LMFDB - Embedded newform 350.2.o.c.243.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(143,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("350.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.o (of order $12$, degree $4$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			243.1
Root			$0.144868 + 1.25092i$ of defining polynomial
Character	$\chi$	$=$	350.243
Dual form			350.2.o.c.157.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-1.95290 - 0.523277i) q^{3} +(-0.866025 + 0.500000i) q^{4} +2.02179i q^{6} +(1.90155 + 1.83959i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.941911 + 0.543813i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-1.95290 - 0.523277i) q^{3} +(-0.866025 + 0.500000i) q^{4} +2.02179i q^{6} +(1.90155 + 1.83959i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.941911 + 0.543813i) q^{9} +(2.01999 + 3.49872i) q^{11} +(1.95290 - 0.523277i) q^{12} +(0.204875 - 0.204875i) q^{13} +(1.28475 - 2.31288i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.527924 - 1.97024i) q^{17} +(0.281498 - 1.05057i) q^{18} +(3.10166 - 5.37224i) q^{19} +(-2.75092 - 4.58757i) q^{21} +(2.85669 - 2.85669i) q^{22} +(4.38350 - 1.17456i) q^{23} +(-1.01089 - 1.75092i) q^{24} +(-0.250919 - 0.144868i) q^{26} +(2.73397 + 2.73397i) q^{27} +(-2.56659 - 0.642357i) q^{28} +7.15869i q^{29} +(6.33287 - 3.65628i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-2.11403 - 7.88965i) q^{33} -2.03974 q^{34} -1.08763 q^{36} +(-1.19723 - 4.46814i) q^{37} +(-5.99195 - 1.60554i) q^{38} +(-0.507306 + 0.292893i) q^{39} +2.58745i q^{41} +(-3.71926 + 3.84454i) q^{42} +(4.97801 + 4.97801i) q^{43} +(-3.49872 - 2.01999i) q^{44} +(-2.26907 - 3.93014i) q^{46} +(0.304388 - 0.0815604i) q^{47} +(-1.42962 + 1.42962i) q^{48} +(0.231803 + 6.99616i) q^{49} +(-2.06196 + 3.57142i) q^{51} +(-0.0749894 + 0.279864i) q^{52} +(-2.14370 + 8.00039i) q^{53} +(1.93321 - 3.34841i) q^{54} +(0.0438127 + 2.64539i) q^{56} +(-8.86840 + 8.86840i) q^{57} +(6.91477 - 1.85281i) q^{58} +(-0.427702 - 0.740802i) q^{59} +(-5.99356 - 3.46038i) q^{61} +(-5.17076 - 5.17076i) q^{62} +(0.790700 + 2.76682i) q^{63} +1.00000i q^{64} +(-7.07367 + 4.08398i) q^{66} +(-3.05106 - 0.817530i) q^{67} +(0.527924 + 1.97024i) q^{68} -9.17514 q^{69} +7.12240 q^{71} +(0.281498 + 1.05057i) q^{72} +(11.1331 + 2.98311i) q^{73} +(-4.00603 + 2.31288i) q^{74} +6.20333i q^{76} +(-2.59511 + 10.3690i) q^{77} +(0.414214 + 0.414214i) q^{78} +(4.39618 + 2.53813i) q^{79} +(-5.53997 - 9.59552i) q^{81} +(2.49929 - 0.669683i) q^{82} +(-3.85372 + 3.85372i) q^{83} +(4.67615 + 2.59749i) q^{84} +(3.51999 - 6.09680i) q^{86} +(3.74598 - 13.9802i) q^{87} +(-1.04562 + 3.90231i) q^{88} +(1.53615 - 2.66069i) q^{89} +(0.766467 - 0.0126942i) q^{91} +(-3.20895 + 3.20895i) q^{92} +(-14.2807 + 3.82650i) q^{93} +(-0.157563 - 0.272906i) q^{94} +(1.75092 + 1.01089i) q^{96} +(-6.63103 - 6.63103i) q^{97} +(6.69778 - 2.03464i) q^{98} +4.39398i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} - 12 q^{11} + 8 q^{16} + 36 q^{17} + 8 q^{18} - 28 q^{21} + 8 q^{22} + 4 q^{23} + 12 q^{26} - 4 q^{28} + 24 q^{31} - 48 q^{33} - 8 q^{36} - 4 q^{37} - 24 q^{38} - 36 q^{42} + 8 q^{43} - 8 q^{46} - 12 q^{47} - 16 q^{51} + 28 q^{53} - 4 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{61} + 36 q^{63} - 32 q^{67} + 36 q^{68} + 16 q^{71} + 8 q^{72} + 12 q^{73} - 16 q^{77} - 16 q^{78} + 48 q^{82} + 12 q^{86} + 24 q^{87} + 4 q^{88} - 16 q^{91} - 8 q^{92} - 28 q^{93} + 12 q^{96} - 40 q^{98}+O(q^{100}) $ 16 * q - 8 * q^7 - 12 * q^11 + 8 * q^16 + 36 * q^17 + 8 * q^18 - 28 * q^21 + 8 * q^22 + 4 * q^23 + 12 * q^26 - 4 * q^28 + 24 * q^31 - 48 * q^33 - 8 * q^36 - 4 * q^37 - 24 * q^38 - 36 * q^42 + 8 * q^43 - 8 * q^46 - 12 * q^47 - 16 * q^51 + 28 * q^53 - 4 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^61 + 36 * q^63 - 32 * q^67 + 36 * q^68 + 16 * q^71 + 8 * q^72 + 12 * q^73 - 16 * q^77 - 16 * q^78 + 48 * q^82 + 12 * q^86 + 24 * q^87 + 4 * q^88 - 16 * q^91 - 8 * q^92 - 28 * q^93 + 12 * q^96 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	−1.95290	−	0.523277i	−1.12751	−	0.302114i	−0.353588	−	0.935401i	$-0.615039\pi$
$3$	−1.95290	−	0.523277i	−1.12751	−	0.302114i	−0.773917	+	0.633287i	$0.781705\pi$
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$			2.02179i			0.825391i
$7$	1.90155	+	1.83959i	0.718719	+	0.695300i
$7$	1.90155	+	1.83959i	0.718719	+	0.695300i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.941911	+	0.543813i	0.313970	+	0.181271i
$10$		0			0
$11$	2.01999	+	3.49872i	0.609049	+	1.05490i	0.991397	+	0.130886i	$0.0417820\pi$
$11$	2.01999	+	3.49872i	0.609049	+	1.05490i	−0.382349	+	0.924018i	$0.624885\pi$
$12$	1.95290	−	0.523277i	0.563753	−	0.151057i
$13$	0.204875	−	0.204875i	0.0568221	−	0.0568221i	−0.678125	−	0.734947i	$-0.737207\pi$
$13$	0.204875	−	0.204875i	0.0568221	−	0.0568221i	0.734947	+	0.678125i	$0.237207\pi$
$14$	1.28475	−	2.31288i	0.343364	−	0.618143i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	0.527924	−	1.97024i	0.128040	−	0.477853i	−0.871890	−	0.489703i	$-0.837105\pi$
$17$	0.527924	−	1.97024i	0.128040	−	0.477853i	0.999930	+	0.0118498i	$0.00377201\pi$
$18$	0.281498	−	1.05057i	0.0663498	−	0.247621i
$19$	3.10166	−	5.37224i	0.711571	−	1.23248i	−0.252697	−	0.967545i	$-0.581318\pi$
$19$	3.10166	−	5.37224i	0.711571	−	1.23248i	0.964267	−	0.264931i	$-0.0853491\pi$
$20$		0			0
$21$	−2.75092	−	4.58757i	−0.600300	−	1.00109i
$22$	2.85669	−	2.85669i	0.609049	−	0.609049i
$23$	4.38350	−	1.17456i	0.914023	−	0.244912i	0.228994	−	0.973428i	$-0.426456\pi$
$23$	4.38350	−	1.17456i	0.914023	−	0.244912i	0.685029	+	0.728516i	$0.259790\pi$
$24$	−1.01089	−	1.75092i	−0.206348	−	0.357405i
$25$		0			0
$26$	−0.250919	−	0.144868i	−0.0492094	−	0.0284110i
$27$	2.73397	+	2.73397i	0.526152	+	0.526152i
$28$	−2.56659	−	0.642357i	−0.485040	−	0.121394i
$29$			7.15869i			1.32934i	0.747139	+	0.664668i	$0.231427\pi$
$29$			7.15869i			1.32934i	−0.747139	+	0.664668i	$0.768573\pi$
$30$		0			0
$31$	6.33287	−	3.65628i	1.13742	−	0.656688i	0.191627	−	0.981468i	$-0.438624\pi$
$31$	6.33287	−	3.65628i	1.13742	−	0.656688i	0.945790	+	0.324780i	$0.105290\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	−2.11403	−	7.88965i	−0.368005	−	1.37341i
$34$	−2.03974			−0.349813
$35$		0			0
$36$	−1.08763			−0.181271
$37$	−1.19723	−	4.46814i	−0.196824	−	0.734558i	−0.991787	−	0.127900i	$-0.959176\pi$
$37$	−1.19723	−	4.46814i	−0.196824	−	0.734558i	0.794963	−	0.606658i	$-0.207490\pi$
$38$	−5.99195	−	1.60554i	−0.972023	−	0.260453i
$39$	−0.507306	+	0.292893i	−0.0812340	+	0.0469005i
$40$		0			0
$41$			2.58745i			0.404093i	0.979376	+	0.202046i	$0.0647591\pi$
$41$			2.58745i			0.404093i	−0.979376	+	0.202046i	$0.935241\pi$
$42$	−3.71926	+	3.84454i	−0.573895	+	0.593225i
$43$	4.97801	+	4.97801i	0.759140	+	0.759140i	0.976166	−	0.217026i	$-0.0696356\pi$
$43$	4.97801	+	4.97801i	0.759140	+	0.759140i	−0.217026	+	0.976166i	$0.569636\pi$
$44$	−3.49872	−	2.01999i	−0.527452	−	0.304524i
$45$		0			0
$46$	−2.26907	−	3.93014i	−0.334556	−	0.579468i
$47$	0.304388	−	0.0815604i	0.0443995	−	0.0118968i	−0.236551	−	0.971619i	$-0.576017\pi$
$47$	0.304388	−	0.0815604i	0.0443995	−	0.0118968i	0.280950	+	0.959722i	$0.409350\pi$
$48$	−1.42962	+	1.42962i	−0.206348	+	0.206348i
$49$	0.231803	+	6.99616i	0.0331148	+	0.999452i
$50$		0			0
$51$	−2.06196	+	3.57142i	−0.288732	+	0.500099i
$52$	−0.0749894	+	0.279864i	−0.0103992	+	0.0388102i
$53$	−2.14370	+	8.00039i	−0.294460	+	1.09894i	0.647186	+	0.762332i	$0.275946\pi$
$53$	−2.14370	+	8.00039i	−0.294460	+	1.09894i	−0.941646	+	0.336606i	$0.890721\pi$
$54$	1.93321	−	3.34841i	0.263076	−	0.455661i
$55$		0			0
$56$	0.0438127	+	2.64539i	0.00585472	+	0.353505i
$57$	−8.86840	+	8.86840i	−1.17465	+	1.17465i
$58$	6.91477	−	1.85281i	0.907953	−	0.243285i
$59$	−0.427702	−	0.740802i	−0.0556821	−	0.0964442i	0.836841	−	0.547446i	$-0.184400\pi$
$59$	−0.427702	−	0.740802i	−0.0556821	−	0.0964442i	−0.892523	+	0.451002i	$0.851067\pi$
$60$		0			0
$61$	−5.99356	−	3.46038i	−0.767397	−	0.443057i	0.0645484	−	0.997915i	$-0.479439\pi$
$61$	−5.99356	−	3.46038i	−0.767397	−	0.443057i	−0.831945	+	0.554858i	$0.812773\pi$
$62$	−5.17076	−	5.17076i	−0.656688	−	0.656688i
$63$	0.790700	+	2.76682i	0.0996189	+	0.348587i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−7.07367	+	4.08398i	−0.870708	+	0.502704i
$67$	−3.05106	−	0.817530i	−0.372747	−	0.0998772i	0.0675822	−	0.997714i	$-0.478472\pi$
$67$	−3.05106	−	0.817530i	−0.372747	−	0.0998772i	−0.440329	+	0.897837i	$0.645138\pi$
$68$	0.527924	+	1.97024i	0.0640201	+	0.238926i
$69$	−9.17514			−1.10456
$70$		0			0
$71$	7.12240			0.845273			0.422637	−	0.906299i	$-0.361105\pi$
$71$	7.12240			0.845273			0.422637	+	0.906299i	$0.361105\pi$
$72$	0.281498	+	1.05057i	0.0331749	+	0.123810i
$73$	11.1331	+	2.98311i	1.30303	+	0.349147i	0.842597	−	0.538545i	$-0.181026\pi$
$73$	11.1331	+	2.98311i	1.30303	+	0.349147i	0.460438	+	0.887692i	$0.347693\pi$
$74$	−4.00603	+	2.31288i	−0.465691	+	0.268867i
$75$		0			0
$76$			6.20333i			0.711571i
$77$	−2.59511	+	10.3690i	−0.295740	+	1.18165i
$78$	0.414214	+	0.414214i	0.0469005	+	0.0469005i
$79$	4.39618	+	2.53813i	0.494609	+	0.285562i	0.726484	−	0.687183i	$-0.241153\pi$
$79$	4.39618	+	2.53813i	0.494609	+	0.285562i	−0.231876	+	0.972745i	$0.574486\pi$
$80$		0			0
$81$	−5.53997	−	9.59552i	−0.615553	−	1.06617i
$82$	2.49929	−	0.669683i	0.276000	−	0.0739541i
$83$	−3.85372	+	3.85372i	−0.423001	+	0.423001i	−0.886236	−	0.463235i	$-0.846689\pi$
$83$	−3.85372	+	3.85372i	−0.423001	+	0.423001i	0.463235	+	0.886236i	$0.346689\pi$
$84$	4.67615	+	2.59749i	0.510210	+	0.283410i
$85$		0			0
$86$	3.51999	−	6.09680i	0.379570	−	0.657434i
$87$	3.74598	−	13.9802i	0.401611	−	1.49883i
$88$	−1.04562	+	3.90231i	−0.111464	+	0.415988i
$89$	1.53615	−	2.66069i	0.162832	−	0.282033i	−0.773051	−	0.634343i	$-0.781271\pi$
$89$	1.53615	−	2.66069i	0.162832	−	0.282033i	0.935883	+	0.352310i	$0.114604\pi$
$90$		0			0
$91$	0.766467	−	0.0126942i	0.0803475	−	0.00133071i
$92$	−3.20895	+	3.20895i	−0.334556	+	0.334556i
$93$	−14.2807	+	3.82650i	−1.48084	+	0.396789i
$94$	−0.157563	−	0.272906i	−0.0162513	−	0.0281481i
$95$		0			0
$96$	1.75092	+	1.01089i	0.178702	+	0.103174i
$97$	−6.63103	−	6.63103i	−0.673279	−	0.673279i	0.285191	−	0.958471i	$-0.407943\pi$
$97$	−6.63103	−	6.63103i	−0.673279	−	0.673279i	−0.958471	+	0.285191i	$0.907943\pi$
$98$	6.69778	−	2.03464i	0.676578	−	0.205530i
$99$			4.39398i			0.441611i
$100$		0			0
$101$	−8.56364	+	4.94422i	−0.852114	+	0.491968i	−0.861364	−	0.507989i	$-0.830389\pi$
$101$	−8.56364	+	4.94422i	−0.852114	+	0.491968i	0.00924966	+	0.999957i	$0.497056\pi$
$102$	3.98340	+	1.06735i	0.394416	+	0.105683i
$103$	−1.10827	−	4.13612i	−0.109201	−	0.407544i	0.889587	−	0.456766i	$-0.150992\pi$
$103$	−1.10827	−	4.13612i	−0.109201	−	0.407544i	−0.998788	+	0.0492221i	$0.984326\pi$
$104$	0.289737			0.0284110
$105$		0			0
$106$	8.28261			0.804479
$107$	3.84918	+	14.3653i	0.372114	+	1.38875i	0.857516	+	0.514457i	$0.172007\pi$
$107$	3.84918	+	14.3653i	0.372114	+	1.38875i	−0.485402	+	0.874291i	$0.661327\pi$
$108$	−3.73467	−	1.00070i	−0.359369	−	0.0962926i
$109$	11.4586	−	6.61564i	1.09754	−	0.633664i	0.161964	−	0.986797i	$-0.448217\pi$
$109$	11.4586	−	6.61564i	1.09754	−	0.633664i	0.935573	+	0.353133i	$0.114884\pi$
$110$		0			0
$111$			9.35230i			0.887681i
$112$	2.54391	−	0.726997i	0.240377	−	0.0686947i
$113$	−9.75336	−	9.75336i	−0.917519	−	0.917519i	0.0793296	−	0.996848i	$-0.474722\pi$
$113$	−9.75336	−	9.75336i	−0.917519	−	0.917519i	−0.996848	+	0.0793296i	$0.974722\pi$
$114$	10.8615	+	6.27091i	1.01728	+	0.587324i
$115$		0			0
$116$	−3.57935	−	6.19961i	−0.332334	−	0.575619i
$117$	0.304388	−	0.0815604i	0.0281406	−	0.00754026i
$118$	−0.604862	+	0.604862i	−0.0556821	+	0.0556821i
$119$	4.62831	−	2.77535i	0.424276	−	0.254416i
$120$		0			0
$121$	−2.66069	+	4.60846i	−0.241881	+	0.418951i
$122$	−1.79123	+	6.68495i	−0.162170	+	0.605227i
$123$	1.35396	−	5.05303i	0.122082	−	0.455617i
$124$	−3.65628	+	6.33287i	−0.328344	+	0.568708i
$125$		0			0
$126$	2.46790	−	1.47986i	0.219858	−	0.131837i
$127$	2.19984	−	2.19984i	0.195204	−	0.195204i	−0.602736	−	0.797940i	$-0.705923\pi$
$127$	2.19984	−	2.19984i	0.195204	−	0.195204i	0.797940	+	0.602736i	$0.205923\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	−7.11667	−	12.3264i	−0.626587	−	1.08528i
$130$		0			0
$131$	−6.32091	−	3.64938i	−0.552260	−	0.318848i	0.197773	−	0.980248i	$-0.436629\pi$
$131$	−6.32091	−	3.64938i	−0.552260	−	0.318848i	−0.750033	+	0.661400i	$0.769963\pi$
$132$	5.77563	+	5.77563i	0.502704	+	0.502704i
$133$	15.7807	−	4.50980i	1.36836	−	0.391049i
$134$			3.15869i			0.272870i
$135$		0			0
$136$	1.76647	−	1.01987i	0.151473	−	0.0874531i
$137$	6.93431	+	1.85804i	0.592438	+	0.158743i	0.542567	−	0.840012i	$-0.317452\pi$
$137$	6.93431	+	1.85804i	0.592438	+	0.158743i	0.0498710	+	0.998756i	$0.484119\pi$
$138$	2.37470	+	8.86251i	0.202148	+	0.754427i
$139$	−12.4172			−1.05321			−0.526605	−	0.850110i	$-0.676535\pi$
$139$	−12.4172			−1.05321			−0.526605	+	0.850110i	$0.676535\pi$
$140$		0			0
$141$	−0.637116			−0.0536549
$142$	−1.84341	−	6.87971i	−0.154696	−	0.577332i
$143$	1.13064	+	0.302955i	0.0945492	+	0.0253344i
$144$	0.941911	−	0.543813i	0.0784926	−	0.0453177i
$145$		0			0
$146$		−	11.5259i		−	0.953887i
$147$	3.20824	−	13.7841i	0.264611	−	1.13689i
$148$	3.27091	+	3.27091i	0.268867	+	0.268867i
$149$	−20.7399	−	11.9742i	−1.69908	−	0.980963i	−0.946637	−	0.322302i	$-0.895543\pi$
$149$	−20.7399	−	11.9742i	−1.69908	−	0.980963i	−0.752440	−	0.658661i	$-0.771123\pi$
$150$		0			0
$151$	1.77167	+	3.06862i	0.144176	+	0.249721i	0.929065	−	0.369916i	$-0.120613\pi$
$151$	1.77167	+	3.06862i	0.144176	+	0.249721i	−0.784889	+	0.619636i	$0.787280\pi$
$152$	5.99195	−	1.60554i	0.486012	−	0.130226i
$153$	1.56870	−	1.56870i	0.126822	−	0.126822i
$154$	10.6873	−	0.177002i	0.861207	−	0.0142632i
$155$		0			0
$156$	0.292893	−	0.507306i	0.0234502	−	0.0406170i
$157$	1.58462	−	5.91389i	0.126467	−	0.471980i	−0.873421	−	0.486966i	$-0.838104\pi$
$157$	1.58462	−	5.91389i	0.126467	−	0.471980i	0.999888	+	0.0149859i	$0.00477033\pi$
$158$	1.31384	−	4.90330i	0.104523	−	0.390086i
$159$	8.37284	−	14.5022i	0.664010	−	1.15010i
$160$		0			0
$161$	10.4962	+	5.83037i	0.827213	+	0.459498i
$162$	−7.83471	+	7.83471i	−0.615553	+	0.615553i
$163$	−15.9937	+	4.28549i	−1.25272	+	0.335666i	−0.823387	−	0.567480i	$-0.807918\pi$
$163$	−15.9937	+	4.28549i	−1.25272	+	0.335666i	−0.429334	+	0.903146i	$0.641252\pi$
$164$	−1.29373	−	2.24080i	−0.101023	−	0.174977i
$165$		0			0
$166$	4.71983	+	2.72499i	0.366329	+	0.211500i
$167$	−10.2873	−	10.2873i	−0.796056	−	0.796056i	0.186415	−	0.982471i	$-0.440313\pi$
$167$	−10.2873	−	10.2873i	−0.796056	−	0.796056i	−0.982471	+	0.186415i	$0.940313\pi$
$168$	1.29871	−	5.18910i	0.100198	−	0.400348i
$169$			12.9161i			0.993543i
$170$		0			0
$171$	5.84298	−	3.37345i	0.446824	−	0.257974i
$172$	−6.80009	−	1.82208i	−0.518502	−	0.138932i
$173$	−2.01155	−	7.50720i	−0.152935	−	0.570762i	−0.999273	−	0.0381159i	$-0.987864\pi$
$173$	−2.01155	−	7.50720i	−0.152935	−	0.570762i	0.846338	−	0.532646i	$-0.178802\pi$
$174$	−14.4734			−1.09722
$175$		0			0
$176$	4.03997			0.304524
$177$	0.447613	+	1.67052i	0.0336447	+	0.125564i
$178$	−2.96762	−	0.795171i	−0.222432	−	0.0596006i
$179$	−3.34695	+	1.93236i	−0.250163	+	0.144431i	−0.619839	−	0.784729i	$-0.712802\pi$
$179$	−3.34695	+	1.93236i	−0.250163	+	0.144431i	0.369676	+	0.929161i	$0.379469\pi$
$180$		0			0
$181$		−	6.99107i		−	0.519642i	−0.965657	−	0.259821i	$-0.916336\pi$
$181$		−	6.99107i		−	0.519642i	0.965657	−	0.259821i	$-0.0836636\pi$
$182$	−0.210638	−	0.737064i	−0.0156135	−	0.0546348i
$183$	9.89407	+	9.89407i	0.731390	+	0.731390i
$184$	3.93014	+	2.26907i	0.289734	+	0.167278i
$185$		0			0
$186$	7.39223	+	12.8037i	0.542024	+	0.938814i
$187$	7.95971	−	2.13280i	0.582071	−	0.155966i
$188$	−0.222827	+	0.222827i	−0.0162513	+	0.0162513i
$189$	0.169398	+	10.2282i	0.0123219	+	0.743990i
$190$		0			0
$191$	−2.23721	+	3.87496i	−0.161879	+	0.280383i	−0.935543	−	0.353214i	$-0.885089\pi$
$191$	−2.23721	+	3.87496i	−0.161879	+	0.280383i	0.773664	+	0.633597i	$0.218422\pi$
$192$	0.523277	−	1.95290i	0.0377643	−	0.140938i
$193$	5.19573	−	19.3907i	0.373997	−	1.39577i	−0.480809	−	0.876825i	$-0.659657\pi$
$193$	5.19573	−	19.3907i	0.373997	−	1.39577i	0.854805	−	0.518949i	$-0.173676\pi$
$194$	−4.68885	+	8.12132i	−0.336640	+	0.583077i
$195$		0			0
$196$	−3.69883	−	5.94295i	−0.264202	−	0.424497i
$197$	7.84901	−	7.84901i	0.559219	−	0.559219i	−0.369866	−	0.929085i	$-0.620596\pi$
$197$	7.84901	−	7.84901i	0.559219	−	0.559219i	0.929085	+	0.369866i	$0.120596\pi$
$198$	4.24426	−	1.13725i	0.301626	−	0.0808205i
$199$	5.40103	+	9.35485i	0.382869	+	0.663148i	0.991471	−	0.130327i	$-0.0416028\pi$
$199$	5.40103	+	9.35485i	0.382869	+	0.663148i	−0.608602	+	0.793475i	$0.708270\pi$
$200$		0			0
$201$	5.53062	+	3.19310i	0.390100	+	0.225224i
$202$	6.99218	+	6.99218i	0.491968	+	0.491968i
$203$	−13.1691	+	13.6126i	−0.924288	+	0.955419i
$204$		−	4.12392i		−	0.288732i
$205$		0			0
$206$	−3.70835	+	2.14101i	−0.258373	+	0.149172i
$207$	4.76761	+	1.27748i	0.331372	+	0.0887908i
$208$	−0.0749894	−	0.279864i	−0.00519958	−	0.0194051i
$209$	25.0613			1.73353
$210$		0			0
$211$	7.56555			0.520834			0.260417	−	0.965496i	$-0.416140\pi$
$211$	7.56555			0.520834			0.260417	+	0.965496i	$0.416140\pi$
$212$	−2.14370	−	8.00039i	−0.147230	−	0.549469i
$213$	−13.9093	−	3.72699i	−0.953050	−	0.255369i
$214$	12.8796	−	7.43604i	0.880431	−	0.508317i
$215$		0			0
$216$			3.86642i			0.263076i
$217$	18.7683	+	4.69728i	1.27408	+	0.318872i
$218$	−9.35593	−	9.35593i	−0.633664	−	0.633664i
$219$	−20.1809	−	11.6514i	−1.36370	−	0.787330i
$220$		0			0
$221$	−0.295494	−	0.511811i	−0.0198771	−	0.0344281i
$222$	9.03363	−	2.42055i	0.606298	−	0.162457i
$223$	9.35230	−	9.35230i	0.626277	−	0.626277i	−0.320853	−	0.947129i	$-0.603969\pi$
$223$	9.35230	−	9.35230i	0.626277	−	0.626277i	0.947129	+	0.320853i	$0.103969\pi$
$224$	−1.36064	−	2.26907i	−0.0909114	−	0.151608i
$225$		0			0
$226$	−6.89667	+	11.9454i	−0.458759	+	0.794595i
$227$	−4.19127	+	15.6420i	−0.278184	+	1.03820i	0.675493	+	0.737367i	$0.263931\pi$
$227$	−4.19127	+	15.6420i	−0.278184	+	1.03820i	−0.953677	+	0.300832i	$0.902736\pi$
$228$	3.24606	−	12.1145i	0.214976	−	0.802300i
$229$	−5.88820	+	10.1987i	−0.389103	+	0.673947i	−0.992329	−	0.123624i	$-0.960548\pi$
$229$	−5.88820	+	10.1987i	−0.389103	+	0.673947i	0.603226	+	0.797570i	$0.293882\pi$
$230$		0			0
$231$	10.4938	−	18.8915i	0.690442	−	1.24297i
$232$	−5.06196	+	5.06196i	−0.332334	+	0.332334i
$233$	−5.52920	+	1.48154i	−0.362230	+	0.0970591i	−0.435343	−	0.900264i	$-0.643373\pi$
$233$	−5.52920	+	1.48154i	−0.362230	+	0.0970591i	0.0731138	+	0.997324i	$0.476706\pi$
$234$	−0.157563	−	0.272906i	−0.0103002	−	0.0178405i
$235$		0			0
$236$	0.740802	+	0.427702i	0.0482221	+	0.0278410i
$237$	−7.25713	−	7.25713i	−0.471402	−	0.471402i
$238$	−3.87867	−	3.75229i	−0.251417	−	0.243225i
$239$		−	8.33794i		−	0.539337i	−0.962953	−	0.269668i	$-0.913086\pi$
$239$		−	8.33794i		−	0.539337i	0.962953	−	0.269668i	$-0.0869141\pi$
$240$		0			0
$241$	2.56723	−	1.48219i	0.165370	−	0.0954763i	−0.415031	−	0.909807i	$-0.636229\pi$
$241$	2.56723	−	1.48219i	0.165370	−	0.0954763i	0.580401	+	0.814331i	$0.302896\pi$
$242$	5.14006	+	1.37728i	0.330416	+	0.0885347i
$243$	2.79578	+	10.4340i	0.179349	+	0.669340i
$244$	6.92077			0.443057
$245$		0			0
$246$	−5.23128			−0.333535
$247$	−0.465184	−	1.73609i	−0.0295989	−	0.110465i
$248$	7.06340	+	1.89263i	0.448526	+	0.120182i
$249$	9.54248	−	5.50936i	0.604730	−	0.349141i
$250$		0			0
$251$			16.1800i			1.02127i	0.859796	+	0.510637i	$0.170590\pi$
$251$			16.1800i			1.02127i	−0.859796	+	0.510637i	$0.829410\pi$
$252$	−2.06818	−	2.00079i	−0.130283	−	0.126038i
$253$	12.9641	+	12.9641i	0.815043	+	0.815043i
$254$	−2.69424	−	1.55552i	−0.169052	−	0.0976020i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.62621	−	1.50754i	0.350954	−	0.0940377i	−0.0790355	−	0.996872i	$-0.525184\pi$
$257$	5.62621	−	1.50754i	0.350954	−	0.0940377i	0.429989	+	0.902834i	$0.358517\pi$
$258$	−10.0645	+	10.0645i	−0.626587	+	0.626587i
$259$	5.94295	−	10.6988i	0.369277	−	0.664793i
$260$		0			0
$261$	−3.89299	+	6.74285i	−0.240970	+	0.417372i
$262$	−1.88906	+	7.05006i	−0.116706	+	0.435554i
$263$	−0.449601	+	1.67793i	−0.0277236	+	0.103466i	−0.978401	−	0.206715i	$-0.933723\pi$
$263$	−0.449601	+	1.67793i	−0.0277236	+	0.103466i	0.950678	+	0.310180i	$0.100389\pi$
$264$	4.08398	−	7.07367i	0.251352	−	0.435354i
$265$		0			0
$266$	−8.44048	−	14.0758i	−0.517519	−	0.863041i
$267$	−4.39223	+	4.39223i	−0.268800	+	0.268800i
$268$	3.05106	−	0.817530i	0.186373	−	0.0499386i
$269$	1.89169	+	3.27650i	0.115338	+	0.199772i	0.917915	−	0.396777i	$-0.129872\pi$
$269$	1.89169	+	3.27650i	0.115338	+	0.199772i	−0.802577	+	0.596549i	$0.796538\pi$
$270$		0			0
$271$	−18.4029	−	10.6249i	−1.11789	−	0.645416i	−0.177032	−	0.984205i	$-0.556649\pi$
$271$	−18.4029	−	10.6249i	−1.11789	−	0.645416i	−0.940862	+	0.338789i	$0.889983\pi$
$272$	−1.44231	−	1.44231i	−0.0874531	−	0.0874531i
$273$	−1.50347	−	0.376284i	−0.0909943	−	0.0227737i
$274$		−	7.17893i		−	0.433695i
$275$		0			0
$276$	7.94591	−	4.58757i	0.478287	−	0.276139i
$277$	−4.72353	−	1.26567i	−0.283810	−	0.0760465i	0.114106	−	0.993469i	$-0.463600\pi$
$277$	−4.72353	−	1.26567i	−0.283810	−	0.0760465i	−0.397916	+	0.917422i	$0.630266\pi$
$278$	3.21380	+	11.9941i	0.192751	+	0.719356i
$279$	7.95333			0.476153
$280$		0			0
$281$	−29.4776			−1.75849			−0.879243	−	0.476373i	$-0.841951\pi$
$281$	−29.4776			−1.75849			−0.879243	+	0.476373i	$0.841951\pi$
$282$	0.164898	+	0.615407i	0.00981952	+	0.0366470i
$283$	10.8991	+	2.92041i	0.647886	+	0.173601i	0.567773	−	0.823185i	$-0.307805\pi$
$283$	10.8991	+	2.92041i	0.647886	+	0.173601i	0.0801133	+	0.996786i	$0.474472\pi$
$284$	−6.16818	+	3.56120i	−0.366014	+	0.211318i
$285$		0			0
$286$		−	1.17053i		−	0.0692148i
$287$	−4.75986	+	4.92018i	−0.280966	+	0.290429i
$288$	−0.769067	−	0.769067i	−0.0453177	−	0.0453177i
$289$	11.1193	+	6.41973i	0.654076	+	0.377631i
$290$		0			0
$291$	9.47985	+	16.4196i	0.555719	+	0.962533i
$292$	−11.1331	+	2.98311i	−0.651517	+	0.174573i
$293$	−7.23407	+	7.23407i	−0.422619	+	0.422619i	−0.886105	−	0.463485i	$-0.846599\pi$
$293$	−7.23407	+	7.23407i	−0.422619	+	0.422619i	0.463485	+	0.886105i	$0.346599\pi$
$294$	−14.1448	+	0.468657i	−0.824939	+	0.0273326i
$295$		0			0
$296$	2.31288	−	4.00603i	0.134433	−	0.232846i
$297$	−4.04281	+	15.0880i	−0.234588	+	0.875493i
$298$	−6.19829	+	23.1323i	−0.359057	+	1.34002i
$299$	0.657432	−	1.13871i	0.0380203	−	0.0658531i
$300$		0			0
$301$	0.308440	+	18.6235i	0.0177782	+	1.07344i
$302$	2.50552	−	2.50552i	0.144176	−	0.144176i
$303$	19.3111	−	5.17439i	1.10939	−	0.297261i
$304$	−3.10166	−	5.37224i	−0.177893	−	0.308119i
$305$		0			0
$306$	−1.92125	−	1.10924i	−0.109831	−	0.0634108i
$307$	−1.07859	−	1.07859i	−0.0615584	−	0.0615584i	0.675657	−	0.737216i	$-0.263860\pi$
$307$	−1.07859	−	1.07859i	−0.0615584	−	0.0615584i	−0.737216	+	0.675657i	$0.763860\pi$
$308$	−2.93705	−	10.2773i	−0.167354	−	0.585605i
$309$			8.65735i			0.492500i
$310$		0			0
$311$	−8.33830	+	4.81412i	−0.472821	+	0.272984i	−0.717420	−	0.696641i	$-0.754677\pi$
$311$	−8.33830	+	4.81412i	−0.472821	+	0.272984i	0.244599	+	0.969624i	$0.421344\pi$
$312$	−0.565826	−	0.151613i	−0.0320336	−	0.00858338i
$313$	−0.783378	−	2.92361i	−0.0442791	−	0.165252i	0.940246	−	0.340496i	$-0.110595\pi$
$313$	−0.783378	−	2.92361i	−0.0442791	−	0.165252i	−0.984525	+	0.175244i	$0.943928\pi$
$314$	−6.12251			−0.345513
$315$		0			0
$316$	−5.07627			−0.285562
$317$	−0.504353	−	1.88227i	−0.0283273	−	0.105719i	0.950315	−	0.311291i	$-0.100761\pi$
$317$	−0.504353	−	1.88227i	−0.0283273	−	0.105719i	−0.978642	+	0.205572i	$0.934095\pi$
$318$	−16.1751	−	4.33410i	−0.907054	−	0.243044i
$319$	−25.0463	+	14.4605i	−1.40232	+	0.809631i
$320$		0			0
$321$		−	30.0682i		−	1.67824i
$322$	2.91510	−	11.6475i	0.162452	−	0.649091i
$323$	−8.94715	−	8.94715i	−0.497833	−	0.497833i
$324$	9.59552	+	5.53997i	0.533084	+	0.307776i
$325$		0			0
$326$	8.27894	+	14.3395i	0.458528	+	0.794194i
$327$	−25.8393	+	6.92363i	−1.42892	+	0.382878i
$328$	−1.82961	+	1.82961i	−0.101023	+	0.101023i
$329$	0.728847	+	0.404858i	0.0401826	+	0.0223205i
$330$		0			0
$331$	14.4468	−	25.0225i	0.794066	−	1.37536i	−0.129365	−	0.991597i	$-0.541294\pi$
$331$	14.4468	−	25.0225i	0.794066	−	1.37536i	0.923431	−	0.383765i	$-0.125373\pi$
$332$	1.41056	−	5.26428i	0.0774145	−	0.288915i
$333$	1.30214	−	4.85966i	0.0713570	−	0.266308i
$334$	−7.27423	+	12.5993i	−0.398028	+	0.689405i
$335$		0			0
$336$	−5.34841	+	0.0885800i	−0.291780	+	0.00483244i
$337$	0.823226	−	0.823226i	0.0448440	−	0.0448440i	−0.684329	−	0.729173i	$-0.739905\pi$
$337$	0.823226	−	0.823226i	0.0448440	−	0.0448440i	0.729173	+	0.684329i	$0.239905\pi$
$338$	12.4759	−	3.34292i	0.678602	−	0.181831i
$339$	13.9436	+	24.1510i	0.757312	+	1.31170i
$340$		0			0
$341$	25.5846	+	14.7713i	1.38548	+	0.799910i
$342$	−4.77078	−	4.77078i	−0.257974	−	0.257974i
$343$	−12.4293	+	13.7300i	−0.671119	+	0.741350i
$344$			7.03997i			0.379570i
$345$		0			0
$346$	−6.73077	+	3.88601i	−0.361849	+	0.208913i
$347$	−16.1350	−	4.32336i	−0.866172	−	0.232090i	−0.201740	−	0.979439i	$-0.564660\pi$
$347$	−16.1350	−	4.32336i	−0.866172	−	0.232090i	−0.664432	+	0.747349i	$0.731326\pi$
$348$	3.74598	+	13.9802i	0.200806	+	0.749417i
$349$	−36.7146			−1.96529			−0.982644	−	0.185503i	$-0.940608\pi$
$349$	−36.7146			−1.96529			−0.982644	+	0.185503i	$0.940608\pi$
$350$		0			0
$351$	1.12024			0.0597942
$352$	−1.04562	−	3.90231i	−0.0557318	−	0.207994i
$353$	13.7845	+	3.69356i	0.733677	+	0.196588i	0.606266	−	0.795262i	$-0.292667\pi$
$353$	13.7845	+	3.69356i	0.733677	+	0.196588i	0.127411	+	0.991850i	$0.459333\pi$
$354$	1.49774	−	0.864723i	0.0796042	−	0.0459595i
$355$		0			0
$356$			3.07230i			0.162832i
$357$	−10.4909	+	2.99808i	−0.555236	+	0.158675i
$358$	2.73277	+	2.73277i	0.144431	+	0.144431i
$359$	23.4596	+	13.5444i	1.23815	+	0.714847i	0.968716	−	0.248172i	$-0.0798298\pi$
$359$	23.4596	+	13.5444i	1.23815	+	0.714847i	0.269435	+	0.963019i	$0.413163\pi$
$360$		0			0
$361$	−9.74064	−	16.8713i	−0.512665	−	0.887962i
$362$	−6.75285	+	1.80942i	−0.354922	+	0.0951011i
$363$	7.60756	−	7.60756i	0.399293	−	0.399293i
$364$	−0.657432	+	0.394227i	−0.0344588	+	0.0206631i
$365$		0			0
$366$	6.99616	−	12.1177i	0.365695	−	0.633403i
$367$	−5.86782	+	21.8990i	−0.306298	+	1.14312i	0.625525	+	0.780204i	$0.284885\pi$
$367$	−5.86782	+	21.8990i	−0.306298	+	1.14312i	−0.931823	+	0.362914i	$0.881782\pi$
$368$	1.17456	−	4.38350i	0.0612279	−	0.228506i
$369$	−1.40709	+	2.43715i	−0.0732502	+	0.126873i
$370$		0			0
$371$	−18.7938	+	11.2696i	−0.975726	+	0.585090i
$372$	10.4542	−	10.4542i	0.542024	−	0.542024i
$373$	−12.3984	+	3.32215i	−0.641966	+	0.172014i	−0.565094	−	0.825027i	$-0.691160\pi$
$373$	−12.3984	+	3.32215i	−0.641966	+	0.172014i	−0.0768720	+	0.997041i	$0.524493\pi$
$374$	−4.12025	−	7.13648i	−0.213053	−	0.369019i
$375$		0			0
$376$	0.272906	+	0.157563i	0.0140741	+	0.00812567i
$377$	1.46664	+	1.46664i	0.0755356	+	0.0755356i
$378$	9.83581	−	2.81087i	0.505900	−	0.144576i
$379$		−	14.4739i		−	0.743476i	−0.928338	−	0.371738i	$-0.878762\pi$
$379$		−	14.4739i		−	0.743476i	0.928338	−	0.371738i	$-0.121238\pi$
$380$		0			0
$381$	−5.44718	+	3.14493i	−0.279068	+	0.161120i
$382$	4.32196	+	1.15807i	0.221131	+	0.0592518i
$383$	−0.453341	−	1.69189i	−0.0231647	−	0.0864517i	0.953376	−	0.301786i	$-0.0975827\pi$
$383$	−0.453341	−	1.69189i	−0.0231647	−	0.0864517i	−0.976540	+	0.215334i	$0.930916\pi$
$384$	−2.02179			−0.103174
$385$		0			0
$386$	−20.0747			−1.02178
$387$	1.98174	+	7.39595i	0.100737	+	0.375957i
$388$	9.05816	+	2.42713i	0.459858	+	0.123219i
$389$	2.40954	−	1.39115i	0.122169	−	0.0705341i	−0.437670	−	0.899135i	$-0.644196\pi$
$389$	2.40954	−	1.39115i	0.122169	−	0.0705341i	0.559839	+	0.828601i	$0.310863\pi$
$390$		0			0
$391$		−	9.25661i		−	0.468127i
$392$	−4.78312	+	5.11094i	−0.241584	+	0.258142i
$393$	10.4344	+	10.4344i	0.526348	+	0.526348i
$394$	−9.61304	−	5.55009i	−0.484298	−	0.279610i
$395$		0			0
$396$	−2.19699	−	3.80530i	−0.110403	−	0.191223i
$397$	−38.3163	+	10.2668i	−1.92304	+	0.515277i	−0.936828	+	0.349791i	$0.886253\pi$
$397$	−38.3163	+	10.2668i	−1.92304	+	0.515277i	−0.986212	+	0.165486i	$0.947081\pi$
$398$	7.63821	−	7.63821i	0.382869	−	0.382869i
$399$	−33.1780	+	0.549491i	−1.66098	+	0.0275089i
$400$		0			0
$401$	9.98528	−	17.2950i	0.498641	−	0.863672i	−0.501358	−	0.865240i	$-0.667166\pi$
$401$	9.98528	−	17.2950i	0.498641	−	0.863672i	0.999999	+	0.00156835i	$0.000499221\pi$
$402$	1.65287	−	6.16860i	0.0824378	−	0.307662i
$403$	0.548365	−	2.04653i	0.0273160	−	0.101945i
$404$	4.94422	−	8.56364i	0.245984	−	0.426057i
$405$		0			0
$406$	16.5572	+	9.19714i	0.821720	+	0.456446i
$407$	13.2144	−	13.2144i	0.655012	−	0.655012i
$408$	−3.98340	+	1.06735i	−0.197208	+	0.0528417i
$409$	7.65280	+	13.2550i	0.378407	+	0.655419i	0.990831	−	0.135110i	$-0.0431388\pi$
$409$	7.65280	+	13.2550i	0.378407	+	0.655419i	−0.612424	+	0.790529i	$0.709805\pi$
$410$		0			0
$411$	−12.5697	−	7.25713i	−0.620019	−	0.357968i
$412$	3.02785	+	3.02785i	0.149172	+	0.149172i
$413$	0.549475	−	2.19547i	0.0270379	−	0.108032i
$414$		−	4.93579i		−	0.242581i
$415$		0			0
$416$	−0.250919	+	0.144868i	−0.0123023	+	0.00710276i
$417$	24.2495	+	6.49762i	1.18750	+	0.318190i
$418$	−6.48634	−	24.2073i	−0.317257	−	1.18402i
$419$	27.7027			1.35337			0.676684	−	0.736274i	$-0.263416\pi$
$419$	27.7027			1.35337			0.676684	+	0.736274i	$0.263416\pi$
$420$		0			0
$421$	33.0159			1.60910			0.804549	−	0.593887i	$-0.202407\pi$
$421$	33.0159			1.60910			0.804549	+	0.593887i	$0.202407\pi$
$422$	−1.95811	−	7.30776i	−0.0953192	−	0.355736i
$423$	0.331060	+	0.0887072i	0.0160967	+	0.00431309i
$424$	−7.17295	+	4.14131i	−0.348349	+	0.201120i
$425$		0			0
$426$			14.4000i			0.697681i
$427$	−5.03138	−	17.6058i	−0.243485	−	0.852005i
$428$	−10.5161	−	10.5161i	−0.508317	−	0.508317i
$429$	−2.04950	−	1.18328i	−0.0989509	−	0.0571293i
$430$		0			0
$431$	−11.9586	−	20.7129i	−0.576027	−	0.997708i	−0.995929	−	0.0901384i	$-0.971269\pi$
$431$	−11.9586	−	20.7129i	−0.576027	−	0.997708i	0.419902	−	0.907569i	$-0.362064\pi$
$432$	3.73467	−	1.00070i	0.179684	−	0.0481463i
$433$	−13.2515	+	13.2515i	−0.636829	+	0.636829i	−0.949772	−	0.312943i	$-0.898685\pi$
$433$	−13.2515	+	13.2515i	−0.636829	+	0.636829i	0.312943	+	0.949772i	$0.398685\pi$
$434$	−0.320383	−	19.3446i	−0.0153789	−	0.928569i
$435$		0			0
$436$	−6.61564	+	11.4586i	−0.316832	+	0.548769i
$437$	7.28615	−	27.1923i	0.348544	−	1.30078i
$438$	−6.03122	+	22.5088i	−0.288183	+	1.07551i
$439$	7.05383	−	12.2176i	0.336661	−	0.583114i	−0.647141	−	0.762370i	$-0.724036\pi$
$439$	7.05383	−	12.2176i	0.336661	−	0.583114i	0.983802	+	0.179256i	$0.0573690\pi$
$440$		0			0
$441$	−3.58626	+	6.71582i	−0.170774	+	0.319801i
$442$	−0.417892	+	0.417892i	−0.0198771	+	0.0198771i
$443$	20.3457	−	5.45161i	0.966652	−	0.259014i	0.259238	−	0.965813i	$-0.416528\pi$
$443$	20.3457	−	5.45161i	0.966652	−	0.259014i	0.707414	+	0.706800i	$0.249862\pi$
$444$	−4.67615	−	8.09933i	−0.221920	−	0.384377i
$445$		0			0
$446$	−11.4542	−	6.61308i	−0.542371	−	0.313138i
$447$	34.2370	+	34.2370i	1.61936	+	1.61936i
$448$	−1.83959	+	1.90155i	−0.0869125	+	0.0898399i
$449$		−	31.3247i		−	1.47831i	−0.673538	−	0.739153i	$-0.735226\pi$
$449$		−	31.3247i		−	1.47831i	0.673538	−	0.739153i	$-0.264774\pi$
$450$		0			0
$451$	−9.05278	+	5.22662i	−0.426279	+	0.246112i
$452$	13.3233	+	3.56998i	0.626677	+	0.167918i
$453$	−1.85415	−	6.91977i	−0.0871154	−	0.325119i
$454$	16.1938			0.760014
$455$		0			0
$456$	−12.5418			−0.587324
$457$	0.740622	+	2.76404i	0.0346448	+	0.129296i	0.981082	−	0.193591i	$-0.0620133\pi$
$457$	0.740622	+	2.76404i	0.0346448	+	0.129296i	−0.946438	+	0.322887i	$0.895347\pi$
$458$	11.3751	+	3.04796i	0.531525	+	0.142422i
$459$	6.82989	−	3.94324i	0.318792	−	0.184055i
$460$		0			0
$461$		−	3.02674i		−	0.140969i	−0.997513	−	0.0704846i	$-0.977545\pi$
$461$		−	3.02674i		−	0.140969i	0.997513	−	0.0704846i	$-0.0224546\pi$
$462$	−20.9638	−	5.24675i	−0.975325	−	0.244101i
$463$	−19.2889	−	19.2889i	−0.896431	−	0.896431i	0.0986876	−	0.995118i	$-0.468536\pi$
$463$	−19.2889	−	19.2889i	−0.896431	−	0.896431i	−0.995118	+	0.0986876i	$0.968536\pi$
$464$	6.19961	+	3.57935i	0.287810	+	0.166167i
$465$		0			0
$466$	2.86212	+	4.95734i	0.132585	+	0.229644i
$467$	24.2727	−	6.50385i	1.12321	−	0.300962i	0.351026	−	0.936366i	$-0.385833\pi$
$467$	24.2727	−	6.50385i	1.12321	−	0.300962i	0.772180	+	0.635403i	$0.219166\pi$
$468$	−0.222827	+	0.222827i	−0.0103002	+	0.0103002i
$469$	−4.29784	−	7.16729i	−0.198456	−	0.330955i
$470$		0			0
$471$	−6.18921	+	10.7200i	−0.285184	+	0.493953i
$472$	0.221395	−	0.826257i	0.0101905	−	0.0380316i
$473$	−7.36115	+	27.4722i	−0.338466	+	1.26317i
$474$	−5.13157	+	8.88814i	−0.235701	+	0.408246i
$475$		0			0
$476$	−2.62056	+	4.71767i	−0.120113	+	0.216234i
$477$	−6.36989	+	6.36989i	−0.291657	+	0.291657i
$478$	−8.05384	+	2.15802i	−0.368374	+	0.0987055i
$479$	4.14346	+	7.17668i	0.189319	+	0.327911i	0.945024	−	0.327002i	$-0.106039\pi$
$479$	4.14346	+	7.17668i	0.189319	+	0.327911i	−0.755704	+	0.654913i	$0.772705\pi$
$480$		0			0
$481$	−1.16069	−	0.670127i	−0.0529231	−	0.0305551i
$482$	−2.09613	−	2.09613i	−0.0954763	−	0.0954763i
$483$	−17.4470	−	16.8785i	−0.793867	−	0.767999i
$484$		−	5.32139i		−	0.241881i
$485$		0			0
$486$	9.35485	−	5.40103i	0.424345	−	0.244996i
$487$	10.3144	+	2.76375i	0.467392	+	0.125237i	0.484826	−	0.874611i	$-0.338883\pi$
$487$	10.3144	+	2.76375i	0.467392	+	0.125237i	−0.0174340	+	0.999848i	$0.505550\pi$
$488$	−1.79123	−	6.68495i	−0.0810850	−	0.302613i
$489$	33.4765			1.51386
$490$		0			0
$491$	25.7259			1.16100			0.580498	−	0.814262i	$-0.302858\pi$
$491$	25.7259			1.16100			0.580498	+	0.814262i	$0.302858\pi$
$492$	1.35396	+	5.05303i	0.0610411	+	0.227808i
$493$	14.1043	+	3.77924i	0.635227	+	0.170209i
$494$	−1.55654	+	0.898666i	−0.0700319	+	0.0404329i
$495$		0			0
$496$		−	7.31256i		−	0.328344i
$497$	13.5436	+	13.1023i	0.607514	+	0.587719i
$498$	−7.79141	−	7.79141i	−0.349141	−	0.349141i
$499$	12.6429	+	7.29940i	0.565975	+	0.326766i	0.755540	−	0.655102i	$-0.227374\pi$
$499$	12.6429	+	7.29940i	0.565975	+	0.326766i	−0.189565	+	0.981868i	$0.560708\pi$
$500$		0			0
$501$	14.7069	+	25.4732i	0.657058	+	1.13806i
$502$	15.6287	−	4.18770i	0.697543	−	0.186906i
$503$	13.9891	−	13.9891i	0.623744	−	0.623744i	−0.322743	−	0.946487i	$-0.604605\pi$
$503$	13.9891	−	13.9891i	0.623744	−	0.623744i	0.946487	+	0.322743i	$0.104605\pi$
$504$	−1.39733	+	2.51555i	−0.0622419	+	0.112051i
$505$		0			0
$506$	9.16697	−	15.8777i	0.407522	−	0.705848i
$507$	6.75868	−	25.2237i	0.300163	−	1.12022i
$508$	−0.805197	+	3.00504i	−0.0357248	+	0.133327i
$509$	−1.42883	+	2.47481i	−0.0633319	+	0.109694i	−0.895953	−	0.444149i	$-0.853506\pi$
$509$	−1.42883	+	2.47481i	−0.0633319	+	0.109694i	0.832621	+	0.553843i	$0.186839\pi$
$510$		0			0
$511$	15.6825	+	26.1530i	0.693754	+	1.15694i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	23.1674	−	6.20768i	1.02287	−	0.274076i
$514$	−2.91234	−	5.04433i	−0.128458	−	0.222496i
$515$		0			0
$516$	12.3264	+	7.11667i	0.542641	+	0.313294i
$517$	0.900216	+	0.900216i	0.0395914	+	0.0395914i
$518$	−11.8724	−	2.97139i	−0.521644	−	0.130555i
$519$			15.7134i			0.689741i
$520$		0			0
$521$	24.7917	−	14.3135i	1.08614	−	0.627084i	0.153595	−	0.988134i	$-0.450915\pi$
$521$	24.7917	−	14.3135i	1.08614	−	0.627084i	0.932547	+	0.361049i	$0.117581\pi$
$522$	7.52068	+	2.01516i	0.329171	+	0.0882011i
$523$	−8.17429	−	30.5069i	−0.357437	−	1.33397i	−0.877390	−	0.479777i	$-0.840717\pi$
$523$	−8.17429	−	30.5069i	−0.357437	−	1.33397i	0.519954	−	0.854195i	$-0.325949\pi$
$524$	7.29876			0.318848
$525$		0			0
$526$	1.73712			0.0757422
$527$	−3.86048	−	14.4075i	−0.168165	−	0.627600i
$528$	−7.88965	−	2.11403i	−0.343353	−	0.0920012i
$529$	−2.08308	+	1.20267i	−0.0905687	+	0.0522899i
$530$		0			0
$531$		−	0.930359i		−	0.0403742i
$532$	−11.4116	+	11.7960i	−0.494755	+	0.511419i
$533$	0.530105	+	0.530105i	0.0229614	+	0.0229614i
$534$	5.37936	+	3.10577i	0.232788	+	0.134400i
$535$		0			0
$536$	−1.57935	−	2.73551i	−0.0682174	−	0.118156i
$537$	7.54741	−	2.02232i	0.325695	−	0.0872696i
$538$	2.67525	−	2.67525i	0.115338	−	0.115338i
$539$	−24.0094	+	14.9432i	−1.03416	+	0.643648i
$540$		0			0
$541$	−18.4994	+	32.0420i	−0.795353	+	1.37759i	0.127262	+	0.991869i	$0.459381\pi$
$541$	−18.4994	+	32.0420i	−0.795353	+	1.37759i	−0.922615	+	0.385722i	$0.873952\pi$
$542$	−5.49985	+	20.5257i	−0.236239	+	0.881655i
$543$	−3.65827	+	13.6528i	−0.156991	+	0.585899i
$544$	−1.01987	+	1.76647i	−0.0437266	+	0.0757366i
$545$		0			0
$546$	0.0256649	+	1.54963i	0.00109836	+	0.0663182i
$547$	20.0765	−	20.0765i	0.858409	−	0.858409i	−0.132742	−	0.991151i	$-0.542378\pi$
$547$	20.0765	−	20.0765i	0.858409	−	0.858409i	0.991151	+	0.132742i	$0.0423781\pi$
$548$	−6.93431	+	1.85804i	−0.296219	+	0.0793717i
$549$	−3.76360	−	6.51875i	−0.160627	−	0.278213i
$550$		0			0
$551$	38.4582	+	22.2039i	1.63838	+	0.945916i
$552$	−6.48781	−	6.48781i	−0.276139	−	0.276139i
$553$	3.69043	+	12.9136i	0.156933	+	0.549141i
$554$			4.89016i			0.207763i
$555$		0			0
$556$	10.7536	−	6.20859i	0.456054	−	0.263303i
$557$	−24.8367	−	6.65499i	−1.05237	−	0.281981i	−0.309137	−	0.951017i	$-0.600040\pi$
$557$	−24.8367	−	6.65499i	−1.05237	−	0.281981i	−0.743229	+	0.669037i	$0.766707\pi$
$558$	−2.05847	−	7.68233i	−0.0871421	−	0.325219i
$559$	2.03974			0.0862718
$560$		0			0
$561$	−16.6605			−0.703408
$562$	7.62937	+	28.4732i	0.321825	+	1.20107i
$563$	−5.18407	−	1.38907i	−0.218482	−	0.0585422i	0.147917	−	0.989000i	$-0.452743\pi$
$563$	−5.18407	−	1.38907i	−0.218482	−	0.0585422i	−0.366400	+	0.930458i	$0.619410\pi$
$564$	0.551759	−	0.318558i	0.0232332	−	0.0134137i
$565$		0			0
$566$		−	11.2836i		−	0.474286i
$567$	7.11728	−	28.4377i	0.298898	−	1.19427i
$568$	5.03630	+	5.03630i	0.211318	+	0.211318i
$569$	−22.0839	−	12.7502i	−0.925806	−	0.534514i	−0.0403234	−	0.999187i	$-0.512839\pi$
$569$	−22.0839	−	12.7502i	−0.925806	−	0.534514i	−0.885483	+	0.464672i	$0.846172\pi$
$570$		0			0
$571$	−7.95235	−	13.7739i	−0.332795	−	0.576419i	0.650263	−	0.759709i	$-0.274659\pi$
$571$	−7.95235	−	13.7739i	−0.332795	−	0.576419i	−0.983059	+	0.183290i	$0.941325\pi$
$572$	−1.13064	+	0.302955i	−0.0472746	+	0.0126672i
$573$	6.39672	−	6.39672i	0.267227	−	0.267227i
$574$	5.98447	+	3.32424i	0.249787	+	0.138751i
$575$		0			0
$576$	−0.543813	+	0.941911i	−0.0226589	+	0.0392463i
$577$	5.96565	−	22.2641i	0.248353	−	0.926867i	−0.723315	−	0.690518i	$-0.757383\pi$
$577$	5.96565	−	22.2641i	0.248353	−	0.926867i	0.971668	−	0.236349i	$-0.0759508\pi$
$578$	3.32310	−	12.4020i	0.138223	−	0.515854i
$579$	−20.2934	+	35.1493i	−0.843366	+	1.46075i
$580$		0			0
$581$	−14.4173	+	0.238779i	−0.598132	+	0.00990621i
$582$	13.4065	−	13.4065i	0.555719	−	0.555719i
$583$	−32.3214	+	8.66048i	−1.33861	+	0.358681i
$584$	5.76293	+	9.98169i	0.238472	+	0.413045i
$585$		0			0
$586$	8.85989	+	5.11526i	0.365999	+	0.211310i
$587$	28.2277	+	28.2277i	1.16508	+	1.16508i	0.983348	+	0.181734i	$0.0581711\pi$
$587$	28.2277	+	28.2277i	1.16508	+	1.16508i	0.181734	+	0.983348i	$0.441829\pi$
$588$	4.11362	+	13.5415i	0.169643	+	0.558441i
$589$		−	45.3622i		−	1.86912i
$590$		0			0
$591$	−19.4355	+	11.2211i	−0.799471	+	0.461575i
$592$	−4.46814	−	1.19723i	−0.183639	−	0.0492060i
$593$	9.16977	+	34.2220i	0.376557	+	1.40533i	0.851056	+	0.525075i	$0.175963\pi$
$593$	9.16977	+	34.2220i	0.376557	+	1.40533i	−0.474499	+	0.880256i	$0.657371\pi$
$594$	15.6202			0.640905
$595$		0			0
$596$	23.9483			0.980963
$597$	−5.65247	−	21.0953i	−0.231340	−	0.863373i
$598$	−1.27006	−	0.340312i	−0.0519367	−	0.0139164i
$599$	−14.5339	+	8.39115i	−0.593839	+	0.342853i	−0.766614	−	0.642108i	$-0.778060\pi$
$599$	−14.5339	+	8.39115i	−0.593839	+	0.342853i	0.172775	+	0.984961i	$0.444727\pi$
$600$		0			0
$601$		−	1.73528i		−	0.0707833i	−0.999374	−	0.0353917i	$-0.988732\pi$
$601$		−	1.73528i		−	0.0707833i	0.999374	−	0.0353917i	$-0.0112679\pi$
$602$	17.9091	−	5.11804i	0.729919	−	0.208596i
$603$	−2.42925	−	2.42925i	−0.0989266	−	0.0989266i
$604$	−3.06862	−	1.77167i	−0.124860	−	0.0720881i
$605$		0			0
$606$	−9.99616	−	17.3139i	−0.406066	−	0.703327i
$607$	−38.0930	+	10.2070i	−1.54615	+	0.414288i	−0.928245	−	0.371968i	$-0.878683\pi$
$607$	−38.0930	+	10.2070i	−1.54615	+	0.414288i	−0.617900	+	0.786257i	$0.712016\pi$
$608$	−4.38642	+	4.38642i	−0.177893	+	0.177893i
$609$	32.8410	−	19.6930i	1.33079	−	0.798000i
$610$		0			0
$611$	0.0456517	−	0.0790711i	0.00184687	−	0.00319887i
$612$	−0.574183	+	2.14288i	−0.0232100	+	0.0866208i
$613$	−0.0885018	+	0.330293i	−0.00357455	+	0.0133404i	−0.967690	−	0.252143i	$-0.918865\pi$
$613$	−0.0885018	+	0.330293i	−0.00357455	+	0.0133404i	0.964116	+	0.265483i	$0.0855314\pi$
$614$	−0.762678	+	1.32100i	−0.0307792	+	0.0533111i
$615$		0			0
$616$	−9.16697	+	5.49694i	−0.369348	+	0.221478i
$617$	−11.1876	+	11.1876i	−0.450397	+	0.450397i	−0.895486	−	0.445089i	$-0.853172\pi$
$617$	−11.1876	+	11.1876i	−0.450397	+	0.450397i	0.445089	+	0.895486i	$0.353172\pi$
$618$	8.36236	−	2.24069i	0.336383	−	0.0901337i
$619$	−18.2682	−	31.6414i	−0.734260	−	1.27178i	−0.955047	−	0.296454i	$-0.904196\pi$
$619$	−18.2682	−	31.6414i	−0.734260	−	1.27178i	0.220787	−	0.975322i	$-0.429138\pi$
$620$		0			0
$621$	15.1956	+	8.77316i	0.609777	+	0.352055i
$622$	6.80819	+	6.80819i	0.272984	+	0.272984i
$623$	7.81566	−	2.23356i	0.313128	−	0.0894855i
$624$			0.585786i			0.0234502i
$625$		0			0
$626$	−2.62123	+	1.51337i	−0.104766	+	0.0604864i
$627$	−48.9421	−	13.1140i	−1.95456	−	0.523723i
$628$	1.58462	+	5.91389i	0.0632333	+	0.235990i
$629$	−9.43535			−0.376212
$630$		0			0
$631$	−35.8189			−1.42593			−0.712964	−	0.701201i	$-0.752648\pi$
$631$	−35.8189			−1.42593			−0.712964	+	0.701201i	$0.752648\pi$
$632$	1.31384	+	4.90330i	0.0522616	+	0.195043i
$633$	−14.7747	−	3.95888i	−0.587243	−	0.157351i
$634$	−1.68760	+	0.974335i	−0.0670231	+	0.0386958i
$635$		0			0
$636$			16.7457i			0.664010i
$637$	1.48083	+	1.38585i	0.0586726	+	0.0549093i
$638$	20.4502	+	20.4502i	0.809631	+	0.809631i
$639$	6.70867	+	3.87325i	0.265391	+	0.153223i
$640$		0			0
$641$	7.16573	+	12.4114i	0.283029	+	0.490221i	0.972129	−	0.234445i	$-0.0753272\pi$
$641$	7.16573	+	12.4114i	0.283029	+	0.490221i	−0.689100	+	0.724666i	$0.741994\pi$
$642$	−29.0436	+	7.78222i	−1.14626	+	0.307140i
$643$	7.65201	−	7.65201i	0.301766	−	0.301766i	−0.539939	−	0.841704i	$-0.681553\pi$
$643$	7.65201	−	7.65201i	0.301766	−	0.301766i	0.841704	+	0.539939i	$0.181553\pi$
$644$	−12.0051	+	0.198828i	−0.473068	+	0.00783492i
$645$		0			0
$646$	−6.32659	+	10.9580i	−0.248916	+	0.431136i
$647$	−8.37254	+	31.2468i	−0.329159	+	1.22844i	0.580906	+	0.813971i	$0.302698\pi$
$647$	−8.37254	+	31.2468i	−0.329159	+	1.22844i	−0.910065	+	0.414466i	$0.863968\pi$
$648$	2.86770	−	10.7024i	0.112654	−	0.420430i
$649$	1.72791	−	2.99282i	0.0678262	−	0.117478i
$650$		0			0
$651$	−34.1947	−	18.9943i	−1.34019	−	0.744447i
$652$	11.7082	−	11.7082i	0.458528	−	0.458528i
$653$	−0.494788	+	0.132578i	−0.0193625	+	0.00518818i	−0.268487	−	0.963283i	$-0.586524\pi$
$653$	−0.494788	+	0.132578i	−0.0193625	+	0.00518818i	0.249125	+	0.968471i	$0.419857\pi$
$654$	13.3754	+	23.1669i	0.523020	+	0.905898i
$655$		0			0
$656$	2.24080	+	1.29373i	0.0874886	+	0.0505116i
$657$	8.86417	+	8.86417i	0.345824	+	0.345824i
$658$	0.202423	−	0.808797i	0.00789127	−	0.0315302i
$659$		−	19.5542i		−	0.761723i	−0.924632	−	0.380862i	$-0.875627\pi$
$659$		−	19.5542i		−	0.761723i	0.924632	−	0.380862i	$-0.124373\pi$
$660$		0			0
$661$	34.0324	−	19.6486i	1.32371	−	0.764242i	0.339388	−	0.940647i	$-0.389780\pi$
$661$	34.0324	−	19.6486i	1.32371	−	0.764242i	0.984318	+	0.176405i	$0.0564468\pi$
$662$	−27.9090	−	7.47819i	−1.08471	−	0.290648i
$663$	0.309250	+	1.15414i	0.0120103	+	0.0448230i
$664$	−5.44998			−0.211500
$665$		0			0
$666$	−5.03109			−0.194951
$667$	8.40828	+	31.3801i	0.325570	+	1.21504i
$668$	14.0527	+	3.76542i	0.543716	+	0.145688i
$669$	−23.1579	+	13.3702i	−0.895337	+	0.516923i
$670$		0			0
$671$		−	27.9597i		−	1.07937i
$672$	1.46983	+	5.14324i	0.0567000	+	0.198405i
$673$	−18.4813	−	18.4813i	−0.712401	−	0.712401i	0.254636	−	0.967037i	$-0.418044\pi$
$673$	−18.4813	−	18.4813i	−0.712401	−	0.712401i	−0.967037	+	0.254636i	$0.918044\pi$
$674$	−1.00824	−	0.582108i	−0.0388360	−	0.0224220i
$675$		0			0
$676$	−6.45803	−	11.1856i	−0.248386	−	0.430217i
$677$	39.7951	−	10.6631i	1.52945	−	0.409815i	0.606611	−	0.794999i	$-0.292528\pi$
$677$	39.7951	−	10.6631i	1.52945	−	0.409815i	0.922840	+	0.385183i	$0.125862\pi$
$678$	19.7192	−	19.7192i	0.757312	−	0.757312i
$679$	−0.410862	−	24.8076i	−0.0157674	−	0.952030i
$680$		0			0
$681$	16.3702	−	28.3541i	0.627309	−	1.08653i
$682$	7.64618	−	28.5359i	0.292787	−	1.09270i
$683$	2.36248	−	8.81689i	0.0903978	−	0.337369i	−0.905884	−	0.423526i	$-0.860792\pi$
$683$	2.36248	−	8.81689i	0.0903978	−	0.337369i	0.996282	+	0.0861573i	$0.0274588\pi$
$684$	−3.37345	+	5.84298i	−0.128987	+	0.223412i
$685$		0			0
$686$	16.4791	+	8.45219i	0.629175	+	0.322706i
$687$	16.8358	−	16.8358i	0.642325	−	0.642325i
$688$	6.80009	−	1.82208i	0.259251	−	0.0694661i
$689$	1.19989	+	2.07827i	0.0457121	+	0.0791758i
$690$		0			0
$691$	−41.9971	−	24.2470i	−1.59765	−	0.922401i	−0.991940	−	0.126712i	$-0.959558\pi$
$691$	−41.9971	−	24.2470i	−1.59765	−	0.922401i	−0.605706	−	0.795689i	$-0.707109\pi$
$692$	5.49565	+	5.49565i	0.208913	+	0.208913i
$693$	−8.08313	+	8.35538i	−0.307053	+	0.317395i
$694$			16.7042i			0.634082i
$695$		0			0
$696$	12.5343	−	7.23668i	0.475111	−	0.274306i
$697$	5.09790	+	1.36598i	0.193097	+	0.0517401i
$698$	9.50244	+	35.4636i	0.359673	+	1.34232i
$699$	11.5732			0.437739
$700$		0			0
$701$	−30.8898			−1.16669			−0.583347	−	0.812223i	$-0.698257\pi$
$701$	−30.8898			−1.16669			−0.583347	+	0.812223i	$0.698257\pi$
$702$	−0.289940	−	1.08207i	−0.0109431	−	0.0408402i
$703$	−27.7173	−	7.42684i	−1.04538	−	0.280109i
$704$	−3.49872	+	2.01999i	−0.131863	+	0.0761311i
$705$		0			0
$706$		−	14.2708i		−	0.537089i
$707$	−25.3796	−	6.35191i	−0.954496	−	0.238888i
$708$	−1.22290	−	1.22290i	−0.0459595	−	0.0459595i
$709$	12.7354	+	7.35277i	0.478287	+	0.276139i	0.719702	−	0.694283i	$-0.244278\pi$
$709$	12.7354	+	7.35277i	0.478287	+	0.276139i	−0.241416	+	0.970422i	$0.577612\pi$
$710$		0			0
$711$	2.76054	+	4.78140i	0.103528	+	0.179316i
$712$	2.96762	−	0.795171i	0.111216	−	0.0298003i
$713$	23.4656	−	23.4656i	0.878795	−	0.878795i
$714$	5.61116	+	9.35745i	0.209992	+	0.350194i
$715$		0			0
$716$	1.93236	−	3.34695i	0.0722157	−	0.125081i
$717$	−4.36306	+	16.2831i	−0.162941	+	0.608105i
$718$	7.01110	−	26.1658i	0.261652	−	0.976499i
$719$	−11.7360	+	20.3273i	−0.437679	+	0.758082i	−0.997510	−	0.0705247i	$-0.977533\pi$
$719$	−11.7360	+	20.3273i	−0.437679	+	0.758082i	0.559831	+	0.828607i	$0.310866\pi$
$720$		0			0
$721$	5.50134	−	9.90382i	0.204881	−	0.368837i
$722$	−13.7753	+	13.7753i	−0.512665	+	0.512665i
$723$	−5.78913	+	1.55119i	−0.215300	+	0.0576895i
$724$	3.49553	+	6.05444i	0.129911	+	0.225012i
$725$		0			0
$726$	−9.31732	−	5.37936i	−0.345798	−	0.199647i
$727$	−14.1380	−	14.1380i	−0.524349	−	0.524349i	0.394533	−	0.918882i	$-0.370907\pi$
$727$	−14.1380	−	14.1380i	−0.524349	−	0.524349i	−0.918882	+	0.394533i	$0.870907\pi$
$728$	0.550950	+	0.532998i	0.0204196	+	0.0197542i
$729$			11.4004i			0.422236i
$730$		0			0
$731$	12.4359	−	7.17986i	0.459958	−	0.265557i
$732$	−13.5155	−	3.62148i	−0.499549	−	0.133854i
$733$	7.17859	+	26.7908i	0.265147	+	0.989543i	0.962160	+	0.272484i	$0.0878452\pi$
$733$	7.17859	+	26.7908i	0.265147	+	0.989543i	−0.697013	+	0.717058i	$0.745488\pi$
$734$	22.6715			0.836821
$735$		0			0
$736$	−4.53813			−0.167278
$737$	−3.30280	−	12.3262i	−0.121660	−	0.454042i
$738$	2.71829	+	0.728364i	0.100062	+	0.0268114i
$739$	11.7451	−	6.78102i	0.432050	−	0.249444i	−0.268170	−	0.963372i	$-0.586419\pi$
$739$	11.7451	−	6.78102i	0.432050	−	0.249444i	0.700219	+	0.713928i	$0.253085\pi$
$740$		0			0
$741$			3.63383i			0.133492i
$742$	15.7498	+	15.2366i	0.578194	+	0.559354i
$743$	−13.5961	−	13.5961i	−0.498791	−	0.498791i	0.412270	−	0.911062i	$-0.364736\pi$
$743$	−13.5961	−	13.5961i	−0.498791	−	0.498791i	−0.911062	+	0.412270i	$0.864736\pi$
$744$	−12.8037	−	7.39223i	−0.469407	−	0.271012i
$745$		0			0
$746$	6.41789	+	11.1161i	0.234976	+	0.406990i
$747$	−5.72557	+	1.53416i	−0.209488	+	0.0561320i
$748$	−5.82691	+	5.82691i	−0.213053	+	0.213053i
$749$	−19.1069	+	34.3973i	−0.698152	+	1.25685i
$750$		0			0
$751$	−21.8309	+	37.8123i	−0.796622	+	1.37979i	0.125182	+	0.992134i	$0.460049\pi$
$751$	−21.8309	+	37.8123i	−0.796622	+	1.37979i	−0.921804	+	0.387656i	$0.873285\pi$
$752$	0.0815604	−	0.304388i	0.00297420	−	0.0110999i
$753$	8.46663	−	31.5979i	0.308541	−	1.15149i
$754$	1.03707	−	1.79626i	0.0377678	−	0.0654158i
$755$		0			0
$756$	−5.26079	−	8.77316i	−0.191333	−	0.319077i
$757$	−7.88896	+	7.88896i	−0.286729	+	0.286729i	−0.835785	−	0.549056i	$-0.814987\pi$
$757$	−7.88896	+	7.88896i	−0.286729	+	0.286729i	0.549056	+	0.835785i	$0.314987\pi$
$758$	−13.9807	+	3.74613i	−0.507803	+	0.136065i
$759$	−18.5337	−	32.1013i	−0.672730	−	1.16520i
$760$		0			0
$761$	−1.70923	−	0.986825i	−0.0619596	−	0.0357724i	0.468700	−	0.883357i	$-0.344722\pi$
$761$	−1.70923	−	0.986825i	−0.0619596	−	0.0357724i	−0.530660	+	0.847585i	$0.678056\pi$
$762$	4.44761	+	4.44761i	0.161120	+	0.161120i
$763$	33.9593	+	8.49921i	1.22941	+	0.307692i
$764$		−	4.47442i		−	0.161879i
$765$		0			0
$766$	−1.51691	+	0.875788i	−0.0548082	+	0.0316435i
$767$	−0.239397	−	0.0641463i	−0.00864413	−	0.00231619i
$768$	0.523277	+	1.95290i	0.0188821	+	0.0704691i
$769$	17.4914			0.630756			0.315378	−	0.948966i	$-0.397869\pi$
$769$	17.4914			0.630756			0.315378	+	0.948966i	$0.397869\pi$
$770$		0			0
$771$	−11.7763			−0.424112
$772$	5.19573	+	19.3907i	0.186998	+	0.697887i
$773$	−43.1933	−	11.5736i	−1.55355	−	0.416274i	−0.622939	−	0.782271i	$-0.714061\pi$
$773$	−43.1933	−	11.5736i	−1.55355	−	0.416274i	−0.930616	+	0.365997i	$0.880728\pi$
$774$	6.63103	−	3.82843i	0.238347	−	0.137610i
$775$		0			0
$776$		−	9.37769i		−	0.336640i
$777$	−17.2044	+	17.7839i	−0.617205	+	0.637994i
$778$	−1.96738	−	1.96738i	−0.0705341	−	0.0705341i
$779$	13.9004	+	8.02542i	0.498035	+	0.287540i
$780$		0			0
$781$	14.3871	+	24.9193i	0.514813	+	0.891682i
$782$	−8.94120	+	2.39579i	−0.319737	+	0.0856732i
$783$	−19.5716	+	19.5716i	−0.699433	+	0.699433i
$784$	6.17475	+	3.29733i	0.220527	+	0.117762i
$785$		0			0
$786$	7.37827	−	12.7795i	0.263174	−	0.455831i
$787$	−6.71595	+	25.0643i	−0.239398	+	0.893445i	0.736719	+	0.676199i	$0.236374\pi$
$787$	−6.71595	+	25.0643i	−0.239398	+	0.893445i	−0.976117	+	0.217246i	$0.930293\pi$
$788$	−2.87294	+	10.7220i	−0.102344	+	0.381954i
$789$	1.75605	−	3.04156i	0.0625170	−	0.108283i
$790$		0			0
$791$	−0.604323	−	36.4887i	−0.0214873	−	1.29739i
$792$	−3.10701	+	3.10701i	−0.110403	+	0.110403i
$793$	−1.93688	+	0.518984i	−0.0687805	+	0.0184297i
$794$	19.8340	+	34.3535i	0.703881	+	1.21916i
$795$		0			0
$796$	−9.35485	−	5.40103i	−0.331574	−	0.191434i
$797$	−37.3374	−	37.3374i	−1.32256	−	1.32256i	−0.911698	−	0.410861i	$-0.865228\pi$
$797$	−37.3374	−	37.3374i	−1.32256	−	1.32256i	−0.410861	−	0.911698i	$-0.634772\pi$
$798$	9.11786	+	31.9052i	0.322769	+	1.12943i
$799$		−	0.642773i		−	0.0227397i
$800$		0			0
$801$	2.89384	−	1.67076i	0.102249	−	0.0590333i
$802$	−19.2901	−	5.16876i	−0.681156	−	0.182515i
$803$	12.0517	+	44.9776i	0.425295	+	1.58722i
$804$	−6.38621			−0.225224
$805$		0			0
$806$	−2.11872			−0.0746287
$807$	−1.97975	−	7.38854i	−0.0696906	−	0.260089i
$808$	−9.55150	−	2.55932i	−0.336021	−	0.0900364i
$809$	13.9001	−	8.02525i	0.488703	−	0.282153i	−0.235333	−	0.971915i	$-0.575618\pi$
$809$	13.9001	−	8.02525i	0.488703	−	0.282153i	0.724036	+	0.689762i	$0.242285\pi$
$810$		0			0
$811$			35.4040i			1.24320i	0.783334	+	0.621602i	$0.213518\pi$
$811$			35.4040i			1.24320i	−0.783334	+	0.621602i	$0.786482\pi$
$812$	4.59844	−	18.3734i	0.161374	−	0.644781i
$813$	30.3791	+	30.3791i	1.06544	+	1.06544i
$814$	−16.1842	−	9.34397i	−0.567257	−	0.327506i
$815$		0			0
$816$	2.06196	+	3.57142i	0.0721831	+	0.125025i
$817$	42.1832	−	11.3030i	1.47580	−	0.395440i
$818$	10.8227	−	10.8227i	0.378407	−	0.378407i
$819$	0.728847	+	0.404858i	0.0254680	+	0.0141469i
$820$		0			0
$821$	−13.4231	+	23.2495i	−0.468469	+	0.811412i	−0.999351	−	0.0360337i	$-0.988528\pi$
$821$	−13.4231	+	23.2495i	−0.468469	+	0.811412i	0.530881	+	0.847446i	$0.321861\pi$
$822$	−3.75657	+	14.0197i	−0.131025	+	0.488993i
$823$	−7.24225	+	27.0285i	−0.252449	+	0.942153i	0.717043	+	0.697029i	$0.245495\pi$
$823$	−7.24225	+	27.0285i	−0.252449	+	0.942153i	−0.969492	+	0.245124i	$0.921171\pi$
$824$	2.14101	−	3.70835i	0.0745858	−	0.129186i
$825$		0			0
$826$	−2.26288	+	0.0374776i	−0.0787355	+	0.00130401i
$827$	−16.8901	+	16.8901i	−0.587325	+	0.587325i	−0.936906	−	0.349581i	$-0.886324\pi$
$827$	−16.8901	+	16.8901i	−0.587325	+	0.587325i	0.349581	+	0.936906i	$0.386324\pi$
$828$	−4.76761	+	1.27748i	−0.165686	+	0.0443954i
$829$	−7.08412	−	12.2701i	−0.246042	−	0.426157i	0.716382	−	0.697708i	$-0.245797\pi$
$829$	−7.08412	−	12.2701i	−0.246042	−	0.426157i	−0.962424	+	0.271551i	$0.912463\pi$
$830$		0			0
$831$	8.56228	+	4.94343i	0.297022	+	0.171486i
$832$	0.204875	+	0.204875i	0.00710276	+	0.00710276i
$833$	13.9065	+	3.23673i	0.481831	+	0.112146i
$834$		−	25.1049i		−	0.869311i
$835$		0			0
$836$	−21.7037	+	12.5306i	−0.750638	+	0.433381i
$837$	27.3100	+	7.31770i	0.943972	+	0.252937i
$838$	−7.17000	−	26.7588i	−0.247683	−	0.924367i
$839$	−18.1874			−0.627900			−0.313950	−	0.949439i	$-0.601652\pi$
$839$	−18.1874			−0.627900			−0.313950	+	0.949439i	$0.601652\pi$
$840$		0			0
$841$	−22.2469			−0.767134
$842$	−8.54515	−	31.8909i	−0.294485	−	1.09903i
$843$	57.5667	+	15.4250i	1.98270	+	0.531264i
$844$	−6.55196	+	3.78278i	−0.225528	+	0.130209i
$845$		0			0
$846$		−	0.342738i		−	0.0117836i
$847$	−13.5371	+	3.86863i	−0.465141	+	0.132928i
$848$	5.85669	+	5.85669i	0.201120	+	0.201120i
$849$	−19.7567	−	11.4065i	−0.678048	−	0.391471i
$850$		0			0
$851$	−10.4962	−	18.1799i	−0.359804	−	0.623198i
$852$	13.9093	−	3.72699i	0.476525	−	0.127685i
$853$	−17.4820	+	17.4820i	−0.598574	+	0.598574i	−0.939933	−	0.341359i	$-0.889113\pi$
$853$	−17.4820	+	17.4820i	−0.598574	+	0.598574i	0.341359	+	0.939933i	$0.389113\pi$
$854$	−15.7037	+	9.41665i	−0.537369	+	0.322231i
$855$		0			0
$856$	−7.43604	+	12.8796i	−0.254159	+	0.440216i
$857$	6.76932	−	25.2634i	0.231235	−	0.862982i	−0.748574	−	0.663051i	$-0.769261\pi$
$857$	6.76932	−	25.2634i	0.231235	−	0.862982i	0.979810	−	0.199932i	$-0.0640720\pi$
$858$	−0.612511	+	2.28592i	−0.0209108	+	0.0780401i
$859$	−24.4126	+	42.2838i	−0.832946	+	1.44271i	0.0627455	+	0.998030i	$0.480014\pi$
$859$	−24.4126	+	42.2838i	−0.832946	+	1.44271i	−0.895692	+	0.444676i	$0.853319\pi$
$860$		0			0
$861$	11.8701	−	7.11788i	0.404533	−	0.242577i
$862$	−16.9121	+	16.9121i	−0.576027	+	0.576027i
$863$	14.8258	−	3.97256i	0.504676	−	0.135228i	0.00250685	−	0.999997i	$-0.499202\pi$
$863$	14.8258	−	3.97256i	0.504676	−	0.135228i	0.502169	+	0.864769i	$0.332535\pi$
$864$	−1.93321	−	3.34841i	−0.0657691	−	0.113915i
$865$		0			0
$866$	16.2298	+	9.37026i	0.551510	+	0.318414i
$867$	−18.3555	−	18.3555i	−0.623387	−	0.623387i
$868$	−18.6025	+	5.31621i	−0.631410	+	0.180444i
$869$			20.5080i			0.695686i
$870$		0			0
$871$	−0.792578	+	0.457595i	−0.0268555	+	0.0155050i
$872$	12.7804	+	3.42451i	0.432800	+	0.115968i
$873$	−2.63980	−	9.85188i	−0.0893438	−	0.333436i
$874$	−28.1515			−0.952240
$875$		0			0
$876$	23.3028			0.787330
$877$	10.2134	+	38.1169i	0.344882	+	1.28712i	0.892750	+	0.450552i	$0.148773\pi$
$877$	10.2134	+	38.1169i	0.344882	+	1.28712i	−0.547868	+	0.836565i	$0.684560\pi$
$878$	−13.6270	−	3.65133i	−0.459888	−	0.123227i
$879$	17.9128	−	10.3420i	0.604185	−	0.348826i
$880$		0			0
$881$			52.5926i			1.77189i	0.463791	+	0.885945i	$0.346489\pi$
$881$			52.5926i			1.77189i	−0.463791	+	0.885945i	$0.653511\pi$
$882$	7.41518	+	1.72588i	0.249682	+	0.0581135i
$883$	−13.0940	−	13.0940i	−0.440649	−	0.440649i	0.451581	−	0.892230i	$-0.350860\pi$
$883$	−13.0940	−	13.0940i	−0.440649	−	0.440649i	−0.892230	+	0.451581i	$0.850860\pi$
$884$	0.511811	+	0.295494i	0.0172141	+	0.00993854i
$885$		0			0
$886$	−10.5317	−	18.2414i	−0.353819	−	0.612833i
$887$	−35.6990	+	9.56553i	−1.19866	+	0.321179i	−0.802302	−	0.596919i	$-0.796391\pi$
$887$	−35.6990	+	9.56553i	−1.19866	+	0.321179i	−0.396354	+	0.918098i	$0.629725\pi$
$888$	−6.61308	+	6.61308i	−0.221920	+	0.221920i
$889$	8.22991	−	0.136303i	0.276022	−	0.00457146i
$890$		0			0
$891$	22.3813	−	38.7656i	0.749803	−	1.29870i
$892$	−3.42318	+	12.7755i	−0.114617	+	0.427755i
$893$	0.505946	−	1.88822i	0.0169308	−	0.0631867i
$894$	24.2092	−	41.9316i	0.809678	−	1.40240i
$895$		0			0
$896$	2.31288	+	1.28475i	0.0772679	+	0.0429205i
$897$	−1.87976	+	1.87976i	−0.0627633	+	0.0627633i
$898$	−30.2574	+	8.10744i	−1.00970	+	0.270549i
$899$	26.1742	+	45.3351i	0.872959	+	1.51201i
$900$		0			0
$901$	14.6310	+	8.44719i	0.487428	+	0.281417i
$902$	7.39156	+	7.39156i	0.246112	+	0.246112i
$903$	9.14288	−	36.5311i	0.304256	−	1.21568i
$904$		−	13.7933i		−	0.458759i
$905$		0			0
$906$	−6.20410	+	3.58194i	−0.206117	+	0.119002i
$907$	−16.0061	−	4.28883i	−0.531474	−	0.142408i	−0.0169054	−	0.999857i	$-0.505381\pi$
$907$	−16.0061	−	4.28883i	−0.531474	−	0.142408i	−0.514569	+	0.857449i	$0.672048\pi$
$908$	−4.19127	−	15.6420i	−0.139092	−	0.519099i
$909$	−10.7549			−0.356718
$910$		0			0
$911$	−1.46770			−0.0486270			−0.0243135	−	0.999704i	$-0.507740\pi$
$911$	−1.46770			−0.0486270			−0.0243135	+	0.999704i	$0.507740\pi$
$912$	3.24606	+	12.1145i	0.107488	+	0.401150i
$913$	−21.2676	−	5.69862i	−0.703853	−	0.188597i
$914$	2.47817	−	1.43077i	0.0819705	−	0.0473257i
$915$		0			0
$916$		−	11.7764i		−	0.389103i
$917$	−5.30617	−	18.5674i	−0.175225	−	0.613149i
$918$	−5.57658	−	5.57658i	−0.184055	−	0.184055i
$919$	−24.1523	−	13.9443i	−0.796710	−	0.459981i	0.0456096	−	0.998959i	$-0.485477\pi$
$919$	−24.1523	−	13.9443i	−0.796710	−	0.459981i	−0.842319	+	0.538979i	$0.818810\pi$
$920$		0			0
$921$	1.54197	+	2.67078i	0.0508098	+	0.0880051i
$922$	−2.92361	+	0.783378i	−0.0962838	+	0.0257992i
$923$	1.45920	−	1.45920i	0.0480302	−	0.0480302i
$924$	0.357861	+	21.6075i	0.0117728	+	0.710833i
$925$		0			0
$926$	−13.6393	+	23.6240i	−0.448215	+	0.776332i
$927$	1.20538	−	4.49855i	0.0395900	−	0.147752i
$928$	1.85281	−	6.91477i	0.0608213	−	0.226988i
$929$	16.6468	−	28.8331i	0.546164	−	0.945984i	−0.452368	−	0.891831i	$-0.649421\pi$
$929$	16.6468	−	28.8331i	0.546164	−	0.945984i	0.998533	−	0.0541530i	$-0.0172459\pi$
$930$		0			0
$931$	38.3040	+	20.4544i	1.25536	+	0.670367i
$932$	4.04765	−	4.04765i	0.132585	−	0.132585i
$933$	18.8030	−	5.03824i	0.615581	−	0.164944i
$934$	−12.5645	−	21.7623i	−0.411122	−	0.712084i
$935$		0			0
$936$	0.272906	+	0.157563i	0.00892023	+	0.00515009i
$937$	25.6651	+	25.6651i	0.838442	+	0.838442i	0.988654	−	0.150212i	$-0.0479957\pi$
$937$	25.6651	+	25.6651i	0.838442	+	0.838442i	−0.150212	+	0.988654i	$0.547996\pi$
$938$	−5.81071	+	6.00642i	−0.189726	+	0.196117i
$939$			6.11942i			0.199700i
$940$		0			0
$941$	−21.0732	+	12.1666i	−0.686967	+	0.396621i	−0.802475	−	0.596686i	$-0.796484\pi$
$941$	−21.0732	+	12.1666i	−0.686967	+	0.396621i	0.115508	+	0.993307i	$0.463151\pi$
$942$	11.9566	+	3.20377i	0.389568	+	0.104384i
$943$	3.03911	+	11.3421i	0.0989670	+	0.369350i
$944$	−0.855404			−0.0278410
$945$		0			0
$946$	28.4413			0.924707
$947$	0.556477	+	2.07680i	0.0180831	+	0.0674869i	0.974378	−	0.224918i	$-0.0722113\pi$
$947$	0.556477	+	2.07680i	0.0180831	+	0.0674869i	−0.956295	+	0.292405i	$0.905545\pi$
$948$	9.91343	+	2.65630i	0.321973	+	0.0862725i
$949$	2.89206	−	1.66973i	0.0938804	−	0.0542019i
$950$		0			0
$951$			3.93980i			0.127757i
$952$	5.23517	+	1.31024i	0.169673	+	0.0424652i
$953$	13.1863	+	13.1863i	0.427146	+	0.427146i	0.887655	−	0.460509i	$-0.152333\pi$
$953$	13.1863	+	13.1863i	0.427146	+	0.427146i	−0.460509	+	0.887655i	$0.652333\pi$
$954$	7.80149	+	4.50419i	0.252582	+	0.145829i
$955$		0			0
$956$	4.16897	+	7.22087i	0.134834	+	0.233540i
$957$	56.4796	−	15.1337i	1.82573	−	0.489202i
$958$	5.85973	−	5.85973i	0.189319	−	0.189319i
$959$	9.76792	+	16.2895i	0.315423	+	0.526015i
$960$		0			0
$961$	11.2368	−	19.4627i	0.362477	−	0.627829i
$962$	−0.346883	+	1.29459i	−0.0111840	+	0.0417391i
$963$	−4.18646	+	15.6241i	−0.134907	+	0.503479i
$964$	−1.48219	+	2.56723i	−0.0477381	+	0.0826849i
$965$		0			0
$966$	−11.7878	+	21.2210i	−0.379266	+	0.682775i
$967$	27.7931	−	27.7931i	0.893766	−	0.893766i	−0.101109	−	0.994875i	$-0.532239\pi$
$967$	27.7931	−	27.7931i	0.893766	−	0.893766i	0.994875	+	0.101109i	$0.0322392\pi$
$968$	−5.14006	+	1.37728i	−0.165208	+	0.0442673i
$969$	12.7910	+	22.1547i	0.410907	+	0.711711i
$970$		0			0
$971$	12.1029	+	6.98760i	0.388400	+	0.224243i	0.681467	−	0.731849i	$-0.261342\pi$
$971$	12.1029	+	6.98760i	0.388400	+	0.224243i	−0.293067	+	0.956092i	$0.594676\pi$
$972$	−7.63821	−	7.63821i	−0.244996	−	0.244996i
$973$	−23.6119	−	22.8425i	−0.756963	−	0.732298i
$974$		−	10.6783i		−	0.342155i
$975$		0			0
$976$	−5.99356	+	3.46038i	−0.191849	+	0.110764i
$977$	8.06456	+	2.16089i	0.258008	+	0.0691331i	0.385505	−	0.922706i	$-0.374027\pi$
$977$	8.06456	+	2.16089i	0.258008	+	0.0691331i	−0.127496	+	0.991839i	$0.540694\pi$
$978$	−8.66436	−	32.3358i	−0.277056	−	1.03399i
$979$	12.4120			0.396690
$980$		0			0
$981$	14.3907			0.459459
$982$	−6.65836	−	24.8494i	−0.212477	−	0.792975i
$983$	23.5262	+	6.30383i	0.750370	+	0.201061i	0.613682	−	0.789553i	$-0.289688\pi$
$983$	23.5262	+	6.30383i	0.750370	+	0.201061i	0.136688	+	0.990614i	$0.456354\pi$
$984$	4.53043	−	2.61564i	0.144425	−	0.0833836i
$985$		0			0
$986$		−	14.6019i		−	0.465018i
$987$	−1.21151	−	1.17203i	−0.0385628	−	0.0373062i
$988$	1.27091	+	1.27091i	0.0404329	+	0.0404329i
$989$	27.6681	+	15.9742i	0.879794	+	0.507949i
$990$		0			0
$991$	−8.72002	−	15.1035i	−0.277000	−	0.479779i	0.693637	−	0.720324i	$-0.256007\pi$
$991$	−8.72002	−	15.1035i	−0.277000	−	0.479779i	−0.970638	+	0.240545i	$0.922674\pi$
$992$	−7.06340	+	1.89263i	−0.224263	+	0.0600911i
$993$	−41.3067	+	41.3067i	−1.31083	+	1.31083i
$994$	9.15051	−	16.4733i	0.290237	−	0.522500i
$995$		0			0
$996$	−5.50936	+	9.54248i	−0.174571	+	0.302365i
$997$	−6.77324	+	25.2781i	−0.214511	+	0.800565i	0.771827	+	0.635832i	$0.219343\pi$
$997$	−6.77324	+	25.2781i	−0.214511	+	0.800565i	−0.986338	+	0.164733i	$0.947324\pi$
$998$	3.77845	−	14.1014i	0.119605	−	0.446371i
$999$	8.94255	−	15.4890i	0.282930	−	0.490049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.o.c.243.1		16
5.2	odd	4	inner	350.2.o.c.257.3		16
5.3	odd	4		70.2.k.a.47.2	yes	16
5.4	even	2		70.2.k.a.33.4	yes	16
7.3	odd	6	inner	350.2.o.c.143.3		16
15.8	even	4		630.2.bv.c.397.4		16
15.14	odd	2		630.2.bv.c.523.2		16
20.3	even	4		560.2.ci.c.257.1		16
20.19	odd	2		560.2.ci.c.33.1		16
35.3	even	12		70.2.k.a.17.4	yes	16
35.4	even	6		490.2.l.c.423.1		16
35.9	even	6		490.2.g.c.293.5		16
35.13	even	4		490.2.l.c.117.1		16
35.17	even	12	inner	350.2.o.c.157.1		16
35.18	odd	12		490.2.l.c.227.3		16
35.19	odd	6		490.2.g.c.293.8		16
35.23	odd	12		490.2.g.c.97.8		16
35.24	odd	6		70.2.k.a.3.2	✓	16
35.33	even	12		490.2.g.c.97.5		16
35.34	odd	2		490.2.l.c.313.3		16
105.38	odd	12		630.2.bv.c.577.2		16
105.59	even	6		630.2.bv.c.73.4		16
140.3	odd	12		560.2.ci.c.17.1		16
140.59	even	6		560.2.ci.c.353.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.2	✓	16	35.24	odd	6
70.2.k.a.17.4	yes	16	35.3	even	12
70.2.k.a.33.4	yes	16	5.4	even	2
70.2.k.a.47.2	yes	16	5.3	odd	4
350.2.o.c.143.3		16	7.3	odd	6	inner
350.2.o.c.157.1		16	35.17	even	12	inner
350.2.o.c.243.1		16	1.1	even	1	trivial
350.2.o.c.257.3		16	5.2	odd	4	inner
490.2.g.c.97.5		16	35.33	even	12
490.2.g.c.97.8		16	35.23	odd	12
490.2.g.c.293.5		16	35.9	even	6
490.2.g.c.293.8		16	35.19	odd	6
490.2.l.c.117.1		16	35.13	even	4
490.2.l.c.227.3		16	35.18	odd	12
490.2.l.c.313.3		16	35.34	odd	2
490.2.l.c.423.1		16	35.4	even	6
560.2.ci.c.17.1		16	140.3	odd	12
560.2.ci.c.33.1		16	20.19	odd	2
560.2.ci.c.257.1		16	20.3	even	4
560.2.ci.c.353.1		16	140.59	even	6
630.2.bv.c.73.4		16	105.59	even	6
630.2.bv.c.397.4		16	15.8	even	4
630.2.bv.c.523.2		16	15.14	odd	2
630.2.bv.c.577.2		16	105.38	odd	12

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.o (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-1.95290 - 0.523277i) q^{3} +(-0.866025 + 0.500000i) q^{4} +2.02179i q^{6} +(1.90155 + 1.83959i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.941911 + 0.543813i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-1.95290 - 0.523277i) q^{3} +(-0.866025 + 0.500000i) q^{4} +2.02179i q^{6} +(1.90155 + 1.83959i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.941911 + 0.543813i) q^{9} +(2.01999 + 3.49872i) q^{11} +(1.95290 - 0.523277i) q^{12} +(0.204875 - 0.204875i) q^{13} +(1.28475 - 2.31288i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.527924 - 1.97024i) q^{17} +(0.281498 - 1.05057i) q^{18} +(3.10166 - 5.37224i) q^{19} +(-2.75092 - 4.58757i) q^{21} +(2.85669 - 2.85669i) q^{22} +(4.38350 - 1.17456i) q^{23} +(-1.01089 - 1.75092i) q^{24} +(-0.250919 - 0.144868i) q^{26} +(2.73397 + 2.73397i) q^{27} +(-2.56659 - 0.642357i) q^{28} +7.15869i q^{29} +(6.33287 - 3.65628i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-2.11403 - 7.88965i) q^{33} -2.03974 q^{34} -1.08763 q^{36} +(-1.19723 - 4.46814i) q^{37} +(-5.99195 - 1.60554i) q^{38} +(-0.507306 + 0.292893i) q^{39} +2.58745i q^{41} +(-3.71926 + 3.84454i) q^{42} +(4.97801 + 4.97801i) q^{43} +(-3.49872 - 2.01999i) q^{44} +(-2.26907 - 3.93014i) q^{46} +(0.304388 - 0.0815604i) q^{47} +(-1.42962 + 1.42962i) q^{48} +(0.231803 + 6.99616i) q^{49} +(-2.06196 + 3.57142i) q^{51} +(-0.0749894 + 0.279864i) q^{52} +(-2.14370 + 8.00039i) q^{53} +(1.93321 - 3.34841i) q^{54} +(0.0438127 + 2.64539i) q^{56} +(-8.86840 + 8.86840i) q^{57} +(6.91477 - 1.85281i) q^{58} +(-0.427702 - 0.740802i) q^{59} +(-5.99356 - 3.46038i) q^{61} +(-5.17076 - 5.17076i) q^{62} +(0.790700 + 2.76682i) q^{63} +1.00000i q^{64} +(-7.07367 + 4.08398i) q^{66} +(-3.05106 - 0.817530i) q^{67} +(0.527924 + 1.97024i) q^{68} -9.17514 q^{69} +7.12240 q^{71} +(0.281498 + 1.05057i) q^{72} +(11.1331 + 2.98311i) q^{73} +(-4.00603 + 2.31288i) q^{74} +6.20333i q^{76} +(-2.59511 + 10.3690i) q^{77} +(0.414214 + 0.414214i) q^{78} +(4.39618 + 2.53813i) q^{79} +(-5.53997 - 9.59552i) q^{81} +(2.49929 - 0.669683i) q^{82} +(-3.85372 + 3.85372i) q^{83} +(4.67615 + 2.59749i) q^{84} +(3.51999 - 6.09680i) q^{86} +(3.74598 - 13.9802i) q^{87} +(-1.04562 + 3.90231i) q^{88} +(1.53615 - 2.66069i) q^{89} +(0.766467 - 0.0126942i) q^{91} +(-3.20895 + 3.20895i) q^{92} +(-14.2807 + 3.82650i) q^{93} +(-0.157563 - 0.272906i) q^{94} +(1.75092 + 1.01089i) q^{96} +(-6.63103 - 6.63103i) q^{97} +(6.69778 - 2.03464i) q^{98} +4.39398i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} - 12 q^{11} + 8 q^{16} + 36 q^{17} + 8 q^{18} - 28 q^{21} + 8 q^{22} + 4 q^{23} + 12 q^{26} - 4 q^{28} + 24 q^{31} - 48 q^{33} - 8 q^{36} - 4 q^{37} - 24 q^{38} - 36 q^{42} + 8 q^{43} - 8 q^{46} - 12 q^{47} - 16 q^{51} + 28 q^{53} - 4 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{61} + 36 q^{63} - 32 q^{67} + 36 q^{68} + 16 q^{71} + 8 q^{72} + 12 q^{73} - 16 q^{77} - 16 q^{78} + 48 q^{82} + 12 q^{86} + 24 q^{87} + 4 q^{88} - 16 q^{91} - 8 q^{92} - 28 q^{93} + 12 q^{96} - 40 q^{98}+O(q^{100}) \) 16 * q - 8 * q^7 - 12 * q^11 + 8 * q^16 + 36 * q^17 + 8 * q^18 - 28 * q^21 + 8 * q^22 + 4 * q^23 + 12 * q^26 - 4 * q^28 + 24 * q^31 - 48 * q^33 - 8 * q^36 - 4 * q^37 - 24 * q^38 - 36 * q^42 + 8 * q^43 - 8 * q^46 - 12 * q^47 - 16 * q^51 + 28 * q^53 - 4 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^61 + 36 * q^63 - 32 * q^67 + 36 * q^68 + 16 * q^71 + 8 * q^72 + 12 * q^73 - 16 * q^77 - 16 * q^78 + 48 * q^82 + 12 * q^86 + 24 * q^87 + 4 * q^88 - 16 * q^91 - 8 * q^92 - 28 * q^93 + 12 * q^96 - 40 * q^98

Introduction

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