LMFDB - Embedded newform 276.2.o.a.35.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(35,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 20]))

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

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

chi := DirichletCharacter("276.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.o (of order $22$, degree $10$, 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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$44$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			35.34
Character	$\chi$	$=$	276.35
Dual form			276.2.o.a.71.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00830 + 0.991633i) q^{2} +(-1.69516 - 0.355553i) q^{3} +(0.0333293 + 1.99972i) q^{4} +(0.252117 + 0.858632i) q^{5} +(-1.35665 - 2.03948i) q^{6} +(-1.92220 + 1.66560i) q^{7} +(-1.94938 + 2.04937i) q^{8} +(2.74716 + 1.20544i) q^{9} +O(q^{10})$	\(q+(1.00830 + 0.991633i) q^{2} +(-1.69516 - 0.355553i) q^{3} +(0.0333293 + 1.99972i) q^{4} +(0.252117 + 0.858632i) q^{5} +(-1.35665 - 2.03948i) q^{6} +(-1.92220 + 1.66560i) q^{7} +(-1.94938 + 2.04937i) q^{8} +(2.74716 + 1.20544i) q^{9} +(-0.597239 + 1.11576i) q^{10} +(-1.26700 - 0.814252i) q^{11} +(0.654508 - 3.40171i) q^{12} +(-0.796709 + 0.919451i) q^{13} +(-3.58982 - 0.226700i) q^{14} +(-0.122091 - 1.54516i) q^{15} +(-3.99778 + 0.133299i) q^{16} +(-6.64432 + 3.03436i) q^{17} +(1.57461 + 3.93962i) q^{18} +(5.60653 + 2.56042i) q^{19} +(-1.70862 + 0.532782i) q^{20} +(3.85066 - 2.14002i) q^{21} +(-0.470075 - 2.07741i) q^{22} +(-0.578761 + 4.76078i) q^{23} +(4.03318 - 2.78090i) q^{24} +(3.53258 - 2.27025i) q^{25} +(-1.71508 + 0.137038i) q^{26} +(-4.22830 - 3.02018i) q^{27} +(-3.39480 - 3.78836i) q^{28} +(6.02903 - 2.75337i) q^{29} +(1.40913 - 1.67906i) q^{30} +(4.18222 - 0.601313i) q^{31} +(-4.16313 - 3.82992i) q^{32} +(1.85827 + 1.83078i) q^{33} +(-9.70842 - 3.52918i) q^{34} +(-1.91476 - 1.23054i) q^{35} +(-2.31898 + 5.53374i) q^{36} +(5.30163 + 1.55670i) q^{37} +(3.11406 + 8.14129i) q^{38} +(1.67747 - 1.27535i) q^{39} +(-2.25113 - 1.15712i) q^{40} +(-1.90201 - 6.47765i) q^{41} +(6.00473 + 1.66066i) q^{42} +(5.31318 + 0.763921i) q^{43} +(1.58605 - 2.56079i) q^{44} +(-0.342423 + 2.66272i) q^{45} +(-5.30451 + 4.22637i) q^{46} -0.483749 q^{47} +(6.82429 + 1.19546i) q^{48} +(-0.0755561 + 0.525504i) q^{49} +(5.81315 + 1.21393i) q^{50} +(12.3421 - 2.78133i) q^{51} +(-1.86520 - 1.56255i) q^{52} +(4.51572 - 3.91290i) q^{53} +(-1.26847 - 7.23816i) q^{54} +(0.379710 - 1.29317i) q^{55} +(0.333691 - 7.18619i) q^{56} +(-8.59363 - 6.33375i) q^{57} +(8.80939 + 3.20237i) q^{58} +(-0.185128 + 0.213649i) q^{59} +(3.08583 - 0.295648i) q^{60} +(1.15091 + 8.00476i) q^{61} +(4.81321 + 3.54093i) q^{62} +(-7.28839 + 2.25857i) q^{63} +(-0.399804 - 7.99000i) q^{64} +(-0.990335 - 0.452271i) q^{65} +(0.0582272 + 3.68868i) q^{66} +(-2.83225 - 4.40707i) q^{67} +(-6.28932 - 13.1857i) q^{68} +(2.67380 - 7.86453i) q^{69} +(-0.710403 - 3.13949i) q^{70} +(-6.21490 + 3.99407i) q^{71} +(-7.82567 + 3.28008i) q^{72} +(-1.39548 + 3.05568i) q^{73} +(3.80195 + 6.82688i) q^{74} +(-6.79550 + 2.59243i) q^{75} +(-4.93326 + 11.2968i) q^{76} +(3.79165 - 0.545157i) q^{77} +(2.95606 + 0.377498i) q^{78} +(4.79347 + 4.15356i) q^{79} +(-1.12236 - 3.39901i) q^{80} +(6.09383 + 6.62309i) q^{81} +(4.50566 - 8.41750i) q^{82} +(11.1296 + 3.26795i) q^{83} +(4.40779 + 7.62893i) q^{84} +(-4.28054 - 4.94001i) q^{85} +(4.59974 + 6.03899i) q^{86} +(-11.1992 + 2.52377i) q^{87} +(4.13857 - 1.00926i) q^{88} +(-7.29656 - 1.04909i) q^{89} +(-2.98570 + 2.34525i) q^{90} -3.09437i q^{91} +(-9.53953 - 0.998688i) q^{92} +(-7.30335 - 0.467676i) q^{93} +(-0.487763 - 0.479701i) q^{94} +(-0.784954 + 5.45948i) q^{95} +(5.69546 + 7.97256i) q^{96} +(-7.46649 + 2.19236i) q^{97} +(-0.597290 + 0.454941i) q^{98} +(-2.49913 - 3.76418i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9}+O(q^{10}) $ 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9	$ 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9} - 30 q^{10} - 18 q^{12} - 36 q^{13} - 30 q^{16} - 10 q^{18} - 22 q^{21} - 48 q^{22} - 14 q^{24} - 8 q^{25} - 34 q^{28} - 21 q^{30} - 6 q^{33} - 32 q^{34} + 22 q^{36} - 36 q^{37} - 168 q^{40} + q^{42} - 44 q^{45} - 110 q^{46} - 6 q^{48} - 16 q^{49} - 94 q^{52} + 21 q^{54} - 46 q^{57} - 116 q^{58} - 47 q^{60} - 68 q^{61} - 28 q^{64} - 20 q^{66} - 22 q^{69} - 44 q^{70} - 23 q^{72} - 36 q^{73} - 74 q^{76} + 134 q^{78} - 130 q^{81} + 36 q^{82} + 105 q^{84} - 60 q^{85} + 38 q^{88} + 162 q^{90} - 332 q^{93} - 40 q^{94} + 225 q^{96} - 36 q^{97}+O(q^{100}) $ 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9 - 30 * q^10 - 18 * q^12 - 36 * q^13 - 30 * q^16 - 10 * q^18 - 22 * q^21 - 48 * q^22 - 14 * q^24 - 8 * q^25 - 34 * q^28 - 21 * q^30 - 6 * q^33 - 32 * q^34 + 22 * q^36 - 36 * q^37 - 168 * q^40 + q^42 - 44 * q^45 - 110 * q^46 - 6 * q^48 - 16 * q^49 - 94 * q^52 + 21 * q^54 - 46 * q^57 - 116 * q^58 - 47 * q^60 - 68 * q^61 - 28 * q^64 - 20 * q^66 - 22 * q^69 - 44 * q^70 - 23 * q^72 - 36 * q^73 - 74 * q^76 + 134 * q^78 - 130 * q^81 + 36 * q^82 + 105 * q^84 - 60 * q^85 + 38 * q^88 + 162 * q^90 - 332 * q^93 - 40 * q^94 + 225 * q^96 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.00830	+	0.991633i	0.712974	+	0.701190i
$2$	1.00830	+	0.991633i	0.712974	+	0.701190i
$3$	−1.69516	−	0.355553i	−0.978704	−	0.205278i
$3$	−1.69516	−	0.355553i	−0.978704	−	0.205278i
$4$	0.0333293	+	1.99972i	0.0166647	+	0.999861i
$5$	0.252117	+	0.858632i	0.112750	+	0.383992i	0.996463	−	0.0840385i	$-0.0267819\pi$
$5$	0.252117	+	0.858632i	0.112750	+	0.383992i	−0.883712	+	0.468031i	$0.844964\pi$
$6$	−1.35665	−	2.03948i	−0.553851	−	0.832616i
$7$	−1.92220	+	1.66560i	−0.726525	+	0.629537i	−0.937513	−	0.347951i	$-0.886877\pi$
$7$	−1.92220	+	1.66560i	−0.726525	+	0.629537i	0.210988	+	0.977489i	$0.432332\pi$
$8$	−1.94938	+	2.04937i	−0.689211	+	0.724560i
$9$	2.74716	+	1.20544i	0.915722	+	0.401813i
$10$	−0.597239	+	1.11576i	−0.188863	+	0.352836i
$11$	−1.26700	−	0.814252i	−0.382015	−	0.245506i	0.335513	−	0.942035i	$-0.391090\pi$
$11$	−1.26700	−	0.814252i	−0.382015	−	0.245506i	−0.717528	+	0.696529i	$0.754727\pi$
$12$	0.654508	−	3.40171i	0.188940	−	0.981989i
$13$	−0.796709	+	0.919451i	−0.220967	+	0.255010i	−0.855400	−	0.517968i	$-0.826688\pi$
$13$	−0.796709	+	0.919451i	−0.220967	+	0.255010i	0.634432	+	0.772978i	$0.281234\pi$
$14$	−3.58982	−	0.226700i	−0.959419	−	0.0605882i
$15$	−0.122091	−	1.54516i	−0.0315238	−	0.398960i
$16$	−3.99778	+	0.133299i	−0.999445	+	0.0333247i
$17$	−6.64432	+	3.03436i	−1.61148	+	0.735940i	−0.998531	−	0.0541802i	$-0.982745\pi$
$17$	−6.64432	+	3.03436i	−1.61148	+	0.735940i	−0.612952	+	0.790120i	$0.710018\pi$
$18$	1.57461	+	3.93962i	0.371138	+	0.928578i
$19$	5.60653	+	2.56042i	1.28623	+	0.587400i	0.936899	−	0.349600i	$-0.113683\pi$
$19$	5.60653	+	2.56042i	1.28623	+	0.587400i	0.349328	+	0.937001i	$0.386410\pi$
$20$	−1.70862	+	0.532782i	−0.382060	+	0.119134i
$21$	3.85066	−	2.14002i	0.840283	−	0.466991i
$22$	−0.470075	−	2.07741i	−0.100220	−	0.442905i
$23$	−0.578761	+	4.76078i	−0.120680	+	0.992691i
$23$	−0.578761	+	4.76078i	−0.120680	+	0.992691i
$24$	4.03318	−	2.78090i	0.823270	−	0.567650i
$25$	3.53258	−	2.27025i	0.706516	−	0.454050i
$26$	−1.71508	+	0.137038i	−0.336354	+	0.0268754i
$27$	−4.22830	−	3.02018i	−0.813736	−	0.581234i
$28$	−3.39480	−	3.78836i	−0.641557	−	0.715933i
$29$	6.02903	−	2.75337i	1.11956	−	0.511287i	0.232343	−	0.972634i	$-0.425361\pi$
$29$	6.02903	−	2.75337i	1.11956	−	0.511287i	0.887220	+	0.461347i	$0.152634\pi$
$30$	1.40913	−	1.67906i	0.257271	−	0.306552i
$31$	4.18222	−	0.601313i	0.751149	−	0.107999i	0.243902	−	0.969800i	$-0.421572\pi$
$31$	4.18222	−	0.601313i	0.751149	−	0.107999i	0.507247	+	0.861801i	$0.330663\pi$
$32$	−4.16313	−	3.82992i	−0.735945	−	0.677041i
$33$	1.85827	+	1.83078i	0.323482	+	0.318697i
$34$	−9.70842	−	3.52918i	−1.66498	−	0.605250i
$35$	−1.91476	−	1.23054i	−0.323653	−	0.207999i
$36$	−2.31898	+	5.53374i	−0.386497	+	0.922290i
$37$	5.30163	+	1.55670i	0.871582	+	0.255920i	0.686788	−	0.726858i	$-0.259020\pi$
$37$	5.30163	+	1.55670i	0.871582	+	0.255920i	0.184794	+	0.982777i	$0.440838\pi$
$38$	3.11406	+	8.14129i	0.505167	+	1.32069i
$39$	1.67747	−	1.27535i	0.268610	−	0.204219i
$40$	−2.25113	−	1.15712i	−0.355934	−	0.182957i
$41$	−1.90201	−	6.47765i	−0.297044	−	1.01164i	−0.963858	−	0.266415i	$-0.914161\pi$
$41$	−1.90201	−	6.47765i	−0.297044	−	1.01164i	0.666814	−	0.745224i	$-0.267658\pi$
$42$	6.00473	+	1.66066i	0.926550	+	0.256246i
$43$	5.31318	+	0.763921i	0.810253	+	0.116497i	0.534975	−	0.844868i	$-0.320321\pi$
$43$	5.31318	+	0.763921i	0.810253	+	0.116497i	0.275278	+	0.961365i	$0.411230\pi$
$44$	1.58605	−	2.56079i	0.239106	−	0.386053i
$45$	−0.342423	+	2.66272i	−0.0510454	+	0.396934i
$46$	−5.30451	+	4.22637i	−0.782107	+	0.623144i
$47$	−0.483749			−0.0705620			−0.0352810	−	0.999377i	$-0.511233\pi$
$47$	−0.483749			−0.0705620			−0.0352810	+	0.999377i	$0.511233\pi$
$48$	6.82429	+	1.19546i	0.985001	+	0.172549i
$49$	−0.0755561	+	0.525504i	−0.0107937	+	0.0750720i
$50$	5.81315	+	1.21393i	0.822104	+	0.171676i
$51$	12.3421	−	2.78133i	1.72824	−	0.389464i
$52$	−1.86520	−	1.56255i	−0.258657	−	0.216687i
$53$	4.51572	−	3.91290i	0.620282	−	0.537478i	−0.287037	−	0.957919i	$-0.592670\pi$
$53$	4.51572	−	3.91290i	0.620282	−	0.537478i	0.907320	+	0.420442i	$0.138125\pi$
$54$	−1.26847	−	7.23816i	−0.172617	−	0.984989i
$55$	0.379710	−	1.29317i	0.0512001	−	0.174372i
$56$	0.333691	−	7.18619i	0.0445914	−	0.960296i
$57$	−8.59363	−	6.33375i	−1.13825	−	0.838925i
$58$	8.80939	+	3.20237i	1.15673	+	0.420492i
$59$	−0.185128	+	0.213649i	−0.0241016	+	0.0278147i	−0.767672	−	0.640842i	$-0.778585\pi$
$59$	−0.185128	+	0.213649i	−0.0241016	+	0.0278147i	0.743571	+	0.668657i	$0.233131\pi$
$60$	3.08583	−	0.295648i	0.398379	−	0.0381679i
$61$	1.15091	+	8.00476i	0.147359	+	1.02490i	0.920520	+	0.390695i	$0.127765\pi$
$61$	1.15091	+	8.00476i	0.147359	+	1.02490i	−0.773161	+	0.634210i	$0.781326\pi$
$62$	4.81321	+	3.54093i	0.611278	+	0.449698i
$63$	−7.28839	+	2.25857i	−0.918251	+	0.284554i
$64$	−0.399804	−	7.99000i	−0.0499754	−	0.998750i
$65$	−0.990335	−	0.452271i	−0.122836	−	0.0560973i
$66$	0.0582272	+	3.68868i	0.00716727	+	0.454046i
$67$	−2.83225	−	4.40707i	−0.346014	−	0.538409i	0.624010	−	0.781416i	$-0.285502\pi$
$67$	−2.83225	−	4.40707i	−0.346014	−	0.538409i	−0.970024	+	0.243007i	$0.921866\pi$
$68$	−6.28932	−	13.1857i	−0.762692	−	1.59900i
$69$	2.67380	−	7.86453i	0.321888	−	0.946778i
$70$	−0.710403	−	3.13949i	−0.0849094	−	0.375241i
$71$	−6.21490	+	3.99407i	−0.737573	+	0.474009i	−0.854710	−	0.519106i	$-0.826265\pi$
$71$	−6.21490	+	3.99407i	−0.737573	+	0.474009i	0.117137	+	0.993116i	$0.462628\pi$
$72$	−7.82567	+	3.28008i	−0.922264	+	0.386561i
$73$	−1.39548	+	3.05568i	−0.163329	+	0.357640i	−0.973546	−	0.228489i	$-0.926621\pi$
$73$	−1.39548	+	3.05568i	−0.163329	+	0.357640i	0.810218	+	0.586129i	$0.199349\pi$
$74$	3.80195	+	6.82688i	0.441967	+	0.793609i
$75$	−6.79550	+	2.59243i	−0.784677	+	0.299348i
$76$	−4.93326	+	11.2968i	−0.565884	+	1.29584i
$77$	3.79165	−	0.545157i	0.432099	−	0.0621264i
$78$	2.95606	+	0.377498i	0.334708	+	0.0427433i
$79$	4.79347	+	4.15356i	0.539307	+	0.467312i	0.881411	−	0.472350i	$-0.156594\pi$
$79$	4.79347	+	4.15356i	0.539307	+	0.467312i	−0.342104	+	0.939662i	$0.611140\pi$
$80$	−1.12236	−	3.39901i	−0.125484	−	0.380021i
$81$	6.09383	+	6.62309i	0.677092	+	0.735898i
$82$	4.50566	−	8.41750i	0.497567	−	0.929557i
$83$	11.1296	+	3.26795i	1.22163	+	0.358704i	0.828086	−	0.560601i	$-0.189430\pi$
$83$	11.1296	+	3.26795i	1.22163	+	0.358704i	0.393547	+	0.919305i	$0.371248\pi$
$84$	4.40779	+	7.62893i	0.480929	+	0.832384i
$85$	−4.28054	−	4.94001i	−0.464290	−	0.535819i
$86$	4.59974	+	6.03899i	0.496003	+	0.651201i
$87$	−11.1992	+	2.52377i	−1.20068	+	0.270577i
$88$	4.13857	−	1.00926i	0.441173	−	0.107587i
$89$	−7.29656	−	1.04909i	−0.773434	−	0.111203i	−0.255713	−	0.966753i	$-0.582310\pi$
$89$	−7.29656	−	1.04909i	−0.773434	−	0.111203i	−0.517721	+	0.855550i	$0.673219\pi$
$90$	−2.98570	+	2.34525i	−0.314721	+	0.247211i
$91$		−	3.09437i		−	0.324378i
$92$	−9.53953	−	0.998688i	−0.994565	−	0.104120i
$93$	−7.30335	−	0.467676i	−0.757322	−	0.0484958i
$94$	−0.487763	−	0.479701i	−0.0503089	−	0.0494774i
$95$	−0.784954	+	5.45948i	−0.0805346	+	0.560130i
$96$	5.69546	+	7.97256i	0.581290	+	0.813696i
$97$	−7.46649	+	2.19236i	−0.758107	+	0.222600i	−0.637869	−	0.770145i	$-0.720184\pi$
$97$	−7.46649	+	2.19236i	−0.758107	+	0.222600i	−0.120238	+	0.992745i	$0.538366\pi$
$98$	−0.597290	+	0.454941i	−0.0603354	+	0.0459560i
$99$	−2.49913	−	3.76418i	−0.251172	−	0.378314i
$100$	4.65761	+	6.98852i	0.465761	+	0.698852i
$101$	−3.58738	+	12.2175i	−0.356958	+	1.21569i	0.563918	+	0.825831i	$0.309294\pi$
$101$	−3.58738	+	12.2175i	−0.356958	+	1.21569i	−0.920876	+	0.389856i	$0.872525\pi$
$102$	15.2026	+	9.43440i	1.50528	+	0.934145i
$103$	−3.64636	+	5.67385i	−0.359287	+	0.559061i	−0.973098	−	0.230392i	$-0.925999\pi$
$103$	−3.64636	+	5.67385i	−0.359287	+	0.559061i	0.613811	+	0.789453i	$0.289636\pi$
$104$	−0.331200	−	3.42511i	−0.0324769	−	0.335860i
$105$	2.80831	+	2.76677i	0.274063	+	0.270009i
$106$	8.43335	+	0.532573i	0.819119	+	0.0517281i
$107$	0.939439	+	6.53395i	0.0908190	+	0.631660i	0.983491	+	0.180954i	$0.0579186\pi$
$107$	0.939439	+	6.53395i	0.0908190	+	0.631660i	−0.892672	+	0.450706i	$0.851172\pi$
$108$	5.89860	−	8.55608i	0.567593	−	0.823309i
$109$	−5.11245	−	11.1947i	−0.489684	−	1.07226i	−0.979686	−	0.200537i	$-0.935731\pi$
$109$	−5.11245	−	11.1947i	−0.489684	−	1.07226i	0.490002	−	0.871721i	$-0.336996\pi$
$110$	1.66522	−	0.927372i	0.158772	−	0.0884215i
$111$	−8.43364	−	4.52387i	−0.800486	−	0.429386i
$112$	7.46252	−	6.91493i	0.705142	−	0.653399i
$113$	−1.98229	−	3.08450i	−0.186478	−	0.290165i	0.735410	−	0.677623i	$-0.236990\pi$
$113$	−1.98229	−	3.08450i	−0.186478	−	0.290165i	−0.921888	+	0.387458i	$0.873353\pi$
$114$	−2.38419	−	14.9080i	−0.223300	−	1.39626i
$115$	−4.23368	+	0.703332i	−0.394792	+	0.0655860i
$116$	5.70691	+	11.9646i	0.529873	+	1.11089i
$117$	−3.29703	+	1.56550i	−0.304811	+	0.144730i
$118$	−0.398525	+	0.0318429i	−0.0366872	+	0.00293138i
$119$	7.71771	−	16.8994i	0.707481	−	1.54917i
$120$	3.40461	+	2.76191i	0.310797	+	0.252127i
$121$	−3.62728	−	7.94264i	−0.329753	−	0.722058i
$122$	−6.77732	+	9.21246i	−0.613590	+	0.834057i
$123$	0.921074	+	11.6570i	0.0830504	+	1.05107i
$124$	1.34185	+	8.34324i	0.120502	+	0.749245i
$125$	6.22147	+	5.39093i	0.556465	+	0.482180i
$126$	−9.58855	−	4.95009i	−0.854216	−	0.440989i
$127$	11.3815	−	17.7100i	1.00995	−	1.57151i	0.204477	−	0.978871i	$-0.434451\pi$
$127$	11.3815	−	17.7100i	1.00995	−	1.57151i	0.805470	−	0.592637i	$-0.201913\pi$
$128$	7.52003	−	8.45276i	0.664683	−	0.747126i
$129$	−8.73511	−	3.18409i	−0.769083	−	0.280343i
$130$	−0.550066	−	1.43807i	−0.0482440	−	0.126127i
$131$	−13.0644	−	15.0771i	−1.14144	−	1.31729i	−0.941318	−	0.337520i	$-0.890412\pi$
$131$	−13.0644	−	15.0771i	−1.14144	−	1.31729i	−0.200121	−	0.979771i	$-0.564134\pi$
$132$	−3.59911	+	3.77703i	−0.313262	+	0.328749i
$133$	−15.0415	+	4.41659i	−1.30427	+	0.382967i
$134$	1.51444	−	7.25219i	0.130828	−	0.626494i
$135$	1.52720	−	4.39199i	0.131440	−	0.378003i
$136$	6.73381	−	19.5318i	0.577420	−	1.67484i
$137$			19.0753i			1.62971i	0.579662	+	0.814857i	$0.303185\pi$
$137$			19.0753i			1.62971i	−0.579662	+	0.814857i	$0.696815\pi$
$138$	10.4947	−	5.27835i	0.893369	−	0.449323i
$139$		−	12.2140i		−	1.03598i	−0.855388	−	0.517988i	$-0.826681\pi$
$139$		−	12.2140i		−	1.03598i	0.855388	−	0.517988i	$-0.173319\pi$
$140$	2.39692	−	3.87000i	0.202577	−	0.327075i
$141$	0.820033	+	0.171998i	0.0690593	+	0.0144849i
$142$	−10.2271	−	2.13568i	−0.858241	−	0.179222i
$143$	1.75810	−	0.516224i	0.147019	−	0.0431688i
$144$	−11.1432	−	4.45289i	−0.928603	−	0.371074i
$145$	3.88415	+	4.48255i	0.322561	+	0.372255i
$146$	−4.43717	+	1.69723i	−0.367223	+	0.140464i
$147$	0.314924	−	0.863952i	0.0259745	−	0.0712575i
$148$	−2.93626	+	10.6537i	−0.241359	+	0.875726i
$149$	0.114192	−	0.177686i	0.00935495	−	0.0145566i	−0.836545	−	0.547899i	$-0.815428\pi$
$149$	0.114192	−	0.177686i	0.00935495	−	0.0145566i	0.845900	+	0.533342i	$0.179064\pi$
$150$	−9.42263	−	4.12470i	−0.769354	−	0.336780i
$151$	8.38713	+	7.26749i	0.682535	+	0.591420i	0.925560	−	0.378600i	$-0.123594\pi$
$151$	8.38713	+	7.26749i	0.682535	+	0.591420i	−0.243025	+	0.970020i	$0.578140\pi$
$152$	−16.1765	+	6.49860i	−1.31209	+	0.527106i
$153$	−21.9108	+	0.326553i	−1.77138	+	0.0264002i
$154$	4.36371	+	3.21025i	0.351638	+	0.258689i
$155$	1.57072	+	3.43939i	0.126163	+	0.276258i
$156$	2.60625	+	3.31196i	0.208667	+	0.265169i
$157$	1.67861	−	3.67565i	0.133968	−	0.293349i	−0.830745	−	0.556654i	$-0.812085\pi$
$157$	1.67861	−	3.67565i	0.133968	−	0.293349i	0.964713	+	0.263304i	$0.0848124\pi$
$158$	0.714434	+	8.94139i	0.0568373	+	0.711338i
$159$	−9.04613	+	5.02743i	−0.717405	+	0.398701i
$160$	2.23890	−	4.54019i	0.177000	−	0.358934i
$161$	−6.81706	−	10.1152i	−0.537259	−	0.797188i
$162$	−0.423276	+	12.7209i	−0.0332557	+	0.999447i
$163$	6.30664	+	9.81332i	0.493974	+	0.768639i	0.995323	−	0.0966068i	$-0.0307989\pi$
$163$	6.30664	+	9.81332i	0.493974	+	0.768639i	−0.501349	+	0.865245i	$0.667163\pi$
$164$	12.8901	−	4.01939i	1.00655	−	0.313862i
$165$	−1.10346	+	2.05714i	−0.0859045	+	0.160148i
$166$	7.98135	+	14.3315i	0.619473	+	1.11234i
$167$	−8.32163	−	18.2218i	−0.643947	−	1.41005i	−0.896753	−	0.442531i	$-0.854081\pi$
$167$	−8.32163	−	18.2218i	−0.643947	−	1.41005i	0.252806	−	0.967517i	$-0.418646\pi$
$168$	−3.12073	+	12.0631i	−0.240770	+	0.930691i
$169$	1.63945	+	11.4026i	0.126111	+	0.877124i
$170$	0.582613	−	9.22573i	0.0446844	−	0.707581i
$171$	12.3156	+	13.7922i	0.941800	+	1.05472i
$172$	−1.35054	+	10.6504i	−0.102978	+	0.812082i
$173$	7.98798	−	12.4295i	0.607315	−	0.945001i	−0.392368	−	0.919808i	$-0.628344\pi$
$173$	7.98798	−	12.4295i	0.607315	−	0.945001i	0.999683	−	0.0251920i	$-0.00801973\pi$
$174$	−13.7947	−	8.56074i	−1.04578	−	0.648988i
$175$	−3.00901	+	10.2478i	−0.227460	+	0.774657i
$176$	5.17373	+	3.08631i	0.389984	+	0.232639i
$177$	0.389785	−	0.296347i	0.0292981	−	0.0222748i
$178$	−6.31680	−	8.29330i	−0.473464	−	0.621609i
$179$	11.7452	−	3.44870i	0.877878	−	0.257768i	0.188415	−	0.982089i	$-0.439665\pi$
$179$	11.7452	−	3.44870i	0.877878	−	0.257768i	0.689463	+	0.724321i	$0.257847\pi$
$180$	−5.33611	−	0.596004i	−0.397730	−	0.0444235i
$181$	−0.701366	+	4.87811i	−0.0521321	+	0.362587i	0.947011	+	0.321201i	$0.104086\pi$
$181$	−0.701366	+	4.87811i	−0.0521321	+	0.362587i	−0.999143	+	0.0413861i	$0.986823\pi$
$182$	3.06848	−	3.12005i	0.227451	−	0.231273i
$183$	0.895131	−	13.9786i	0.0661700	−	1.03333i
$184$	−8.62836	−	10.4667i	−0.636091	−	0.771614i
$185$			4.94462i			0.363536i
$186$	−6.90019	−	7.71380i	−0.505947	−	0.565603i
$187$	10.8891	+	1.56561i	0.796289	+	0.114489i
$188$	−0.0161230	−	0.967363i	−0.00117589	−	0.0705522i
$189$	13.1581	−	1.23725i	0.957108	−	0.0899964i
$190$	−6.20526	+	4.72639i	−0.450177	+	0.342889i
$191$	11.5586	+	13.3393i	0.836350	+	0.965200i	0.999772	−	0.0213564i	$-0.00679848\pi$
$191$	11.5586	+	13.3393i	0.836350	+	0.965200i	−0.163421	+	0.986556i	$0.552253\pi$
$192$	−2.16313	+	13.6865i	−0.156111	+	0.987740i
$193$	−0.269554	−	0.0791481i	−0.0194029	−	0.00569720i	0.272017	−	0.962293i	$-0.412309\pi$
$193$	−0.269554	−	0.0791481i	−0.0194029	−	0.00569720i	−0.291420	+	0.956595i	$0.594128\pi$
$194$	−9.70246	−	5.19346i	−0.696596	−	0.372869i
$195$	1.51797	+	1.11879i	0.108704	+	0.0801182i
$196$	−1.05338	−	0.133576i	−0.0752415	−	0.00954118i
$197$	16.1860	+	14.0252i	1.15320	+	0.999255i	0.999939	+	0.0110696i	$0.00352362\pi$
$197$	16.1860	+	14.0252i	1.15320	+	0.999255i	0.153263	+	0.988185i	$0.451022\pi$
$198$	1.21282	−	6.27363i	0.0861912	−	0.445847i
$199$	−6.76489	+	0.972645i	−0.479551	+	0.0689490i	−0.377851	−	0.925866i	$-0.623337\pi$
$199$	−6.76489	+	0.972645i	−0.479551	+	0.0689490i	−0.101699	+	0.994815i	$0.532428\pi$
$200$	−2.23378	+	11.6651i	−0.157952	+	0.824850i
$201$	3.23419	+	8.47772i	0.228122	+	0.597972i
$202$	−15.7324	+	8.76152i	−1.10693	+	0.616458i
$203$	−7.00302	+	15.3345i	−0.491516	+	1.07627i
$204$	5.97324	+	24.5880i	0.418211	+	1.72151i
$205$	5.08239	−	3.26626i	0.354970	−	0.228125i
$206$	−9.30300	+	2.10508i	−0.648171	+	0.146668i
$207$	−7.32879	+	12.3810i	−0.509386	+	0.860538i
$208$	3.06250	−	3.78196i	0.212346	−	0.262232i
$209$	−5.01866	−	7.80918i	−0.347148	−	0.540172i
$210$	0.0879960	+	5.57453i	0.00607230	+	0.384679i
$211$	−14.6613	−	6.69561i	−1.00933	−	0.460945i	−0.159045	−	0.987271i	$-0.550842\pi$
$211$	−14.6613	−	6.69561i	−1.00933	−	0.460945i	−0.850282	+	0.526327i	$0.823569\pi$
$212$	7.97521	+	8.89978i	0.547740	+	0.611239i
$213$	11.9554	−	4.56089i	0.819169	−	0.312507i
$214$	−5.53204	+	7.51974i	−0.378162	+	0.514039i
$215$	0.683618	+	4.75467i	0.0466224	+	0.324266i
$216$	14.4320	−	2.77784i	0.981976	−	0.189008i
$217$	−7.03754	+	8.12175i	−0.477739	+	0.551340i
$218$	5.94616	−	16.3573i	0.402725	−	1.10785i
$219$	3.45202	−	4.68371i	0.233266	−	0.316495i
$220$	2.59865	+	0.716215i	0.175201	+	0.0482872i
$221$	2.50364	−	8.52662i	0.168413	−	0.573563i
$222$	−4.01761	−	12.9245i	−0.269644	−	0.867434i
$223$	−6.92303	+	5.99884i	−0.463600	+	0.401712i	−0.855097	−	0.518467i	$-0.826503\pi$
$223$	−6.92303	+	5.99884i	−0.463600	+	0.401712i	0.391497	+	0.920179i	$0.371957\pi$
$224$	14.3815	+	0.427779i	0.960905	+	0.0285822i
$225$	12.4412	−	1.97844i	0.829416	−	0.131896i
$226$	1.05995	−	5.07579i	0.0705071	−	0.337637i
$227$	3.23806	−	22.5212i	0.214918	−	1.49479i	−0.541502	−	0.840699i	$-0.682144\pi$
$227$	3.23806	−	22.5212i	0.214918	−	1.49479i	0.756420	−	0.654086i	$-0.226947\pi$
$228$	12.3793	−	17.3960i	0.819840	−	1.15208i
$229$	15.4954			1.02397			0.511983	−	0.858995i	$-0.328911\pi$
$229$	15.4954			1.02397			0.511983	+	0.858995i	$0.328911\pi$
$230$	−4.96625	−	3.48908i	−0.327465	−	0.230063i
$231$	−6.62131	−	0.424001i	−0.435650	−	0.0278972i
$232$	−6.11024	+	17.7231i	−0.401157	+	1.16358i
$233$	−14.5695	−	2.09478i	−0.954479	−	0.137233i	−0.352559	−	0.935790i	$-0.614688\pi$
$233$	−14.5695	−	2.09478i	−0.954479	−	0.137233i	−0.601920	+	0.798556i	$0.705597\pi$
$234$	−4.87679	−	1.69096i	−0.318806	−	0.110541i
$235$	−0.121961	−	0.415362i	−0.00795588	−	0.0270952i
$236$	−0.433408	−	0.363083i	−0.0282125	−	0.0236347i
$237$	−6.64890	−	8.74530i	−0.431893	−	0.568068i
$238$	24.5398	−	9.38652i	1.59068	−	0.608438i
$239$	4.90891	+	1.44139i	0.317531	+	0.0932355i	0.436614	−	0.899649i	$-0.356177\pi$
$239$	4.90891	+	1.44139i	0.317531	+	0.0932355i	−0.119083	+	0.992884i	$0.537996\pi$
$240$	0.694062	+	6.16095i	0.0448015	+	0.397688i
$241$	−1.20704	−	0.775718i	−0.0777523	−	0.0499684i	0.501187	−	0.865339i	$-0.332897\pi$
$241$	−1.20704	−	0.775718i	−0.0777523	−	0.0499684i	−0.578939	+	0.815371i	$0.696533\pi$
$242$	4.21880	−	11.6055i	0.271195	−	0.746028i
$243$	−7.97518	−	13.3939i	−0.511608	−	0.859219i
$244$	−15.9689	+	2.56830i	−1.02231	+	0.164418i
$245$	−0.470264	+	0.0676137i	−0.0300441	+	0.00431968i
$246$	−10.6307	+	12.6670i	−0.677789	+	0.807622i
$247$	−6.82095	+	3.11503i	−0.434007	+	0.198204i
$248$	−6.92045	+	9.74309i	−0.439449	+	0.618687i
$249$	−17.7046	−	9.49687i	−1.12198	−	0.601839i
$250$	0.927268	+	11.6051i	0.0586456	+	0.733969i
$251$	−15.1964	+	9.76612i	−0.959187	+	0.616432i	−0.923773	−	0.382941i	$-0.874911\pi$
$251$	−15.1964	+	9.76612i	−0.959187	+	0.616432i	−0.0354141	+	0.999373i	$0.511275\pi$
$252$	−4.75944	−	14.4995i	−0.299816	−	0.913382i
$253$	4.60977	−	5.56066i	0.289814	−	0.349595i
$254$	29.0378	−	6.57066i	1.82199	−	0.412280i
$255$	5.49979	+	9.89609i	0.344410	+	0.619717i
$256$	15.9645	−	1.06580i	0.997779	−	0.0666123i
$257$	−1.35868	−	0.620488i	−0.0847520	−	0.0387050i	0.372588	−	0.927997i	$-0.378470\pi$
$257$	−1.35868	−	0.620488i	−0.0847520	−	0.0387050i	−0.457340	+	0.889292i	$0.651198\pi$
$258$	−5.65014	−	11.8725i	−0.351763	−	0.739151i
$259$	−12.7836	+	5.83810i	−0.794337	+	0.362762i
$260$	0.871409	−	1.99547i	0.0540425	−	0.123754i
$261$	19.8818	−	0.296313i	1.23065	−	0.0183413i
$262$	1.77816	−	28.1573i	0.109855	−	1.73956i
$263$	17.6809	−	20.4048i	1.09025	−	1.25822i	0.126341	−	0.991987i	$-0.459677\pi$
$263$	17.6809	−	20.4048i	1.09025	−	1.25822i	0.963910	−	0.266229i	$-0.0857778\pi$
$264$	−7.37440	+	0.239379i	−0.453863	+	0.0147328i
$265$	4.49823	+	2.89084i	0.276324	+	0.177583i
$266$	−19.5460	−	10.4624i	−1.19844	−	0.641493i
$267$	11.9959	+	4.37269i	0.734135	+	0.267604i
$268$	8.71851	−	5.81060i	0.532568	−	0.354939i
$269$	19.9009	−	17.2443i	1.21338	−	1.05140i	0.216202	−	0.976349i	$-0.430633\pi$
$269$	19.9009	−	17.2443i	1.21338	−	1.05140i	0.997180	−	0.0750520i	$-0.0239123\pi$
$270$	5.89512	−	2.91402i	0.358765	−	0.177341i
$271$	−0.989518	−	3.36999i	−0.0601089	−	0.204712i	0.923963	−	0.382481i	$-0.124930\pi$
$271$	−0.989518	−	3.36999i	−0.0601089	−	0.204712i	−0.984072	+	0.177769i	$0.943112\pi$
$272$	26.1580	−	13.0164i	1.58606	−	0.789233i
$273$	−1.10021	+	5.24547i	−0.0665879	+	0.317470i
$274$	−18.9157	+	19.2336i	−1.14274	+	1.16194i
$275$	−6.32434			−0.381372
$276$	15.8160	+	5.08475i	0.952010	+	0.306066i
$277$	23.2924			1.39950			0.699752	−	0.714386i	$-0.253294\pi$
$277$	23.2924			1.39950			0.699752	+	0.714386i	$0.253294\pi$
$278$	12.1118	−	12.3153i	0.726417	−	0.738625i
$279$	12.2141	+	3.38951i	0.731239	+	0.202925i
$280$	6.25443	−	1.52525i	0.373774	−	0.0911508i
$281$	4.53568	+	15.4471i	0.270576	+	0.921498i	0.976916	+	0.213625i	$0.0685269\pi$
$281$	4.53568	+	15.4471i	0.270576	+	0.921498i	−0.706340	+	0.707873i	$0.749655\pi$
$282$	0.656279	+	0.986597i	0.0390808	+	0.0587510i
$283$	−20.0340	+	17.3595i	−1.19090	+	1.03192i	−0.192174	+	0.981361i	$0.561554\pi$
$283$	−20.0340	+	17.3595i	−1.19090	+	1.03192i	−0.998721	+	0.0505561i	$0.983901\pi$
$284$	−8.19418	−	12.2950i	−0.486235	−	0.729571i
$285$	3.27176	−	8.97562i	0.193802	−	0.531670i
$286$	2.28459	+	1.22288i	0.135091	+	0.0723103i
$287$	14.4452	+	9.28339i	0.852675	+	0.547981i
$288$	−6.82007	−	15.5398i	−0.401877	−	0.915694i
$289$	23.8070	−	27.4747i	1.40041	−	1.61616i
$290$	−0.528661	+	8.37140i	−0.0310440	+	0.491585i
$291$	13.4364	−	1.06168i	0.787657	−	0.0622367i
$292$	−6.15701	−	2.68873i	−0.360312	−	0.157346i
$293$	−2.87530	+	1.31311i	−0.167977	+	0.0767125i	−0.497629	−	0.867390i	$-0.665796\pi$
$293$	−2.87530	+	1.31311i	−0.167977	+	0.0767125i	0.329652	+	0.944103i	$0.393069\pi$
$294$	1.17426	−	0.558831i	0.0684843	−	0.0325917i
$295$	−0.230120	−	0.105092i	−0.0133981	−	0.00611870i
$296$	−13.5252	+	7.83037i	−0.786133	+	0.455131i
$297$	2.89807	+	7.26947i	0.168163	+	0.421818i
$298$	0.291338	−	0.0659240i	0.0168768	−	0.00381887i
$299$	−3.91620	−	4.32510i	−0.226480	−	0.250127i
$300$	−5.41063	−	13.5027i	−0.312383	−	0.779579i
$301$	−11.4854	+	7.38123i	−0.662008	+	0.425447i
$302$	1.25005	+	15.6447i	0.0719321	+	0.900254i
$303$	10.4252	−	19.4352i	0.598910	−	1.11652i
$304$	−22.7550	−	9.48864i	−1.30509	−	0.544211i
$305$	−6.58298	+	3.00635i	−0.376940	+	0.172143i
$306$	−22.4164	−	21.3982i	−1.28146	−	1.22325i
$307$	23.9785	−	3.44759i	1.36853	−	0.196764i	0.581431	−	0.813596i	$-0.302493\pi$
$307$	23.9785	−	3.44759i	1.36853	−	0.196764i	0.787095	+	0.616832i	$0.211584\pi$
$308$	1.21654	+	7.56408i	0.0693186	+	0.431004i
$309$	8.19854	−	8.32164i	0.466399	−	0.473401i
$310$	−1.82686	+	5.02550i	−0.103759	+	0.285429i
$311$	29.4574	+	18.9311i	1.67038	+	1.07349i	0.899992	+	0.435906i	$0.143572\pi$
$311$	29.4574	+	18.9311i	1.67038	+	1.07349i	0.770384	+	0.637580i	$0.220064\pi$
$312$	−0.656369	+	5.92389i	−0.0371596	+	0.335374i
$313$	−14.9268	−	4.38289i	−0.843711	−	0.247736i	−0.168814	−	0.985648i	$-0.553994\pi$
$313$	−14.9268	−	4.38289i	−0.843711	−	0.247736i	−0.674897	+	0.737912i	$0.735812\pi$
$314$	5.33744	−	2.04158i	0.301209	−	0.115213i
$315$	−3.77681	−	5.68862i	−0.212799	−	0.320518i
$316$	−8.14621	+	9.72404i	−0.458260	+	0.547020i
$317$	−3.54627	−	12.0775i	−0.199179	−	0.678340i	−0.997136	−	0.0756264i	$-0.975904\pi$
$317$	−3.54627	−	12.0775i	−0.199179	−	0.678340i	0.797958	−	0.602714i	$-0.205914\pi$
$318$	−14.1066	−	3.90130i	−0.791056	−	0.218774i
$319$	−9.88072	−	1.42063i	−0.553214	−	0.0795402i
$320$	6.75968	−	2.35770i	0.377878	−	0.131800i
$321$	0.730657	−	11.4101i	0.0407813	−	0.636851i
$322$	3.15692	−	16.9591i	0.175928	−	0.945095i
$323$	−45.0208			−2.50502
$324$	−13.0412	+	12.4067i	−0.724513	+	0.689261i
$325$	−0.727053	+	5.05677i	−0.0403297	+	0.280499i
$326$	−3.37224	+	16.1486i	−0.186771	+	0.894389i
$327$	4.68614	+	20.7946i	0.259144	+	1.14994i
$328$	16.9828	+	8.72952i	0.937720	+	0.482007i
$329$	0.929864	−	0.805731i	0.0512650	−	0.0444214i
$330$	−3.15254	+	0.979977i	−0.173542	+	0.0539459i
$331$	3.55143	−	12.0950i	0.195204	−	0.664804i	−0.802473	−	0.596688i	$-0.796483\pi$
$331$	3.55143	−	12.0950i	0.195204	−	0.664804i	0.997677	−	0.0681159i	$-0.0216988\pi$
$332$	−6.16404	+	22.3650i	−0.338296	+	1.22744i
$333$	12.6879	+	10.6673i	0.695295	+	0.584564i
$334$	9.67868	−	26.6250i	0.529594	−	1.45686i
$335$	3.06999	−	3.54296i	0.167732	−	0.193573i
$336$	−15.1088	+	9.06861i	−0.824254	+	0.494733i
$337$	−0.974611	−	6.77857i	−0.0530905	−	0.369252i	−0.998996	−	0.0448089i	$-0.985732\pi$
$337$	−0.974611	−	6.77857i	−0.0530905	−	0.369252i	0.945905	−	0.324443i	$-0.105177\pi$
$338$	−9.65415	+	13.1230i	−0.525116	+	0.713795i
$339$	2.26360	+	5.93354i	0.122942	+	0.322266i
$340$	9.73598	−	8.72455i	0.528008	−	0.473155i
$341$	−5.78850	−	2.64352i	−0.313465	−	0.143155i
$342$	−1.25899	+	26.1193i	−0.0680786	+	1.41237i
$343$	−10.3557	−	16.1137i	−0.559153	−	0.870059i
$344$	−11.9230	+	9.39949i	−0.642844	+	0.506786i
$345$	7.42685	+	0.313032i	0.399848	+	0.0168531i
$346$	20.3798	−	4.61154i	1.09563	−	0.247918i
$347$	−23.6115	+	15.1742i	−1.26753	+	0.814593i	−0.989296	−	0.145920i	$-0.953386\pi$
$347$	−23.6115	+	15.1742i	−1.26753	+	0.814593i	−0.278235	+	0.960513i	$0.589749\pi$
$348$	−5.42010	−	22.3111i	−0.290548	−	1.19600i
$349$	10.2308	−	22.4024i	0.547645	−	1.19917i	−0.410229	−	0.911983i	$-0.634551\pi$
$349$	10.2308	−	22.4024i	0.547645	−	1.19917i	0.957873	−	0.287192i	$-0.0927216\pi$
$350$	−13.1960	+	7.34895i	−0.705355	+	0.392818i
$351$	6.14563	−	1.48151i	0.328030	−	0.0790771i
$352$	2.15617	+	8.24236i	0.114924	+	0.439319i
$353$	7.08525	−	1.01870i	0.377110	−	0.0542202i	0.0488460	−	0.998806i	$-0.484446\pi$
$353$	7.08525	−	1.01870i	0.377110	−	0.0542202i	0.328264	+	0.944586i	$0.393537\pi$
$354$	0.686887	+	0.0877176i	0.0365076	+	0.00466214i
$355$	−4.99632	−	4.32934i	−0.265177	−	0.229778i
$356$	1.85469	−	14.6261i	0.0982986	−	0.775180i
$357$	−19.0914	+	25.9033i	−1.01043	+	1.37095i
$358$	15.2625	+	8.16961i	0.806649	+	0.431777i
$359$	15.8738	+	4.66096i	0.837786	+	0.245996i	0.672358	−	0.740226i	$-0.265281\pi$
$359$	15.8738	+	4.66096i	0.837786	+	0.245996i	0.165428	+	0.986222i	$0.447100\pi$
$360$	−4.78937	−	5.89241i	−0.252422	−	0.310557i
$361$	12.4351	+	14.3509i	0.654480	+	0.755310i
$362$	−5.54448	+	4.22309i	−0.291411	+	0.221961i
$363$	3.32481	+	14.7538i	0.174507	+	0.774372i
$364$	6.18788	−	0.103133i	0.324333	−	0.00540565i
$365$	−2.97553	−	0.427816i	−0.155746	−	0.0223929i
$366$	14.7642	−	13.2069i	0.771737	−	0.690338i
$367$			0.0283362i			0.00147914i	1.00000		0.000739568i	$0.000235412\pi$
$367$			0.0283362i			0.00147914i	−1.00000		0.000739568i	$0.999765\pi$
$368$	1.67915	−	19.1097i	0.0875319	−	0.996162i
$369$	2.58329	−	20.0879i	0.134481	−	1.04574i
$370$	−4.90325	+	4.98565i	−0.254908	+	0.259192i
$371$	−2.16282	+	15.0428i	−0.112288	+	0.780982i
$372$	0.691807	−	14.6203i	0.0358685	−	0.758025i
$373$	−16.2386	+	4.76807i	−0.840801	+	0.246882i	−0.673651	−	0.739050i	$-0.735275\pi$
$373$	−16.2386	+	4.76807i	−0.840801	+	0.246882i	−0.167151	+	0.985931i	$0.553457\pi$
$374$	9.42693	+	12.3766i	0.487455	+	0.639978i
$375$	−8.62965	−	11.3506i	−0.445633	−	0.586141i
$376$	0.943012	−	0.991378i	0.0486321	−	0.0511264i
$377$	−2.27180	+	7.73703i	−0.117003	+	0.398477i
$378$	14.4941	+	11.8005i	0.745498	+	0.606950i
$379$	−9.71366	+	15.1148i	−0.498957	+	0.776393i	−0.995810	−	0.0914418i	$-0.970852\pi$
$379$	−9.71366	+	15.1148i	−0.498957	+	0.776393i	0.496853	+	0.867835i	$0.334489\pi$
$380$	−10.9436	−	1.38773i	−0.561395	−	0.0711890i
$381$	−25.5904	+	25.9746i	−1.31104	+	1.33072i
$382$	−1.57321	+	24.9119i	−0.0804923	+	1.27460i
$383$	0.754662	+	5.24879i	0.0385614	+	0.268201i	0.999976	−	0.00690243i	$-0.00219713\pi$
$383$	0.754662	+	5.24879i	0.0385614	+	0.268201i	−0.961415	+	0.275103i	$0.911288\pi$
$384$	−15.7531	+	11.6551i	−0.803896	+	0.594770i
$385$	1.42403	+	3.11819i	0.0725753	+	0.158918i
$386$	−0.193304	−	0.347103i	−0.00983894	−	0.0176671i
$387$	13.6753	+	8.50334i	0.695156	+	0.432249i
$388$	−4.63296	−	14.8578i	−0.235203	−	0.754292i
$389$	4.03413	+	6.27723i	0.204539	+	0.318268i	0.928335	−	0.371746i	$-0.121241\pi$
$389$	4.03413	+	6.27723i	0.204539	+	0.318268i	−0.723796	+	0.690014i	$0.757604\pi$
$390$	0.421142	+	2.63335i	0.0213254	+	0.133345i
$391$	−10.6004	−	33.3883i	−0.536087	−	1.68852i
$392$	−0.929663	−	1.17925i	−0.0469550	−	0.0595612i
$393$	16.7856	+	30.2032i	0.846719	+	1.52355i
$394$	2.41241	+	30.1921i	0.121535	+	1.52106i
$395$	−2.35787	+	5.16301i	−0.118637	+	0.259779i
$396$	7.44402	−	5.12302i	0.374076	−	0.257441i
$397$	3.95821	+	8.66727i	0.198657	+	0.434998i	0.982575	−	0.185866i	$-0.0595091\pi$
$397$	3.95821	+	8.66727i	0.198657	+	0.434998i	−0.783918	+	0.620864i	$0.786782\pi$
$398$	−7.78553	−	5.72757i	−0.390254	−	0.287097i
$399$	27.0682	−	2.13879i	1.35511	−	0.107074i
$400$	−13.8199	+	9.54685i	−0.690993	+	0.477343i
$401$	−11.1679	−	9.67704i	−0.557699	−	0.483249i	0.329805	−	0.944049i	$-0.393017\pi$
$401$	−11.1679	−	9.67704i	−0.557699	−	0.483249i	−0.887504	+	0.460800i	$0.847562\pi$
$402$	−5.14576	+	11.7552i	−0.256647	+	0.586296i
$403$	−2.77914	+	4.32442i	−0.138439	+	0.215415i
$404$	−24.5512	−	6.76657i	−1.22147	−	0.336649i
$405$	−4.15044	+	6.90215i	−0.206237	+	0.342971i
$406$	−22.2673	+	8.51730i	−1.10511	+	0.422706i
$407$	−5.44962	−	6.28920i	−0.270128	−	0.311744i
$408$	−18.3595	+	30.7153i	−0.908930	+	1.52064i
$409$	16.1986	−	4.75634i	0.800970	−	0.235186i	0.144467	−	0.989510i	$-0.453853\pi$
$409$	16.1986	−	4.75634i	0.800970	−	0.235186i	0.656503	+	0.754324i	$0.272035\pi$
$410$	8.36349	+	1.74651i	0.413043	+	0.0862539i
$411$	6.78228	−	32.3358i	0.334545	−	1.59501i
$412$	−11.4677	−	7.10261i	−0.564971	−	0.349920i
$413$		−	0.719025i		−	0.0353809i
$414$	−19.6670	+	5.21626i	−0.966580	+	0.256365i
$415$			10.3801i			0.509541i
$416$	6.83823	−	0.776465i	0.335272	−	0.0380693i
$417$	−4.34271	+	20.7047i	−0.212664	+	1.01391i
$418$	2.68354	−	12.8506i	0.131256	−	0.628546i
$419$	7.24752	−	2.12806i	0.354064	−	0.103963i	−0.0998634	−	0.995001i	$-0.531841\pi$
$419$	7.24752	−	2.12806i	0.354064	−	0.103963i	0.453928	+	0.891038i	$0.350022\pi$
$420$	−5.43916	+	5.70805i	−0.265404	+	0.278524i
$421$	−10.1793	−	11.7476i	−0.496111	−	0.572543i	0.451377	−	0.892333i	$-0.350933\pi$
$421$	−10.1793	−	11.7476i	−0.496111	−	0.572543i	−0.947488	+	0.319791i	$0.896387\pi$
$422$	−8.14341	−	21.2898i	−0.396415	−	1.03637i
$423$	−1.32894	−	0.583130i	−0.0646151	−	0.0283528i
$424$	−0.783921	+	16.8821i	−0.0380706	+	0.819868i
$425$	−16.5828	+	25.8034i	−0.804385	+	1.25165i
$426$	16.5773	+	7.25661i	0.803173	+	0.351584i
$427$	−15.5450	−	13.4698i	−0.752276	−	0.651851i
$428$	−13.0348	+	2.09639i	−0.630059	+	0.101333i
$429$	−3.16381	+	0.249988i	−0.152750	+	0.0120695i
$430$	−4.02559	+	5.47202i	−0.194131	+	0.263884i
$431$	−12.5112	−	27.3957i	−0.602643	−	1.31960i	−0.927494	−	0.373839i	$-0.878041\pi$
$431$	−12.5112	−	27.3957i	−0.602643	−	1.31960i	0.324851	−	0.945765i	$-0.394686\pi$
$432$	17.3064	+	11.5104i	0.832654	+	0.553794i
$433$	−11.8115	+	25.8636i	−0.567624	+	1.24292i	0.380429	+	0.924810i	$0.375777\pi$
$433$	−11.8115	+	25.8636i	−0.567624	+	1.24292i	−0.948053	+	0.318113i	$0.896951\pi$
$434$	−15.1497	+	1.21049i	−0.727210	+	0.0581055i
$435$	−4.99049	−	8.97968i	−0.239276	−	0.430543i
$436$	22.2159	−	10.5966i	1.06395	−	0.507485i
$437$	−15.4344	+	25.2096i	−0.738329	+	1.20594i
$438$	8.12518	−	1.29943i	0.388236	−	0.0620893i
$439$	1.88020	+	2.92565i	0.0897370	+	0.139634i	0.883220	−	0.468959i	$-0.155371\pi$
$439$	1.88020	+	2.92565i	0.0897370	+	0.139634i	−0.793483	+	0.608593i	$0.791734\pi$
$440$	1.90999	+	3.29906i	0.0910551	+	0.157277i
$441$	−0.841029	+	1.35257i	−0.0400490	+	0.0644080i
$442$	10.9797	−	6.11468i	0.522251	−	0.290846i
$443$	−9.42060	−	20.6282i	−0.447586	−	0.980077i	−0.990143	−	0.140058i	$-0.955271\pi$
$443$	−9.42060	−	20.6282i	−0.447586	−	0.980077i	0.542557	−	0.840019i	$-0.317456\pi$
$444$	8.76539	−	17.0157i	0.415987	−	0.807530i
$445$	−0.938808	−	6.52956i	−0.0445038	−	0.309531i
$446$	−12.9291	−	0.816485i	−0.612212	−	0.0386617i
$447$	−0.256750	+	0.260605i	−0.0121439	+	0.0123262i
$448$	14.0767	+	14.6925i	0.665059	+	0.694156i
$449$	0.151898	−	0.236358i	0.00716852	−	0.0111544i	−0.837651	−	0.546206i	$-0.816072\pi$
$449$	0.151898	−	0.236358i	0.00716852	−	0.0111544i	0.844819	+	0.535052i	$0.179708\pi$
$450$	14.5064	+	10.3423i	0.683836	+	0.487540i
$451$	−2.86459	+	9.75591i	−0.134888	+	0.459388i
$452$	6.10207	−	4.06683i	0.287017	−	0.191287i
$453$	−11.6336	−	15.3017i	−0.546594	−	0.718935i
$454$	25.5977	−	19.4971i	1.20136	−	0.915046i
$455$	2.65693	−	0.780144i	0.124559	−	0.0365737i
$456$	29.7325	−	5.26459i	1.39235	−	0.246537i
$457$	4.82992	−	33.5929i	0.225934	−	1.57141i	−0.489043	−	0.872260i	$-0.662654\pi$
$457$	4.82992	−	33.5929i	0.225934	−	1.57141i	0.714977	−	0.699148i	$-0.246437\pi$
$458$	15.6240	+	15.3658i	0.730062	+	0.717996i
$459$	37.2585	+	7.23687i	1.73908	+	0.337788i
$460$	−1.54757	−	8.44274i	−0.0721560	−	0.393645i
$461$		−	14.0254i		−	0.653227i	−0.945158	−	0.326614i	$-0.894092\pi$
$461$		−	14.0254i		−	0.653227i	0.945158	−	0.326614i	$-0.105908\pi$
$462$	−6.25580	−	6.99342i	−0.291046	−	0.325363i
$463$	−7.89428	−	1.13503i	−0.366878	−	0.0527491i	−0.0435896	−	0.999050i	$-0.513879\pi$
$463$	−7.89428	−	1.13503i	−0.366878	−	0.0527491i	−0.323289	+	0.946300i	$0.604788\pi$
$464$	−23.7357	+	11.8110i	−1.10190	+	0.548312i
$465$	−1.43974	−	6.38880i	−0.0667663	−	0.296274i
$466$	−12.6131	−	16.5597i	−0.584292	−	0.767115i
$467$	−10.6309	−	12.2687i	−0.491937	−	0.567726i	0.454445	−	0.890775i	$-0.349838\pi$
$467$	−10.6309	−	12.2687i	−0.491937	−	0.567726i	−0.946382	+	0.323049i	$0.895292\pi$
$468$	−3.24045	−	6.54098i	−0.149790	−	0.302357i
$469$	12.7846	+	3.75389i	0.590337	+	0.173339i
$470$	0.288913	−	0.539750i	0.0133266	−	0.0248968i
$471$	−4.15242	+	5.63400i	−0.191333	+	0.259601i
$472$	−0.0769596	−	0.795878i	−0.00354235	−	0.0366333i
$473$	−6.10979	−	5.29416i	−0.280928	−	0.243426i
$474$	1.96805	−	15.4111i	0.0903955	−	0.707857i
$475$	25.6183	−	3.68336i	1.17545	−	0.169004i
$476$	34.0514	+	14.8700i	1.56074	+	0.681567i
$477$	17.1222	−	5.30594i	0.783972	−	0.242942i
$478$	3.52032	+	6.32118i	0.161016	+	0.289124i
$479$	−15.9635	+	34.9552i	−0.729392	+	1.59715i	0.0708636	+	0.997486i	$0.477424\pi$
$479$	−15.9635	+	34.9552i	−0.729392	+	1.59715i	−0.800255	+	0.599659i	$0.795303\pi$
$480$	−5.40958	+	6.90033i	−0.246912	+	0.314955i
$481$	−5.65516	+	3.63435i	−0.257853	+	0.165712i
$482$	−0.447829	−	1.97910i	−0.0203981	−	0.0901453i
$483$	7.95955	+	19.5707i	0.362172	+	0.890498i
$484$	15.7622	−	7.51828i	0.716462	−	0.341740i
$485$	−3.76486	−	5.85824i	−0.170954	−	0.266009i
$486$	5.24047	−	21.4135i	0.237712	−	0.971336i
$487$	10.0628	+	4.59553i	0.455989	+	0.208243i	0.630149	−	0.776474i	$-0.282994\pi$
$487$	10.0628	+	4.59553i	0.455989	+	0.208243i	−0.174160	+	0.984717i	$0.555721\pi$
$488$	−18.6483	−	13.2457i	−0.844167	−	0.599605i
$489$	−7.20164	−	18.8775i	−0.325669	−	0.853672i
$490$	−0.541214	−	0.398154i	−0.0244496	−	0.0179868i
$491$	2.11883	+	14.7368i	0.0956212	+	0.665060i	0.980104	+	0.198487i	$0.0636026\pi$
$491$	2.11883	+	14.7368i	0.0956212	+	0.665060i	−0.884482	+	0.466574i	$0.845488\pi$
$492$	−23.2800	+	2.23041i	−1.04954	+	0.100555i
$493$	−31.7041	+	36.5885i	−1.42788	+	1.64786i
$494$	−9.96652	−	3.62301i	−0.448415	−	0.163007i
$495$	2.60197	−	3.09485i	0.116950	−	0.139103i
$496$	−16.6394	+	2.96140i	−0.747133	+	0.132971i
$497$	5.29378	−	18.0290i	0.237459	−	0.808710i
$498$	−8.43409	−	27.1321i	−0.377941	−	1.21582i
$499$	−8.61943	+	7.46878i	−0.385859	+	0.334348i	−0.826092	−	0.563535i	$-0.809441\pi$
$499$	−8.61943	+	7.46878i	−0.385859	+	0.334348i	0.440234	+	0.897883i	$0.354896\pi$
$500$	−10.5730	+	12.6209i	−0.472839	+	0.564423i
$501$	7.62771	+	33.8478i	0.340781	+	1.51221i
$502$	−25.0069	−	5.22207i	−1.11611	−	0.233072i
$503$	3.35735	−	23.3509i	0.149697	−	1.04117i	−0.767019	−	0.641625i	$-0.778261\pi$
$503$	3.35735	−	23.3509i	0.149697	−	1.04117i	0.916716	−	0.399541i	$-0.130830\pi$
$504$	9.57923	−	19.3394i	0.426693	−	0.861446i
$505$	−11.3948			−0.507061
$506$	10.1621	−	1.03560i	0.451763	−	0.0460382i
$507$	1.27509	−	19.9122i	0.0566289	−	0.884332i
$508$	35.7944	+	22.1696i	1.58812	+	0.983618i
$509$	3.51588	+	0.505508i	0.155839	+	0.0224062i	0.219793	−	0.975547i	$-0.429462\pi$
$509$	3.51588	+	0.505508i	0.155839	+	0.0224062i	−0.0639538	+	0.997953i	$0.520371\pi$
$510$	−4.26786	+	15.4320i	−0.188984	+	0.683340i
$511$	−2.40713	−	8.19794i	−0.106485	−	0.362656i
$512$	17.1538	+	14.7562i	0.758099	+	0.652140i
$513$	−15.9732	−	27.7590i	−0.705233	−	1.22559i
$514$	−0.754657	−	1.97295i	−0.0332865	−	0.0870229i
$515$	−5.79106	−	1.70041i	−0.255185	−	0.0749290i
$516$	6.07616	−	17.5739i	0.267488	−	0.773648i
$517$	0.612910	+	0.393893i	0.0269557	+	0.0173234i
$518$	−18.6790	−	6.79014i	−0.820707	−	0.298342i
$519$	−17.9603	+	18.2300i	−0.788370	+	0.800207i
$520$	2.85741	−	1.14791i	0.125306	−	0.0503391i
$521$	32.8173	−	4.71842i	1.43775	−	0.206718i	0.621047	−	0.783773i	$-0.286708\pi$
$521$	32.8173	−	4.71842i	1.43775	−	0.206718i	0.816705	+	0.577056i	$0.195798\pi$
$522$	20.3406	+	19.4166i	0.890282	+	0.849843i
$523$	6.44512	−	2.94339i	0.281826	−	0.128705i	−0.269487	−	0.963004i	$-0.586854\pi$
$523$	6.44512	−	2.94339i	0.281826	−	0.128705i	0.551313	+	0.834298i	$0.314127\pi$
$524$	29.7146	−	26.6276i	1.29809	−	1.16323i
$525$	8.74439	−	16.3018i	0.381636	−	0.711467i
$526$	38.0617	−	3.04120i	1.65957	−	0.132603i
$527$	−25.9634	+	16.6857i	−1.13098	+	0.726839i
$528$	−7.67297	−	7.07133i	−0.333923	−	0.307740i
$529$	−22.3301	−	5.51071i	−0.970873	−	0.239596i
$530$	1.66891	+	7.37542i	0.0724927	+	0.320368i
$531$	−0.766117	+	0.363768i	−0.0332467	+	0.0157862i
$532$	−9.33328	−	29.9317i	−0.404649	−	1.29770i
$533$	7.47124	+	3.41200i	0.323615	+	0.147790i
$534$	7.75931	+	16.3045i	0.335778	+	0.705563i
$535$	−5.37341	+	2.45395i	−0.232313	+	0.106094i
$536$	14.5528	+	2.78675i	0.628587	+	0.120369i
$537$	−21.1363	+	1.67008i	−0.912097	+	0.0720693i
$538$	37.1660	+	2.34707i	1.60234	+	0.101189i
$539$	0.523622	−	0.604292i	0.0225540	−	0.0260287i
$540$	8.83367	+	2.90759i	0.380141	+	0.125123i
$541$	−23.8046	−	15.2983i	−1.02344	−	0.657724i	−0.0826016	−	0.996583i	$-0.526323\pi$
$541$	−23.8046	−	15.2983i	−1.02344	−	0.657724i	−0.940837	+	0.338858i	$0.889959\pi$
$542$	2.34406	−	4.37919i	0.100686	−	0.188102i
$543$	2.92336	−	8.01982i	0.125453	−	0.344164i
$544$	39.2825	+	12.8148i	1.68422	+	0.549429i
$545$	8.32320	−	7.21209i	0.356527	−	0.308932i
$546$	−6.31092	+	4.19799i	−0.270082	+	0.179657i
$547$	−1.19561	−	4.07189i	−0.0511207	−	0.174101i	0.929976	−	0.367621i	$-0.119828\pi$
$547$	−1.19561	−	4.07189i	−0.0511207	−	0.174101i	−0.981096	+	0.193520i	$0.938010\pi$
$548$	−38.1453	+	0.635767i	−1.62949	+	0.0271586i
$549$	−6.48752	+	23.3778i	−0.276881	+	0.997738i
$550$	−6.37682	−	6.27142i	−0.271909	−	0.267414i
$551$	40.8517			1.74034
$552$	10.9050	+	20.8106i	0.464149	+	0.885757i
$553$	−16.1322			−0.686011
$554$	23.4856	+	23.0975i	0.997810	+	0.981318i
$555$	1.75807	−	8.38194i	0.0746260	−	0.355794i
$556$	24.4246	−	0.407084i	1.03583	−	0.0172642i
$557$	−5.26734	−	17.9389i	−0.223184	−	0.760096i	−0.992609	−	0.121358i	$-0.961275\pi$
$557$	−5.26734	−	17.9389i	−0.223184	−	0.760096i	0.769424	−	0.638738i	$-0.220543\pi$
$558$	8.95430	+	15.5295i	0.379066	+	0.657418i
$559$	−4.93545	+	4.27659i	−0.208747	+	0.180881i
$560$	7.81881	+	4.66419i	0.330405	+	0.197098i
$561$	−17.9021	−	6.52562i	−0.755829	−	0.275512i
$562$	−10.7445	+	20.0730i	−0.453231	+	0.846729i
$563$	27.1735	+	17.4633i	1.14523	+	0.735991i	0.968683	−	0.248302i	$-0.0798724\pi$
$563$	27.1735	+	17.4633i	1.14523	+	0.735991i	0.176542	+	0.984293i	$0.443509\pi$
$564$	−0.316617	+	1.64557i	−0.0133320	+	0.0692911i
$565$	2.14868	−	2.47971i	0.0903957	−	0.104322i
$566$	−37.4145	−	2.36276i	−1.57265	−	0.0993141i
$567$	−22.7450	−	2.58105i	−0.955200	−	0.108394i
$568$	3.92991	−	20.5226i	0.164895	−	0.861109i
$569$	0.615380	−	0.281035i	0.0257981	−	0.0117816i	−0.402474	−	0.915431i	$-0.631850\pi$
$569$	0.615380	−	0.281035i	0.0257981	−	0.0117816i	0.428272	+	0.903650i	$0.359122\pi$
$570$	12.1994	−	5.80571i	0.510978	−	0.243175i
$571$	−32.8804	−	15.0160i	−1.37600	−	0.628399i	−0.416251	−	0.909250i	$-0.636656\pi$
$571$	−32.8804	−	15.0160i	−1.37600	−	0.628399i	−0.959752	+	0.280851i	$0.909383\pi$
$572$	1.09090	+	3.49850i	0.0456128	+	0.146280i
$573$	−14.8509	−	26.7220i	−0.620405	−	1.11633i
$574$	5.35939	+	23.6848i	0.223697	+	0.988584i
$575$	8.76365	+	18.1318i	0.365470	+	0.756147i
$576$	8.53315	−	22.4318i	0.355548	−	0.934658i
$577$	−25.1184	+	16.1426i	−1.04569	+	0.672026i	−0.946388	−	0.323031i	$-0.895298\pi$
$577$	−25.1184	+	16.1426i	−1.04569	+	0.672026i	−0.0993047	+	0.995057i	$0.531662\pi$
$578$	51.2494	−	4.09492i	2.13169	−	0.170326i
$579$	0.428796	+	0.230009i	0.0178202	+	0.00955887i
$580$	−8.83440	+	7.91662i	−0.366828	+	0.328720i
$581$	−26.8365	+	12.2558i	−1.11336	+	0.508456i
$582$	14.6007	+	12.2535i	0.605219	+	0.507924i
$583$	−8.90751	+	1.28071i	−0.368911	+	0.0530414i
$584$	−3.54187	−	8.81653i	−0.146564	−	0.364831i
$585$	−2.17543	−	2.43625i	−0.0899428	−	0.100727i
$586$	−4.20128	−	1.52724i	−0.173553	−	0.0630898i
$587$	12.8654	+	8.26810i	0.531013	+	0.341261i	0.778515	−	0.627626i	$-0.215973\pi$
$587$	12.8654	+	8.26810i	0.531013	+	0.341261i	−0.247502	+	0.968887i	$0.579610\pi$
$588$	1.73816	+	0.600966i	0.0716805	+	0.0247834i
$589$	24.9874	+	7.33695i	1.02959	+	0.302314i
$590$	−0.127816	−	0.334158i	−0.00526212	−	0.0137571i
$591$	−22.4512	−	29.5300i	−0.923517	−	1.21470i
$592$	−21.4022	−	5.51663i	−0.879626	−	0.226732i
$593$	−4.46501	−	15.2064i	−0.183356	−	0.624453i	−0.998949	−	0.0458275i	$-0.985408\pi$
$593$	−4.46501	−	15.2064i	−0.183356	−	0.624453i	0.815593	−	0.578625i	$-0.196411\pi$
$594$	−4.28653	+	10.2036i	−0.175878	+	0.418659i
$595$	16.4562	+	2.36604i	0.674637	+	0.0969981i
$596$	0.359128	+	0.222430i	0.0147105	+	0.00911107i
$597$	11.8134	+	0.756483i	0.483492	+	0.0309608i
$598$	0.340213	−	8.24442i	0.0139123	−	0.337140i
$599$	−27.9464			−1.14186			−0.570929	−	0.821000i	$-0.693417\pi$
$599$	−27.9464			−1.14186			−0.570929	+	0.821000i	$0.693417\pi$
$600$	7.93420	−	18.9801i	0.323912	−	0.774860i
$601$	2.97472	−	20.6896i	0.121341	−	0.843948i	−0.834698	−	0.550709i	$-0.814358\pi$
$601$	2.97472	−	20.6896i	0.121341	−	0.843948i	0.956039	−	0.293240i	$-0.0947334\pi$
$602$	−18.9002	−	3.94683i	−0.770314	−	0.160861i
$603$	−2.46820	−	15.5210i	−0.100513	−	0.632066i
$604$	−14.2534	+	17.0142i	−0.579964	+	0.692296i
$605$	5.90530	−	5.11698i	0.240085	−	0.208035i
$606$	29.7842	−	9.25851i	1.20990	−	0.376101i
$607$	−5.93201	+	20.2026i	−0.240773	+	0.819997i	0.747097	+	0.664715i	$0.231447\pi$
$607$	−5.93201	+	20.2026i	−0.240773	+	0.819997i	−0.987870	+	0.155282i	$0.950371\pi$
$608$	−13.5346	−	32.1320i	−0.548898	−	1.30312i
$609$	17.3235	−	23.5045i	0.701983	−	0.952451i
$610$	−9.61880	−	3.49661i	−0.389454	−	0.141573i
$611$	0.385407	−	0.444783i	0.0155919	−	0.0179940i
$612$	−1.38329	−	43.8046i	−0.0559160	−	1.77069i
$613$	−1.52458	−	10.6037i	−0.0615772	−	0.428279i	−0.997169	−	0.0751948i	$-0.976042\pi$
$613$	−1.52458	−	10.6037i	−0.0615772	−	0.428279i	0.935592	−	0.353084i	$-0.114867\pi$
$614$	27.5962	+	20.3017i	1.11369	+	0.819309i
$615$	−9.77682	+	3.72978i	−0.394239	+	0.150399i
$616$	−6.27416	+	8.83321i	−0.252793	+	0.355900i
$617$	33.9727	+	15.5148i	1.36769	+	0.624603i	0.957774	−	0.287521i	$-0.0928311\pi$
$617$	33.9727	+	15.5148i	1.36769	+	0.624603i	0.409915	+	0.912124i	$0.365558\pi$
$618$	16.5186	−	0.260751i	0.664475	−	0.0104890i
$619$	3.57908	+	5.56916i	0.143856	+	0.223844i	0.905703	−	0.423913i	$-0.139344\pi$
$619$	3.57908	+	5.56916i	0.143856	+	0.223844i	−0.761847	+	0.647757i	$0.775707\pi$
$620$	−6.82547	+	3.25563i	−0.274118	+	0.130749i
$621$	16.8256	−	18.3820i	0.675188	−	0.737646i
$622$	10.9291	+	48.2991i	0.438218	+	1.93662i
$623$	15.7728	−	10.1366i	0.631926	−	0.406114i
$624$	−6.53614	+	5.32217i	−0.261655	+	0.213057i
$625$	5.66174	−	12.3975i	0.226470	−	0.495899i
$626$	−10.7044	−	19.2211i	−0.427834	−	0.768231i
$627$	5.73087	+	15.0222i	0.228869	+	0.599931i
$628$	7.40623	+	3.23426i	0.295541	+	0.129061i
$629$	−39.9493	+	5.74384i	−1.59288	+	0.229022i
$630$	1.83287	−	9.48104i	0.0730234	−	0.377734i
$631$	27.9037	+	24.1787i	1.11083	+	0.962538i	0.999512	−	0.0312466i	$-0.00994772\pi$
$631$	27.9037	+	24.1787i	1.11083	+	0.962538i	0.111317	+	0.993785i	$0.464493\pi$
$632$	−17.8565	+	1.72668i	−0.710292	+	0.0686836i
$633$	22.4727	+	16.5630i	0.893211	+	0.658321i
$634$	8.40074	−	15.6943i	0.333636	−	0.623301i
$635$	18.0759	+	5.30755i	0.717318	+	0.210624i
$636$	−10.3550	−	17.9222i	−0.410601	−	0.710661i
$637$	−0.422979	−	0.488144i	−0.0167590	−	0.0193410i
$638$	−8.55396	−	11.2305i	−0.338655	−	0.444618i
$639$	−21.8880	+	3.48069i	−0.865875	+	0.137694i
$640$	9.15374	+	4.32585i	0.361833	+	0.170994i
$641$	43.6092	+	6.27005i	1.72246	+	0.247652i	0.931377	−	0.364057i	$-0.118609\pi$
$641$	43.6092	+	6.27005i	1.72246	+	0.247652i	0.791083	+	0.611709i	$0.209518\pi$
$642$	12.0514	−	10.7803i	0.475630	−	0.425463i
$643$		−	42.1685i		−	1.66296i	−0.555553	−	0.831481i	$-0.687494\pi$
$643$		−	42.1685i		−	1.66296i	0.555553	−	0.831481i	$-0.312506\pi$
$644$	20.0003	−	13.9694i	0.788124	−	0.550470i
$645$	0.531690	−	8.30301i	0.0209353	−	0.326931i
$646$	−45.3944	−	44.6441i	−1.78602	−	1.75650i
$647$	2.84386	−	19.7795i	0.111804	−	0.777612i	−0.854360	−	0.519682i	$-0.826050\pi$
$647$	2.84386	−	19.7795i	0.111804	−	0.777612i	0.966164	−	0.257930i	$-0.0830405\pi$
$648$	−25.4523	−	0.422456i	−0.999862	−	0.0165956i
$649$	0.408521	−	0.119953i	0.0160358	−	0.00470855i
$650$	−5.74754	+	4.37776i	−0.225437	+	0.171710i
$651$	14.8175	−	11.2655i	0.580743	−	0.441529i
$652$	−19.4137	+	12.9386i	−0.760300	+	0.506715i
$653$	−0.199242	+	0.678557i	−0.00779695	+	0.0265540i	−0.963300	−	0.268429i	$-0.913496\pi$
$653$	−0.199242	+	0.678557i	−0.00779695	+	0.0265540i	0.955503	+	0.294983i	$0.0953138\pi$
$654$	−15.8956	+	25.6141i	−0.621567	+	1.00159i
$655$	9.65192	−	15.0187i	0.377132	−	0.586829i
$656$	8.46728	+	25.6427i	0.330592	+	1.00118i
$657$	−7.51705	+	6.71227i	−0.293268	+	0.261871i
$658$	1.73657	+	0.109666i	0.0676985	+	0.00427522i
$659$	−1.83098	−	12.7347i	−0.0713247	−	0.496074i	−0.993902	−	0.110263i	$-0.964831\pi$
$659$	−1.83098	−	12.7347i	−0.0713247	−	0.496074i	0.922578	−	0.385811i	$-0.126078\pi$
$660$	−4.15048	−	2.13806i	−0.161557	−	0.0832238i
$661$	−3.16875	−	6.93859i	−0.123250	−	0.269880i	0.837942	−	0.545759i	$-0.183758\pi$
$661$	−3.16875	−	6.93859i	−0.123250	−	0.269880i	−0.961192	+	0.275879i	$0.911031\pi$
$662$	15.5747	−	8.67370i	0.605329	−	0.337113i
$663$	−7.27575	+	13.5639i	−0.282567	+	0.526776i
$664$	−28.3931	+	16.4382i	−1.10187	+	0.637924i
$665$	−7.58446	−	11.8016i	−0.294113	−	0.457648i
$666$	2.21517	+	23.3376i	0.0858362	+	0.904313i
$667$	9.61880	+	30.2964i	0.372441	+	1.17308i
$668$	36.1612	−	17.2483i	1.39912	−	0.667356i
$669$	13.8686	−	7.70752i	0.536190	−	0.297990i
$670$	6.60878	−	0.528054i	0.255319	−	0.0204005i
$671$	5.05969	−	11.0792i	0.195327	−	0.427707i
$672$	−24.2269	−	5.83854i	−0.934574	−	0.225227i
$673$	13.9697	+	30.5894i	0.538493	+	1.17913i	0.961952	+	0.273219i	$0.0880885\pi$
$673$	13.9697	+	30.5894i	0.538493	+	1.17913i	−0.423459	+	0.905915i	$0.639184\pi$
$674$	5.73915	−	7.80127i	0.221064	−	0.300494i
$675$	−21.7934	−	1.06973i	−0.838828	−	0.0411740i
$676$	−22.7474	+	3.65848i	−0.874900	+	0.140711i
$677$	7.55804	+	6.54908i	0.290479	+	0.251702i	0.787894	−	0.615811i	$-0.211172\pi$
$677$	7.55804	+	6.54908i	0.290479	+	0.251702i	−0.497414	+	0.867513i	$0.665717\pi$
$678$	−3.60151	+	8.22744i	−0.138315	+	0.315973i
$679$	10.7005	−	16.6503i	0.410649	−	0.638982i
$680$	18.4683	+	0.857577i	0.708228	+	0.0328866i
$681$	−13.4965	+	37.0259i	−0.517188	+	1.41883i
$682$	−3.21513	−	8.40552i	−0.123114	−	0.321864i
$683$	−2.01654	−	2.32721i	−0.0771607	−	0.0890482i	0.715857	−	0.698247i	$-0.246036\pi$
$683$	−2.01654	−	2.32721i	−0.0771607	−	0.0890482i	−0.793017	+	0.609199i	$0.791491\pi$
$684$	−27.1702	+	25.0875i	−1.03888	+	0.959246i
$685$	−16.3787	+	4.80922i	−0.625797	+	0.183751i
$686$	5.53730	−	26.5164i	0.211415	−	1.01240i
$687$	−26.2673	−	5.50944i	−1.00216	−	0.210198i
$688$	−21.3428	−	2.34574i	−0.813685	−	0.0894307i
$689$			7.26943i			0.276943i
$690$	7.17806	+	7.68034i	0.273264	+	0.292385i
$691$			34.1984i			1.30097i	0.759519	+	0.650485i	$0.225434\pi$
$691$			34.1984i			1.30097i	−0.759519	+	0.650485i	$0.774566\pi$
$692$	25.1219	+	15.5595i	0.954990	+	0.591483i
$693$	11.0734	+	3.07297i	0.420646	+	0.116733i
$694$	−38.8546	−	8.11383i	−1.47490	−	0.307997i
$695$	10.4873	−	3.07936i	0.397807	−	0.116807i
$696$	16.6593	−	27.8710i	0.631471	−	1.05645i
$697$	32.2931	+	37.2682i	1.22319	+	1.41163i
$698$	32.5307	−	12.4431i	1.23131	−	0.470977i
$699$	23.9529	+	8.73121i	0.905981	+	0.330245i
$700$	−20.5930	−	5.67564i	−0.778340	−	0.214519i
$701$	−7.87469	+	12.2533i	−0.297423	+	0.462799i	−0.957514	−	0.288386i	$-0.906881\pi$
$701$	−7.87469	+	12.2533i	−0.297423	+	0.462799i	0.660091	+	0.751186i	$0.270518\pi$
$702$	7.66574	+	4.60041i	0.289325	+	0.173631i
$703$	25.7379	+	22.3021i	0.970725	+	0.841138i
$704$	−5.99933	+	10.4489i	−0.226108	+	0.393807i
$705$	0.0590614	+	0.747471i	0.00222438	+	0.0281514i
$706$	8.15422	+	5.99880i	0.306888	+	0.225768i
$707$	−13.4538	−	29.4597i	−0.505982	−	1.10795i
$708$	0.605603	+	0.769585i	0.0227600	+	0.0289228i
$709$	2.69486	−	5.90093i	0.101208	−	0.221614i	−0.852254	−	0.523128i	$-0.824765\pi$
$709$	2.69486	−	5.90093i	0.101208	−	0.221614i	0.953462	+	0.301514i	$0.0974921\pi$
$710$	−0.744669	−	9.31978i	−0.0279469	−	0.349765i
$711$	8.16157	+	17.1888i	0.306083	+	0.644629i
$712$	16.3738	−	12.9083i	0.613633	−	0.483757i
$713$	0.442210	+	20.2587i	0.0165609	+	0.758693i
$714$	−44.9364	+	7.18652i	−1.68170	+	0.268949i
$715$	0.886493	+	1.37941i	0.0331529	+	0.0515870i
$716$	7.28791	+	23.3722i	0.272362	+	0.873461i
$717$	−7.80892	−	4.18876i	−0.291630	−	0.156432i
$718$	11.3835	+	20.4406i	0.424830	+	0.762836i
$719$	12.0750	+	26.4406i	0.450323	+	0.986070i	0.989587	+	0.143933i	$0.0459750\pi$
$719$	12.0750	+	26.4406i	0.450323	+	0.986070i	−0.539265	+	0.842136i	$0.681298\pi$
$720$	1.01399	−	10.6906i	0.0377893	−	0.398415i
$721$	−2.44131	−	16.9797i	−0.0909191	−	0.632357i
$722$	−1.69251	+	26.8010i	−0.0629887	+	0.997432i
$723$	1.77032	+	1.74414i	0.0658391	+	0.0648651i
$724$	−9.77824	−	1.23995i	−0.363405	−	0.0460825i
$725$	15.0472	−	23.4139i	0.558839	−	0.869571i
$726$	−11.2779	+	18.1732i	−0.418563	+	0.674470i
$727$	6.61631	−	22.5331i	0.245385	−	0.835706i	−0.741035	−	0.671466i	$-0.765665\pi$
$727$	6.61631	−	22.5331i	0.245385	−	0.835706i	0.986421	−	0.164239i	$-0.0525169\pi$
$728$	6.34150	+	6.03212i	0.235032	+	0.223565i
$729$	8.75701	+	25.5405i	0.324334	+	0.945943i
$730$	−2.57598	−	3.38199i	−0.0953413	−	0.125173i
$731$	−37.6205	+	11.0464i	−1.39144	+	0.408565i
$732$	27.9831	+	1.32412i	1.03429	+	0.0489407i
$733$	−3.65831	+	25.4441i	−0.135123	+	0.939800i	0.803610	+	0.595156i	$0.202910\pi$
$733$	−3.65831	+	25.4441i	−0.135123	+	0.939800i	−0.938733	+	0.344644i	$0.887999\pi$
$734$	−0.0280991	+	0.0285713i	−0.00103716	+	0.00105459i
$735$	0.821215	+	0.0525872i	0.0302910	+	0.00193971i
$736$	20.6429	−	17.6032i	0.760907	−	0.648861i
$737$			7.88992i			0.290629i
$738$	22.5246	−	17.6930i	0.829141	−	0.651287i
$739$	24.0773	+	3.46180i	0.885699	+	0.127344i	0.570126	−	0.821557i	$-0.306894\pi$
$739$	24.0773	+	3.46180i	0.885699	+	0.127344i	0.315572	+	0.948901i	$0.397803\pi$
$740$	−9.88786	+	0.164801i	−0.363485	+	0.00605819i
$741$	12.6702	−	2.85527i	0.465451	−	0.104891i
$742$	−17.0977	+	13.0229i	−0.627676	+	0.478085i
$743$	−16.4886	−	19.0288i	−0.604907	−	0.698100i	0.367861	−	0.929881i	$-0.380090\pi$
$743$	−16.4886	−	19.0288i	−0.604907	−	0.698100i	−0.972768	+	0.231781i	$0.925545\pi$
$744$	15.1955	−	14.0556i	0.557093	−	0.515302i
$745$	0.181356	+	0.0532511i	0.00664439	+	0.00195097i
$746$	−21.1015	−	11.2951i	−0.772581	−	0.413541i
$747$	26.6355	+	22.3937i	0.974543	+	0.819341i
$748$	−2.76787	+	21.8273i	−0.101203	+	0.798086i
$749$	−12.6887	−	10.9948i	−0.463636	−	0.401743i
$750$	2.55434	−	20.0022i	0.0932714	−	0.730377i
$751$	−10.2521	+	1.47403i	−0.374105	+	0.0537881i	−0.326803	−	0.945093i	$-0.605971\pi$
$751$	−10.2521	+	1.47403i	−0.374105	+	0.0537881i	−0.0473018	+	0.998881i	$0.515062\pi$
$752$	1.93392	−	0.0644831i	0.0705228	−	0.00235145i
$753$	29.2327	−	11.1521i	1.06530	−	0.406404i
$754$	−9.96294	+	5.54844i	−0.362829	+	0.202062i
$755$	−4.12556	+	9.03372i	−0.150145	+	0.328771i
$756$	2.91270	+	26.2712i	0.105934	+	0.955476i
$757$	−17.4925	+	11.2418i	−0.635776	+	0.408589i	−0.818444	−	0.574586i	$-0.805163\pi$
$757$	−17.4925	+	11.2418i	−0.635776	+	0.408589i	0.182668	+	0.983175i	$0.441527\pi$
$758$	−24.7826	+	5.60779i	−0.900143	+	0.203684i
$759$	−9.79142	+	7.78721i	−0.355406	+	0.282658i
$760$	−9.65829	−	12.2513i	−0.350343	−	0.444400i
$761$	−20.0730	−	31.2342i	−0.727646	−	1.13224i	−0.986090	−	0.166213i	$-0.946846\pi$
$761$	−20.0730	−	31.2342i	−0.727646	−	1.13224i	0.258444	−	0.966026i	$-0.416790\pi$
$762$	−51.5600	+	0.813893i	−1.86782	+	0.0294842i
$763$	28.4731	+	13.0032i	1.03079	+	0.470748i
$764$	−26.2897	+	23.5586i	−0.951128	+	0.852319i
$765$	−5.80447	−	18.7310i	−0.209861	−	0.677219i
$766$	−4.44395	+	6.04069i	−0.160566	+	0.218259i
$767$	−0.0489467	−	0.340432i	−0.00176736	−	0.0122923i
$768$	−27.4413	−	3.86951i	−0.990204	−	0.139629i
$769$	26.3502	−	30.4098i	0.950214	−	1.09660i	−0.0450103	−	0.998987i	$-0.514332\pi$
$769$	26.3502	−	30.4098i	0.950214	−	1.09660i	0.995224	−	0.0976185i	$-0.0311225\pi$
$770$	−1.65625	+	4.55618i	−0.0596873	+	0.164193i
$771$	2.08257	+	1.53491i	0.0750018	+	0.0552785i
$772$	0.149290	−	0.541670i	0.00537307	−	0.0194951i
$773$	−7.98788	+	27.2042i	−0.287304	+	0.978468i	0.681743	+	0.731592i	$0.261222\pi$
$773$	−7.98788	+	27.2042i	−0.287304	+	0.978468i	−0.969047	+	0.246876i	$0.920596\pi$
$774$	5.35662	+	22.1348i	0.192540	+	0.795619i
$775$	13.4089	−	11.6189i	0.481662	−	0.417363i
$776$	10.0621	−	19.5753i	0.361209	−	0.702713i
$777$	23.7461	−	5.35127i	0.851888	−	0.191976i
$778$	−2.15710	+	10.3297i	−0.0773358	+	0.370338i
$779$	5.92181	−	41.1871i	0.212171	−	1.47568i
$780$	−2.18667	+	3.07281i	−0.0782955	+	0.110024i
$781$	11.1265			0.398136
$782$	22.4205	−	44.1771i	0.801757	−	1.57977i
$783$	−33.8082	−	6.56671i	−1.20821	−	0.234675i
$784$	0.232007	−	2.11092i	0.00828598	−	0.0753900i
$785$	3.57924	+	0.514617i	0.127749	+	0.0183675i
$786$	−13.0257	+	47.0989i	−0.464610	+	1.67996i
$787$	−2.30422	−	7.84746i	−0.0821367	−	0.279732i	0.908176	−	0.418589i	$-0.137475\pi$
$787$	−2.30422	−	7.84746i	−0.0821367	−	0.279732i	−0.990312	+	0.138857i	$0.955657\pi$
$788$	−27.5071	+	32.8349i	−0.979899	+	1.16969i
$789$	−37.2270	+	28.3031i	−1.32532	+	1.00762i
$790$	−7.49724	+	2.86771i	−0.266740	+	0.102029i
$791$	8.94790	+	2.62734i	0.318151	+	0.0934175i
$792$	12.5859	+	2.21620i	0.447222	+	0.0787493i
$793$	−8.27693	−	5.31926i	−0.293922	−	0.188892i
$794$	−4.60369	+	12.6643i	−0.163379	+	0.449438i
$795$	−6.59740	−	6.49980i	−0.233986	−	0.230524i
$796$	−2.17049	−	13.4955i	−0.0769309	−	0.478335i
$797$	16.5836	−	2.38435i	0.587420	−	0.0844582i	0.157805	−	0.987470i	$-0.449558\pi$
$797$	16.5836	−	2.38435i	0.587420	−	0.0844582i	0.429615	+	0.903012i	$0.358649\pi$
$798$	29.4137	+	24.6852i	1.04123	+	0.873846i
$799$	3.21418	−	1.46787i	0.113709	−	0.0519294i
$800$	−23.4015	−	4.07815i	−0.827368	−	0.144184i
$801$	−18.7802	−	11.6776i	−0.663567	−	0.412607i
$802$	−1.66450	−	20.8318i	−0.0587756	−	0.735596i
$803$	4.25616	−	2.73527i	0.150197	−	0.0965256i
$804$	−16.8453	+	6.75003i	−0.594088	+	0.238055i
$805$	6.96652	−	8.40356i	0.245538	−	0.296186i
$806$	−7.09043	+	1.60442i	−0.249750	+	0.0565133i
$807$	−39.8666	+	22.1560i	−1.40337	+	0.779929i
$808$	−18.0450	−	31.1685i	−0.634819	−	1.09650i
$809$	20.8546	+	9.52397i	0.733208	+	0.334845i	0.746787	−	0.665063i	$-0.231595\pi$
$809$	20.8546	+	9.52397i	0.733208	+	0.334845i	−0.0135793	+	0.999908i	$0.504323\pi$
$810$	−11.0293	+	2.84371i	−0.387529	+	0.0999180i
$811$	−10.3706	+	4.73609i	−0.364160	+	0.166306i	−0.589088	−	0.808069i	$-0.700513\pi$
$811$	−10.3706	+	4.73609i	−0.364160	+	0.166306i	0.224927	+	0.974376i	$0.427786\pi$
$812$	−30.8981	−	13.4930i	−1.08431	−	0.473512i
$813$	0.479187	+	6.06451i	0.0168058	+	0.212692i
$814$	0.741733	−	11.7454i	0.0259977	−	0.411676i
$815$	−6.83602	+	7.88919i	−0.239455	+	0.276346i
$816$	−48.9702	+	12.7643i	−1.71430	+	0.446841i
$817$	27.8326	+	17.8869i	0.973739	+	0.625784i
$818$	21.0496	+	11.2673i	0.735981	+	0.393951i
$819$	3.73008	−	8.50075i	0.130340	−	0.297040i
$820$	6.70100	+	10.0545i	0.234009	+	0.351119i
$821$	−35.6784	+	30.9155i	−1.24518	+	1.07896i	−0.251371	+	0.967891i	$0.580881\pi$
$821$	−35.6784	+	30.9155i	−1.24518	+	1.07896i	−0.993813	+	0.111067i	$0.964573\pi$
$822$	38.9038	−	25.8786i	1.35693	−	0.902619i
$823$	−3.77705	−	12.8635i	−0.131660	−	0.448392i	0.867103	−	0.498130i	$-0.165980\pi$
$823$	−3.77705	−	12.8635i	−0.131660	−	0.448392i	−0.998762	+	0.0497377i	$0.984161\pi$
$824$	−4.51964	−	18.5333i	−0.157449	−	0.645636i
$825$	10.7208	+	2.24864i	0.373250	+	0.0782875i
$826$	0.713009	−	0.724992i	0.0248088	−	0.0252257i
$827$	32.8908			1.14373			0.571863	−	0.820349i	$-0.306221\pi$
$827$	32.8908			1.14373			0.571863	+	0.820349i	$0.306221\pi$
$828$	−25.0028	−	14.2429i	−0.868907	−	0.494975i
$829$	23.5541			0.818066			0.409033	−	0.912520i	$-0.365866\pi$
$829$	23.5541			0.818066			0.409033	+	0.912520i	$0.365866\pi$
$830$	−10.2933	+	10.4663i	−0.357285	+	0.363290i
$831$	−39.4844	−	8.28166i	−1.36970	−	0.287288i
$832$	7.66495	+	5.99811i	0.265734	+	0.207947i
$833$	−1.09255	−	3.72088i	−0.0378546	−	0.128921i
$834$	−24.9102	+	16.5701i	−0.862570	+	0.573777i
$835$	13.5478	−	11.7393i	0.468842	−	0.406254i
$836$	15.4489	−	10.2962i	0.534312	−	0.356101i
$837$	−19.4998	−	10.0885i	−0.674010	−	0.348711i
$838$	9.41791	+	5.04115i	0.325336	+	0.174144i
$839$	−10.5978	−	6.81077i	−0.365875	−	0.235134i	0.344765	−	0.938689i	$-0.387958\pi$
$839$	−10.5978	−	6.81077i	−0.365875	−	0.235134i	−0.710641	+	0.703555i	$0.751595\pi$
$840$	−11.1446	+	0.361763i	−0.384525	+	0.0124820i
$841$	9.77721	−	11.2835i	0.337145	−	0.389086i
$842$	1.38548	−	21.9392i	0.0477469	−	0.756076i
$843$	−2.19646	−	27.7981i	−0.0756503	−	0.957417i
$844$	12.9007	−	29.5418i	0.444060	−	1.01687i
$845$	−9.37732	+	4.28248i	−0.322589	+	0.147322i
$846$	−0.761713	−	1.90579i	−0.0261882	−	0.0655223i
$847$	20.2016	+	9.22577i	0.694136	+	0.317001i
$848$	−17.5313	+	16.2448i	−0.602027	+	0.557850i
$849$	40.1331	−	22.3041i	1.37736	−	0.765476i
$850$	−42.3079	+	9.57343i	−1.45115	+	0.328366i
$851$	−10.4795	+	24.3389i	−0.359232	+	0.834328i
$852$	9.51897	+	23.7554i	0.326115	+	0.813848i
$853$	41.5108	−	26.6774i	1.42130	−	0.913415i	0.421323	−	0.906911i	$-0.361566\pi$
$853$	41.5108	−	26.6774i	1.42130	−	0.913415i	0.999979	−	0.00650434i	$-0.00207041\pi$
$854$	−2.31688	−	28.9965i	−0.0792820	−	0.992241i
$855$	−8.73747	+	14.0519i	−0.298815	+	0.480564i
$856$	−15.2218	−	10.8119i	−0.520270	−	0.369544i
$857$	−19.3900	+	8.85510i	−0.662348	+	0.302484i	−0.718079	−	0.695961i	$-0.754978\pi$
$857$	−19.3900	+	8.85510i	−0.662348	+	0.302484i	0.0557308	+	0.998446i	$0.482251\pi$
$858$	−3.43796	−	2.88527i	−0.117370	−	0.0985015i
$859$	−26.4229	+	3.79904i	−0.901538	+	0.129622i	−0.577470	−	0.816412i	$-0.695960\pi$
$859$	−26.4229	+	3.79904i	−0.901538	+	0.129622i	−0.324068	+	0.946034i	$0.605051\pi$
$860$	−9.48523	+	1.52552i	−0.323444	+	0.0520197i
$861$	−21.1863	−	20.8729i	−0.722028	−	0.711347i
$862$	14.5515	−	40.0295i	0.495624	−	1.36341i
$863$	10.9390	+	7.03006i	0.372368	+	0.239306i	0.713418	−	0.700739i	$-0.247146\pi$
$863$	10.9390	+	7.03006i	0.372368	+	0.239306i	−0.341050	+	0.940045i	$0.610783\pi$
$864$	6.03591	+	28.7675i	0.205346	+	0.978689i
$865$	12.6863	+	3.72504i	0.431348	+	0.126655i
$866$	−37.5567	+	14.3655i	−1.27623	+	0.488160i
$867$	−50.1255	+	38.1095i	−1.70235	+	1.29427i
$868$	−16.4758	−	13.8024i	−0.559225	−	0.468485i
$869$	−2.69128	−	9.16566i	−0.0912954	−	0.310924i
$870$	3.87264	−	14.0029i	0.131295	−	0.474744i
$871$	6.30856	+	0.907034i	0.213757	+	0.0307337i
$872$	32.9082	+	11.3455i	1.11441	+	0.384207i
$873$	−23.1544	−	2.97764i	−0.783659	−	0.100778i
$874$	−40.5612	+	10.1135i	−1.37200	+	0.342094i
$875$	−20.9381			−0.707836
$876$	9.48116	+	6.74698i	0.320339	+	0.227959i
$877$	6.58241	−	45.7817i	0.222272	−	1.54594i	−0.507140	−	0.861864i	$-0.669297\pi$
$877$	6.58241	−	45.7817i	0.222272	−	1.54594i	0.729412	−	0.684074i	$-0.239794\pi$
$878$	−1.00537	+	4.81439i	−0.0339295	+	0.162478i
$879$	5.34099	−	1.20361i	0.180147	−	0.0405968i
$880$	−1.34562	+	5.22044i	−0.0453608	+	0.175981i
$881$	6.99947	−	6.06508i	0.235818	−	0.204338i	−0.528933	−	0.848664i	$-0.677408\pi$
$881$	6.99947	−	6.06508i	0.235818	−	0.204338i	0.764751	+	0.644326i	$0.222862\pi$
$882$	−2.18926	+	0.529800i	−0.0737162	+	0.0178393i
$883$	4.42183	−	15.0594i	0.148806	−	0.506788i	−0.851026	−	0.525124i	$-0.824019\pi$
$883$	4.42183	−	15.0594i	0.148806	−	0.506788i	0.999832	+	0.0183366i	$0.00583703\pi$
$884$	17.1343	+	4.72240i	0.576290	+	0.158832i
$885$	0.352725	+	0.259968i	0.0118567	+	0.00873873i
$886$	10.9569	−	30.1412i	0.368103	−	1.01261i
$887$	7.37544	−	8.51171i	0.247643	−	0.285795i	−0.618295	−	0.785946i	$-0.712176\pi$
$887$	7.37544	−	8.51171i	0.247643	−	0.285795i	0.865939	+	0.500150i	$0.166722\pi$
$888$	25.7115	−	8.46486i	0.862820	−	0.284062i
$889$	7.62015	+	52.9993i	0.255572	+	1.77754i
$890$	5.52832	−	7.51469i	0.185310	−	0.251893i
$891$	−2.32802	−	13.3534i	−0.0779917	−	0.447355i
$892$	−12.2268	−	13.6442i	−0.409382	−	0.456842i
$893$	−2.71215	−	1.23860i	−0.0907587	−	0.0414481i
$894$	−0.517306	+	0.00816585i	−0.0173013	+	0.000273107i
$895$	5.92234	+	9.21534i	0.197962	+	0.308035i
$896$	−0.376113	+	28.7733i	−0.0125650	+	0.961248i
$897$	5.10080	+	8.72417i	0.170311	+	0.291292i
$898$	0.387539	−	0.0876922i	0.0129323	−	0.00292633i
$899$	23.5591	−	15.1405i	0.785740	−	0.504964i
$900$	4.37099	+	24.8131i	0.145700	+	0.827103i
$901$	−18.1308	+	39.7008i	−0.604023	+	1.32263i
$902$	−12.5626	+	6.99624i	−0.418290	+	0.232949i
$903$	22.0941	−	8.42872i	0.735245	−	0.280490i
$904$	10.1855	+	1.95044i	0.338765	+	0.0648707i
$905$	−4.36533	+	0.627639i	−0.145108	+	0.0208634i
$906$	3.44350	−	26.9649i	0.114403	−	0.895848i
$907$	−27.8499	−	24.1321i	−0.924740	−	0.801292i	0.0556316	−	0.998451i	$-0.482283\pi$
$907$	−27.8499	−	24.1321i	−0.924740	−	0.801292i	−0.980371	+	0.197160i	$0.936828\pi$
$908$	45.1441	+	5.72461i	1.49816	+	0.189978i
$909$	−24.5826	+	29.2391i	−0.815354	+	0.969801i
$910$	3.45259	+	1.84808i	0.114452	+	0.0612632i
$911$	12.7033	+	3.73003i	0.420880	+	0.123582i	0.485313	−	0.874340i	$-0.338706\pi$
$911$	12.7033	+	3.73003i	0.420880	+	0.123582i	−0.0644329	+	0.997922i	$0.520524\pi$
$912$	35.1997	+	24.1754i	1.16558	+	0.800527i
$913$	−11.4403	−	13.2028i	−0.378618	−	0.436949i
$914$	38.1818	−	29.0821i	1.26294	−	0.961950i
$915$	12.2282	−	2.75566i	0.404250	−	0.0910992i
$916$	0.516452	+	30.9866i	0.0170641	+	1.02382i
$917$	50.2248	+	7.22123i	1.65857	+	0.238466i
$918$	30.3913	+	44.2436i	1.00306	+	1.46026i
$919$			52.5903i			1.73479i	0.497617	+	0.867397i	$0.334208\pi$
$919$			52.5903i			1.73479i	−0.497617	+	0.867397i	$0.665792\pi$
$920$	6.81168	−	10.0474i	0.224574	−	0.331254i
$921$	−41.8733	−	2.68139i	−1.37977	−	0.0883549i
$922$	13.9080	−	14.1418i	0.458036	−	0.465734i
$923$	1.27911	−	8.89641i	0.0421025	−	0.292829i
$924$	0.627200	−	13.2549i	0.0206334	−	0.436054i
$925$	22.2625	−	6.53687i	0.731987	−	0.214931i
$926$	−6.83426	−	8.97267i	−0.224588	−	0.294860i
$927$	−16.8567	+	11.1915i	−0.553645	+	0.367578i
$928$	−35.6448	−	11.6281i	−1.17010	−	0.381711i
$929$	8.54254	−	29.0932i	0.280272	−	0.954518i	−0.692241	−	0.721667i	$-0.743376\pi$
$929$	8.54254	−	29.0932i	0.280272	−	0.954518i	0.972512	−	0.232851i	$-0.0748055\pi$
$930$	4.88366	−	7.86951i	0.160142	−	0.258051i
$931$	−1.76912	+	2.75280i	−0.0579805	+	0.0902194i
$932$	3.70338	−	29.2047i	0.121308	−	0.956633i
$933$	−43.2041	−	42.5650i	−1.41444	−	1.39352i
$934$	1.44694	−	22.9124i	0.0473452	−	0.749716i
$935$	1.40104	+	9.74444i	0.0458189	+	0.318677i
$936$	3.21891	−	9.80859i	0.105213	−	0.320604i
$937$	−15.4701	−	33.8748i	−0.505386	−	1.10664i	−0.974681	−	0.223600i	$-0.928219\pi$
$937$	−15.4701	−	33.8748i	−0.505386	−	1.10664i	0.469295	−	0.883042i	$-0.344508\pi$
$938$	9.16818	+	16.4626i	0.299352	+	0.537524i
$939$	23.7450	+	12.7370i	0.774888	+	0.415656i
$940$	0.826544	−	0.257733i	0.0269589	−	0.00840631i
$941$	7.55222	+	11.7515i	0.246195	+	0.383087i	0.942255	−	0.334897i	$-0.108701\pi$
$941$	7.55222	+	11.7515i	0.246195	+	0.383087i	−0.696060	+	0.717984i	$0.745065\pi$
$942$	−9.77373	+	1.56308i	−0.318445	+	0.0509279i
$943$	31.9395	−	5.30604i	1.04009	−	0.172788i
$944$	0.711620	−	0.878798i	0.0231613	−	0.0286024i
$945$	4.37971	+	10.9860i	0.142472	+	0.357375i
$946$	−0.910623	−	11.3968i	−0.0296069	−	0.370540i
$947$	10.3291	−	22.6176i	0.335651	−	0.734973i	−0.664271	−	0.747492i	$-0.731258\pi$
$947$	10.3291	−	22.6176i	0.335651	−	0.734973i	0.999922	+	0.0125191i	$0.00398507\pi$
$948$	17.2666	−	13.5874i	0.560792	−	0.441299i
$949$	−1.69775	−	3.71756i	−0.0551114	−	0.120677i
$950$	29.4834	+	21.6900i	0.956569	+	0.703718i
$951$	1.71733	+	21.7342i	0.0556882	+	0.704781i
$952$	19.5883	+	48.7599i	0.634862	+	1.58032i
$953$	27.8415	+	24.1248i	0.901876	+	0.781480i	0.976452	−	0.215736i	$-0.0692149\pi$
$953$	27.8415	+	24.1248i	0.901876	+	0.781480i	−0.0745762	+	0.997215i	$0.523760\pi$
$954$	22.5258	+	11.6290i	0.729300	+	0.376502i
$955$	−8.53946	+	13.2877i	−0.276330	+	0.429978i
$956$	−2.71876	+	9.86450i	−0.0879310	+	0.319041i
$957$	16.2443	+	5.92132i	0.525105	+	0.191409i
$958$	−50.7587	+	19.4153i	−1.63994	+	0.627281i
$959$	−31.7718	−	36.6667i	−1.02597	−	1.18403i
$960$	−12.2971	+	1.59327i	−0.396886	+	0.0514226i
$961$	−12.6149	+	3.70406i	−0.406932	+	0.119486i
$962$	−9.30603	−	1.94333i	−0.300038	−	0.0626556i
$963$	−5.29549	+	19.0823i	−0.170645	+	0.614917i
$964$	1.51099	−	2.43960i	0.0486657	−	0.0785742i
$965$		−	0.251402i		−	0.00809292i
$966$	−11.3814	+	27.6261i	−0.366189	+	0.888854i
$967$			5.27841i			0.169742i	0.996392	+	0.0848711i	$0.0270478\pi$
$967$			5.27841i			0.169742i	−0.996392	+	0.0848711i	$0.972952\pi$
$968$	23.3483	+	8.04962i	0.750444	+	0.258725i
$969$	76.3177	+	16.0073i	2.45168	+	0.514227i
$970$	2.01312	−	9.64021i	0.0646374	−	0.309528i
$971$	−35.4402	+	10.4062i	−1.13733	+	0.333950i	−0.795584	−	0.605843i	$-0.792836\pi$
$971$	−35.4402	+	10.4062i	−1.13733	+	0.333950i	−0.341745	+	0.939793i	$0.611018\pi$
$972$	26.5183	−	16.3946i	0.850574	−	0.525856i
$973$	20.3436	+	23.4778i	0.652186	+	0.752663i
$974$	5.58923	+	14.6123i	0.179091	+	0.468207i
$975$	3.03042	−	8.31354i	0.0970512	−	0.266247i
$976$	−5.66811	−	31.8478i	−0.181432	−	1.01942i
$977$	8.95434	−	13.9332i	0.286475	−	0.445763i	−0.667954	−	0.744203i	$-0.732830\pi$
$977$	8.95434	−	13.9332i	0.286475	−	0.445763i	0.954429	+	0.298439i	$0.0964660\pi$
$978$	11.4582	−	26.1756i	0.366392	−	0.837002i
$979$	8.39053	+	7.27043i	0.268162	+	0.232364i
$980$	−0.150882	−	0.938144i	−0.00481976	−	0.0299679i
$981$	−0.550194	−	36.9165i	−0.0175663	−	1.17865i
$982$	−12.4770	+	16.9601i	−0.398158	+	0.541220i
$983$	25.1195	+	55.0039i	0.801186	+	1.75435i	0.641407	+	0.767200i	$0.278351\pi$
$983$	25.1195	+	55.0039i	0.801186	+	1.75435i	0.159779	+	0.987153i	$0.448922\pi$
$984$	−25.6849	−	20.8363i	−0.818804	−	0.664236i
$985$	−7.96174	+	17.4338i	−0.253682	+	0.555487i
$986$	−68.2495	+	5.45327i	−2.17351	+	0.173667i
$987$	−1.86275	+	1.03523i	−0.0592920	+	0.0329518i
$988$	−6.45652	−	13.5362i	−0.205409	−	0.430644i
$989$	−6.71192	+	24.8528i	−0.213427	+	0.790272i
$990$	5.69251	−	0.540326i	0.180920	−	0.0171727i
$991$	−16.2294	−	25.2535i	−0.515544	−	0.802202i	0.481704	−	0.876334i	$-0.340018\pi$
$991$	−16.2294	−	25.2535i	−0.515544	−	0.802202i	−0.997248	+	0.0741315i	$0.976382\pi$
$992$	−19.7141	−	13.5142i	−0.625924	−	0.429078i
$993$	−10.3207	+	19.2404i	−0.327517	+	0.610575i
$994$	23.2158	−	12.9291i	0.736361	−	0.410086i
$995$	−2.54069	−	5.56334i	−0.0805453	−	0.176370i
$996$	18.4010	−	35.7208i	0.583058	−	1.13186i
$997$	8.73142	+	60.7283i	0.276527	+	1.92329i	0.372762	+	0.927927i	$0.378411\pi$
$997$	8.73142	+	60.7283i	0.276527	+	1.92329i	−0.0962351	+	0.995359i	$0.530680\pi$
$998$	−16.0972	−	1.01655i	−0.509549	−	0.0321785i
$999$	−17.7153	−	22.5941i	−0.560489	−	0.714844i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.o.a.35.34	yes	440
3.2	odd	2	inner	276.2.o.a.35.11	✓	440
4.3	odd	2	inner	276.2.o.a.35.27	yes	440
12.11	even	2	inner	276.2.o.a.35.18	yes	440
23.2	even	11	inner	276.2.o.a.71.18	yes	440
69.2	odd	22	inner	276.2.o.a.71.27	yes	440
92.71	odd	22	inner	276.2.o.a.71.11	yes	440
276.71	even	22	inner	276.2.o.a.71.34	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.o.a.35.11	✓	440	3.2	odd	2	inner
276.2.o.a.35.18	yes	440	12.11	even	2	inner
276.2.o.a.35.27	yes	440	4.3	odd	2	inner
276.2.o.a.35.34	yes	440	1.1	even	1	trivial
276.2.o.a.71.11	yes	440	92.71	odd	22	inner
276.2.o.a.71.18	yes	440	23.2	even	11	inner
276.2.o.a.71.27	yes	440	69.2	odd	22	inner
276.2.o.a.71.34	yes	440	276.71	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00830 + 0.991633i) q^{2} +(-1.69516 - 0.355553i) q^{3} +(0.0333293 + 1.99972i) q^{4} +(0.252117 + 0.858632i) q^{5} +(-1.35665 - 2.03948i) q^{6} +(-1.92220 + 1.66560i) q^{7} +(-1.94938 + 2.04937i) q^{8} +(2.74716 + 1.20544i) q^{9} +O(q^{10})\)	\(q+(1.00830 + 0.991633i) q^{2} +(-1.69516 - 0.355553i) q^{3} +(0.0333293 + 1.99972i) q^{4} +(0.252117 + 0.858632i) q^{5} +(-1.35665 - 2.03948i) q^{6} +(-1.92220 + 1.66560i) q^{7} +(-1.94938 + 2.04937i) q^{8} +(2.74716 + 1.20544i) q^{9} +(-0.597239 + 1.11576i) q^{10} +(-1.26700 - 0.814252i) q^{11} +(0.654508 - 3.40171i) q^{12} +(-0.796709 + 0.919451i) q^{13} +(-3.58982 - 0.226700i) q^{14} +(-0.122091 - 1.54516i) q^{15} +(-3.99778 + 0.133299i) q^{16} +(-6.64432 + 3.03436i) q^{17} +(1.57461 + 3.93962i) q^{18} +(5.60653 + 2.56042i) q^{19} +(-1.70862 + 0.532782i) q^{20} +(3.85066 - 2.14002i) q^{21} +(-0.470075 - 2.07741i) q^{22} +(-0.578761 + 4.76078i) q^{23} +(4.03318 - 2.78090i) q^{24} +(3.53258 - 2.27025i) q^{25} +(-1.71508 + 0.137038i) q^{26} +(-4.22830 - 3.02018i) q^{27} +(-3.39480 - 3.78836i) q^{28} +(6.02903 - 2.75337i) q^{29} +(1.40913 - 1.67906i) q^{30} +(4.18222 - 0.601313i) q^{31} +(-4.16313 - 3.82992i) q^{32} +(1.85827 + 1.83078i) q^{33} +(-9.70842 - 3.52918i) q^{34} +(-1.91476 - 1.23054i) q^{35} +(-2.31898 + 5.53374i) q^{36} +(5.30163 + 1.55670i) q^{37} +(3.11406 + 8.14129i) q^{38} +(1.67747 - 1.27535i) q^{39} +(-2.25113 - 1.15712i) q^{40} +(-1.90201 - 6.47765i) q^{41} +(6.00473 + 1.66066i) q^{42} +(5.31318 + 0.763921i) q^{43} +(1.58605 - 2.56079i) q^{44} +(-0.342423 + 2.66272i) q^{45} +(-5.30451 + 4.22637i) q^{46} -0.483749 q^{47} +(6.82429 + 1.19546i) q^{48} +(-0.0755561 + 0.525504i) q^{49} +(5.81315 + 1.21393i) q^{50} +(12.3421 - 2.78133i) q^{51} +(-1.86520 - 1.56255i) q^{52} +(4.51572 - 3.91290i) q^{53} +(-1.26847 - 7.23816i) q^{54} +(0.379710 - 1.29317i) q^{55} +(0.333691 - 7.18619i) q^{56} +(-8.59363 - 6.33375i) q^{57} +(8.80939 + 3.20237i) q^{58} +(-0.185128 + 0.213649i) q^{59} +(3.08583 - 0.295648i) q^{60} +(1.15091 + 8.00476i) q^{61} +(4.81321 + 3.54093i) q^{62} +(-7.28839 + 2.25857i) q^{63} +(-0.399804 - 7.99000i) q^{64} +(-0.990335 - 0.452271i) q^{65} +(0.0582272 + 3.68868i) q^{66} +(-2.83225 - 4.40707i) q^{67} +(-6.28932 - 13.1857i) q^{68} +(2.67380 - 7.86453i) q^{69} +(-0.710403 - 3.13949i) q^{70} +(-6.21490 + 3.99407i) q^{71} +(-7.82567 + 3.28008i) q^{72} +(-1.39548 + 3.05568i) q^{73} +(3.80195 + 6.82688i) q^{74} +(-6.79550 + 2.59243i) q^{75} +(-4.93326 + 11.2968i) q^{76} +(3.79165 - 0.545157i) q^{77} +(2.95606 + 0.377498i) q^{78} +(4.79347 + 4.15356i) q^{79} +(-1.12236 - 3.39901i) q^{80} +(6.09383 + 6.62309i) q^{81} +(4.50566 - 8.41750i) q^{82} +(11.1296 + 3.26795i) q^{83} +(4.40779 + 7.62893i) q^{84} +(-4.28054 - 4.94001i) q^{85} +(4.59974 + 6.03899i) q^{86} +(-11.1992 + 2.52377i) q^{87} +(4.13857 - 1.00926i) q^{88} +(-7.29656 - 1.04909i) q^{89} +(-2.98570 + 2.34525i) q^{90} -3.09437i q^{91} +(-9.53953 - 0.998688i) q^{92} +(-7.30335 - 0.467676i) q^{93} +(-0.487763 - 0.479701i) q^{94} +(-0.784954 + 5.45948i) q^{95} +(5.69546 + 7.97256i) q^{96} +(-7.46649 + 2.19236i) q^{97} +(-0.597290 + 0.454941i) q^{98} +(-2.49913 - 3.76418i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9}+O(q^{10}) \) 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9	\( 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9} - 30 q^{10} - 18 q^{12} - 36 q^{13} - 30 q^{16} - 10 q^{18} - 22 q^{21} - 48 q^{22} - 14 q^{24} - 8 q^{25} - 34 q^{28} - 21 q^{30} - 6 q^{33} - 32 q^{34} + 22 q^{36} - 36 q^{37} - 168 q^{40} + q^{42} - 44 q^{45} - 110 q^{46} - 6 q^{48} - 16 q^{49} - 94 q^{52} + 21 q^{54} - 46 q^{57} - 116 q^{58} - 47 q^{60} - 68 q^{61} - 28 q^{64} - 20 q^{66} - 22 q^{69} - 44 q^{70} - 23 q^{72} - 36 q^{73} - 74 q^{76} + 134 q^{78} - 130 q^{81} + 36 q^{82} + 105 q^{84} - 60 q^{85} + 38 q^{88} + 162 q^{90} - 332 q^{93} - 40 q^{94} + 225 q^{96} - 36 q^{97}+O(q^{100}) \) 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9 - 30 * q^10 - 18 * q^12 - 36 * q^13 - 30 * q^16 - 10 * q^18 - 22 * q^21 - 48 * q^22 - 14 * q^24 - 8 * q^25 - 34 * q^28 - 21 * q^30 - 6 * q^33 - 32 * q^34 + 22 * q^36 - 36 * q^37 - 168 * q^40 + q^42 - 44 * q^45 - 110 * q^46 - 6 * q^48 - 16 * q^49 - 94 * q^52 + 21 * q^54 - 46 * q^57 - 116 * q^58 - 47 * q^60 - 68 * q^61 - 28 * q^64 - 20 * q^66 - 22 * q^69 - 44 * q^70 - 23 * q^72 - 36 * q^73 - 74 * q^76 + 134 * q^78 - 130 * q^81 + 36 * q^82 + 105 * q^84 - 60 * q^85 + 38 * q^88 + 162 * q^90 - 332 * q^93 - 40 * q^94 + 225 * q^96 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more