	4
75.3.f.c.7.1		4	5.2	odd	4	inner
75.3.f.c.43.1		4	1.1	even	1	trivial
225.3.g.a.82.2		4	15.2	even	4
225.3.g.a.118.2		4	3.2	odd	2
240.3.bg.a.97.2		4	20.3	even	4
240.3.bg.a.193.2		4	20.19	odd	2
405.3.l.f.28.2		8	45.29	odd	6
405.3.l.f.217.2		8	45.23	even	12
405.3.l.f.298.1		8	45.14	odd	6
405.3.l.f.352.1		8	45.38	even	12
405.3.l.h.28.1		8	45.34	even	6
405.3.l.h.217.1		8	45.13	odd	12
405.3.l.h.298.2		8	45.4	even	6
405.3.l.h.352.2		8	45.43	odd	12
720.3.bh.k.433.2		4	60.59	even	2
720.3.bh.k.577.2		4	60.23	odd	4
960.3.bg.h.193.1		4	40.19	odd	2
960.3.bg.h.577.1		4	40.3	even	4
960.3.bg.i.193.2		4	40.29	even	2
960.3.bg.i.577.2		4	40.13	odd	4
1200.3.bg.k.193.1		4	4.3	odd	2
1200.3.bg.k.1057.1		4	20.7	even	4

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	75.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.224745 + 0.224745i) q^{2} +(1.22474 + 1.22474i) q^{3} +3.89898i q^{4} -0.550510 q^{6} +(-3.44949 + 3.44949i) q^{7} +(-1.77526 - 1.77526i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-0.224745 + 0.224745i) q^{2} +(1.22474 + 1.22474i) q^{3} +3.89898i q^{4} -0.550510 q^{6} +(-3.44949 + 3.44949i) q^{7} +(-1.77526 - 1.77526i) q^{8} +3.00000i q^{9} +11.3485 q^{11} +(-4.77526 + 4.77526i) q^{12} +(5.55051 + 5.55051i) q^{13} -1.55051i q^{14} -14.7980 q^{16} +(17.3485 - 17.3485i) q^{17} +(-0.674235 - 0.674235i) q^{18} -8.69694i q^{19} -8.44949 q^{21} +(-2.55051 + 2.55051i) q^{22} +(-11.5505 - 11.5505i) q^{23} -4.34847i q^{24} -2.49490 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-13.4495 - 13.4495i) q^{28} -35.1464i q^{29} +10.6969 q^{31} +(10.4268 - 10.4268i) q^{32} +(13.8990 + 13.8990i) q^{33} +7.79796i q^{34} -11.6969 q^{36} +(6.04541 - 6.04541i) q^{37} +(1.95459 + 1.95459i) q^{38} +13.5959i q^{39} +0.696938 q^{41} +(1.89898 - 1.89898i) q^{42} +(26.4949 + 26.4949i) q^{43} +44.2474i q^{44} +5.19184 q^{46} +(-44.2474 + 44.2474i) q^{47} +(-18.1237 - 18.1237i) q^{48} +25.2020i q^{49} +42.4949 q^{51} +(-21.6413 + 21.6413i) q^{52} +(0.696938 + 0.696938i) q^{53} -1.65153i q^{54} +12.2474 q^{56} +(10.6515 - 10.6515i) q^{57} +(7.89898 + 7.89898i) q^{58} +39.9342i q^{59} +5.90918 q^{61} +(-2.40408 + 2.40408i) q^{62} +(-10.3485 - 10.3485i) q^{63} -54.5051i q^{64} -6.24745 q^{66} +(45.1010 - 45.1010i) q^{67} +(67.6413 + 67.6413i) q^{68} -28.2929i q^{69} -68.0000 q^{71} +(5.32577 - 5.32577i) q^{72} +(-77.7878 - 77.7878i) q^{73} +2.71735i q^{74} +33.9092 q^{76} +(-39.1464 + 39.1464i) q^{77} +(-3.05561 - 3.05561i) q^{78} +24.4949i q^{79} -9.00000 q^{81} +(-0.156633 + 0.156633i) q^{82} +(-13.1464 - 13.1464i) q^{83} -32.9444i q^{84} -11.9092 q^{86} +(43.0454 - 43.0454i) q^{87} +(-20.1464 - 20.1464i) q^{88} -82.1816i q^{89} -38.2929 q^{91} +(45.0352 - 45.0352i) q^{92} +(13.1010 + 13.1010i) q^{93} -19.8888i q^{94} +25.5403 q^{96} +(24.5959 - 24.5959i) q^{97} +(-5.66403 - 5.66403i) q^{98} +34.0454i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 12 q^{6} - 4 q^{7} - 12 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 12 * q^6 - 4 * q^7 - 12 * q^8	\( 4 q + 4 q^{2} - 12 q^{6} - 4 q^{7} - 12 q^{8} + 16 q^{11} - 24 q^{12} + 32 q^{13} - 20 q^{16} + 40 q^{17} + 12 q^{18} - 24 q^{21} - 20 q^{22} - 56 q^{23} + 88 q^{26} - 44 q^{28} - 16 q^{31} + 76 q^{32} + 36 q^{33} + 12 q^{36} - 64 q^{37} + 96 q^{38} - 56 q^{41} - 12 q^{42} + 8 q^{43} - 136 q^{46} - 128 q^{47} - 48 q^{48} + 72 q^{51} + 80 q^{52} - 56 q^{53} + 72 q^{57} + 12 q^{58} + 200 q^{61} - 88 q^{62} - 12 q^{63} + 24 q^{66} + 200 q^{67} + 104 q^{68} - 272 q^{71} + 36 q^{72} - 76 q^{73} + 312 q^{76} - 88 q^{77} - 120 q^{78} - 36 q^{81} - 128 q^{82} + 16 q^{83} - 224 q^{86} + 84 q^{87} - 12 q^{88} - 16 q^{91} - 104 q^{92} + 72 q^{93} - 84 q^{96} + 20 q^{97} + 188 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 12 * q^6 - 4 * q^7 - 12 * q^8 + 16 * q^11 - 24 * q^12 + 32 * q^13 - 20 * q^16 + 40 * q^17 + 12 * q^18 - 24 * q^21 - 20 * q^22 - 56 * q^23 + 88 * q^26 - 44 * q^28 - 16 * q^31 + 76 * q^32 + 36 * q^33 + 12 * q^36 - 64 * q^37 + 96 * q^38 - 56 * q^41 - 12 * q^42 + 8 * q^43 - 136 * q^46 - 128 * q^47 - 48 * q^48 + 72 * q^51 + 80 * q^52 - 56 * q^53 + 72 * q^57 + 12 * q^58 + 200 * q^61 - 88 * q^62 - 12 * q^63 + 24 * q^66 + 200 * q^67 + 104 * q^68 - 272 * q^71 + 36 * q^72 - 76 * q^73 + 312 * q^76 - 88 * q^77 - 120 * q^78 - 36 * q^81 - 128 * q^82 + 16 * q^83 - 224 * q^86 + 84 * q^87 - 12 * q^88 - 16 * q^91 - 104 * q^92 + 72 * q^93 - 84 * q^96 + 20 * q^97 + 188 * q^98

Introduction

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