LMFDB - Embedded newform 475.2.l.b.251.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(101,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("475.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.l (of order $9$, degree $6$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 12 x^{16} - 8 x^{15} + 96 x^{14} - 75 x^{13} + 448 x^{12} - 405 x^{11} + 1521 x^{10} + \cdots + 361 $ x^18 + 12x^16 - 8x^15 + 96x^14 - 75x^13 + 448x^12 - 405x^11 + 1521x^10 - 1294x^9 + 3333x^8 - 2616x^7 + 5113x^6 - 3126x^5 + 4032x^4 - 1359x^3 + 1698x^2 - 513x + 361
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			251.1
Root			$1.01081 + 1.75077i$ of defining polynomial
Character	$\chi$	$=$	475.251
Dual form			475.2.l.b.176.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.89970 - 0.691434i) q^{2} +(0.330026 + 1.87167i) q^{3} +(1.59869 + 1.34146i) q^{4} +(0.667187 - 3.78381i) q^{6} +(1.54609 - 2.67790i) q^{7} +(-0.0878797 - 0.152212i) q^{8} +(-0.575162 + 0.209342i) q^{9} +(-0.481594 - 0.834145i) q^{11} +(-1.98316 + 3.43494i) q^{12} +(0.513859 - 2.91424i) q^{13} +(-4.78870 + 4.01819i) q^{14} +(-0.663086 - 3.76055i) q^{16} +(0.0366124 + 0.0133258i) q^{17} +1.23738 q^{18} +(-4.31788 - 0.596607i) q^{19} +(5.52241 + 2.00999i) q^{21} +(0.338127 + 1.91762i) q^{22} +(-2.97348 - 2.49504i) q^{23} +(0.255888 - 0.214716i) q^{24} +(-2.99118 + 5.18088i) q^{26} +(2.26918 + 3.93034i) q^{27} +(6.06401 - 2.20712i) q^{28} +(8.76529 - 3.19030i) q^{29} +(4.68894 - 8.12148i) q^{31} +(-1.40155 + 7.94857i) q^{32} +(1.40231 - 1.17668i) q^{33} +(-0.0603386 - 0.0506301i) q^{34} +(-1.20033 - 0.436884i) q^{36} +1.11739 q^{37} +(7.79016 + 4.11890i) q^{38} +5.62409 q^{39} +(2.09674 + 11.8912i) q^{41} +(-9.10114 - 7.63676i) q^{42} +(3.79459 - 3.18404i) q^{43} +(0.349053 - 1.97958i) q^{44} +(3.92356 + 6.79580i) q^{46} +(7.53217 - 2.74148i) q^{47} +(6.81968 - 2.48216i) q^{48} +(-1.28078 - 2.21837i) q^{49} +(-0.0128585 + 0.0729242i) q^{51} +(4.73083 - 3.96964i) q^{52} +(-4.64208 - 3.89517i) q^{53} +(-1.59319 - 9.03545i) q^{54} -0.543479 q^{56} +(-0.308361 - 8.27855i) q^{57} -18.8573 q^{58} +(-2.60732 - 0.948987i) q^{59} +(-7.68360 - 6.44731i) q^{61} +(-14.5230 + 12.1863i) q^{62} +(-0.328654 + 1.86389i) q^{63} +(4.33987 - 7.51688i) q^{64} +(-3.47756 + 1.26573i) q^{66} +(8.78501 - 3.19748i) q^{67} +(0.0406557 + 0.0704178i) q^{68} +(3.68858 - 6.38881i) q^{69} +(9.64404 - 8.09231i) q^{71} +(0.0824094 + 0.0691497i) q^{72} +(-0.155782 - 0.883486i) q^{73} +(-2.12271 - 0.772603i) q^{74} +(-6.10262 - 6.74604i) q^{76} -2.97835 q^{77} +(-10.6841 - 3.88869i) q^{78} +(1.54415 + 8.75731i) q^{79} +(-8.01404 + 6.72458i) q^{81} +(4.23882 - 24.0395i) q^{82} +(-4.80224 + 8.31772i) q^{83} +(6.13229 + 10.6214i) q^{84} +(-9.41012 + 3.42500i) q^{86} +(8.86398 + 15.3529i) q^{87} +(-0.0846446 + 0.146609i) q^{88} +(-1.51886 + 8.61386i) q^{89} +(-7.00958 - 5.88173i) q^{91} +(-1.40667 - 7.97760i) q^{92} +(16.7482 + 6.09585i) q^{93} -16.2044 q^{94} -15.3397 q^{96} +(7.31855 + 2.66374i) q^{97} +(0.899233 + 5.09981i) q^{98} +(0.451616 + 0.378951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 12 q^{8} - 21 q^{9} - 6 q^{12} + 3 q^{13} + 24 q^{14} + 21 q^{16} + 24 q^{17} + 12 q^{18} - 12 q^{19} + 3 q^{21} - 15 q^{22} - 21 q^{23} + 21 q^{24} - 21 q^{26}+ \cdots + 3 q^{99}+O(q^{100}) $ 18 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 12 * q^8 - 21 * q^9 - 6 * q^12 + 3 * q^13 + 24 * q^14 + 21 * q^16 + 24 * q^17 + 12 * q^18 - 12 * q^19 + 3 * q^21 - 15 * q^22 - 21 * q^23 + 21 * q^24 - 21 * q^26 - 6 * q^27 + 24 * q^28 - 9 * q^29 + 30 * q^31 - 45 * q^32 + 3 * q^33 + 24 * q^34 - 21 * q^36 + 60 * q^37 + 15 * q^38 + 12 * q^39 - 6 * q^41 - 39 * q^42 + 6 * q^43 - 30 * q^44 + 21 * q^46 - 33 * q^47 + 63 * q^48 - 3 * q^49 + 27 * q^51 - 9 * q^52 - 24 * q^53 + 30 * q^54 - 72 * q^56 + 30 * q^57 - 36 * q^58 + 18 * q^59 + 6 * q^61 - 12 * q^62 - 24 * q^63 - 24 * q^64 - 33 * q^66 + 24 * q^67 + 3 * q^68 + 27 * q^69 + 24 * q^71 - 18 * q^72 - 6 * q^73 - 39 * q^74 + 27 * q^76 - 24 * q^77 - 72 * q^78 + 9 * q^79 + 15 * q^81 + 57 * q^82 - 12 * q^84 - 33 * q^86 + 45 * q^87 - 39 * q^88 - 6 * q^89 - 6 * q^91 + 66 * q^92 + 72 * q^93 - 66 * q^94 - 18 * q^96 + 87 * q^97 - 39 * q^98 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−1.89970	−	0.691434i	−1.34329	−	0.488918i	−0.432443	−	0.901661i	$-0.642348\pi$
$2$	−1.89970	−	0.691434i	−1.34329	−	0.488918i	−0.910847	+	0.412743i	$0.864571\pi$
$3$	0.330026	+	1.87167i	0.190541	+	1.08061i	0.918627	+	0.395125i	$0.129299\pi$
$3$	0.330026	+	1.87167i	0.190541	+	1.08061i	−0.728086	+	0.685485i	$0.759590\pi$
$4$	1.59869	+	1.34146i	0.799344	+	0.670730i
$5$		0			0
$5$		0			0
$6$	0.667187	−	3.78381i	0.272378	−	1.54473i
$7$	1.54609	−	2.67790i	0.584366	−	1.01215i	−0.410588	−	0.911821i	$-0.634676\pi$
$7$	1.54609	−	2.67790i	0.584366	−	1.01215i	0.994954	−	0.100331i	$-0.0319902\pi$
$8$	−0.0878797	−	0.152212i	−0.0310701	−	0.0538151i
$9$	−0.575162	+	0.209342i	−0.191721	+	0.0697806i
$10$		0			0
$11$	−0.481594	−	0.834145i	−0.145206	−	0.251504i	0.784244	−	0.620453i	$-0.213051\pi$
$11$	−0.481594	−	0.834145i	−0.145206	−	0.251504i	−0.929450	+	0.368949i	$0.879718\pi$
$12$	−1.98316	+	3.43494i	−0.572490	+	0.991581i
$13$	0.513859	−	2.91424i	0.142519	−	0.808264i	−0.826807	−	0.562486i	$-0.809845\pi$
$13$	0.513859	−	2.91424i	0.142519	−	0.808264i	0.969326	−	0.245779i	$-0.0790437\pi$
$14$	−4.78870	+	4.01819i	−1.27983	+	1.07391i
$15$		0			0
$16$	−0.663086	−	3.76055i	−0.165772	−	0.940137i
$17$	0.0366124	+	0.0133258i	0.00887980	+	0.00323198i	0.346456	−	0.938066i	$-0.387385\pi$
$17$	0.0366124	+	0.0133258i	0.00887980	+	0.00323198i	−0.337576	+	0.941298i	$0.609607\pi$
$18$	1.23738			0.291654
$19$	−4.31788	−	0.596607i	−0.990589	−	0.136871i
$19$	−4.31788	−	0.596607i	−0.990589	−	0.136871i
$20$		0			0
$21$	5.52241	+	2.00999i	1.20509	+	0.438616i
$22$	0.338127	+	1.91762i	0.0720890	+	0.408837i
$23$	−2.97348	−	2.49504i	−0.620013	−	0.520253i	0.277795	−	0.960641i	$-0.410397\pi$
$23$	−2.97348	−	2.49504i	−0.620013	−	0.520253i	−0.897808	+	0.440388i	$0.854841\pi$
$24$	0.255888	−	0.214716i	0.0522330	−	0.0438287i
$25$		0			0
$26$	−2.99118	+	5.18088i	−0.586619	+	1.01605i
$27$	2.26918	+	3.93034i	0.436704	+	0.756394i
$28$	6.06401	−	2.20712i	1.14599	−	0.417106i
$29$	8.76529	−	3.19030i	1.62767	−	0.592425i	0.642851	−	0.765991i	$-0.277751\pi$
$29$	8.76529	−	3.19030i	1.62767	−	0.592425i	0.984822	+	0.173566i	$0.0555291\pi$
$30$		0			0
$31$	4.68894	−	8.12148i	0.842158	−	1.45866i	−0.0459085	−	0.998946i	$-0.514618\pi$
$31$	4.68894	−	8.12148i	0.842158	−	1.45866i	0.888067	−	0.459715i	$-0.152048\pi$
$32$	−1.40155	+	7.94857i	−0.247761	+	1.40512i
$33$	1.40231	−	1.17668i	0.244110	−	0.204833i
$34$	−0.0603386	−	0.0506301i	−0.0103480	−	0.00868299i
$35$		0			0
$36$	−1.20033	−	0.436884i	−0.200055	−	0.0728140i
$37$	1.11739			0.183698			0.0918491	−	0.995773i	$-0.470722\pi$
$37$	1.11739			0.183698			0.0918491	+	0.995773i	$0.470722\pi$
$38$	7.79016	+	4.11890i	1.26373	+	0.668174i
$39$	5.62409			0.900575
$40$		0			0
$41$	2.09674	+	11.8912i	0.327456	+	1.85710i	0.491818	+	0.870698i	$0.336332\pi$
$41$	2.09674	+	11.8912i	0.327456	+	1.85710i	−0.164362	+	0.986400i	$0.552557\pi$
$42$	−9.10114	−	7.63676i	−1.40434	−	1.17838i
$43$	3.79459	−	3.18404i	0.578669	−	0.485561i	−0.305841	−	0.952083i	$-0.598938\pi$
$43$	3.79459	−	3.18404i	0.578669	−	0.485561i	0.884510	+	0.466522i	$0.154493\pi$
$44$	0.349053	−	1.97958i	0.0526217	−	0.298432i
$45$		0			0
$46$	3.92356	+	6.79580i	0.578497	+	1.00199i
$47$	7.53217	−	2.74148i	1.09868	−	0.399887i	0.271850	−	0.962340i	$-0.412364\pi$
$47$	7.53217	−	2.74148i	1.09868	−	0.399887i	0.826829	+	0.562453i	$0.190142\pi$
$48$	6.81968	−	2.48216i	0.984336	−	0.358269i
$49$	−1.28078	−	2.21837i	−0.182968	−	0.316910i
$50$		0			0
$51$	−0.0128585	+	0.0729242i	−0.00180055	+	0.0102114i
$52$	4.73083	−	3.96964i	0.656048	−	0.550490i
$53$	−4.64208	−	3.89517i	−0.637639	−	0.535043i	0.265653	−	0.964069i	$-0.414412\pi$
$53$	−4.64208	−	3.89517i	−0.637639	−	0.535043i	−0.903292	+	0.429026i	$0.858857\pi$
$54$	−1.59319	−	9.03545i	−0.216806	−	1.22957i
$55$		0			0
$56$	−0.543479			−0.0726254
$57$	−0.308361	−	8.27855i	−0.0408434	−	1.09652i
$58$	−18.8573			−2.47609
$59$	−2.60732	−	0.948987i	−0.339444	−	0.123548i	0.166673	−	0.986012i	$-0.446698\pi$
$59$	−2.60732	−	0.948987i	−0.339444	−	0.123548i	−0.506117	+	0.862465i	$0.668920\pi$
$60$		0			0
$61$	−7.68360	−	6.44731i	−0.983784	−	0.825493i	0.000871917	−	1.00000i	$-0.499722\pi$
$61$	−7.68360	−	6.44731i	−0.983784	−	0.825493i	−0.984656	+	0.174507i	$0.944167\pi$
$62$	−14.5230	+	12.1863i	−1.84443	+	1.54766i
$63$	−0.328654	+	1.86389i	−0.0414065	+	0.234828i
$64$	4.33987	−	7.51688i	0.542484	−	0.939610i
$65$		0			0
$66$	−3.47756	+	1.26573i	−0.428058	+	0.155800i
$67$	8.78501	−	3.19748i	1.07326	−	0.390635i	0.255865	−	0.966713i	$-0.417640\pi$
$67$	8.78501	−	3.19748i	1.07326	−	0.390635i	0.817395	+	0.576078i	$0.195418\pi$
$68$	0.0406557	+	0.0704178i	0.00493023	+	0.00853941i
$69$	3.68858	−	6.38881i	0.444053	−	0.769122i
$70$		0			0
$71$	9.64404	−	8.09231i	1.14454	−	0.960381i	0.144959	−	0.989438i	$-0.453695\pi$
$71$	9.64404	−	8.09231i	1.14454	−	0.960381i	0.999578	+	0.0290571i	$0.00925045\pi$
$72$	0.0824094	+	0.0691497i	0.00971204	+	0.00814937i
$73$	−0.155782	−	0.883486i	−0.0182330	−	0.103404i	0.974333	−	0.225111i	$-0.0722744\pi$
$73$	−0.155782	−	0.883486i	−0.0182330	−	0.103404i	−0.992566	+	0.121707i	$0.961163\pi$
$74$	−2.12271	−	0.772603i	−0.246760	−	0.0898133i
$75$		0			0
$76$	−6.10262	−	6.74604i	−0.700018	−	0.773824i
$77$	−2.97835			−0.339414
$78$	−10.6841	−	3.88869i	−1.20973	−	0.440307i
$79$	1.54415	+	8.75731i	0.173731	+	0.985275i	0.939599	+	0.342277i	$0.111198\pi$
$79$	1.54415	+	8.75731i	0.173731	+	0.985275i	−0.765868	+	0.642997i	$0.777691\pi$
$80$		0			0
$81$	−8.01404	+	6.72458i	−0.890449	+	0.747176i
$82$	4.23882	−	24.0395i	0.468099	−	2.65472i
$83$	−4.80224	+	8.31772i	−0.527114	+	0.912988i	0.472387	+	0.881391i	$0.343393\pi$
$83$	−4.80224	+	8.31772i	−0.527114	+	0.912988i	−0.999501	+	0.0315966i	$0.989941\pi$
$84$	6.13229	+	10.6214i	0.669087	+	1.15889i
$85$		0			0
$86$	−9.41012	+	3.42500i	−1.01472	+	0.369328i
$87$	8.86398	+	15.3529i	0.950319	+	1.64600i
$88$	−0.0846446	+	0.146609i	−0.00902315	+	0.0156285i
$89$	−1.51886	+	8.61386i	−0.160998	+	0.913068i	0.792096	+	0.610396i	$0.208990\pi$
$89$	−1.51886	+	8.61386i	−0.160998	+	0.913068i	−0.953095	+	0.302672i	$0.902121\pi$
$90$		0			0
$91$	−7.00958	−	5.88173i	−0.734803	−	0.616573i
$92$	−1.40667	−	7.97760i	−0.146655	−	0.831722i
$93$	16.7482	+	6.09585i	1.73671	+	0.632111i
$94$	−16.2044			−1.67136
$95$		0			0
$96$	−15.3397			−1.56560
$97$	7.31855	+	2.66374i	0.743087	+	0.270461i	0.685694	−	0.727890i	$-0.259499\pi$
$97$	7.31855	+	2.66374i	0.743087	+	0.270461i	0.0573929	+	0.998352i	$0.481721\pi$
$98$	0.899233	+	5.09981i	0.0908363	+	0.515158i
$99$	0.451616	+	0.378951i	0.0453891	+	0.0380860i
$100$		0			0
$101$	−0.528521	+	2.99739i	−0.0525898	+	0.298251i	−0.999746	−	0.0225200i	$-0.992831\pi$
$101$	−0.528521	+	2.99739i	−0.0525898	+	0.298251i	0.947157	+	0.320771i	$0.103942\pi$
$102$	0.0748496	−	0.129643i	0.00741121	−	0.0128366i
$103$	−0.164287	−	0.284553i	−0.0161876	−	0.0280378i	0.857818	−	0.513953i	$-0.171820\pi$
$103$	−0.164287	−	0.284553i	−0.0161876	−	0.0280378i	−0.874006	+	0.485916i	$0.838486\pi$
$104$	−0.488740	+	0.177887i	−0.0479249	+	0.0174432i
$105$		0			0
$106$	6.12531	+	10.6093i	0.594943	+	1.03047i
$107$	−6.39366	+	11.0741i	−0.618099	+	1.07058i	0.371734	+	0.928339i	$0.378763\pi$
$107$	−6.39366	+	11.0741i	−0.618099	+	1.07058i	−0.989832	+	0.142239i	$0.954570\pi$
$108$	−1.64467	+	9.32740i	−0.158259	+	0.897529i
$109$	−11.6754	+	9.79682i	−1.11830	+	0.938366i	−0.998517	−	0.0544346i	$-0.982664\pi$
$109$	−11.6754	+	9.79682i	−1.11830	+	0.938366i	−0.119783	+	0.992800i	$0.538220\pi$
$110$		0			0
$111$	0.368769	+	2.09139i	0.0350020	+	0.198506i
$112$	−11.0956	−	4.03846i	−1.04843	−	0.381598i
$113$	−2.56380			−0.241182			−0.120591	−	0.992702i	$-0.538479\pi$
$113$	−2.56380			−0.241182			−0.120591	+	0.992702i	$0.538479\pi$
$114$	−5.13828	+	15.9400i	−0.481244	+	1.49291i
$115$		0			0
$116$	18.2926	+	6.65797i	1.69843	+	0.618177i
$117$	0.314520	+	1.78373i	0.0290774	+	0.164906i
$118$	4.29697	+	3.60558i	0.395568	+	0.331921i
$119$	0.0922912	−	0.0774415i	0.00846032	−	0.00709905i
$120$		0			0
$121$	5.03613	−	8.72284i	0.457830	−	0.792986i
$122$	10.1386	+	17.5606i	0.917910	+	1.58987i
$123$	−21.5645	+	7.84884i	−1.94441	+	0.707706i
$124$	18.3908	−	6.69370i	1.65154	−	0.601112i
$125$		0			0
$126$	1.91310	−	3.31359i	0.170433	−	0.295198i
$127$	2.68740	−	15.2410i	0.238468	−	1.35242i	−0.596718	−	0.802451i	$-0.703529\pi$
$127$	2.68740	−	15.2410i	0.238468	−	1.35242i	0.835186	−	0.549968i	$-0.185360\pi$
$128$	−1.07610	+	0.902953i	−0.0951145	+	0.0798105i
$129$	7.21178	+	6.05141i	0.634962	+	0.532797i
$130$		0			0
$131$	−0.791413	−	0.288051i	−0.0691461	−	0.0251671i	0.307216	−	0.951640i	$-0.400603\pi$
$131$	−0.791413	−	0.288051i	−0.0691461	−	0.0251671i	−0.376362	+	0.926473i	$0.622825\pi$
$132$	3.82032			0.332516
$133$	−8.27347	+	10.6404i	−0.717401	+	0.922644i
$134$	−18.8997			−1.63269
$135$		0			0
$136$	−0.00118913	−	0.00674391i	−0.000101967	−	0.000578285i
$137$	3.88675	+	3.26137i	0.332068	+	0.278638i	0.793542	−	0.608516i	$-0.208235\pi$
$137$	3.88675	+	3.26137i	0.332068	+	0.278638i	−0.461474	+	0.887154i	$0.652679\pi$
$138$	−11.4246	+	9.58641i	−0.972529	+	0.816049i
$139$	0.474127	−	2.68891i	0.0402150	−	0.228070i	−0.958076	−	0.286515i	$-0.907503\pi$
$139$	0.474127	−	2.68891i	0.0402150	−	0.228070i	0.998291	+	0.0584449i	$0.0186142\pi$
$140$		0			0
$141$	7.61698	+	13.1930i	0.641465	+	1.11105i
$142$	−23.9161	+	8.70474i	−2.00699	+	0.730486i
$143$	−2.67837	+	0.974847i	−0.223977	+	0.0815208i
$144$	1.16862	+	2.02411i	0.0973852	+	0.168676i
$145$		0			0
$146$	−0.314933	+	1.78607i	−0.0260640	+	0.147816i
$147$	3.72937	−	3.12931i	0.307593	−	0.258101i
$148$	1.78636	+	1.49894i	0.146838	+	0.123212i
$149$	−1.15401	−	6.54471i	−0.0945401	−	0.536164i	−0.994887	−	0.100991i	$-0.967799\pi$
$149$	−1.15401	−	6.54471i	−0.0945401	−	0.536164i	0.900347	−	0.435172i	$-0.143313\pi$
$150$		0			0
$151$	−5.19059			−0.422404			−0.211202	−	0.977442i	$-0.567738\pi$
$151$	−5.19059			−0.422404			−0.211202	+	0.977442i	$0.567738\pi$
$152$	0.288643	+	0.709662i	0.0234120	+	0.0575612i
$153$	−0.0238477			−0.00192797
$154$	5.65796	+	2.05933i	0.455932	+	0.165946i
$155$		0			0
$156$	8.99116	+	7.54448i	0.719869	+	0.604042i
$157$	−8.92275	+	7.48708i	−0.712113	+	0.597534i	−0.925191	−	0.379501i	$-0.876096\pi$
$157$	−8.92275	+	7.48708i	−0.712113	+	0.597534i	0.213078	+	0.977035i	$0.431651\pi$
$158$	3.12168	−	17.7039i	0.248348	−	1.40845i
$159$	5.75847	−	9.97396i	0.456676	−	0.790987i
$160$		0			0
$161$	−11.2787	+	4.10513i	−0.888890	+	0.323529i
$162$	19.8739	−	7.23350i	1.56144	−	0.568317i
$163$	−0.278398	−	0.482199i	−0.0218058	−	0.0377688i	0.854917	−	0.518765i	$-0.173608\pi$
$163$	−0.278398	−	0.482199i	−0.0218058	−	0.0377688i	−0.876722	+	0.480997i	$0.840275\pi$
$164$	−12.5996	+	21.8231i	−0.983860	+	1.70410i
$165$		0			0
$166$	14.8740	−	12.4807i	1.15444	−	0.968693i
$167$	−16.9727	−	14.2418i	−1.31339	−	1.10206i	−0.987662	−	0.156600i	$-0.949947\pi$
$167$	−16.9727	−	14.2418i	−1.31339	−	1.10206i	−0.325727	−	0.945464i	$-0.605609\pi$
$168$	−0.179362	−	1.01721i	−0.0138381	−	0.0784798i
$169$	3.98727	+	1.45125i	0.306713	+	0.111634i
$170$		0			0
$171$	2.60837	−	0.560767i	0.199467	−	0.0428829i
$172$	10.3376			0.788236
$173$	−10.7653	−	3.91823i	−0.818467	−	0.297898i	−0.101350	−	0.994851i	$-0.532316\pi$
$173$	−10.7653	−	3.91823i	−0.818467	−	0.297898i	−0.717117	+	0.696953i	$0.754539\pi$
$174$	−6.22341	−	35.2947i	−0.471795	−	2.67568i
$175$		0			0
$176$	−2.81751	+	2.36417i	−0.212377	+	0.178206i
$177$	0.915709	−	5.19324i	0.0688289	−	0.390348i
$178$	8.84129	−	15.3136i	0.662683	−	1.14780i
$179$	−2.98306	−	5.16681i	−0.222964	−	0.386185i	0.732743	−	0.680506i	$-0.238240\pi$
$179$	−2.98306	−	5.16681i	−0.222964	−	0.386185i	−0.955707	+	0.294321i	$0.904907\pi$
$180$		0			0
$181$	5.80527	−	2.11294i	0.431502	−	0.157054i	−0.117132	−	0.993116i	$-0.537370\pi$
$181$	5.80527	−	2.11294i	0.431502	−	0.157054i	0.548634	+	0.836062i	$0.315148\pi$
$182$	9.24926	+	16.0202i	0.685601	+	1.18750i
$183$	9.53145	−	16.5090i	0.704585	−	1.22038i
$184$	−0.118468	+	0.671863i	−0.00873354	+	0.0495304i
$185$		0			0
$186$	−27.6017	−	23.1606i	−2.02386	−	1.69822i
$187$	−0.00651663	−	0.0369577i	−0.000476543	−	0.00270261i
$188$	15.7192	+	5.72131i	1.14644	+	0.417270i
$189$	14.0334			1.02078
$190$		0			0
$191$	−18.6639			−1.35047			−0.675235	−	0.737602i	$-0.735958\pi$
$191$	−18.6639			−1.35047			−0.675235	+	0.737602i	$0.735958\pi$
$192$	15.5014	+	5.64205i	1.11872	+	0.407180i
$193$	4.15136	+	23.5435i	0.298821	+	1.69470i	0.651252	+	0.758861i	$0.274244\pi$
$193$	4.15136	+	23.5435i	0.298821	+	1.69470i	−0.352431	+	0.935838i	$0.614645\pi$
$194$	−12.0613	−	10.1206i	−0.865948	−	0.726616i
$195$		0			0
$196$	0.928289	−	5.26459i	0.0663064	−	0.376042i
$197$	−3.35076	+	5.80368i	−0.238732	+	0.413495i	−0.960351	−	0.278795i	$-0.910065\pi$
$197$	−3.35076	+	5.80368i	−0.238732	+	0.413495i	0.721619	+	0.692290i	$0.243398\pi$
$198$	−0.595916	−	1.03216i	−0.0423499	−	0.0733521i
$199$	−2.96836	+	1.08040i	−0.210422	+	0.0765872i	−0.445080	−	0.895491i	$-0.646825\pi$
$199$	−2.96836	+	1.08040i	−0.210422	+	0.0765872i	0.234659	+	0.972078i	$0.424603\pi$
$200$		0			0
$201$	8.88392	+	15.3874i	0.626624	+	1.08534i
$202$	3.07653	−	5.32870i	0.216464	−	0.374926i
$203$	5.00858	−	28.4051i	0.351534	−	1.99365i
$204$	−0.118382	+	0.0993340i	−0.00828837	+	0.00695477i
$205$		0			0
$206$	0.115346	+	0.654158i	0.00803652	+	0.0455774i
$207$	2.23255	+	0.812582i	0.155173	+	0.0564783i
$208$	−11.2999			−0.783505
$209$	1.58181	+	3.88906i	0.109416	+	0.269012i
$210$		0			0
$211$	10.7670	+	3.91887i	0.741231	+	0.269786i	0.684911	−	0.728627i	$-0.259841\pi$
$211$	10.7670	+	3.91887i	0.741231	+	0.269786i	0.0563198	+	0.998413i	$0.482063\pi$
$212$	−2.19603	−	12.4543i	−0.150824	−	0.855367i
$213$	18.3289	+	15.3798i	1.25588	+	1.05381i
$214$	19.8031	−	16.6168i	1.35371	−	1.13590i
$215$		0			0
$216$	0.398830	−	0.690793i	0.0271369	−	0.0470025i
$217$	−14.4990	−	25.1130i	−0.984258	−	1.70478i
$218$	28.9536	−	10.5383i	1.96099	−	0.713741i
$219$	1.60218	−	0.583148i	0.108266	−	0.0394055i
$220$		0			0
$221$	0.0576482	−	0.0998496i	0.00387784	−	0.00671661i
$222$	0.745510	−	4.22800i	0.0500354	−	0.283765i
$223$	5.75623	−	4.83005i	0.385465	−	0.323444i	−0.429378	−	0.903125i	$-0.641267\pi$
$223$	5.75623	−	4.83005i	0.385465	−	0.323444i	0.814844	+	0.579681i	$0.196823\pi$
$224$	19.1186	+	16.0424i	1.27741	+	1.07188i
$225$		0			0
$226$	4.87044	+	1.77270i	0.323977	+	0.117918i
$227$	4.20184			0.278886			0.139443	−	0.990230i	$-0.455469\pi$
$227$	4.20184			0.278886			0.139443	+	0.990230i	$0.455469\pi$
$228$	10.6124	−	13.6485i	0.702821	−	0.903892i
$229$	22.5758			1.49185			0.745927	−	0.666028i	$-0.232007\pi$
$229$	22.5758			1.49185			0.745927	+	0.666028i	$0.232007\pi$
$230$		0			0
$231$	−0.982933	−	5.57449i	−0.0646722	−	0.366774i
$232$	−1.25589	−	1.05382i	−0.0824534	−	0.0691867i
$233$	8.41032	−	7.05710i	0.550978	−	0.462326i	−0.324294	−	0.945956i	$-0.605127\pi$
$233$	8.41032	−	7.05710i	0.550978	−	0.462326i	0.875272	+	0.483631i	$0.160682\pi$
$234$	0.635840	−	3.60603i	0.0415661	−	0.235733i
$235$		0			0
$236$	−2.89527	−	5.01475i	−0.188466	−	0.326432i
$237$	−15.8812	+	5.78029i	−1.03160	+	0.375470i
$238$	−0.228871	+	0.0833023i	−0.0148355	+	0.00539969i
$239$	1.36280	+	2.36043i	0.0881520	+	0.152684i	0.906730	−	0.421712i	$-0.138571\pi$
$239$	1.36280	+	2.36043i	0.0881520	+	0.152684i	−0.818578	+	0.574395i	$0.805237\pi$
$240$		0			0
$241$	1.93687	−	10.9846i	0.124765	−	0.707577i	−0.856682	−	0.515845i	$-0.827478\pi$
$241$	1.93687	−	10.9846i	0.124765	−	0.707577i	0.981447	−	0.191733i	$-0.0614107\pi$
$242$	−15.5984	+	13.0886i	−1.00270	+	0.841369i
$243$	−4.80130	−	4.02877i	−0.308003	−	0.258445i
$244$	−3.63489	−	20.6145i	−0.232700	−	1.31971i
$245$		0			0
$246$	46.3930			2.95791
$247$	−3.95743	+	12.2768i	−0.251805	+	0.781151i
$248$	−1.64825			−0.104664
$249$	−17.1529	−	6.24315i	−1.08702	−	0.395643i
$250$		0			0
$251$	−20.9654	−	17.5920i	−1.32332	−	1.11040i	−0.985589	−	0.169156i	$-0.945896\pi$
$251$	−20.9654	−	17.5920i	−1.32332	−	1.11040i	−0.337732	−	0.941242i	$-0.609660\pi$
$252$	−3.02575	+	2.53890i	−0.190604	+	0.159936i
$253$	−0.649220	+	3.68191i	−0.0408161	+	0.231480i
$254$	−15.6434	+	27.0951i	−0.981553	+	1.70010i
$255$		0			0
$256$	−13.6440	+	4.96601i	−0.852749	+	0.310375i
$257$	−19.0408	+	6.93029i	−1.18773	+	0.432300i	−0.858927	−	0.512098i	$-0.828869\pi$
$257$	−19.0408	+	6.93029i	−1.18773	+	0.432300i	−0.328806	+	0.944397i	$0.606646\pi$
$258$	−9.51608	−	16.4823i	−0.592445	−	1.02614i
$259$	1.72759	−	2.99227i	0.107347	−	0.185931i
$260$		0			0
$261$	−4.37360	+	3.66989i	−0.270719	+	0.227160i
$262$	1.30428	+	1.09442i	0.0805786	+	0.0676135i
$263$	−1.66049	−	9.41708i	−0.102390	−	0.580682i	−0.992231	−	0.124411i	$-0.960296\pi$
$263$	−1.66049	−	9.41708i	−0.102390	−	0.580682i	0.889841	−	0.456271i	$-0.150815\pi$
$264$	−0.302339	−	0.110042i	−0.0186077	−	0.00677263i
$265$		0			0
$266$	23.0743	−	14.4931i	1.41477	−	0.888629i
$267$	−16.6236			−1.01735
$268$	18.3338	+	6.67295i	1.11991	+	0.407615i
$269$	0.794363	+	4.50506i	0.0484332	+	0.274678i	0.999401	−	0.0346123i	$-0.0110196\pi$
$269$	0.794363	+	4.50506i	0.0484332	+	0.274678i	−0.950968	+	0.309290i	$0.899909\pi$
$270$		0			0
$271$	−16.9571	+	14.2287i	−1.03007	+	0.864330i	−0.990859	−	0.134901i	$-0.956928\pi$
$271$	−16.9571	+	14.2287i	−1.03007	+	0.864330i	−0.0392098	+	0.999231i	$0.512484\pi$
$272$	0.0258352	−	0.146519i	0.00156649	−	0.00888400i
$273$	8.69533	−	15.0608i	0.526265	−	0.911518i
$274$	−5.12864	−	8.88306i	−0.309832	−	0.536645i
$275$		0			0
$276$	14.4672	−	5.26564i	0.870824	−	0.316954i
$277$	11.7771	+	20.3985i	0.707617	+	1.22563i	0.965739	+	0.259516i	$0.0835629\pi$
$277$	11.7771	+	20.3985i	0.707617	+	1.22563i	−0.258122	+	0.966112i	$0.583104\pi$
$278$	−2.75990	+	4.78029i	−0.165528	+	0.286703i
$279$	−0.996734	+	5.65276i	−0.0596729	+	0.338422i
$280$		0			0
$281$	7.90783	+	6.63545i	0.471741	+	0.395838i	0.847429	−	0.530908i	$-0.178149\pi$
$281$	7.90783	+	6.63545i	0.471741	+	0.395838i	−0.375688	+	0.926746i	$0.622594\pi$
$282$	−5.34788	−	30.3294i	−0.318462	−	1.80609i
$283$	−29.0110	−	10.5592i	−1.72453	−	0.627676i	−0.726310	−	0.687367i	$-0.758766\pi$
$283$	−29.0110	−	10.5592i	−1.72453	−	0.627676i	−0.998217	+	0.0596910i	$0.980988\pi$
$284$	26.2733			1.55903
$285$		0			0
$286$	5.76214			0.340722
$287$	35.0853	+	12.7700i	2.07102	+	0.753790i
$288$	−0.857852	−	4.86512i	−0.0505494	−	0.286680i
$289$	−13.0216	−	10.9264i	−0.765976	−	0.642730i
$290$		0			0
$291$	−2.57033	+	14.5770i	−0.150675	+	0.854521i
$292$	0.936113	−	1.62140i	0.0547819	−	0.0948850i
$293$	3.18052	+	5.50882i	0.185808	+	0.321828i	0.943848	−	0.330379i	$-0.107176\pi$
$293$	3.18052	+	5.50882i	0.185808	+	0.321828i	−0.758041	+	0.652207i	$0.773843\pi$
$294$	−9.24839	+	3.36614i	−0.539377	+	0.196317i
$295$		0			0
$296$	−0.0981961	−	0.170081i	−0.00570753	−	0.00988573i
$297$	2.18565	−	3.78565i	0.126824	−	0.219666i
$298$	−2.33297	+	13.2309i	−0.135145	+	0.766446i
$299$	−8.79910	+	7.38332i	−0.508865	+	0.426989i
$300$		0			0
$301$	−2.65977	−	15.0843i	−0.153307	−	0.869446i
$302$	9.86055	+	3.58895i	0.567411	+	0.206521i
$303$	−5.78456			−0.332314
$304$	0.619557	+	16.6332i	0.0355340	+	0.953979i
$305$		0			0
$306$	0.0453035	+	0.0164891i	0.00258983	+	0.000942620i
$307$	1.02217	+	5.79702i	0.0583384	+	0.330854i	0.999983	−	0.00575393i	$-0.00183154\pi$
$307$	1.02217	+	5.79702i	0.0583384	+	0.330854i	−0.941645	+	0.336608i	$0.890720\pi$
$308$	−4.76145	−	3.99533i	−0.271309	−	0.227655i
$309$	0.478371	−	0.401401i	0.0272136	−	0.0228349i
$310$		0			0
$311$	12.6942	−	21.9871i	0.719825	−	1.24677i	−0.241245	−	0.970464i	$-0.577556\pi$
$311$	12.6942	−	21.9871i	0.719825	−	1.24677i	0.961069	−	0.276308i	$-0.0891111\pi$
$312$	−0.494243	−	0.856054i	−0.0279810	−	0.0484645i
$313$	5.67434	−	2.06529i	0.320733	−	0.116737i	−0.176637	−	0.984276i	$-0.556522\pi$
$313$	5.67434	−	2.06529i	0.320733	−	0.116737i	0.497369	+	0.867539i	$0.334299\pi$
$314$	22.1274	−	8.05371i	1.24872	−	0.454497i
$315$		0			0
$316$	−9.27896	+	16.0716i	−0.521982	+	0.904100i
$317$	−2.75679	+	15.6346i	−0.154837	+	0.878124i	0.804098	+	0.594497i	$0.202649\pi$
$317$	−2.75679	+	15.6346i	−0.154837	+	0.878124i	−0.958935	+	0.283627i	$0.908462\pi$
$318$	−17.8357	+	14.9659i	−1.00018	+	0.839248i
$319$	−6.88249	−	5.77509i	−0.385345	−	0.323343i
$320$		0			0
$321$	−22.8373	−	8.31208i	−1.27465	−	0.463935i
$322$	24.2647			1.35222
$323$	−0.150137	−	0.0793824i	−0.00835387	−	0.00441695i
$324$	−21.8327			−1.21293
$325$		0			0
$326$	0.195463	+	1.10853i	0.0108257	+	0.0613956i
$327$	−22.1896	−	18.6193i	−1.22709	−	1.02965i
$328$	1.62573	−	1.36415i	0.0897657	−	0.0753224i
$329$	4.30396	−	24.4090i	0.237285	−	1.34571i
$330$		0			0
$331$	7.08478	+	12.2712i	0.389414	+	0.674486i	0.992371	−	0.123288i	$-0.0393440\pi$
$331$	7.08478	+	12.2712i	0.389414	+	0.674486i	−0.602956	+	0.797774i	$0.706011\pi$
$332$	−18.8352	+	6.85544i	−1.03371	+	0.376241i
$333$	−0.642682	+	0.233917i	−0.0352188	+	0.0128186i
$334$	22.3958	+	38.7907i	1.22544	+	2.12253i
$335$		0			0
$336$	3.89684	−	22.1001i	0.212590	−	1.20566i
$337$	1.64694	−	1.38195i	0.0897147	−	0.0752796i	−0.596827	−	0.802370i	$-0.703572\pi$
$337$	1.64694	−	1.38195i	0.0897147	−	0.0752796i	0.686542	+	0.727090i	$0.259128\pi$
$338$	−6.57117	−	5.51387i	−0.357425	−	0.299915i
$339$	−0.846120	−	4.79859i	−0.0459550	−	0.260623i
$340$		0			0
$341$	−9.03266			−0.489146
$342$	−5.34286	−	0.738230i	−0.288909	−	0.0399189i
$343$	13.7245			0.741051
$344$	−0.818115	−	0.297770i	−0.0441098	−	0.0160547i
$345$		0			0
$346$	17.7415	+	14.8869i	0.953791	+	0.800326i
$347$	8.46670	−	7.10441i	0.454516	−	0.381385i	−0.386592	−	0.922251i	$-0.626348\pi$
$347$	8.46670	−	7.10441i	0.454516	−	0.381385i	0.841109	+	0.540866i	$0.181903\pi$
$348$	−6.42450	+	36.4351i	−0.344389	+	1.95313i
$349$	−17.6725	+	30.6097i	−0.945989	+	1.63850i	−0.192229	+	0.981350i	$0.561572\pi$
$349$	−17.6725	+	30.6097i	−0.945989	+	1.63850i	−0.753759	+	0.657151i	$0.771762\pi$
$350$		0			0
$351$	12.6200	−	4.59330i	0.673604	−	0.245172i
$352$	7.30524	−	2.65889i	0.389371	−	0.141719i
$353$	11.0952	+	19.2174i	0.590538	+	1.02284i	0.994160	+	0.107916i	$0.0344176\pi$
$353$	11.0952	+	19.2174i	0.590538	+	1.02284i	−0.403622	+	0.914926i	$0.632249\pi$
$354$	−5.33036	+	9.23245i	−0.283305	+	0.490699i
$355$		0			0
$356$	−13.9833	+	11.7334i	−0.741115	+	0.621869i
$357$	0.175404	+	0.147181i	0.00928334	+	0.00778965i
$358$	2.09441	+	11.8780i	0.110693	+	0.627770i
$359$	8.93517	+	3.25214i	0.471580	+	0.171641i	0.566868	−	0.823809i	$-0.308155\pi$
$359$	8.93517	+	3.25214i	0.471580	+	0.171641i	−0.0952879	+	0.995450i	$0.530377\pi$
$360$		0			0
$361$	18.2881	+	5.15215i	0.962533	+	0.271166i
$362$	−12.4892			−0.656419
$363$	17.9884	+	6.54723i	0.944144	+	0.343640i
$364$	−3.31603	−	18.8061i	−0.173807	−	0.985709i
$365$		0			0
$366$	−29.5218	+	24.7717i	−1.54313	+	1.29484i
$367$	0.379110	−	2.15004i	0.0197894	−	0.112231i	−0.973313	−	0.229482i	$-0.926297\pi$
$367$	0.379110	−	2.15004i	0.0197894	−	0.112231i	0.993102	+	0.117250i	$0.0374080\pi$
$368$	−7.41107	+	12.8363i	−0.386328	+	0.669141i
$369$	−3.69530	−	6.40045i	−0.192370	−	0.333194i
$370$		0			0
$371$	−17.6079	+	6.40877i	−0.914159	+	0.332727i
$372$	18.5979	+	32.2124i	0.964254	+	1.67014i
$373$	−6.17035	+	10.6874i	−0.319488	+	0.553370i	−0.980381	−	0.197110i	$-0.936844\pi$
$373$	−6.17035	+	10.6874i	−0.319488	+	0.553370i	0.660893	+	0.750480i	$0.270178\pi$
$374$	−0.0131741	+	0.0747143i	−0.000681219	+	0.00386338i
$375$		0			0
$376$	−1.07921	−	0.905566i	−0.0556561	−	0.0467010i
$377$	−4.79319	−	27.1835i	−0.246862	−	1.40002i
$378$	−26.6593	−	9.70318i	−1.37120	−	0.499078i
$379$	−18.5014			−0.950352			−0.475176	−	0.879891i	$-0.657616\pi$
$379$	−18.5014			−0.950352			−0.475176	+	0.879891i	$0.657616\pi$
$380$		0			0
$381$	29.4130			1.50688
$382$	35.4558	+	12.9048i	1.81407	+	0.660269i
$383$	1.98517	+	11.2585i	0.101438	+	0.575282i	0.992584	+	0.121565i	$0.0387912\pi$
$383$	1.98517	+	11.2585i	0.101438	+	0.575282i	−0.891146	+	0.453717i	$0.850098\pi$
$384$	−2.04517	−	1.71610i	−0.104367	−	0.0875746i
$385$		0			0
$386$	8.39246	−	47.5960i	0.427165	−	2.42257i
$387$	−1.51595	+	2.62570i	−0.0770601	+	0.133472i
$388$	8.12680	+	14.0760i	0.412576	+	0.714602i
$389$	−11.7685	+	4.28337i	−0.596684	+	0.217175i	−0.622667	−	0.782487i	$-0.713951\pi$
$389$	−11.7685	+	4.28337i	−0.596684	+	0.217175i	0.0259826	+	0.999662i	$0.491729\pi$
$390$		0			0
$391$	−0.0756176	−	0.130974i	−0.00382415	−	0.00662361i
$392$	−0.225108	+	0.389899i	−0.0113697	+	0.0196929i
$393$	0.277949	−	1.57633i	0.0140207	−	0.0795153i
$394$	10.3783	−	8.70843i	0.522851	−	0.438724i
$395$		0			0
$396$	0.213646	+	1.21165i	0.0107361	+	0.0608877i
$397$	11.0417	+	4.01886i	0.554168	+	0.201701i	0.603898	−	0.797062i	$-0.293614\pi$
$397$	11.0417	+	4.01886i	0.554168	+	0.201701i	−0.0497292	+	0.998763i	$0.515836\pi$
$398$	6.38602			0.320102
$399$	−22.6459	−	11.9736i	−1.13371	−	0.599430i
$400$		0			0
$401$	13.7588	+	5.00780i	0.687083	+	0.250078i	0.661886	−	0.749605i	$-0.269756\pi$
$401$	13.7588	+	5.00780i	0.687083	+	0.250078i	0.0251970	+	0.999683i	$0.491979\pi$
$402$	−6.23741	−	35.3741i	−0.311094	−	1.76430i
$403$	−21.2585	−	17.8380i	−1.05896	−	0.888573i
$404$	−4.86582	+	4.08290i	−0.242083	+	0.203132i
$405$		0			0
$406$	−29.1551	+	50.4980i	−1.44694	+	2.50618i
$407$	−0.538130	−	0.932068i	−0.0266741	−	0.0462009i
$408$	0.0122299	−	0.00445134i	0.000605472	−	0.000220374i
$409$	−11.9790	+	4.36001i	−0.592324	+	0.215588i	−0.620751	−	0.784007i	$-0.713172\pi$
$409$	−11.9790	+	4.36001i	−0.592324	+	0.215588i	0.0284271	+	0.999596i	$0.490950\pi$
$410$		0			0
$411$	−4.82149	+	8.35106i	−0.237827	+	0.411928i
$412$	0.119073	−	0.675295i	0.00586630	−	0.0332694i
$413$	−6.57244	+	5.51494i	−0.323409	+	0.271372i
$414$	−3.67933	−	3.08732i	−0.180829	−	0.151734i
$415$		0			0
$416$	22.4438	+	8.16889i	1.10040	+	0.400513i
$417$	5.18923			0.254118
$418$	−0.315930	−	8.48176i	−0.0154527	−	0.414856i
$419$	2.84601			0.139037			0.0695184	−	0.997581i	$-0.477854\pi$
$419$	2.84601			0.139037			0.0695184	+	0.997581i	$0.477854\pi$
$420$		0			0
$421$	1.93626	+	10.9811i	0.0943677	+	0.535186i	0.994939	+	0.100478i	$0.0320372\pi$
$421$	1.93626	+	10.9811i	0.0943677	+	0.535186i	−0.900572	+	0.434708i	$0.856852\pi$
$422$	−17.7444	−	14.8893i	−0.863785	−	0.724802i
$423$	−3.75831	+	3.15360i	−0.182735	+	0.153333i
$424$	−0.184947	+	1.04889i	−0.00898182	+	0.0509384i
$425$		0			0
$426$	−24.1854	−	41.8903i	−1.17178	−	2.02959i
$427$	−29.1448	+	10.6078i	−1.41041	+	0.513349i
$428$	−25.0770	+	9.12728i	−1.21214	+	0.441184i
$429$	−2.70853	−	4.69131i	−0.130769	−	0.226498i
$430$		0			0
$431$	−2.59366	+	14.7094i	−0.124932	+	0.708525i	0.856416	+	0.516286i	$0.172686\pi$
$431$	−2.59366	+	14.7094i	−0.124932	+	0.708525i	−0.981348	+	0.192239i	$0.938425\pi$
$432$	13.2756	−	11.1395i	0.638721	−	0.535950i
$433$	29.6894	+	24.9123i	1.42678	+	1.19721i	0.947585	+	0.319503i	$0.103516\pi$
$433$	29.6894	+	24.9123i	1.42678	+	1.19721i	0.479195	+	0.877708i	$0.340929\pi$
$434$	10.1798	+	57.7323i	0.488645	+	2.77124i
$435$		0			0
$436$	−31.8074			−1.52330
$437$	11.3506	+	12.5473i	0.542971	+	0.600218i
$438$	−3.44688			−0.164698
$439$	29.5331	+	10.7492i	1.40954	+	0.513030i	0.930994	−	0.365034i	$-0.118943\pi$
$439$	29.5331	+	10.7492i	1.40954	+	0.513030i	0.478544	+	0.878064i	$0.341165\pi$
$440$		0			0
$441$	1.20105	+	1.00780i	0.0571929	+	0.0479906i
$442$	−0.178554	+	0.149824i	−0.00849293	+	0.00712641i
$443$	−1.84950	+	10.4890i	−0.0878722	+	0.498348i	0.908828	+	0.417172i	$0.136979\pi$
$443$	−1.84950	+	10.4890i	−0.0878722	+	0.498348i	−0.996700	+	0.0811761i	$0.974132\pi$
$444$	−2.21597	+	3.83817i	−0.105165	+	0.182152i
$445$		0			0
$446$	−14.2748	+	5.19559i	−0.675930	+	0.246018i
$447$	11.8687	−	4.31985i	0.561370	−	0.204322i
$448$	−13.4196	−	23.2435i	−0.634019	−	1.09815i
$449$	−2.05200	+	3.55417i	−0.0968399	+	0.167732i	−0.910375	−	0.413784i	$-0.864207\pi$
$449$	−2.05200	+	3.55417i	−0.0968399	+	0.167732i	0.813535	+	0.581516i	$0.197540\pi$
$450$		0			0
$451$	8.90923	−	7.47573i	0.419519	−	0.352019i
$452$	−4.09871	−	3.43923i	−0.192787	−	0.161768i
$453$	−1.71303	−	9.71508i	−0.0804852	−	0.456454i
$454$	−7.98224	−	2.90530i	−0.374625	−	0.136352i
$455$		0			0
$456$	−1.23300	+	0.774452i	−0.0577403	+	0.0362670i
$457$	−9.25947			−0.433140			−0.216570	−	0.976267i	$-0.569487\pi$
$457$	−9.25947			−0.433140			−0.216570	+	0.976267i	$0.569487\pi$
$458$	−42.8873	−	15.6097i	−2.00399	−	0.729394i
$459$	0.0307052	+	0.174138i	0.00143319	+	0.00812805i
$460$		0			0
$461$	5.09121	−	4.27203i	0.237121	−	0.198968i	−0.516482	−	0.856298i	$-0.672759\pi$
$461$	5.09121	−	4.27203i	0.237121	−	0.198968i	0.753603	+	0.657330i	$0.228314\pi$
$462$	−1.98711	+	11.2695i	−0.0924489	+	0.524304i
$463$	11.1474	−	19.3079i	0.518064	−	0.897313i	−0.481716	−	0.876327i	$-0.659986\pi$
$463$	11.1474	−	19.3079i	0.518064	−	0.897313i	0.999780	−	0.0209853i	$-0.00668032\pi$
$464$	−17.8094	−	30.8469i	−0.826783	−	1.43203i
$465$		0			0
$466$	−20.8566	+	7.59118i	−0.966163	+	0.351655i
$467$	−7.73697	−	13.4008i	−0.358024	−	0.620116i	0.629606	−	0.776914i	$-0.283216\pi$
$467$	−7.73697	−	13.4008i	−0.358024	−	0.620116i	−0.987631	+	0.156798i	$0.949883\pi$
$468$	−1.88998	+	3.27355i	−0.0873645	+	0.151320i
$469$	5.01985	−	28.4690i	0.231795	−	1.31458i
$470$		0			0
$471$	−16.9581	−	14.2295i	−0.781388	−	0.655663i
$472$	0.0846832	+	0.480262i	0.00389786	+	0.0221059i
$473$	−4.48340	−	1.63182i	−0.206147	−	0.0750313i
$474$	34.1662			1.56931
$475$		0			0
$476$	0.251429			0.0115242
$477$	3.48537	+	1.26857i	0.159584	+	0.0580839i
$478$	−0.956820	−	5.42640i	−0.0437639	−	0.248198i
$479$	24.6710	+	20.7014i	1.12725	+	0.945872i	0.998948	−	0.0458635i	$-0.0146039\pi$
$479$	24.6710	+	20.7014i	1.12725	+	0.945872i	0.128299	+	0.991736i	$0.459048\pi$
$480$		0			0
$481$	0.574182	−	3.25635i	0.0261805	−	0.148477i
$482$	−11.2746	+	19.5281i	−0.513543	+	0.889482i
$483$	−11.4057	−	19.7553i	−0.518979	−	0.898898i
$484$	19.7525	−	7.18934i	0.897843	−	0.326788i
$485$		0			0
$486$	6.33539	+	10.9732i	0.287379	+	0.497755i
$487$	−1.82569	+	3.16219i	−0.0827301	+	0.143293i	−0.904422	−	0.426640i	$-0.859697\pi$
$487$	−1.82569	+	3.16219i	−0.0827301	+	0.143293i	0.821692	+	0.569932i	$0.193031\pi$
$488$	−0.306125	+	1.73612i	−0.0138576	+	0.0785906i
$489$	0.810640	−	0.680208i	0.0366584	−	0.0307601i
$490$		0			0
$491$	0.789859	+	4.47952i	0.0356459	+	0.202158i	0.997430	−	0.0716523i	$-0.0228272\pi$
$491$	0.789859	+	4.47952i	0.0356459	+	0.202158i	−0.961784	+	0.273810i	$0.911716\pi$
$492$	−45.0038	−	16.3801i	−2.02893	−	0.738470i
$493$	0.363431			0.0163681
$494$	16.0065	−	20.5858i	0.720166	−	0.926201i
$495$		0			0
$496$	−33.6504	−	12.2477i	−1.51095	−	0.549940i
$497$	−6.75989	−	38.3372i	−0.303222	−	1.71966i
$498$	28.2686	+	23.7202i	1.26675	+	1.06293i
$499$	−16.7177	+	14.0278i	−0.748387	+	0.627972i	−0.935076	−	0.354448i	$-0.884669\pi$
$499$	−16.7177	+	14.0278i	−0.748387	+	0.627972i	0.186689	+	0.982419i	$0.440224\pi$
$500$		0			0
$501$	21.0545	−	36.4675i	0.940648	−	1.62925i
$502$	27.6641	+	47.9157i	1.23471	+	2.13858i
$503$	−23.2469	+	8.46117i	−1.03653	+	0.377265i	−0.803562	−	0.595221i	$-0.797065\pi$
$503$	−23.2469	+	8.46117i	−1.03653	+	0.377265i	−0.232964	+	0.972485i	$0.574842\pi$
$504$	0.312588	−	0.113773i	0.0139238	−	0.00506785i
$505$		0			0
$506$	3.77912	−	6.54563i	0.168003	−	0.290989i
$507$	−1.40036	+	7.94181i	−0.0621920	+	0.352708i
$508$	24.7415	−	20.7606i	1.09773	−	0.921101i
$509$	−13.2902	−	11.1518i	−0.589078	−	0.494295i	0.298836	−	0.954305i	$-0.403402\pi$
$509$	−13.2902	−	11.1518i	−0.589078	−	0.494295i	−0.887914	+	0.460009i	$0.847846\pi$
$510$		0			0
$511$	−2.60674	−	0.948777i	−0.115316	−	0.0419714i
$512$	32.1626			1.42140
$513$	−7.45318	−	18.3245i	−0.329066	−	0.809047i
$514$	40.9637			1.80683
$515$		0			0
$516$	3.41168	+	19.3486i	0.150191	+	0.851776i
$517$	−5.91424	−	4.96264i	−0.260108	−	0.218257i
$518$	−5.35085	+	4.48990i	−0.235103	+	0.197275i
$519$	3.78083	−	21.4421i	0.165960	−	0.941206i
$520$		0			0
$521$	−0.228337	−	0.395492i	−0.0100036	−	0.0173268i	0.860980	−	0.508638i	$-0.169851\pi$
$521$	−0.228337	−	0.395492i	−0.0100036	−	0.0173268i	−0.870984	+	0.491312i	$0.836518\pi$
$522$	10.8460	−	3.94762i	0.474717	−	0.172783i
$523$	−35.5171	+	12.9272i	−1.55305	+	0.565265i	−0.969132	−	0.246544i	$-0.920705\pi$
$523$	−35.5171	+	12.9272i	−1.55305	+	0.565265i	−0.583922	+	0.811810i	$0.698483\pi$
$524$	−0.878815	−	1.52215i	−0.0383912	−	0.0664955i
$525$		0			0
$526$	−3.35687	+	19.0377i	−0.146366	+	0.830085i
$527$	0.279898	−	0.234863i	0.0121926	−	0.0102308i
$528$	−5.35480	−	4.49321i	−0.233038	−	0.195542i
$529$	−1.37758	−	7.81265i	−0.0598949	−	0.339681i
$530$		0			0
$531$	1.69830			0.0736998
$532$	−27.5004	+	5.91224i	−1.19229	+	0.256328i
$533$	35.7313			1.54769
$534$	31.5798	+	11.4941i	1.36659	+	0.497399i
$535$		0			0
$536$	−1.25872	−	1.05619i	−0.0543684	−	0.0456205i
$537$	8.68608	−	7.28849i	0.374832	−	0.314522i
$538$	1.60590	−	9.10750i	0.0692352	−	0.392652i
$539$	−1.23363	+	2.13671i	−0.0531361	+	0.0920344i
$540$		0			0
$541$	19.8556	−	7.22684i	0.853658	−	0.310706i	0.122127	−	0.992514i	$-0.461028\pi$
$541$	19.8556	−	7.22684i	0.853658	−	0.310706i	0.731531	+	0.681808i	$0.238806\pi$
$542$	42.0515	−	15.3055i	1.80627	−	0.657428i
$543$	5.87063	+	10.1682i	0.251933	+	0.436361i
$544$	−0.157235	+	0.272339i	−0.00674140	+	0.0116765i
$545$		0			0
$546$	−26.9320	+	22.5987i	−1.15258	+	0.967134i
$547$	9.60806	+	8.06212i	0.410811	+	0.344711i	0.824655	−	0.565637i	$-0.191369\pi$
$547$	9.60806	+	8.06212i	0.410811	+	0.344711i	−0.413843	+	0.910348i	$0.635814\pi$
$548$	1.83871	+	10.4278i	0.0785458	+	0.445455i
$549$	5.76901	+	2.09975i	0.246215	+	0.0896150i
$550$		0			0
$551$	−39.7508	+	8.54591i	−1.69344	+	0.364068i
$552$	−1.29660			−0.0551872
$553$	25.8386	+	9.40449i	1.09877	+	0.399920i
$554$	−8.26870	−	46.8941i	−0.351303	−	1.99234i
$555$		0			0
$556$	4.36504	−	3.66271i	0.185119	−	0.155333i
$557$	5.56111	−	31.5386i	0.235632	−	1.33633i	−0.605647	−	0.795733i	$-0.707086\pi$
$557$	5.56111	−	31.5386i	0.235632	−	1.33633i	0.841279	−	0.540601i	$-0.181803\pi$
$558$	5.80201	−	10.0494i	0.245618	−	0.425424i
$559$	−7.32916	−	12.6945i	−0.309990	−	0.536919i
$560$		0			0
$561$	0.0670220	−	0.0243940i	0.00282967	−	0.00102992i
$562$	−10.4345	−	18.0731i	−0.440153	−	0.762368i
$563$	9.79034	−	16.9574i	0.412614	−	0.714668i	−0.582561	−	0.812787i	$-0.697949\pi$
$563$	9.79034	−	16.9574i	0.412614	−	0.714668i	0.995175	+	0.0981190i	$0.0312826\pi$
$564$	−5.52068	+	31.3093i	−0.232463	+	1.31836i
$565$		0			0
$566$	47.8113	+	40.1184i	2.00966	+	1.68630i
$567$	5.61736	+	31.8576i	0.235907	+	1.33789i
$568$	−2.07926	−	0.756789i	−0.0872439	−	0.0317542i
$569$	−18.6525			−0.781953			−0.390977	−	0.920401i	$-0.627863\pi$
$569$	−18.6525			−0.781953			−0.390977	+	0.920401i	$0.627863\pi$
$570$		0			0
$571$	−0.460181			−0.0192580			−0.00962899	−	0.999954i	$-0.503065\pi$
$571$	−0.460181			−0.0192580			−0.00962899	+	0.999954i	$0.503065\pi$
$572$	−5.58960	−	2.03445i	−0.233713	−	0.0850645i
$573$	−6.15957	−	34.9327i	−0.257320	−	1.45933i
$574$	−57.8219	−	48.5184i	−2.41344	−	2.02512i
$575$		0			0
$576$	−0.922533	+	5.23194i	−0.0384389	+	0.217998i
$577$	5.87392	−	10.1739i	0.244534	−	0.423546i	−0.717466	−	0.696593i	$-0.754698\pi$
$577$	5.87392	−	10.1739i	0.244534	−	0.423546i	0.962001	+	0.273047i	$0.0880316\pi$
$578$	17.1822	+	29.7605i	0.714686	+	1.23787i
$579$	−42.6957	+	15.5400i	−1.77437	+	0.645819i
$580$		0			0
$581$	14.8494	+	25.7198i	0.616055	+	1.06704i
$582$	14.9619	−	25.9148i	0.620191	−	1.07420i
$583$	−1.01354	+	5.74806i	−0.0419765	+	0.238060i
$584$	−0.120787	+	0.101352i	−0.00499821	+	0.00419399i
$585$		0			0
$586$	−2.23304	−	12.6642i	−0.0922461	−	0.523154i
$587$	−4.60486	−	1.67603i	−0.190063	−	0.0691773i	0.245235	−	0.969464i	$-0.421135\pi$
$587$	−4.60486	−	1.67603i	−0.190063	−	0.0691773i	−0.435298	+	0.900286i	$0.643357\pi$
$588$	10.1599			0.418989
$589$	−25.0916	+	32.2701i	−1.03388	+	1.32967i
$590$		0			0
$591$	−11.9684	−	4.35615i	−0.492316	−	0.179188i
$592$	−0.740928	−	4.20201i	−0.0304519	−	0.172702i
$593$	14.1700	+	11.8900i	0.581892	+	0.488265i	0.885568	−	0.464510i	$-0.153770\pi$
$593$	14.1700	+	11.8900i	0.581892	+	0.488265i	−0.303676	+	0.952775i	$0.598214\pi$
$594$	−6.76960	+	5.68037i	−0.277760	+	0.233068i
$595$		0			0
$596$	6.93456	−	12.0110i	0.284051	−	0.491990i
$597$	−3.00178	−	5.19924i	−0.122855	−	0.212791i
$598$	21.8207	−	7.94210i	0.892316	−	0.324777i
$599$	20.1336	−	7.32805i	0.822638	−	0.299416i	0.103804	−	0.994598i	$-0.466898\pi$
$599$	20.1336	−	7.32805i	0.822638	−	0.299416i	0.718834	+	0.695182i	$0.244676\pi$
$600$		0			0
$601$	−15.0195	+	26.0146i	−0.612659	+	1.06116i	0.378132	+	0.925752i	$0.376567\pi$
$601$	−15.0195	+	26.0146i	−0.612659	+	1.06116i	−0.990790	+	0.135404i	$0.956767\pi$
$602$	−5.37705	+	30.4948i	−0.219152	+	1.24287i
$603$	−4.38344	+	3.67814i	−0.178507	+	0.149785i
$604$	−8.29813	−	6.96296i	−0.337646	−	0.283319i
$605$		0			0
$606$	10.9889	+	3.99964i	0.446394	+	0.162474i
$607$	−29.3882			−1.19283			−0.596415	−	0.802676i	$-0.703409\pi$
$607$	−29.3882			−1.19283			−0.596415	+	0.802676i	$0.703409\pi$
$608$	10.7939	−	33.4848i	0.437750	−	1.35799i
$609$	54.8180			2.22134
$610$		0			0
$611$	−4.11887	−	23.3593i	−0.166632	−	0.945015i
$612$	−0.0381250	−	0.0319907i	−0.00154111	−	0.00129315i
$613$	4.22183	−	3.54254i	0.170518	−	0.143082i	−0.553535	−	0.832826i	$-0.686721\pi$
$613$	4.22183	−	3.54254i	0.170518	−	0.143082i	0.724053	+	0.689744i	$0.242277\pi$
$614$	2.06644	−	11.7194i	0.0833948	−	0.472955i
$615$		0			0
$616$	0.261736	+	0.453340i	0.0105456	+	0.0182656i
$617$	43.1381	−	15.7010i	1.73667	−	0.632098i	0.737606	−	0.675232i	$-0.235956\pi$
$617$	43.1381	−	15.7010i	1.73667	−	0.632098i	0.999069	+	0.0431340i	$0.0137342\pi$
$618$	−1.18630	+	0.431779i	−0.0477201	+	0.0173687i
$619$	0.239303	+	0.414484i	0.00961839	+	0.0166595i	0.870795	−	0.491647i	$-0.163605\pi$
$619$	0.239303	+	0.414484i	0.00961839	+	0.0166595i	−0.861176	+	0.508307i	$0.830272\pi$
$620$		0			0
$621$	3.05900	−	17.3485i	0.122754	−	0.696170i
$622$	−39.3179	+	32.9916i	−1.57650	+	1.32284i
$623$	20.7188	+	17.3851i	0.830081	+	0.696521i
$624$	−3.72925	−	21.1497i	−0.149290	−	0.846664i
$625$		0			0
$626$	−12.2075			−0.487912
$627$	−6.75701	+	4.24412i	−0.269849	+	0.169494i
$628$	−24.3083			−0.970008
$629$	0.0409104	+	0.0148902i	0.00163120	+	0.000593710i
$630$		0			0
$631$	12.9110	+	10.8336i	0.513980	+	0.431281i	0.862527	−	0.506011i	$-0.168880\pi$
$631$	12.9110	+	10.8336i	0.513980	+	0.431281i	−0.348547	+	0.937291i	$0.613325\pi$
$632$	1.19727	−	1.00463i	0.0476248	−	0.0399620i
$633$	−3.78144	+	21.4456i	−0.150299	+	0.852387i
$634$	16.0473	−	27.7948i	0.637321	−	1.10387i
$635$		0			0
$636$	22.5857	−	8.22051i	0.895580	−	0.325964i
$637$	−7.12299	+	2.59256i	−0.282223	+	0.102721i
$638$	9.08156	+	15.7297i	0.359543	+	0.622746i
$639$	−3.85283	+	6.67329i	−0.152416	+	0.263991i
$640$		0			0
$641$	17.5433	−	14.7206i	0.692920	−	0.581429i	−0.226830	−	0.973934i	$-0.572836\pi$
$641$	17.5433	−	14.7206i	0.692920	−	0.581429i	0.919750	+	0.392506i	$0.128392\pi$
$642$	37.6367	+	31.5809i	1.48540	+	1.24640i
$643$	1.49019	+	8.45131i	0.0587675	+	0.333287i	0.999990	−	0.00450051i	$-0.00143256\pi$
$643$	1.49019	+	8.45131i	0.0587675	+	0.333287i	−0.941222	+	0.337788i	$0.890321\pi$
$644$	−23.5381	−	8.56716i	−0.927530	−	0.337593i
$645$		0			0
$646$	0.230328	+	0.254613i	0.00906215	+	0.0100176i
$647$	27.2647			1.07188			0.535942	−	0.844255i	$-0.319957\pi$
$647$	27.2647			1.07188			0.535942	+	0.844255i	$0.319957\pi$
$648$	1.72783	+	0.628880i	0.0678757	+	0.0247047i
$649$	0.464077	+	2.63191i	0.0182166	+	0.103312i
$650$		0			0
$651$	42.2183	−	35.4254i	1.65467	−	1.38843i
$652$	0.201779	−	1.14435i	0.00790228	−	0.0448160i
$653$	−13.1299	+	22.7417i	−0.513813	+	0.889950i	0.486059	+	0.873926i	$0.338434\pi$
$653$	−13.1299	+	22.7417i	−0.513813	+	0.889950i	−0.999872	+	0.0160238i	$0.994899\pi$
$654$	29.2796	+	50.7138i	1.14492	+	1.98307i
$655$		0			0
$656$	43.3272	−	15.7698i	1.69164	−	0.615708i
$657$	0.274551	+	0.475536i	0.0107113	+	0.0185524i
$658$	−25.0534	+	43.3938i	−0.976685	+	1.69167i
$659$	−3.99590	+	22.6619i	−0.155658	+	0.882781i	0.802524	+	0.596620i	$0.203490\pi$
$659$	−3.99590	+	22.6619i	−0.155658	+	0.882781i	−0.958182	+	0.286160i	$0.907621\pi$
$660$		0			0
$661$	23.4408	+	19.6692i	0.911742	+	0.765042i	0.972450	−	0.233114i	$-0.0748914\pi$
$661$	23.4408	+	19.6692i	0.911742	+	0.765042i	−0.0607080	+	0.998156i	$0.519336\pi$
$662$	−4.97423	−	28.2102i	−0.193329	−	1.09642i
$663$	0.205911	+	0.0749455i	0.00799693	+	0.00291064i
$664$	1.68807			0.0655100
$665$		0			0
$666$	1.38264			0.0535763
$667$	−34.0234	−	12.3835i	−1.31739	−	0.479491i
$668$	−8.02930	−	45.5364i	−0.310663	−	1.76186i
$669$	10.9400	+	9.17973i	0.422964	+	0.354909i
$670$		0			0
$671$	−1.67761	+	9.51422i	−0.0647636	+	0.367292i
$672$	−23.7165	+	41.0781i	−0.914883	+	1.58462i
$673$	−18.9334	−	32.7936i	−0.729828	−	1.26410i	−0.956956	−	0.290234i	$-0.906267\pi$
$673$	−18.9334	−	32.7936i	−0.729828	−	1.26410i	0.227128	−	0.973865i	$-0.427066\pi$
$674$	−4.08422	+	1.48654i	−0.157318	+	0.0572592i
$675$		0			0
$676$	4.42761	+	7.66885i	0.170293	+	0.294956i
$677$	−21.8471	+	37.8403i	−0.839654	+	1.45432i	0.0505308	+	0.998723i	$0.483909\pi$
$677$	−21.8471	+	37.8403i	−0.839654	+	1.45432i	−0.890184	+	0.455600i	$0.849425\pi$
$678$	−1.71053	+	9.70091i	−0.0656926	+	0.372561i
$679$	18.4484	−	15.4800i	0.707983	−	0.594068i
$680$		0			0
$681$	1.38672	+	7.86447i	0.0531392	+	0.301367i
$682$	17.1593	+	6.24549i	0.657065	+	0.239152i
$683$	−15.0878			−0.577320			−0.288660	−	0.957432i	$-0.593210\pi$
$683$	−15.0878			−0.577320			−0.288660	+	0.957432i	$0.593210\pi$
$684$	4.92222	+	2.60254i	0.188206	+	0.0995104i
$685$		0			0
$686$	−26.0724	−	9.48956i	−0.995447	−	0.362313i
$687$	7.45062	+	42.2546i	0.284259	+	1.61211i
$688$	−14.4899	−	12.1584i	−0.552421	−	0.463536i
$689$	−13.7368	+	11.5266i	−0.523331	+	0.439127i
$690$		0			0
$691$	−5.36034	+	9.28438i	−0.203917	+	0.353194i	−0.949787	−	0.312897i	$-0.898701\pi$
$691$	−5.36034	+	9.28438i	−0.203917	+	0.353194i	0.745870	+	0.666091i	$0.232034\pi$
$692$	−11.9541	−	20.7052i	−0.454428	−	0.787093i
$693$	1.71303	−	0.623493i	0.0650727	−	0.0236845i
$694$	−20.9964	+	7.64207i	−0.797013	+	0.290089i
$695$		0			0
$696$	1.55793	−	2.69841i	0.0590531	−	0.102283i
$697$	−0.0816935	+	0.463307i	−0.00309436	+	0.0175490i
$698$	54.7371	−	45.9299i	2.07183	−	1.73847i
$699$	15.9842	+	13.4123i	0.604578	+	0.507301i
$700$		0			0
$701$	−23.0611	−	8.39354i	−0.871005	−	0.317020i	−0.132431	−	0.991192i	$-0.542278\pi$
$701$	−23.0611	−	8.39354i	−0.871005	−	0.317020i	−0.738574	+	0.674172i	$0.764500\pi$
$702$	−27.1501			−1.02472
$703$	−4.82476	−	0.666644i	−0.181969	−	0.0251429i
$704$	−8.36023			−0.315088
$705$		0			0
$706$	−7.78994	−	44.1790i	−0.293178	−	1.66270i
$707$	7.20958	+	6.04956i	0.271144	+	0.227517i
$708$	8.43046	−	7.07399i	0.316836	−	0.265857i
$709$	−7.43295	+	42.1543i	−0.279150	+	1.58314i	0.446312	+	0.894878i	$0.352737\pi$
$709$	−7.43295	+	42.1543i	−0.279150	+	1.58314i	−0.725462	+	0.688262i	$0.758374\pi$
$710$		0			0
$711$	−2.72141	−	4.71362i	−0.102061	−	0.176775i
$712$	1.44461	−	0.525795i	0.0541391	−	0.0197050i
$713$	−34.2059	+	12.4499i	−1.28102	+	0.466254i
$714$	−0.231448	−	0.400880i	−0.00866173	−	0.0150026i
$715$		0			0
$716$	2.16208	−	12.2618i	0.0808007	−	0.458244i
$717$	−3.96820	+	3.32971i	−0.148195	+	0.124350i
$718$	−14.7255	−	12.3562i	−0.549551	−	0.461128i
$719$	3.69371	+	20.9481i	0.137752	+	0.781231i	0.972904	+	0.231211i	$0.0742688\pi$
$719$	3.69371	+	20.9481i	0.137752	+	0.781231i	−0.835152	+	0.550020i	$0.814620\pi$
$720$		0			0
$721$	−1.01601			−0.0378381
$722$	−31.1796	−	22.4326i	−1.16038	−	0.834854i
$723$	21.1987			0.788388
$724$	12.1152	+	4.40959i	0.450259	+	0.163881i
$725$		0			0
$726$	−29.6455	−	24.8755i	−1.10025	−	0.923217i
$727$	8.06976	−	6.77133i	0.299291	−	0.251135i	−0.480758	−	0.876853i	$-0.659639\pi$
$727$	8.06976	−	6.77133i	0.299291	−	0.251135i	0.780049	+	0.625718i	$0.215194\pi$
$728$	−0.279271	+	1.58383i	−0.0103505	+	0.0587005i
$729$	−9.73641	+	16.8640i	−0.360608	+	0.624591i
$730$		0			0
$731$	0.181359	−	0.0660091i	0.00670779	−	0.00244144i
$732$	37.3839	−	13.6066i	1.38175	−	0.502916i
$733$	−12.5446	−	21.7279i	−0.463346	−	0.802538i	0.535779	−	0.844358i	$-0.320018\pi$
$733$	−12.5446	−	21.7279i	−0.463346	−	0.802538i	−0.999125	+	0.0418196i	$0.986685\pi$
$734$	−2.20681	+	3.82230i	−0.0814548	+	0.141084i
$735$		0			0
$736$	23.9995	−	20.1380i	0.884634	−	0.742296i
$737$	−6.89797	−	5.78809i	−0.254090	−	0.213207i
$738$	2.59447	+	14.7140i	0.0955039	+	0.541629i
$739$	−26.7511	−	9.73660i	−0.984054	−	0.358166i	−0.200639	−	0.979665i	$-0.564302\pi$
$739$	−26.7511	−	9.73660i	−0.984054	−	0.358166i	−0.783415	+	0.621499i	$0.786524\pi$
$740$		0			0
$741$	−24.2841	−	3.35537i	−0.892099	−	0.123262i
$742$	37.8811			1.39066
$743$	−9.54830	−	3.47530i	−0.350293	−	0.127496i	0.160880	−	0.986974i	$-0.448567\pi$
$743$	−9.54830	−	3.47530i	−0.350293	−	0.127496i	−0.511173	+	0.859478i	$0.670789\pi$
$744$	−0.543966	−	3.08498i	−0.0199427	−	0.113101i
$745$		0			0
$746$	19.1114	−	16.0364i	0.699718	−	0.587133i
$747$	1.02082	−	5.78934i	0.0373498	−	0.211821i
$748$	0.0391591	−	0.0678256i	0.00143180	−	0.00247995i
$749$	19.7703	+	34.2432i	0.722392	+	1.25122i
$750$		0			0
$751$	24.1407	−	8.78648i	0.880905	−	0.320623i	0.138330	−	0.990386i	$-0.455826\pi$
$751$	24.1407	−	8.78648i	0.880905	−	0.320623i	0.742575	+	0.669763i	$0.233604\pi$
$752$	−15.3040	−	26.5072i	−0.558078	−	0.966620i
$753$	26.0074	−	45.0461i	0.947762	−	1.64157i
$754$	−9.68999	+	54.9547i	−0.352889	+	2.00133i
$755$		0			0
$756$	22.4351	+	18.8252i	0.815955	+	0.684668i
$757$	5.48348	+	31.0983i	0.199300	+	1.13029i	0.906160	+	0.422935i	$0.139000\pi$
$757$	5.48348	+	31.0983i	0.199300	+	1.13029i	−0.706860	+	0.707354i	$0.749889\pi$
$758$	35.1471	+	12.7925i	1.27660	+	0.464644i
$759$	−7.10559			−0.257917
$760$		0			0
$761$	−3.42183			−0.124041			−0.0620207	−	0.998075i	$-0.519754\pi$
$761$	−3.42183			−0.124041			−0.0620207	+	0.998075i	$0.519754\pi$
$762$	−55.8760	−	20.3372i	−2.02417	−	0.736738i
$763$	8.18375	+	46.4123i	0.296272	+	1.68024i
$764$	−29.8377	−	25.0368i	−1.07949	−	0.905801i
$765$		0			0
$766$	4.01327	−	22.7604i	0.145005	−	0.822365i
$767$	−4.10537	+	7.11071i	−0.148236	+	0.256753i
$768$	−13.7976	−	23.8982i	−0.497878	−	0.862351i
$769$	26.7893	−	9.75052i	0.966048	−	0.351613i	0.189648	−	0.981852i	$-0.439265\pi$
$769$	26.7893	−	9.75052i	0.966048	−	0.351613i	0.776401	+	0.630239i	$0.217043\pi$
$770$		0			0
$771$	−19.2552	−	33.3510i	−0.693459	−	1.20111i
$772$	−24.9459	+	43.2076i	−0.897824	+	1.55508i
$773$	−0.247597	+	1.40419i	−0.00890545	+	0.0505053i	−0.988937	−	0.148338i	$-0.952608\pi$
$773$	−0.247597	+	1.40419i	−0.00890545	+	0.0505053i	0.980031	+	0.198844i	$0.0637186\pi$
$774$	4.69535	−	3.93987i	0.168771	−	0.141616i
$775$		0			0
$776$	−0.237699	−	1.34806i	−0.00853291	−	0.0483925i
$777$	6.17070	+	2.24595i	0.221372	+	0.0805730i
$778$	25.3182			0.907701
$779$	−1.95910	−	52.5958i	−0.0701920	−	1.88444i
$780$		0			0
$781$	−11.3947	−	4.14732i	−0.407733	−	0.148403i
$782$	0.0530912	+	0.301095i	0.00189854	+	0.0107671i
$783$	32.4290	+	27.2112i	1.15892	+	0.972448i
$784$	−7.49302	+	6.28739i	−0.267608	+	0.224550i
$785$		0			0
$786$	−1.61795	+	2.80237i	−0.0577103	+	0.0999572i
$787$	12.1600	+	21.0617i	0.433456	+	0.750768i	0.997168	−	0.0752034i	$-0.0239606\pi$
$787$	12.1600	+	21.0617i	0.433456	+	0.750768i	−0.563712	+	0.825971i	$0.690627\pi$
$788$	−13.1422	+	4.78338i	−0.468172	+	0.170401i
$789$	17.0777	−	6.21577i	0.607982	−	0.221287i
$790$		0			0
$791$	−3.96386	+	6.86560i	−0.140938	+	0.244113i
$792$	0.0179930	−	0.102043i	0.000639354	−	0.00362596i
$793$	−22.7373	+	19.0788i	−0.807424	+	0.677509i
$794$	−18.1972	−	15.2693i	−0.645794	−	0.541885i
$795$		0			0
$796$	−6.19479	−	2.25472i	−0.219569	−	0.0799164i
$797$	−33.5714			−1.18916			−0.594580	−	0.804037i	$-0.702681\pi$
$797$	−33.5714			−1.18916			−0.594580	+	0.804037i	$0.702681\pi$
$798$	34.7414	+	38.4044i	1.22983	+	1.35950i
$799$	0.312303			0.0110485
$800$		0			0
$801$	−0.929654	−	5.27233i	−0.0328477	−	0.186289i
$802$	−22.6751	−	19.0266i	−0.800684	−	0.671854i
$803$	−0.661932	+	0.555427i	−0.0233591	+	0.0196006i
$804$	−6.43895	+	36.5171i	−0.227084	+	1.28786i
$805$		0			0
$806$	28.0509	+	48.5856i	0.988052	+	1.71136i
$807$	−8.16983	+	2.97357i	−0.287592	+	0.104675i
$808$	0.502685	−	0.182962i	0.0176844	−	0.00643659i
$809$	−9.12037	−	15.7970i	−0.320655	−	0.555391i	0.659968	−	0.751294i	$-0.270570\pi$
$809$	−9.12037	−	15.7970i	−0.320655	−	0.555391i	−0.980623	+	0.195902i	$0.937236\pi$
$810$		0			0
$811$	−6.34578	+	35.9887i	−0.222830	+	1.26373i	0.643959	+	0.765060i	$0.277291\pi$
$811$	−6.34578	+	35.9887i	−0.222830	+	1.26373i	−0.866790	+	0.498674i	$0.833820\pi$
$812$	46.1114	−	38.6921i	1.61819	−	1.35783i
$813$	−32.2277	−	27.0422i	−1.13027	−	0.948413i
$814$	0.377821	+	2.14273i	0.0132426	+	0.0751026i
$815$		0			0
$816$	0.282761			0.00989863
$817$	−18.2842	+	11.4844i	−0.639682	+	0.401788i
$818$	25.7712			0.901069
$819$	5.26294	+	1.91555i	0.183902	+	0.0669348i
$820$		0			0
$821$	8.13847	+	6.82899i	0.284035	+	0.238333i	0.773662	−	0.633598i	$-0.218423\pi$
$821$	8.13847	+	6.82899i	0.284035	+	0.238333i	−0.489628	+	0.871932i	$0.662867\pi$
$822$	14.9336	−	12.5308i	0.520869	−	0.437061i
$823$	6.43574	−	36.4989i	0.224336	−	1.27227i	−0.639615	−	0.768696i	$-0.720906\pi$
$823$	6.43574	−	36.4989i	0.224336	−	1.27227i	0.863951	−	0.503577i	$-0.167983\pi$
$824$	−0.0288749	+	0.0500128i	−0.00100591	+	0.00174228i
$825$		0			0
$826$	16.2989	−	5.93231i	0.567111	−	0.206411i
$827$	26.1420	−	9.51490i	0.909045	−	0.330865i	0.155174	−	0.987887i	$-0.450406\pi$
$827$	26.1420	−	9.51490i	0.909045	−	0.330865i	0.753871	+	0.657022i	$0.228184\pi$
$828$	2.47911	+	4.29394i	0.0861549	+	0.149225i
$829$	6.90991	−	11.9683i	0.239991	−	0.415677i	−0.720720	−	0.693226i	$-0.756189\pi$
$829$	6.90991	−	11.9683i	0.239991	−	0.415677i	0.960711	+	0.277549i	$0.0895221\pi$
$830$		0			0
$831$	−34.2926	+	28.7749i	−1.18960	+	0.998190i
$832$	−19.6759	−	16.5100i	−0.682139	−	0.572383i
$833$	−0.0173307	−	0.0982871i	−0.000600472	−	0.00340545i
$834$	−9.85798	−	3.58801i	−0.341354	−	0.124243i
$835$		0			0
$836$	−2.68820	+	8.33932i	−0.0929732	+	0.288422i
$837$	42.5602			1.47110
$838$	−5.40657	−	1.96783i	−0.186767	−	0.0679776i
$839$	−1.11616	−	6.33006i	−0.0385341	−	0.218538i	0.959460	−	0.281845i	$-0.0909464\pi$
$839$	−1.11616	−	6.33006i	−0.0385341	−	0.218538i	−0.997994	+	0.0633071i	$0.979835\pi$
$840$		0			0
$841$	44.4370	−	37.2871i	1.53231	−	1.28576i
$842$	3.91439	−	22.1996i	0.134899	−	0.765048i
$843$	−9.80960	+	16.9907i	−0.337861	+	0.585192i
$844$	11.9561	+	20.7085i	0.411545	+	0.712817i
$845$		0			0
$846$	9.32017	−	3.39226i	0.320434	−	0.116628i
$847$	−15.5726	−	26.9726i	−0.535081	−	0.926788i
$848$	−11.5699	+	20.0396i	−0.397311	+	0.688163i
$849$	10.1889	−	57.7839i	0.349681	−	1.98314i
$850$		0			0
$851$	−3.32254	−	2.78794i	−0.113895	−	0.0955695i
$852$	8.67089	+	49.1751i	0.297060	+	1.68471i
$853$	24.8033	+	9.02767i	0.849250	+	0.309102i	0.729734	−	0.683731i	$-0.239644\pi$
$853$	24.8033	+	9.02767i	0.849250	+	0.309102i	0.119515	+	0.992832i	$0.461866\pi$
$854$	62.7009			2.14558
$855$		0			0
$856$	2.24749			0.0768177
$857$	16.0036	+	5.82483i	0.546672	+	0.198973i	0.600567	−	0.799574i	$-0.294941\pi$
$857$	16.0036	+	5.82483i	0.546672	+	0.198973i	−0.0538950	+	0.998547i	$0.517164\pi$
$858$	1.90166	+	10.7848i	0.0649215	+	0.368188i
$859$	18.9375	+	15.8905i	0.646140	+	0.542176i	0.905897	−	0.423498i	$-0.139198\pi$
$859$	18.9375	+	15.8905i	0.646140	+	0.542176i	−0.259757	+	0.965674i	$0.583642\pi$
$860$		0			0
$861$	−12.3222	+	69.8826i	−0.419939	+	2.38159i
$862$	15.0977	−	26.1500i	0.514230	−	0.890673i
$863$	−0.519450	−	0.899714i	−0.0176823	−	0.0306266i	0.857049	−	0.515235i	$-0.172295\pi$
$863$	−0.519450	−	0.899714i	−0.0176823	−	0.0306266i	−0.874731	+	0.484609i	$0.838962\pi$
$864$	−34.4209	+	12.5282i	−1.17102	+	0.426218i
$865$		0			0
$866$	−39.1757	−	67.8542i	−1.33124	−	2.30578i
$867$	16.1532	−	27.9782i	0.548591	−	0.950188i
$868$	10.5087	−	59.5978i	0.356688	−	2.02288i
$869$	6.56122	−	5.50552i	0.222574	−	0.186762i
$870$		0			0
$871$	−4.80397	−	27.2447i	−0.162776	−	0.923150i
$872$	2.51722	+	0.916195i	0.0852440	+	0.0310263i
$873$	−4.76699			−0.161338
$874$	−12.8870	−	31.6842i	−0.435910	−	1.07174i
$875$		0			0
$876$	3.34366	+	1.21699i	0.112972	+	0.0411184i
$877$	−3.68173	−	20.8801i	−0.124323	−	0.705071i	−0.981708	−	0.190395i	$-0.939023\pi$
$877$	−3.68173	−	20.8801i	−0.124323	−	0.705071i	0.857385	−	0.514676i	$-0.172088\pi$
$878$	−48.6717	−	40.8404i	−1.64259	−	1.37830i
$879$	−9.26105	+	7.77094i	−0.312367	+	0.262107i
$880$		0			0
$881$	−7.84097	+	13.5810i	−0.264169	+	0.457554i	−0.967346	−	0.253461i	$-0.918431\pi$
$881$	−7.84097	+	13.5810i	−0.264169	+	0.457554i	0.703176	+	0.711015i	$0.251764\pi$
$882$	−1.58481	−	2.74497i	−0.0533633	−	0.0924279i
$883$	18.4562	−	6.71750i	0.621100	−	0.226062i	−0.0122532	−	0.999925i	$-0.503900\pi$
$883$	18.4562	−	6.71750i	0.621100	−	0.226062i	0.633353	+	0.773863i	$0.281678\pi$
$884$	0.226106	−	0.0822957i	0.00760476	−	0.00276790i
$885$		0			0
$886$	10.7659	−	18.6472i	0.361689	−	0.626464i
$887$	−4.30310	+	24.4041i	−0.144484	+	0.819408i	0.823296	+	0.567612i	$0.192133\pi$
$887$	−4.30310	+	24.4041i	−0.144484	+	0.819408i	−0.967780	+	0.251797i	$0.918979\pi$
$888$	0.285928	−	0.239922i	0.00959511	−	0.00805125i
$889$	−36.6589	−	30.7605i	−1.22950	−	1.03167i
$890$		0			0
$891$	9.46879	+	3.44636i	0.317216	+	0.115457i
$892$	15.6817			0.525063
$893$	−34.1586	+	7.34365i	−1.14307	+	0.245746i
$894$	−25.5339			−0.853980
$895$		0			0
$896$	0.754279	+	4.27773i	0.0251987	+	0.142909i
$897$	−16.7231	−	14.0323i	−0.558368	−	0.468526i
$898$	6.35566	−	5.33303i	0.212091	−	0.177966i
$899$	15.1899	−	86.1463i	0.506612	−	2.87314i
$900$		0			0
$901$	−0.118051	−	0.204471i	−0.00393286	−	0.00681191i
$902$	−22.0938	+	8.04150i	−0.735644	+	0.267753i
$903$	27.3551	−	9.95645i	0.910322	−	0.331330i
$904$	0.225306	+	0.390241i	0.00749355	+	0.0129792i
$905$		0			0
$906$	−3.46309	+	19.6402i	−0.115054	+	0.652501i
$907$	16.3342	−	13.7060i	0.542368	−	0.455100i	−0.329979	−	0.943988i	$-0.607042\pi$
$907$	16.3342	−	13.7060i	0.542368	−	0.455100i	0.872347	+	0.488888i	$0.162597\pi$
$908$	6.71744	+	5.63660i	0.222926	+	0.187057i
$909$	−0.323494	−	1.83463i	−0.0107296	−	0.0608507i
$910$		0			0
$911$	−34.0175			−1.12705			−0.563524	−	0.826100i	$-0.690555\pi$
$911$	−34.0175			−1.12705			−0.563524	+	0.826100i	$0.690555\pi$
$912$	−30.9274	+	6.64900i	−1.02411	+	0.220170i
$913$	9.25091			0.306160
$914$	17.5902	+	6.40232i	0.581833	+	0.211770i
$915$		0			0
$916$	36.0917	+	30.2846i	1.19250	+	1.00063i
$917$	−1.99497	+	1.67397i	−0.0658796	+	0.0552795i
$918$	0.0620741	−	0.352040i	0.00204875	−	0.0116190i
$919$	20.8710	−	36.1496i	0.688470	−	1.19246i	−0.283863	−	0.958865i	$-0.591616\pi$
$919$	20.8710	−	36.1496i	0.688470	−	1.19246i	0.972333	−	0.233600i	$-0.0750505\pi$
$920$		0			0
$921$	−10.5128	+	3.82634i	−0.346408	+	0.126082i
$922$	−12.6256	+	4.59534i	−0.415802	+	0.151340i
$923$	−18.6272	−	32.2633i	−0.613123	−	1.06196i
$924$	5.90655	−	10.2304i	0.194311	−	0.336557i
$925$		0			0
$926$	−34.5268	+	28.9715i	−1.13462	+	0.952061i
$927$	0.154060	+	0.129272i	0.00506001	+	0.00424585i
$928$	13.0734	+	74.1429i	0.429155	+	2.43386i
$929$	21.5234	+	7.83389i	0.706161	+	0.257022i	0.670039	−	0.742326i	$-0.266277\pi$
$929$	21.5234	+	7.83389i	0.706161	+	0.257022i	0.0361220	+	0.999347i	$0.488500\pi$
$930$		0			0
$931$	4.20674	+	10.3428i	0.137870	+	0.338970i
$932$	22.9123			0.750517
$933$	45.3420	+	16.5032i	1.48443	+	0.540289i
$934$	5.43213	+	30.8071i	0.177745	+	1.00804i
$935$		0			0
$936$	0.243866	−	0.204627i	0.00797099	−	0.00668846i
$937$	−2.02604	+	11.4902i	−0.0661877	+	0.375369i	0.933664	+	0.358150i	$0.116592\pi$
$937$	−2.02604	+	11.4902i	−0.0661877	+	0.375369i	−0.999852	+	0.0172191i	$0.994519\pi$
$938$	−29.2206	+	50.6116i	−0.954088	+	1.65253i
$939$	5.73823	+	9.93890i	0.187260	+	0.324344i
$940$		0			0
$941$	−52.0967	+	18.9616i	−1.69830	+	0.618132i	−0.995630	−	0.0933820i	$-0.970232\pi$
$941$	−52.0967	+	18.9616i	−1.69830	+	0.618132i	−0.702672	+	0.711514i	$0.748010\pi$
$942$	22.3765	+	38.7573i	0.729066	+	1.26278i
$943$	23.4345	−	40.5898i	0.763133	−	1.32179i
$944$	−1.83983	+	10.4342i	−0.0598815	+	0.339605i
$945$		0			0
$946$	7.38881	+	6.19995i	0.240231	+	0.201578i
$947$	1.61575	+	9.16340i	0.0525049	+	0.297770i	0.999741	−	0.0227671i	$-0.00724762\pi$
$947$	1.61575	+	9.16340i	0.0525049	+	0.297770i	−0.947236	+	0.320537i	$0.896137\pi$
$948$	−33.1431	−	12.0631i	−1.07644	−	0.391792i
$949$	−2.65474			−0.0861765
$950$		0			0
$951$	−30.1726			−0.978413
$952$	−0.0198980	−	0.00724229i	−0.000644899	−	0.000234724i
$953$	2.99473	+	16.9840i	0.0970090	+	0.550165i	0.994113	+	0.108346i	$0.0345555\pi$
$953$	2.99473	+	16.9840i	0.0970090	+	0.550165i	−0.897104	+	0.441819i	$0.854333\pi$
$954$	−5.74403	−	4.81981i	−0.185970	−	0.156047i
$955$		0			0
$956$	−0.987737	+	5.60173i	−0.0319457	+	0.181173i
$957$	8.53768	−	14.7877i	0.275984	−	0.478018i
$958$	−32.5538	−	56.3848i	−1.05177	−	1.82171i
$959$	14.7429	−	5.36598i	0.476073	−	0.173276i
$960$		0			0
$961$	−28.4723	−	49.3154i	−0.918460	−	1.59082i
$962$	−3.34232	+	5.78908i	−0.107761	+	0.186647i
$963$	1.35911	−	7.70789i	0.0437967	−	0.248383i
$964$	17.8318	−	14.9626i	0.574323	−	0.481914i
$965$		0			0
$966$	8.00798	+	45.4155i	0.257652	+	1.46122i
$967$	3.46405	+	1.26081i	0.111396	+	0.0405449i	0.397117	−	0.917768i	$-0.370011\pi$
$967$	3.46405	+	1.26081i	0.111396	+	0.0405449i	−0.285721	+	0.958313i	$0.592233\pi$
$968$	−1.77029			−0.0568994
$969$	0.0990285	−	0.307206i	0.00318125	−	0.00986889i
$970$		0			0
$971$	21.3740	+	7.77948i	0.685923	+	0.249656i	0.661389	−	0.750043i	$-0.269967\pi$
$971$	21.3740	+	7.77948i	0.685923	+	0.249656i	0.0245344	+	0.999699i	$0.492190\pi$
$972$	−2.27135	−	12.8815i	−0.0728537	−	0.413174i
$973$	−6.46760	−	5.42696i	−0.207342	−	0.173980i
$974$	5.65472	−	4.74487i	0.181189	−	0.152036i
$975$		0			0
$976$	−19.1505	+	33.1697i	−0.612993	+	1.06174i
$977$	−22.5088	−	38.9865i	−0.720122	−	1.24729i	−0.960951	−	0.276720i	$-0.910753\pi$
$977$	−22.5088	−	38.9865i	−0.720122	−	1.24729i	0.240829	−	0.970568i	$-0.422581\pi$
$978$	−2.01029	+	0.731686i	−0.0642820	+	0.0233968i
$979$	7.91669	−	2.88144i	0.253018	−	0.0920911i
$980$		0			0
$981$	4.66436	−	8.07891i	0.148922	−	0.257940i
$982$	1.59679	−	9.05587i	0.0509557	−	0.288984i
$983$	−32.4157	+	27.2000i	−1.03390	+	0.867544i	−0.991310	−	0.131548i	$-0.958005\pi$
$983$	−32.4157	+	27.2000i	−1.03390	+	0.867544i	−0.0425891	+	0.999093i	$0.513561\pi$
$984$	3.08977	+	2.59262i	0.0984982	+	0.0826498i
$985$		0			0
$986$	−0.690411	−	0.251289i	−0.0219872	−	0.00800267i
$987$	47.1061			1.49940
$988$	−22.7955	+	14.3180i	−0.725220	+	0.455515i
$989$	−19.2274			−0.611397
$990$		0			0
$991$	5.41069	+	30.6856i	0.171876	+	0.974759i	0.941688	+	0.336488i	$0.109239\pi$
$991$	5.41069	+	30.6856i	0.171876	+	0.974759i	−0.769812	+	0.638271i	$0.779650\pi$
$992$	57.9824	+	48.6530i	1.84094	+	1.54473i
$993$	−20.6295	+	17.3102i	−0.654657	+	0.549322i
$994$	−13.6659	+	77.5032i	−0.433456	+	2.45825i
$995$		0			0
$996$	−19.0472	−	32.9908i	−0.603534	−	1.04535i
$997$	36.5451	−	13.3013i	1.15740	−	0.421258i	0.309229	−	0.950987i	$-0.399929\pi$
$997$	36.5451	−	13.3013i	1.15740	−	0.421258i	0.848166	+	0.529730i	$0.177707\pi$
$998$	41.4579	−	15.0895i	1.31233	−	0.477648i
$999$	2.53557	+	4.39173i	0.0802218	+	0.138948i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.l.b.251.1		18
5.2	odd	4		475.2.u.c.99.6		36
5.3	odd	4		475.2.u.c.99.1		36
5.4	even	2		95.2.k.b.61.3	✓	18
15.14	odd	2		855.2.bs.b.631.1		18
19.5	even	9	inner	475.2.l.b.176.1		18
19.9	even	9		9025.2.a.ce.1.9		9
19.10	odd	18		9025.2.a.cd.1.1		9
95.9	even	18		1805.2.a.t.1.1		9
95.24	even	18		95.2.k.b.81.3	yes	18
95.29	odd	18		1805.2.a.u.1.9		9
95.43	odd	36		475.2.u.c.24.6		36
95.62	odd	36		475.2.u.c.24.1		36
285.119	odd	18		855.2.bs.b.271.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.61.3	✓	18	5.4	even	2
95.2.k.b.81.3	yes	18	95.24	even	18
475.2.l.b.176.1		18	19.5	even	9	inner
475.2.l.b.251.1		18	1.1	even	1	trivial
475.2.u.c.24.1		36	95.62	odd	36
475.2.u.c.24.6		36	95.43	odd	36
475.2.u.c.99.1		36	5.3	odd	4
475.2.u.c.99.6		36	5.2	odd	4
855.2.bs.b.271.1		18	285.119	odd	18
855.2.bs.b.631.1		18	15.14	odd	2
1805.2.a.t.1.1		9	95.9	even	18
1805.2.a.u.1.9		9	95.29	odd	18
9025.2.a.cd.1.1		9	19.10	odd	18
9025.2.a.ce.1.9		9	19.9	even	9

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.89970 - 0.691434i) q^{2} +(0.330026 + 1.87167i) q^{3} +(1.59869 + 1.34146i) q^{4} +(0.667187 - 3.78381i) q^{6} +(1.54609 - 2.67790i) q^{7} +(-0.0878797 - 0.152212i) q^{8} +(-0.575162 + 0.209342i) q^{9} +(-0.481594 - 0.834145i) q^{11} +(-1.98316 + 3.43494i) q^{12} +(0.513859 - 2.91424i) q^{13} +(-4.78870 + 4.01819i) q^{14} +(-0.663086 - 3.76055i) q^{16} +(0.0366124 + 0.0133258i) q^{17} +1.23738 q^{18} +(-4.31788 - 0.596607i) q^{19} +(5.52241 + 2.00999i) q^{21} +(0.338127 + 1.91762i) q^{22} +(-2.97348 - 2.49504i) q^{23} +(0.255888 - 0.214716i) q^{24} +(-2.99118 + 5.18088i) q^{26} +(2.26918 + 3.93034i) q^{27} +(6.06401 - 2.20712i) q^{28} +(8.76529 - 3.19030i) q^{29} +(4.68894 - 8.12148i) q^{31} +(-1.40155 + 7.94857i) q^{32} +(1.40231 - 1.17668i) q^{33} +(-0.0603386 - 0.0506301i) q^{34} +(-1.20033 - 0.436884i) q^{36} +1.11739 q^{37} +(7.79016 + 4.11890i) q^{38} +5.62409 q^{39} +(2.09674 + 11.8912i) q^{41} +(-9.10114 - 7.63676i) q^{42} +(3.79459 - 3.18404i) q^{43} +(0.349053 - 1.97958i) q^{44} +(3.92356 + 6.79580i) q^{46} +(7.53217 - 2.74148i) q^{47} +(6.81968 - 2.48216i) q^{48} +(-1.28078 - 2.21837i) q^{49} +(-0.0128585 + 0.0729242i) q^{51} +(4.73083 - 3.96964i) q^{52} +(-4.64208 - 3.89517i) q^{53} +(-1.59319 - 9.03545i) q^{54} -0.543479 q^{56} +(-0.308361 - 8.27855i) q^{57} -18.8573 q^{58} +(-2.60732 - 0.948987i) q^{59} +(-7.68360 - 6.44731i) q^{61} +(-14.5230 + 12.1863i) q^{62} +(-0.328654 + 1.86389i) q^{63} +(4.33987 - 7.51688i) q^{64} +(-3.47756 + 1.26573i) q^{66} +(8.78501 - 3.19748i) q^{67} +(0.0406557 + 0.0704178i) q^{68} +(3.68858 - 6.38881i) q^{69} +(9.64404 - 8.09231i) q^{71} +(0.0824094 + 0.0691497i) q^{72} +(-0.155782 - 0.883486i) q^{73} +(-2.12271 - 0.772603i) q^{74} +(-6.10262 - 6.74604i) q^{76} -2.97835 q^{77} +(-10.6841 - 3.88869i) q^{78} +(1.54415 + 8.75731i) q^{79} +(-8.01404 + 6.72458i) q^{81} +(4.23882 - 24.0395i) q^{82} +(-4.80224 + 8.31772i) q^{83} +(6.13229 + 10.6214i) q^{84} +(-9.41012 + 3.42500i) q^{86} +(8.86398 + 15.3529i) q^{87} +(-0.0846446 + 0.146609i) q^{88} +(-1.51886 + 8.61386i) q^{89} +(-7.00958 - 5.88173i) q^{91} +(-1.40667 - 7.97760i) q^{92} +(16.7482 + 6.09585i) q^{93} -16.2044 q^{94} -15.3397 q^{96} +(7.31855 + 2.66374i) q^{97} +(0.899233 + 5.09981i) q^{98} +(0.451616 + 0.378951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 12 q^{8} - 21 q^{9} - 6 q^{12} + 3 q^{13} + 24 q^{14} + 21 q^{16} + 24 q^{17} + 12 q^{18} - 12 q^{19} + 3 q^{21} - 15 q^{22} - 21 q^{23} + 21 q^{24} - 21 q^{26}+ \cdots + 3 q^{99}+O(q^{100}) \) 18 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 12 * q^8 - 21 * q^9 - 6 * q^12 + 3 * q^13 + 24 * q^14 + 21 * q^16 + 24 * q^17 + 12 * q^18 - 12 * q^19 + 3 * q^21 - 15 * q^22 - 21 * q^23 + 21 * q^24 - 21 * q^26 - 6 * q^27 + 24 * q^28 - 9 * q^29 + 30 * q^31 - 45 * q^32 + 3 * q^33 + 24 * q^34 - 21 * q^36 + 60 * q^37 + 15 * q^38 + 12 * q^39 - 6 * q^41 - 39 * q^42 + 6 * q^43 - 30 * q^44 + 21 * q^46 - 33 * q^47 + 63 * q^48 - 3 * q^49 + 27 * q^51 - 9 * q^52 - 24 * q^53 + 30 * q^54 - 72 * q^56 + 30 * q^57 - 36 * q^58 + 18 * q^59 + 6 * q^61 - 12 * q^62 - 24 * q^63 - 24 * q^64 - 33 * q^66 + 24 * q^67 + 3 * q^68 + 27 * q^69 + 24 * q^71 - 18 * q^72 - 6 * q^73 - 39 * q^74 + 27 * q^76 - 24 * q^77 - 72 * q^78 + 9 * q^79 + 15 * q^81 + 57 * q^82 - 12 * q^84 - 33 * q^86 + 45 * q^87 - 39 * q^88 - 6 * q^89 - 6 * q^91 + 66 * q^92 + 72 * q^93 - 66 * q^94 - 18 * q^96 + 87 * q^97 - 39 * q^98 + 3 * q^99

Introduction

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