LMFDB - Embedded newform 810.2.f.c.323.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(323,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("810.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.5
Root			$0.500000 + 0.410882i$ of defining polynomial
Character	$\chi$	$=$	810.323
Dual form			810.2.f.c.647.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-2.21569 - 0.301182i) q^{5} +(1.87542 - 1.87542i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.35376 - 1.77970i) q^{10} +4.79792i q^{11} +(-0.425935 - 0.425935i) q^{13} +2.65225 q^{14} -1.00000 q^{16} +(4.40865 + 4.40865i) q^{17} +5.19145i q^{19} +(0.301182 - 2.21569i) q^{20} +(-3.39264 + 3.39264i) q^{22} +(-1.86115 + 1.86115i) q^{23} +(4.81858 + 1.33465i) q^{25} -0.602363i q^{26} +(1.87542 + 1.87542i) q^{28} +1.84040 q^{29} +4.07776 q^{31} +(-0.707107 - 0.707107i) q^{32} +6.23478i q^{34} +(-4.72021 + 3.59052i) q^{35} +(0.632057 - 0.632057i) q^{37} +(-3.67091 + 3.67091i) q^{38} +(1.77970 - 1.35376i) q^{40} +6.44958i q^{41} +(-1.76059 - 1.76059i) q^{43} -4.79792 q^{44} -2.63206 q^{46} +(-2.80140 - 2.80140i) q^{47} -0.0344378i q^{49} +(2.46351 + 4.35099i) q^{50} +(0.425935 - 0.425935i) q^{52} +(-1.31215 + 1.31215i) q^{53} +(1.44505 - 10.6307i) q^{55} +2.65225i q^{56} +(1.30136 + 1.30136i) q^{58} +0.129095 q^{59} -12.5450 q^{61} +(2.88341 + 2.88341i) q^{62} -1.00000i q^{64} +(0.815457 + 1.07203i) q^{65} +(7.80770 - 7.80770i) q^{67} +(-4.40865 + 4.40865i) q^{68} +(-5.87657 - 0.798810i) q^{70} -10.4203i q^{71} +(3.30021 + 3.30021i) q^{73} +0.893864 q^{74} -5.19145 q^{76} +(8.99814 + 8.99814i) q^{77} +4.18916i q^{79} +(2.21569 + 0.301182i) q^{80} +(-4.56054 + 4.56054i) q^{82} +(-8.13293 + 8.13293i) q^{83} +(-8.44041 - 11.0960i) q^{85} -2.48985i q^{86} +(-3.39264 - 3.39264i) q^{88} +2.04989 q^{89} -1.59762 q^{91} +(-1.86115 - 1.86115i) q^{92} -3.96178i q^{94} +(1.56357 - 11.5027i) q^{95} +(12.2336 - 12.2336i) q^{97} +(0.0243512 - 0.0243512i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{7} - 8 q^{10} - 16 q^{16} - 16 q^{22} + 32 q^{25} - 16 q^{28} + 16 q^{31} + 8 q^{40} - 32 q^{46} + 24 q^{55} - 32 q^{58} + 48 q^{61} + 32 q^{67} - 32 q^{70} + 16 q^{73} - 32 q^{76} - 16 q^{82}+ \cdots + 96 q^{97}+O(q^{100}) $ 16 * q - 16 * q^7 - 8 * q^10 - 16 * q^16 - 16 * q^22 + 32 * q^25 - 16 * q^28 + 16 * q^31 + 8 * q^40 - 32 * q^46 + 24 * q^55 - 32 * q^58 + 48 * q^61 + 32 * q^67 - 32 * q^70 + 16 * q^73 - 32 * q^76 - 16 * q^82 + 8 * q^85 - 16 * q^88 + 96 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	−2.21569	−	0.301182i	−0.990887	−	0.134693i
$5$	−2.21569	−	0.301182i	−0.990887	−	0.134693i
$6$		0			0
$7$	1.87542	−	1.87542i	0.708844	−	0.708844i	−0.257448	−	0.966292i	$-0.582882\pi$
$7$	1.87542	−	1.87542i	0.708844	−	0.708844i	0.966292	+	0.257448i	$0.0828816\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	−1.35376	−	1.77970i	−0.428097	−	0.562790i
$11$			4.79792i			1.44663i	0.690519	+	0.723314i	$0.257382\pi$
$11$			4.79792i			1.44663i	−0.690519	+	0.723314i	$0.742618\pi$
$12$		0			0
$13$	−0.425935	−	0.425935i	−0.118133	−	0.118133i	0.645569	−	0.763702i	$-0.276620\pi$
$13$	−0.425935	−	0.425935i	−0.118133	−	0.118133i	−0.763702	+	0.645569i	$0.776620\pi$
$14$	2.65225			0.708844
$15$		0			0
$16$	−1.00000			−0.250000
$17$	4.40865	+	4.40865i	1.06926	+	1.06926i	0.997416	+	0.0718393i	$0.0228869\pi$
$17$	4.40865	+	4.40865i	1.06926	+	1.06926i	0.0718393	+	0.997416i	$0.477113\pi$
$18$		0			0
$19$			5.19145i			1.19100i	0.803355	+	0.595501i	$0.203046\pi$
$19$			5.19145i			1.19100i	−0.803355	+	0.595501i	$0.796954\pi$
$20$	0.301182	−	2.21569i	0.0673463	−	0.495444i
$21$		0			0
$22$	−3.39264	+	3.39264i	−0.723314	+	0.723314i
$23$	−1.86115	+	1.86115i	−0.388076	+	0.388076i	−0.874001	−	0.485925i	$-0.838483\pi$
$23$	−1.86115	+	1.86115i	−0.388076	+	0.388076i	0.485925	+	0.874001i	$0.338483\pi$
$24$		0			0
$25$	4.81858	+	1.33465i	0.963716	+	0.266930i
$26$		−	0.602363i		−	0.118133i
$27$		0			0
$28$	1.87542	+	1.87542i	0.354422	+	0.354422i
$29$	1.84040			0.341754			0.170877	−	0.985292i	$-0.445340\pi$
$29$	1.84040			0.341754			0.170877	+	0.985292i	$0.445340\pi$
$30$		0			0
$31$	4.07776			0.732388			0.366194	−	0.930539i	$-0.380661\pi$
$31$	4.07776			0.732388			0.366194	+	0.930539i	$0.380661\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$			6.23478i			1.06926i
$35$	−4.72021	+	3.59052i	−0.797861	+	0.606909i
$36$		0			0
$37$	0.632057	−	0.632057i	0.103910	−	0.103910i	−0.653241	−	0.757150i	$-0.726591\pi$
$37$	0.632057	−	0.632057i	0.103910	−	0.103910i	0.757150	+	0.653241i	$0.226591\pi$
$38$	−3.67091	+	3.67091i	−0.595501	+	0.595501i
$39$		0			0
$40$	1.77970	−	1.35376i	0.281395	−	0.214049i
$41$			6.44958i			1.00726i	0.863921	+	0.503628i	$0.168002\pi$
$41$			6.44958i			1.00726i	−0.863921	+	0.503628i	$0.831998\pi$
$42$		0			0
$43$	−1.76059	−	1.76059i	−0.268487	−	0.268487i	0.560003	−	0.828490i	$-0.310800\pi$
$43$	−1.76059	−	1.76059i	−0.268487	−	0.268487i	−0.828490	+	0.560003i	$0.810800\pi$
$44$	−4.79792			−0.723314
$45$		0			0
$46$	−2.63206			−0.388076
$47$	−2.80140	−	2.80140i	−0.408626	−	0.408626i	0.472633	−	0.881259i	$-0.343304\pi$
$47$	−2.80140	−	2.80140i	−0.408626	−	0.408626i	−0.881259	+	0.472633i	$0.843304\pi$
$48$		0			0
$49$		−	0.0344378i		−	0.00491969i
$50$	2.46351	+	4.35099i	0.348393	+	0.615323i
$51$		0			0
$52$	0.425935	−	0.425935i	0.0590666	−	0.0590666i
$53$	−1.31215	+	1.31215i	−0.180237	+	0.180237i	−0.791459	−	0.611222i	$-0.790678\pi$
$53$	−1.31215	+	1.31215i	−0.180237	+	0.180237i	0.611222	+	0.791459i	$0.290678\pi$
$54$		0			0
$55$	1.44505	−	10.6307i	0.194850	−	1.43345i
$56$			2.65225i			0.354422i
$57$		0			0
$58$	1.30136	+	1.30136i	0.170877	+	0.170877i
$59$	0.129095			0.0168067			0.00840334	−	0.999965i	$-0.497325\pi$
$59$	0.129095			0.0168067			0.00840334	+	0.999965i	$0.497325\pi$
$60$		0			0
$61$	−12.5450			−1.60623			−0.803113	−	0.595827i	$-0.796824\pi$
$61$	−12.5450			−1.60623			−0.803113	+	0.595827i	$0.796824\pi$
$62$	2.88341	+	2.88341i	0.366194	+	0.366194i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	0.815457	+	1.07203i	0.101145	+	0.132968i
$66$		0			0
$67$	7.80770	−	7.80770i	0.953862	−	0.953862i	−0.0451197	−	0.998982i	$-0.514367\pi$
$67$	7.80770	−	7.80770i	0.953862	−	0.953862i	0.998982	+	0.0451197i	$0.0143669\pi$
$68$	−4.40865	+	4.40865i	−0.534628	+	0.534628i
$69$		0			0
$70$	−5.87657	−	0.798810i	−0.702385	−	0.0954760i
$71$		−	10.4203i		−	1.23666i	−0.785919	−	0.618329i	$-0.787810\pi$
$71$		−	10.4203i		−	1.23666i	0.785919	−	0.618329i	$-0.212190\pi$
$72$		0			0
$73$	3.30021	+	3.30021i	0.386261	+	0.386261i	0.873351	−	0.487091i	$-0.161942\pi$
$73$	3.30021	+	3.30021i	0.386261	+	0.386261i	−0.487091	+	0.873351i	$0.661942\pi$
$74$	0.893864			0.103910
$75$		0			0
$76$	−5.19145			−0.595501
$77$	8.99814	+	8.99814i	1.02543	+	1.02543i
$78$		0			0
$79$			4.18916i			0.471317i	0.971836	+	0.235659i	$0.0757247\pi$
$79$			4.18916i			0.471317i	−0.971836	+	0.235659i	$0.924275\pi$
$80$	2.21569	+	0.301182i	0.247722	+	0.0336731i
$81$		0			0
$82$	−4.56054	+	4.56054i	−0.503628	+	0.503628i
$83$	−8.13293	+	8.13293i	−0.892705	+	0.892705i	−0.994777	−	0.102072i	$-0.967453\pi$
$83$	−8.13293	+	8.13293i	−0.892705	+	0.892705i	0.102072	+	0.994777i	$0.467453\pi$
$84$		0			0
$85$	−8.44041	−	11.0960i	−0.915491	−	1.20353i
$86$		−	2.48985i		−	0.268487i
$87$		0			0
$88$	−3.39264	−	3.39264i	−0.361657	−	0.361657i
$89$	2.04989			0.217288			0.108644	−	0.994081i	$-0.465349\pi$
$89$	2.04989			0.217288			0.108644	+	0.994081i	$0.465349\pi$
$90$		0			0
$91$	−1.59762			−0.167476
$92$	−1.86115	−	1.86115i	−0.194038	−	0.194038i
$93$		0			0
$94$		−	3.96178i		−	0.408626i
$95$	1.56357	−	11.5027i	0.160419	−	1.18015i
$96$		0			0
$97$	12.2336	−	12.2336i	1.24214	−	1.24214i	0.283024	−	0.959113i	$-0.408662\pi$
$97$	12.2336	−	12.2336i	1.24214	−	1.24214i	0.959113	−	0.283024i	$-0.0913377\pi$
$98$	0.0243512	−	0.0243512i	0.00245984	−	0.00245984i
$99$		0			0
$100$	−1.33465	+	4.81858i	−0.133465	+	0.481858i
$101$		−	11.9619i		−	1.19026i	−0.803630	−	0.595129i	$-0.797101\pi$
$101$		−	11.9619i		−	1.19026i	0.803630	−	0.595129i	$-0.202899\pi$
$102$		0			0
$103$	7.61739	+	7.61739i	0.750564	+	0.750564i	0.974584	−	0.224021i	$-0.0719183\pi$
$103$	7.61739	+	7.61739i	0.750564	+	0.750564i	−0.224021	+	0.974584i	$0.571918\pi$
$104$	0.602363			0.0590666
$105$		0			0
$106$	−1.85566			−0.180237
$107$	4.35367	+	4.35367i	0.420885	+	0.420885i	0.885508	−	0.464623i	$-0.153810\pi$
$107$	4.35367	+	4.35367i	0.420885	+	0.420885i	−0.464623	+	0.885508i	$0.653810\pi$
$108$		0			0
$109$		−	15.4546i		−	1.48028i	−0.672452	−	0.740141i	$-0.734759\pi$
$109$		−	15.4546i		−	1.48028i	0.672452	−	0.740141i	$-0.265241\pi$
$110$	8.53886	−	6.49525i	0.814148	−	0.619298i
$111$		0			0
$112$	−1.87542	+	1.87542i	−0.177211	+	0.177211i
$113$	4.19556	−	4.19556i	0.394685	−	0.394685i	−0.481668	−	0.876354i	$-0.659969\pi$
$113$	4.19556	−	4.19556i	0.394685	−	0.394685i	0.876354	+	0.481668i	$0.159969\pi$
$114$		0			0
$115$	4.68427	−	3.56318i	0.436810	−	0.332268i
$116$			1.84040i			0.170877i
$117$		0			0
$118$	0.0912837	+	0.0912837i	0.00840334	+	0.00840334i
$119$	16.5362			1.51587
$120$		0			0
$121$	−12.0201			−1.09273
$122$	−8.87067	−	8.87067i	−0.803113	−	0.803113i
$123$		0			0
$124$			4.07776i			0.366194i
$125$	−10.2745	−	4.40844i	−0.918980	−	0.394303i
$126$		0			0
$127$	2.51837	−	2.51837i	0.223469	−	0.223469i	−0.586489	−	0.809957i	$-0.699490\pi$
$127$	2.51837	−	2.51837i	0.223469	−	0.223469i	0.809957	+	0.586489i	$0.199490\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$	−0.181421	+	1.33465i	−0.0159117	+	0.117057i
$131$		−	13.0599i		−	1.14105i	−0.821279	−	0.570526i	$-0.806739\pi$
$131$		−	13.0599i		−	1.14105i	0.821279	−	0.570526i	$-0.193261\pi$
$132$		0			0
$133$	9.73618	+	9.73618i	0.844234	+	0.844234i
$134$	11.0417			0.953862
$135$		0			0
$136$	−6.23478			−0.534628
$137$	2.29750	+	2.29750i	0.196288	+	0.196288i	0.798407	−	0.602118i	$-0.205677\pi$
$137$	2.29750	+	2.29750i	0.196288	+	0.196288i	−0.602118	+	0.798407i	$0.705677\pi$
$138$		0			0
$139$			21.9945i			1.86555i	0.360459	+	0.932775i	$0.382620\pi$
$139$			21.9945i			1.86555i	−0.360459	+	0.932775i	$0.617380\pi$
$140$	−3.59052	−	4.72021i	−0.303454	−	0.398930i
$141$		0			0
$142$	7.36824	−	7.36824i	0.618329	−	0.618329i
$143$	2.04360	−	2.04360i	0.170895	−	0.170895i
$144$		0			0
$145$	−4.07776	−	0.554295i	−0.338640	−	0.0460317i
$146$			4.66721i			0.386261i
$147$		0			0
$148$	0.632057	+	0.632057i	0.0519548	+	0.0519548i
$149$	−13.1334			−1.07593			−0.537964	−	0.842968i	$-0.680806\pi$
$149$	−13.1334			−1.07593			−0.537964	+	0.842968i	$0.680806\pi$
$150$		0			0
$151$	0.335798			0.0273269			0.0136634	−	0.999907i	$-0.495651\pi$
$151$	0.335798			0.0273269			0.0136634	+	0.999907i	$0.495651\pi$
$152$	−3.67091	−	3.67091i	−0.297750	−	0.297750i
$153$		0			0
$154$			12.7253i			1.02543i
$155$	−9.03506	−	1.22815i	−0.725714	−	0.0986472i
$156$		0			0
$157$	−3.22360	+	3.22360i	−0.257271	+	0.257271i	−0.823943	−	0.566672i	$-0.808231\pi$
$157$	−3.22360	+	3.22360i	−0.257271	+	0.257271i	0.566672	+	0.823943i	$0.308231\pi$
$158$	−2.96218	+	2.96218i	−0.235659	+	0.235659i
$159$		0			0
$160$	1.35376	+	1.77970i	0.107024	+	0.140697i
$161$			6.98088i			0.550170i
$162$		0			0
$163$	9.01496	+	9.01496i	0.706106	+	0.706106i	0.965714	−	0.259608i	$-0.0835932\pi$
$163$	9.01496	+	9.01496i	0.706106	+	0.706106i	−0.259608	+	0.965714i	$0.583593\pi$
$164$	−6.44958			−0.503628
$165$		0			0
$166$	−11.5017			−0.892705
$167$	0.00628350	+	0.00628350i	0.000486232	+	0.000486232i	0.707350	−	0.706864i	$-0.249891\pi$
$167$	0.00628350	+	0.00628350i	0.000486232	+	0.000486232i	−0.706864	+	0.707350i	$0.749891\pi$
$168$		0			0
$169$		−	12.6372i		−	0.972089i
$170$	1.87780	−	13.8143i	0.144021	−	1.05951i
$171$		0			0
$172$	1.76059	−	1.76059i	0.134243	−	0.134243i
$173$	7.34182	−	7.34182i	0.558189	−	0.558189i	−0.370603	−	0.928791i	$-0.620849\pi$
$173$	7.34182	−	7.34182i	0.558189	−	0.558189i	0.928791	+	0.370603i	$0.120849\pi$
$174$		0			0
$175$	11.5399	−	6.53384i	0.872336	−	0.493912i
$176$		−	4.79792i		−	0.361657i
$177$		0			0
$178$	1.44949	+	1.44949i	0.108644	+	0.108644i
$179$	1.46292			0.109343			0.0546717	−	0.998504i	$-0.482589\pi$
$179$	1.46292			0.109343			0.0546717	+	0.998504i	$0.482589\pi$
$180$		0			0
$181$	−8.68576			−0.645607			−0.322804	−	0.946466i	$-0.604625\pi$
$181$	−8.68576			−0.645607			−0.322804	+	0.946466i	$0.604625\pi$
$182$	−1.12969	−	1.12969i	−0.0837380	−	0.0837380i
$183$		0			0
$184$		−	2.63206i		−	0.194038i
$185$	−1.59081	+	1.21008i	−0.116959	+	0.0889668i
$186$		0			0
$187$	−21.1524	+	21.1524i	−1.54682	+	1.54682i
$188$	2.80140	−	2.80140i	0.204313	−	0.204313i
$189$		0			0
$190$	9.23922	−	7.02800i	0.670284	−	0.509865i
$191$		−	5.00903i		−	0.362441i	−0.983443	−	0.181220i	$-0.941995\pi$
$191$		−	5.00903i		−	0.362441i	0.983443	−	0.181220i	$-0.0580047\pi$
$192$		0			0
$193$	2.38176	+	2.38176i	0.171443	+	0.171443i	0.787613	−	0.616170i	$-0.211317\pi$
$193$	2.38176	+	2.38176i	0.171443	+	0.171443i	−0.616170	+	0.787613i	$0.711317\pi$
$194$	17.3010			1.24214
$195$		0			0
$196$	0.0344378			0.00245984
$197$	−15.5027	−	15.5027i	−1.10452	−	1.10452i	−0.993858	−	0.110665i	$-0.964702\pi$
$197$	−15.5027	−	15.5027i	−1.10452	−	1.10452i	−0.110665	−	0.993858i	$-0.535298\pi$
$198$		0			0
$199$			18.4607i			1.30864i	0.756217	+	0.654321i	$0.227045\pi$
$199$			18.4607i			1.30864i	−0.756217	+	0.654321i	$0.772955\pi$
$200$	−4.35099	+	2.46351i	−0.307662	+	0.174196i
$201$		0			0
$202$	8.45838	−	8.45838i	0.595129	−	0.595129i
$203$	3.45153	−	3.45153i	0.242250	−	0.242250i
$204$		0			0
$205$	1.94250	−	14.2903i	0.135670	−	0.998077i
$206$			10.7726i			0.750564i
$207$		0			0
$208$	0.425935	+	0.425935i	0.0295333	+	0.0295333i
$209$	−24.9082			−1.72294
$210$		0			0
$211$	−1.30893			−0.0901105			−0.0450552	−	0.998984i	$-0.514346\pi$
$211$	−1.30893			−0.0901105			−0.0450552	+	0.998984i	$0.514346\pi$
$212$	−1.31215	−	1.31215i	−0.0901186	−	0.0901186i
$213$		0			0
$214$			6.15702i			0.420885i
$215$	3.37066	+	4.43117i	0.229877	+	0.302204i
$216$		0			0
$217$	7.64754	−	7.64754i	0.519149	−	0.519149i
$218$	10.9280	−	10.9280i	0.740141	−	0.740141i
$219$		0			0
$220$	10.6307	+	1.44505i	0.716723	+	0.0974250i
$221$		−	3.75560i		−	0.252629i
$222$		0			0
$223$	14.8324	+	14.8324i	0.993251	+	0.993251i	0.999977	−	0.00672662i	$-0.00214117\pi$
$223$	14.8324	+	14.8324i	0.993251	+	0.993251i	−0.00672662	+	0.999977i	$0.502141\pi$
$224$	−2.65225			−0.177211
$225$		0			0
$226$	5.93342			0.394685
$227$	4.21080	+	4.21080i	0.279481	+	0.279481i	0.832902	−	0.553421i	$-0.186678\pi$
$227$	4.21080	+	4.21080i	0.279481	+	0.279481i	−0.553421	+	0.832902i	$0.686678\pi$
$228$		0			0
$229$		−	11.7574i		−	0.776954i	−0.921458	−	0.388477i	$-0.873001\pi$
$229$		−	11.7574i		−	0.776954i	0.921458	−	0.388477i	$-0.126999\pi$
$230$	5.83183	+	0.792727i	0.384539	+	0.0522709i
$231$		0			0
$232$	−1.30136	+	1.30136i	−0.0854385	+	0.0854385i
$233$	13.4322	−	13.4322i	0.879973	−	0.879973i	−0.113558	−	0.993531i	$-0.536225\pi$
$233$	13.4322	−	13.4322i	0.879973	−	0.879973i	0.993531	+	0.113558i	$0.0362249\pi$
$234$		0			0
$235$	5.36331	+	7.05077i	0.349864	+	0.459941i
$236$			0.129095i			0.00840334i
$237$		0			0
$238$	11.6929	+	11.6929i	0.757935	+	0.757935i
$239$	4.55886			0.294888			0.147444	−	0.989070i	$-0.452895\pi$
$239$	4.55886			0.294888			0.147444	+	0.989070i	$0.452895\pi$
$240$		0			0
$241$	−16.0621			−1.03465			−0.517325	−	0.855789i	$-0.673072\pi$
$241$	−16.0621			−1.03465			−0.517325	+	0.855789i	$0.673072\pi$
$242$	−8.49947	−	8.49947i	−0.546367	−	0.546367i
$243$		0			0
$244$		−	12.5450i		−	0.803113i
$245$	−0.0103720	+	0.0763036i	−0.000662646	+	0.00487486i
$246$		0			0
$247$	2.21122	−	2.21122i	0.140697	−	0.140697i
$248$	−2.88341	+	2.88341i	−0.183097	+	0.183097i
$249$		0			0
$250$	−4.14794	−	10.3824i	−0.262339	−	0.656642i
$251$		−	18.9981i		−	1.19915i	−0.800319	−	0.599574i	$-0.795337\pi$
$251$		−	18.9981i		−	1.19915i	0.800319	−	0.599574i	$-0.204663\pi$
$252$		0			0
$253$	−8.92963	−	8.92963i	−0.561401	−	0.561401i
$254$	3.56151			0.223469
$255$		0			0
$256$	1.00000			0.0625000
$257$	−2.36971	−	2.36971i	−0.147819	−	0.147819i	0.629324	−	0.777143i	$-0.283332\pi$
$257$	−2.36971	−	2.36971i	−0.147819	−	0.147819i	−0.777143	+	0.629324i	$0.783332\pi$
$258$		0			0
$259$		−	2.37075i		−	0.147311i
$260$	−1.07203	+	0.815457i	−0.0664842	+	0.0505725i
$261$		0			0
$262$	9.23478	−	9.23478i	0.570526	−	0.570526i
$263$	11.8408	−	11.8408i	0.730133	−	0.730133i	−0.240513	−	0.970646i	$-0.577316\pi$
$263$	11.8408	−	11.8408i	0.730133	−	0.730133i	0.970646	+	0.240513i	$0.0773158\pi$
$264$		0			0
$265$	3.30251	−	2.51212i	0.202871	−	0.154318i
$266$			13.7690i			0.844234i
$267$		0			0
$268$	7.80770	+	7.80770i	0.476931	+	0.476931i
$269$	0.535741			0.0326647			0.0163324	−	0.999867i	$-0.494801\pi$
$269$	0.535741			0.0326647			0.0163324	+	0.999867i	$0.494801\pi$
$270$		0			0
$271$	−15.5412			−0.944063			−0.472032	−	0.881582i	$-0.656479\pi$
$271$	−15.5412			−0.944063			−0.472032	+	0.881582i	$0.656479\pi$
$272$	−4.40865	−	4.40865i	−0.267314	−	0.267314i
$273$		0			0
$274$			3.24915i			0.196288i
$275$	−6.40356	+	23.1192i	−0.386149	+	1.39414i
$276$		0			0
$277$	−12.2399	+	12.2399i	−0.735423	+	0.735423i	−0.971689	−	0.236265i	$-0.924076\pi$
$277$	−12.2399	+	12.2399i	−0.735423	+	0.735423i	0.236265	+	0.971689i	$0.424076\pi$
$278$	−15.5525	+	15.5525i	−0.932775	+	0.932775i
$279$		0			0
$280$	0.798810	−	5.87657i	0.0477380	−	0.351192i
$281$		−	24.1227i		−	1.43904i	−0.694472	−	0.719519i	$-0.744362\pi$
$281$		−	24.1227i		−	1.43904i	0.694472	−	0.719519i	$-0.255638\pi$
$282$		0			0
$283$	−11.7037	−	11.7037i	−0.695715	−	0.695715i	0.267768	−	0.963483i	$-0.413714\pi$
$283$	−11.7037	−	11.7037i	−0.695715	−	0.695715i	−0.963483	+	0.267768i	$0.913714\pi$
$284$	10.4203			0.618329
$285$		0			0
$286$	2.89009			0.170895
$287$	12.0957	+	12.0957i	0.713987	+	0.713987i
$288$		0			0
$289$			21.8725i			1.28661i
$290$	−2.49147	−	3.27536i	−0.146304	−	0.192336i
$291$		0			0
$292$	−3.30021	+	3.30021i	−0.193130	+	0.193130i
$293$	11.4209	−	11.4209i	0.667214	−	0.667214i	−0.289857	−	0.957070i	$-0.593608\pi$
$293$	11.4209	−	11.4209i	0.667214	−	0.667214i	0.957070	+	0.289857i	$0.0936076\pi$
$294$		0			0
$295$	−0.286034	−	0.0388809i	−0.0166535	−	0.00226374i
$296$			0.893864i			0.0519548i
$297$		0			0
$298$	−9.28669	−	9.28669i	−0.537964	−	0.537964i
$299$	1.58545			0.0916892
$300$		0			0
$301$	−6.60370			−0.380631
$302$	0.237445	+	0.237445i	0.0136634	+	0.0136634i
$303$		0			0
$304$		−	5.19145i		−	0.297750i
$305$	27.7959	+	3.77833i	1.59159	+	0.216347i
$306$		0			0
$307$	−1.45642	+	1.45642i	−0.0831222	+	0.0831222i	−0.747445	−	0.664323i	$-0.768720\pi$
$307$	−1.45642	+	1.45642i	−0.0831222	+	0.0831222i	0.664323	+	0.747445i	$0.268720\pi$
$308$	−8.99814	+	8.99814i	−0.512717	+	0.512717i
$309$		0			0
$310$	−5.52032	−	7.25719i	−0.313533	−	0.412180i
$311$			2.09535i			0.118816i	0.998234	+	0.0594081i	$0.0189213\pi$
$311$			2.09535i			0.118816i	−0.998234	+	0.0594081i	$0.981079\pi$
$312$		0			0
$313$	−13.9667	−	13.9667i	−0.789445	−	0.789445i	0.191958	−	0.981403i	$-0.438516\pi$
$313$	−13.9667	−	13.9667i	−0.789445	−	0.789445i	−0.981403	+	0.191958i	$0.938516\pi$
$314$	−4.55886			−0.257271
$315$		0			0
$316$	−4.18916			−0.235659
$317$	24.1026	+	24.1026i	1.35374	+	1.35374i	0.881437	+	0.472301i	$0.156577\pi$
$317$	24.1026	+	24.1026i	1.35374	+	1.35374i	0.472301	+	0.881437i	$0.343423\pi$
$318$		0			0
$319$			8.83010i			0.494391i
$320$	−0.301182	+	2.21569i	−0.0168366	+	0.123861i
$321$		0			0
$322$	−4.93623	+	4.93623i	−0.275085	+	0.275085i
$323$	−22.8873	+	22.8873i	−1.27348	+	1.27348i
$324$		0			0
$325$	−1.48393	−	2.62088i	−0.0823135	−	0.145380i
$326$			12.7491i			0.706106i
$327$		0			0
$328$	−4.56054	−	4.56054i	−0.251814	−	0.251814i
$329$	−10.5076			−0.579304
$330$		0			0
$331$	24.0280			1.32070			0.660348	−	0.750959i	$-0.270409\pi$
$331$	24.0280			1.32070			0.660348	+	0.750959i	$0.270409\pi$
$332$	−8.13293	−	8.13293i	−0.446353	−	0.446353i
$333$		0			0
$334$			0.00888621i			0.000486232i
$335$	−19.6510	+	14.9479i	−1.07365	+	0.816692i
$336$		0			0
$337$	8.66306	−	8.66306i	0.471907	−	0.471907i	−0.430624	−	0.902531i	$-0.641707\pi$
$337$	8.66306	−	8.66306i	0.471907	−	0.471907i	0.902531	+	0.430624i	$0.141707\pi$
$338$	8.93582	−	8.93582i	0.486045	−	0.486045i
$339$		0			0
$340$	11.0960	−	8.44041i	0.601766	−	0.457746i
$341$			19.5648i			1.05949i
$342$		0			0
$343$	13.0634	+	13.0634i	0.705357	+	0.705357i
$344$	2.48985			0.134243
$345$		0			0
$346$	10.3829			0.558189
$347$	13.1446	+	13.1446i	0.705641	+	0.705641i	0.965616	−	0.259974i	$-0.0837141\pi$
$347$	13.1446	+	13.1446i	0.705641	+	0.705641i	−0.259974	+	0.965616i	$0.583714\pi$
$348$		0			0
$349$			31.4430i			1.68311i	0.540174	+	0.841553i	$0.318358\pi$
$349$			31.4430i			1.68311i	−0.540174	+	0.841553i	$0.681642\pi$
$350$	12.7801	+	3.53983i	0.683124	+	0.189212i
$351$		0			0
$352$	3.39264	−	3.39264i	0.180829	−	0.180829i
$353$	−8.59724	+	8.59724i	−0.457585	+	0.457585i	−0.897862	−	0.440277i	$-0.854880\pi$
$353$	−8.59724	+	8.59724i	−0.457585	+	0.457585i	0.440277	+	0.897862i	$0.354880\pi$
$354$		0			0
$355$	−3.13839	+	23.0881i	−0.166569	+	1.22539i
$356$			2.04989i			0.108644i
$357$		0			0
$358$	1.03444	+	1.03444i	0.0546717	+	0.0546717i
$359$	−4.31606			−0.227793			−0.113896	−	0.993493i	$-0.536333\pi$
$359$	−4.31606			−0.227793			−0.113896	+	0.993493i	$0.536333\pi$
$360$		0			0
$361$	−7.95119			−0.418484
$362$	−6.14176	−	6.14176i	−0.322804	−	0.322804i
$363$		0			0
$364$		−	1.59762i		−	0.0837380i
$365$	−6.31829	−	8.30622i	−0.330715	−	0.434767i
$366$		0			0
$367$	14.0560	−	14.0560i	0.733717	−	0.733717i	−0.237637	−	0.971354i	$-0.576373\pi$
$367$	14.0560	−	14.0560i	0.733717	−	0.733717i	0.971354	+	0.237637i	$0.0763729\pi$
$368$	1.86115	−	1.86115i	0.0970189	−	0.0970189i
$369$		0			0
$370$	−1.98053	−	0.269215i	−0.102963	−	0.0139958i
$371$			4.92166i			0.255520i
$372$		0			0
$373$	−1.85795	−	1.85795i	−0.0962009	−	0.0962009i	0.657368	−	0.753569i	$-0.271670\pi$
$373$	−1.85795	−	1.85795i	−0.0962009	−	0.0962009i	−0.753569	+	0.657368i	$0.771670\pi$
$374$	−29.9140			−1.54682
$375$		0			0
$376$	3.96178			0.204313
$377$	−0.783892	−	0.783892i	−0.0403725	−	0.0403725i
$378$		0			0
$379$			3.03124i			0.155705i	0.996965	+	0.0778523i	$0.0248063\pi$
$379$			3.03124i			0.155705i	−0.996965	+	0.0778523i	$0.975194\pi$
$380$	11.5027	+	1.56357i	0.590074	+	0.0802095i
$381$		0			0
$382$	3.54192	−	3.54192i	0.181220	−	0.181220i
$383$	−16.7944	+	16.7944i	−0.858153	+	0.858153i	−0.991120	−	0.132967i	$-0.957549\pi$
$383$	−16.7944	+	16.7944i	−0.858153	+	0.858153i	0.132967	+	0.991120i	$0.457549\pi$
$384$		0			0
$385$	−17.2270	−	22.6472i	−0.877971	−	1.15421i
$386$			3.36832i			0.171443i
$387$		0			0
$388$	12.2336	+	12.2336i	0.621069	+	0.621069i
$389$	−6.66508			−0.337933			−0.168966	−	0.985622i	$-0.554043\pi$
$389$	−6.66508			−0.337933			−0.168966	+	0.985622i	$0.554043\pi$
$390$		0			0
$391$	−16.4103			−0.829904
$392$	0.0243512	+	0.0243512i	0.00122992	+	0.00122992i
$393$		0			0
$394$		−	21.9241i		−	1.10452i
$395$	1.26170	−	9.28189i	0.0634829	−	0.467022i
$396$		0			0
$397$	−13.2242	+	13.2242i	−0.663703	+	0.663703i	−0.956251	−	0.292548i	$-0.905497\pi$
$397$	−13.2242	+	13.2242i	−0.663703	+	0.663703i	0.292548	+	0.956251i	$0.405497\pi$
$398$	−13.0537	+	13.0537i	−0.654321	+	0.654321i
$399$		0			0
$400$	−4.81858	−	1.33465i	−0.240929	−	0.0667326i
$401$		−	5.39169i		−	0.269248i	−0.990897	−	0.134624i	$-0.957017\pi$
$401$		−	5.39169i		−	0.269248i	0.990897	−	0.134624i	$-0.0429827\pi$
$402$		0			0
$403$	−1.73686	−	1.73686i	−0.0865193	−	0.0865193i
$404$	11.9619			0.595129
$405$		0			0
$406$	4.88121			0.242250
$407$	3.03256	+	3.03256i	0.150318	+	0.150318i
$408$		0			0
$409$			8.58606i			0.424553i	0.977210	+	0.212277i	$0.0680878\pi$
$409$			8.58606i			0.424553i	−0.977210	+	0.212277i	$0.931912\pi$
$410$	11.4783	−	8.73120i	0.566873	−	0.431203i
$411$		0			0
$412$	−7.61739	+	7.61739i	−0.375282	+	0.375282i
$413$	0.242107	−	0.242107i	0.0119133	−	0.0119133i
$414$		0			0
$415$	20.4696	−	15.5706i	1.00481	−	0.764329i
$416$			0.602363i			0.0295333i
$417$		0			0
$418$	−17.6128	−	17.6128i	−0.861468	−	0.861468i
$419$	−15.4550			−0.755025			−0.377512	−	0.926005i	$-0.623220\pi$
$419$	−15.4550			−0.755025			−0.377512	+	0.926005i	$0.623220\pi$
$420$		0			0
$421$	−18.9026			−0.921256			−0.460628	−	0.887593i	$-0.652376\pi$
$421$	−18.9026			−0.921256			−0.460628	+	0.887593i	$0.652376\pi$
$422$	−0.925553	−	0.925553i	−0.0450552	−	0.0450552i
$423$		0			0
$424$		−	1.85566i		−	0.0901186i
$425$	15.3594	+	27.1275i	0.745042	+	1.31588i
$426$		0			0
$427$	−23.5273	+	23.5273i	−1.13856	+	1.13856i
$428$	−4.35367	+	4.35367i	−0.210442	+	0.210442i
$429$		0			0
$430$	−0.749896	+	5.51673i	−0.0361632	+	0.266040i
$431$			3.91428i			0.188544i	0.995546	+	0.0942720i	$0.0300523\pi$
$431$			3.91428i			0.188544i	−0.995546	+	0.0942720i	$0.969948\pi$
$432$		0			0
$433$	−27.2049	−	27.2049i	−1.30738	−	1.30738i	−0.923297	−	0.384086i	$-0.874517\pi$
$433$	−27.2049	−	27.2049i	−1.30738	−	1.30738i	−0.384086	−	0.923297i	$-0.625483\pi$
$434$	10.8152			0.519149
$435$		0			0
$436$	15.4546			0.740141
$437$	−9.66205	−	9.66205i	−0.462199	−	0.462199i
$438$		0			0
$439$		−	15.3257i		−	0.731457i	−0.930722	−	0.365728i	$-0.880820\pi$
$439$		−	15.3257i		−	0.731457i	0.930722	−	0.365728i	$-0.119180\pi$
$440$	6.49525	+	8.53886i	0.309649	+	0.407074i
$441$		0			0
$442$	2.65561	−	2.65561i	0.126315	−	0.126315i
$443$	19.6716	−	19.6716i	0.934626	−	0.934626i	−0.0633641	−	0.997990i	$-0.520183\pi$
$443$	19.6716	−	19.6716i	0.934626	−	0.934626i	0.997990	+	0.0633641i	$0.0201830\pi$
$444$		0			0
$445$	−4.54192	−	0.617389i	−0.215308	−	0.0292670i
$446$			20.9762i			0.993251i
$447$		0			0
$448$	−1.87542	−	1.87542i	−0.0886055	−	0.0886055i
$449$	−24.3627			−1.14975			−0.574874	−	0.818242i	$-0.694949\pi$
$449$	−24.3627			−1.14975			−0.574874	+	0.818242i	$0.694949\pi$
$450$		0			0
$451$	−30.9446			−1.45712
$452$	4.19556	+	4.19556i	0.197343	+	0.197343i
$453$		0			0
$454$			5.95497i			0.279481i
$455$	3.53983	+	0.481174i	0.165950	+	0.0225578i
$456$		0			0
$457$	9.27546	−	9.27546i	0.433888	−	0.433888i	−0.456061	−	0.889949i	$-0.650740\pi$
$457$	9.27546	−	9.27546i	0.433888	−	0.433888i	0.889949	+	0.456061i	$0.150740\pi$
$458$	8.31377	−	8.31377i	0.388477	−	0.388477i
$459$		0			0
$460$	3.56318	+	4.68427i	0.166134	+	0.218405i
$461$			40.1471i			1.86984i	0.354861	+	0.934919i	$0.384528\pi$
$461$			40.1471i			1.86984i	−0.354861	+	0.934919i	$0.615472\pi$
$462$		0			0
$463$	8.46896	+	8.46896i	0.393586	+	0.393586i	0.875964	−	0.482377i	$-0.160227\pi$
$463$	8.46896	+	8.46896i	0.393586	+	0.393586i	−0.482377	+	0.875964i	$0.660227\pi$
$464$	−1.84040			−0.0854385
$465$		0			0
$466$	18.9960			0.879973
$467$	8.63124	+	8.63124i	0.399406	+	0.399406i	0.878024	−	0.478617i	$-0.158862\pi$
$467$	8.63124	+	8.63124i	0.399406	+	0.399406i	−0.478617	+	0.878024i	$0.658862\pi$
$468$		0			0
$469$		−	29.2855i		−	1.35228i
$470$	−1.19321	+	8.77808i	−0.0550389	+	0.404902i
$471$		0			0
$472$	−0.0912837	+	0.0912837i	−0.00420167	+	0.00420167i
$473$	8.44716	−	8.44716i	0.388401	−	0.388401i
$474$		0			0
$475$	−6.92878	+	25.0154i	−0.317914	+	1.14779i
$476$			16.5362i			0.757935i
$477$		0			0
$478$	3.22360	+	3.22360i	0.147444	+	0.147444i
$479$	−10.2698			−0.469238			−0.234619	−	0.972087i	$-0.575384\pi$
$479$	−10.2698			−0.469238			−0.234619	+	0.972087i	$0.575384\pi$
$480$		0			0
$481$	−0.538431			−0.0245503
$482$	−11.3576	−	11.3576i	−0.517325	−	0.517325i
$483$		0			0
$484$		−	12.0201i		−	0.546367i
$485$	−30.7905	+	23.4214i	−1.39812	+	1.06351i
$486$		0			0
$487$	17.5218	−	17.5218i	0.793987	−	0.793987i	−0.188153	−	0.982140i	$-0.560250\pi$
$487$	17.5218	−	17.5218i	0.793987	−	0.793987i	0.982140	+	0.188153i	$0.0602500\pi$
$488$	8.87067	−	8.87067i	0.401556	−	0.401556i
$489$		0			0
$490$	−0.0612889	+	0.0466207i	−0.00276875	+	0.00210611i
$491$			8.89235i			0.401306i	0.979662	+	0.200653i	$0.0643064\pi$
$491$			8.89235i			0.401306i	−0.979662	+	0.200653i	$0.935694\pi$
$492$		0			0
$493$	8.11369	+	8.11369i	0.365422	+	0.365422i
$494$	3.12714			0.140697
$495$		0			0
$496$	−4.07776			−0.183097
$497$	−19.5424	−	19.5424i	−0.876597	−	0.876597i
$498$		0			0
$499$		−	29.3509i		−	1.31393i	−0.753923	−	0.656963i	$-0.771841\pi$
$499$		−	29.3509i		−	1.31393i	0.753923	−	0.656963i	$-0.228159\pi$
$500$	4.40844	−	10.2745i	0.197152	−	0.459490i
$501$		0			0
$502$	13.4337	−	13.4337i	0.599574	−	0.599574i
$503$	10.0766	−	10.0766i	0.449293	−	0.449293i	−0.445826	−	0.895120i	$-0.647090\pi$
$503$	10.0766	−	10.0766i	0.449293	−	0.449293i	0.895120	+	0.445826i	$0.147090\pi$
$504$		0			0
$505$	−3.60272	+	26.5040i	−0.160319	+	1.17941i
$506$		−	12.6284i		−	0.561401i
$507$		0			0
$508$	2.51837	+	2.51837i	0.111734	+	0.111734i
$509$	30.0048			1.32994			0.664970	−	0.746870i	$-0.268444\pi$
$509$	30.0048			1.32994			0.664970	+	0.746870i	$0.268444\pi$
$510$		0			0
$511$	12.3786			0.547597
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$		−	3.35128i		−	0.147819i
$515$	−14.5836	−	19.1720i	−0.642629	−	0.844819i
$516$		0			0
$517$	13.4409	−	13.4409i	0.591130	−	0.591130i
$518$	1.67637	−	1.67637i	0.0736557	−	0.0736557i
$519$		0			0
$520$	−1.33465	−	0.181421i	−0.0585283	−	0.00795583i
$521$			6.40485i			0.280602i	0.990109	+	0.140301i	$0.0448070\pi$
$521$			6.40485i			0.280602i	−0.990109	+	0.140301i	$0.955193\pi$
$522$		0			0
$523$	16.0596	+	16.0596i	0.702237	+	0.702237i	0.964890	−	0.262653i	$-0.0845974\pi$
$523$	16.0596	+	16.0596i	0.702237	+	0.702237i	−0.262653	+	0.964890i	$0.584597\pi$
$524$	13.0599			0.570526
$525$		0			0
$526$	16.7454			0.730133
$527$	17.9774	+	17.9774i	0.783110	+	0.783110i
$528$		0			0
$529$			16.0723i			0.698795i
$530$	4.11156	+	0.558889i	0.178595	+	0.0242766i
$531$		0			0
$532$	−9.73618	+	9.73618i	−0.422117	+	0.422117i
$533$	2.74710	−	2.74710i	0.118990	−	0.118990i
$534$		0			0
$535$	−8.33514	−	10.9576i	−0.360360	−	0.473740i
$536$			11.0417i			0.476931i
$537$		0			0
$538$	0.378826	+	0.378826i	0.0163324	+	0.0163324i
$539$	0.165230			0.00711696
$540$		0			0
$541$	44.6389			1.91917			0.959587	−	0.281412i	$-0.0908026\pi$
$541$	44.6389			1.91917			0.959587	+	0.281412i	$0.0908026\pi$
$542$	−10.9893	−	10.9893i	−0.472032	−	0.472032i
$543$		0			0
$544$		−	6.23478i		−	0.267314i
$545$	−4.65464	+	34.2426i	−0.199383	+	1.46679i
$546$		0			0
$547$	−3.77045	+	3.77045i	−0.161213	+	0.161213i	−0.783104	−	0.621891i	$-0.786365\pi$
$547$	−3.77045	+	3.77045i	−0.161213	+	0.161213i	0.621891	+	0.783104i	$0.286365\pi$
$548$	−2.29750	+	2.29750i	−0.0981442	+	0.0981442i
$549$		0			0
$550$	−20.8757	+	11.8197i	−0.890144	+	0.503995i
$551$			9.55436i			0.407029i
$552$		0			0
$553$	7.85646	+	7.85646i	0.334091	+	0.334091i
$554$	−17.3098			−0.735423
$555$		0			0
$556$	−21.9945			−0.932775
$557$	4.10329	+	4.10329i	0.173862	+	0.173862i	0.788674	−	0.614812i	$-0.210768\pi$
$557$	4.10329	+	4.10329i	0.173862	+	0.173862i	−0.614812	+	0.788674i	$0.710768\pi$
$558$		0			0
$559$			1.49979i			0.0634344i
$560$	4.72021	−	3.59052i	0.199465	−	0.151727i
$561$		0			0
$562$	17.0573	−	17.0573i	0.719519	−	0.719519i
$563$	4.19499	−	4.19499i	0.176798	−	0.176798i	−0.613160	−	0.789958i	$-0.710102\pi$
$563$	4.19499	−	4.19499i	0.176798	−	0.176798i	0.789958	+	0.613160i	$0.210102\pi$
$564$		0			0
$565$	−10.5597	+	8.03244i	−0.444250	+	0.337927i
$566$		−	16.5516i		−	0.695715i
$567$		0			0
$568$	7.36824	+	7.36824i	0.309164	+	0.309164i
$569$	−35.3427			−1.48164			−0.740822	−	0.671702i	$-0.765564\pi$
$569$	−35.3427			−1.48164			−0.740822	+	0.671702i	$0.765564\pi$
$570$		0			0
$571$	−3.01059			−0.125989			−0.0629946	−	0.998014i	$-0.520065\pi$
$571$	−3.01059			−0.125989			−0.0629946	+	0.998014i	$0.520065\pi$
$572$	2.04360	+	2.04360i	0.0854474	+	0.0854474i
$573$		0			0
$574$			17.1059i			0.713987i
$575$	−11.4521	+	6.48410i	−0.477584	+	0.270405i
$576$		0			0
$577$	−11.5350	+	11.5350i	−0.480208	+	0.480208i	−0.905198	−	0.424990i	$-0.860278\pi$
$577$	−11.5350	+	11.5350i	−0.480208	+	0.480208i	0.424990	+	0.905198i	$0.360278\pi$
$578$	−15.4662	+	15.4662i	−0.643307	+	0.643307i
$579$		0			0
$580$	0.554295	−	4.07776i	0.0230159	−	0.169320i
$581$			30.5054i			1.26558i
$582$		0			0
$583$	−6.29558	−	6.29558i	−0.260736	−	0.260736i
$584$	−4.66721			−0.193130
$585$		0			0
$586$	16.1515			0.667214
$587$	−8.06405	−	8.06405i	−0.332839	−	0.332839i	0.520825	−	0.853664i	$-0.325625\pi$
$587$	−8.06405	−	8.06405i	−0.332839	−	0.332839i	−0.853664	+	0.520825i	$0.825625\pi$
$588$		0			0
$589$			21.1695i			0.872275i
$590$	−0.174763	−	0.229749i	−0.00719490	−	0.00945863i
$591$		0			0
$592$	−0.632057	+	0.632057i	−0.0259774	+	0.0259774i
$593$	23.4664	−	23.4664i	0.963651	−	0.963651i	−0.0357109	−	0.999362i	$-0.511370\pi$
$593$	23.4664	−	23.4664i	0.963651	−	0.963651i	0.999362	+	0.0357109i	$0.0113696\pi$
$594$		0			0
$595$	−36.6391	−	4.98040i	−1.50206	−	0.204177i
$596$		−	13.1334i		−	0.537964i
$597$		0			0
$598$	1.12109	+	1.12109i	0.0458446	+	0.0458446i
$599$	34.5367			1.41113			0.705566	−	0.708645i	$-0.250693\pi$
$599$	34.5367			1.41113			0.705566	+	0.708645i	$0.250693\pi$
$600$		0			0
$601$	3.15518			0.128703			0.0643513	−	0.997927i	$-0.479502\pi$
$601$	3.15518			0.128703			0.0643513	+	0.997927i	$0.479502\pi$
$602$	−4.66952	−	4.66952i	−0.190315	−	0.190315i
$603$		0			0
$604$			0.335798i			0.0136634i
$605$	26.6328	+	3.62022i	1.08278	+	0.147183i
$606$		0			0
$607$	3.60821	−	3.60821i	0.146453	−	0.146453i	−0.630079	−	0.776531i	$-0.716977\pi$
$607$	3.60821	−	3.60821i	0.146453	−	0.146453i	0.776531	+	0.630079i	$0.216977\pi$
$608$	3.67091	−	3.67091i	0.148875	−	0.148875i
$609$		0			0
$610$	16.9830	+	22.3264i	0.687621	+	0.903968i
$611$			2.38643i			0.0965446i
$612$		0			0
$613$	−9.09622	−	9.09622i	−0.367393	−	0.367393i	0.499133	−	0.866525i	$-0.333652\pi$
$613$	−9.09622	−	9.09622i	−0.367393	−	0.367393i	−0.866525	+	0.499133i	$0.833652\pi$
$614$	−2.05969			−0.0831222
$615$		0			0
$616$	−12.7253			−0.512717
$617$	−17.0566	−	17.0566i	−0.686673	−	0.686673i	0.274822	−	0.961495i	$-0.411381\pi$
$617$	−17.0566	−	17.0566i	−0.686673	−	0.686673i	−0.961495	+	0.274822i	$0.911381\pi$
$618$		0			0
$619$			31.0938i			1.24977i	0.780718	+	0.624883i	$0.214853\pi$
$619$			31.0938i			1.24977i	−0.780718	+	0.624883i	$0.785147\pi$
$620$	1.22815	−	9.03506i	0.0493236	−	0.362857i
$621$		0			0
$622$	−1.48163	+	1.48163i	−0.0594081	+	0.0594081i
$623$	3.84441	−	3.84441i	0.154023	−	0.154023i
$624$		0			0
$625$	21.4374	+	12.8622i	0.857496	+	0.514490i
$626$		−	19.7519i		−	0.789445i
$627$		0			0
$628$	−3.22360	−	3.22360i	−0.128636	−	0.128636i
$629$	5.57304			0.222212
$630$		0			0
$631$	46.1604			1.83762			0.918809	−	0.394703i	$-0.129153\pi$
$631$	46.1604			1.83762			0.918809	+	0.394703i	$0.129153\pi$
$632$	−2.96218	−	2.96218i	−0.117829	−	0.117829i
$633$		0			0
$634$			34.0863i			1.35374i
$635$	−6.33841	+	4.82144i	−0.251532	+	0.191333i
$636$		0			0
$637$	−0.0146683	+	0.0146683i	−0.000581179	+	0.000581179i
$638$	−6.24383	+	6.24383i	−0.247195	+	0.247195i
$639$		0			0
$640$	−1.77970	+	1.35376i	−0.0703487	+	0.0535122i
$641$		−	3.93850i		−	0.155562i	−0.996970	−	0.0777808i	$-0.975217\pi$
$641$		−	3.93850i		−	0.155562i	0.996970	−	0.0777808i	$-0.0247834\pi$
$642$		0			0
$643$	21.9554	+	21.9554i	0.865838	+	0.865838i	0.992009	−	0.126171i	$-0.0402686\pi$
$643$	21.9554	+	21.9554i	0.865838	+	0.865838i	−0.126171	+	0.992009i	$0.540269\pi$
$644$	−6.98088			−0.275085
$645$		0			0
$646$	−32.3676			−1.27348
$647$	−18.0986	−	18.0986i	−0.711531	−	0.711531i	0.255325	−	0.966855i	$-0.417818\pi$
$647$	−18.0986	−	18.0986i	−0.711531	−	0.711531i	−0.966855	+	0.255325i	$0.917818\pi$
$648$		0			0
$649$			0.619386i			0.0243130i
$650$	0.803945	−	2.90254i	0.0315333	−	0.113847i
$651$		0			0
$652$	−9.01496	+	9.01496i	−0.353053	+	0.353053i
$653$	9.93605	−	9.93605i	0.388828	−	0.388828i	−0.485442	−	0.874269i	$-0.661341\pi$
$653$	9.93605	−	9.93605i	0.388828	−	0.388828i	0.874269	+	0.485442i	$0.161341\pi$
$654$		0			0
$655$	−3.93342	+	28.9368i	−0.153691	+	1.13066i
$656$		−	6.44958i		−	0.251814i
$657$		0			0
$658$	−7.43002	−	7.43002i	−0.289652	−	0.289652i
$659$	36.5419			1.42347			0.711734	−	0.702449i	$-0.247910\pi$
$659$	36.5419			1.42347			0.711734	+	0.702449i	$0.247910\pi$
$660$		0			0
$661$	35.8730			1.39530			0.697650	−	0.716439i	$-0.254229\pi$
$661$	35.8730			1.39530			0.697650	+	0.716439i	$0.254229\pi$
$662$	16.9903	+	16.9903i	0.660348	+	0.660348i
$663$		0			0
$664$		−	11.5017i		−	0.446353i
$665$	−18.6400	−	24.5047i	−0.722829	−	0.950253i
$666$		0			0
$667$	−3.42525	+	3.42525i	−0.132626	+	0.132626i
$668$	−0.00628350	+	0.00628350i	−0.000243116	+	0.000243116i
$669$		0			0
$670$	−24.4651	−	3.32557i	−0.945170	−	0.128478i
$671$		−	60.1901i		−	2.32361i
$672$		0			0
$673$	−17.7365	−	17.7365i	−0.683691	−	0.683691i	0.277139	−	0.960830i	$-0.410614\pi$
$673$	−17.7365	−	17.7365i	−0.683691	−	0.683691i	−0.960830	+	0.277139i	$0.910614\pi$
$674$	12.2514			0.471907
$675$		0			0
$676$	12.6372			0.486045
$677$	3.82902	+	3.82902i	0.147161	+	0.147161i	0.776849	−	0.629687i	$-0.216817\pi$
$677$	3.82902	+	3.82902i	0.147161	+	0.147161i	−0.629687	+	0.776849i	$0.716817\pi$
$678$		0			0
$679$		−	45.8865i		−	1.76096i
$680$	13.8143	+	1.87780i	0.529756	+	0.0720104i
$681$		0			0
$682$	−13.8344	+	13.8344i	−0.529746	+	0.529746i
$683$	14.3302	−	14.3302i	0.548331	−	0.548331i	−0.377627	−	0.925958i	$-0.623260\pi$
$683$	14.3302	−	14.3302i	0.548331	−	0.548331i	0.925958	+	0.377627i	$0.123260\pi$
$684$		0			0
$685$	−4.39858	−	5.78251i	−0.168061	−	0.220938i
$686$			18.4744i			0.705357i
$687$		0			0
$688$	1.76059	+	1.76059i	0.0671217	+	0.0671217i
$689$	1.11778			0.0425840
$690$		0			0
$691$	11.7198			0.445843			0.222921	−	0.974836i	$-0.428441\pi$
$691$	11.7198			0.445843			0.222921	+	0.974836i	$0.428441\pi$
$692$	7.34182	+	7.34182i	0.279094	+	0.279094i
$693$		0			0
$694$			18.5893i			0.705641i
$695$	6.62435	−	48.7331i	0.251276	−	1.84855i
$696$		0			0
$697$	−28.4340	+	28.4340i	−1.07701	+	1.07701i
$698$	−22.2336	+	22.2336i	−0.841553	+	0.841553i
$699$		0			0
$700$	6.53384	+	11.5399i	0.246956	+	0.436168i
$701$		−	30.7235i		−	1.16041i	−0.814471	−	0.580205i	$-0.802972\pi$
$701$		−	30.7235i		−	1.16041i	0.814471	−	0.580205i	$-0.197028\pi$
$702$		0			0
$703$	3.28129	+	3.28129i	0.123756	+	0.123756i
$704$	4.79792			0.180829
$705$		0			0
$706$	−12.1583			−0.457585
$707$	−22.4337	−	22.4337i	−0.843708	−	0.843708i
$708$		0			0
$709$		−	31.7403i		−	1.19203i	−0.802973	−	0.596015i	$-0.796750\pi$
$709$		−	31.7403i		−	1.19203i	0.802973	−	0.596015i	$-0.203250\pi$
$710$	−18.5449	+	14.1066i	−0.695979	+	0.529410i
$711$		0			0
$712$	−1.44949	+	1.44949i	−0.0543219	+	0.0543219i
$713$	−7.58931	+	7.58931i	−0.284222	+	0.284222i
$714$		0			0
$715$	−5.14349	+	3.91250i	−0.192356	+	0.146319i
$716$			1.46292i			0.0546717i
$717$		0			0
$718$	−3.05191	−	3.05191i	−0.113896	−	0.113896i
$719$	−7.79879			−0.290846			−0.145423	−	0.989370i	$-0.546454\pi$
$719$	−7.79879			−0.290846			−0.145423	+	0.989370i	$0.546454\pi$
$720$		0			0
$721$	28.5717			1.06407
$722$	−5.62234	−	5.62234i	−0.209242	−	0.209242i
$723$		0			0
$724$		−	8.68576i		−	0.322804i
$725$	8.86812	+	2.45629i	0.329354	+	0.0912245i
$726$		0			0
$727$	31.3217	−	31.3217i	1.16166	−	1.16166i	0.177546	−	0.984113i	$-0.443184\pi$
$727$	31.3217	−	31.3217i	1.16166	−	1.16166i	0.984113	−	0.177546i	$-0.0568158\pi$
$728$	1.12969	−	1.12969i	0.0418690	−	0.0418690i
$729$		0			0
$730$	1.40568	−	10.3411i	0.0520265	−	0.382741i
$731$		−	15.5236i		−	0.574162i
$732$		0			0
$733$	−19.7144	−	19.7144i	−0.728169	−	0.728169i	0.242086	−	0.970255i	$-0.422168\pi$
$733$	−19.7144	−	19.7144i	−0.728169	−	0.728169i	−0.970255	+	0.242086i	$0.922168\pi$
$734$	19.8782			0.733717
$735$		0			0
$736$	2.63206			0.0970189
$737$	37.4607	+	37.4607i	1.37988	+	1.37988i
$738$		0			0
$739$		−	10.8068i		−	0.397536i	−0.980047	−	0.198768i	$-0.936306\pi$
$739$		−	10.8068i		−	0.397536i	0.980047	−	0.198768i	$-0.0636941\pi$
$740$	−1.21008	−	1.59081i	−0.0444834	−	0.0584793i
$741$		0			0
$742$	−3.48014	+	3.48014i	−0.127760	+	0.127760i
$743$	−15.7301	+	15.7301i	−0.577082	+	0.577082i	−0.934098	−	0.357016i	$-0.883794\pi$
$743$	−15.7301	+	15.7301i	−0.577082	+	0.577082i	0.357016	+	0.934098i	$0.383794\pi$
$744$		0			0
$745$	29.0995	+	3.95553i	1.06612	+	0.144919i
$746$		−	2.62754i		−	0.0962009i
$747$		0			0
$748$	−21.1524	−	21.1524i	−0.773408	−	0.773408i
$749$	16.3300			0.596684
$750$		0			0
$751$	41.2469			1.50512			0.752561	−	0.658523i	$-0.228818\pi$
$751$	41.2469			1.50512			0.752561	+	0.658523i	$0.228818\pi$
$752$	2.80140	+	2.80140i	0.102157	+	0.102157i
$753$		0			0
$754$		−	1.10859i		−	0.0403725i
$755$	−0.744025	−	0.101136i	−0.0270778	−	0.00368072i
$756$		0			0
$757$	−20.5246	+	20.5246i	−0.745978	+	0.745978i	−0.973721	−	0.227743i	$-0.926865\pi$
$757$	−20.5246	+	20.5246i	−0.745978	+	0.745978i	0.227743	+	0.973721i	$0.426865\pi$
$758$	−2.14341	+	2.14341i	−0.0778523	+	0.0778523i
$759$		0			0
$760$	7.02800	+	9.23922i	0.254932	+	0.335142i
$761$		−	45.9788i		−	1.66673i	−0.552724	−	0.833365i	$-0.686411\pi$
$761$		−	45.9788i		−	1.66673i	0.552724	−	0.833365i	$-0.313589\pi$
$762$		0			0
$763$	−28.9839	−	28.9839i	−1.04929	−	1.04929i
$764$	5.00903			0.181220
$765$		0			0
$766$	−23.7508			−0.858153
$767$	−0.0549859	−	0.0549859i	−0.00198543	−	0.00198543i
$768$		0			0
$769$		−	30.7961i		−	1.11054i	−0.831672	−	0.555268i	$-0.812616\pi$
$769$		−	30.7961i		−	1.11054i	0.831672	−	0.555268i	$-0.187384\pi$
$770$	3.83263	−	28.1953i	0.138118	−	1.01609i
$771$		0			0
$772$	−2.38176	+	2.38176i	−0.0857214	+	0.0857214i
$773$	29.6376	−	29.6376i	1.06599	−	1.06599i	0.0683287	−	0.997663i	$-0.478233\pi$
$773$	29.6376	−	29.6376i	1.06599	−	1.06599i	0.997663	−	0.0683287i	$-0.0217667\pi$
$774$		0			0
$775$	19.6490	+	5.44239i	0.705814	+	0.195496i
$776$			17.3010i			0.621069i
$777$		0			0
$778$	−4.71292	−	4.71292i	−0.168966	−	0.168966i
$779$	−33.4827			−1.19964
$780$		0			0
$781$	49.9956			1.78898
$782$	−11.6038	−	11.6038i	−0.414952	−	0.414952i
$783$		0			0
$784$			0.0344378i			0.00122992i
$785$	8.11339	−	6.17161i	0.289579	−	0.220274i
$786$		0			0
$787$	−19.0784	+	19.0784i	−0.680070	+	0.680070i	−0.960016	−	0.279946i	$-0.909683\pi$
$787$	−19.0784	+	19.0784i	−0.680070	+	0.680070i	0.279946	+	0.960016i	$0.409683\pi$
$788$	15.5027	−	15.5027i	0.552261	−	0.552261i
$789$		0			0
$790$	7.45544	−	5.67113i	0.265253	−	0.201770i
$791$		−	15.7369i		−	0.559540i
$792$		0			0
$793$	5.34337	+	5.34337i	0.189749	+	0.189749i
$794$	−18.7018			−0.663703
$795$		0			0
$796$	−18.4607			−0.654321
$797$	−4.59865	−	4.59865i	−0.162893	−	0.162893i	0.620954	−	0.783847i	$-0.286745\pi$
$797$	−4.59865	−	4.59865i	−0.162893	−	0.162893i	−0.783847	+	0.620954i	$0.786745\pi$
$798$		0			0
$799$		−	24.7008i		−	0.873851i
$800$	−2.46351	−	4.35099i	−0.0870982	−	0.153831i
$801$		0			0
$802$	3.81250	−	3.81250i	0.134624	−	0.134624i
$803$	−15.8342	+	15.8342i	−0.558776	+	0.558776i
$804$		0			0
$805$	2.10251	−	15.4675i	0.0741038	−	0.545157i
$806$		−	2.45629i		−	0.0865193i
$807$		0			0
$808$	8.45838	+	8.45838i	0.297565	+	0.297565i
$809$	−5.79431			−0.203717			−0.101859	−	0.994799i	$-0.532479\pi$
$809$	−5.79431			−0.203717			−0.101859	+	0.994799i	$0.532479\pi$
$810$		0			0
$811$	1.90498			0.0668929			0.0334465	−	0.999441i	$-0.489352\pi$
$811$	1.90498			0.0668929			0.0334465	+	0.999441i	$0.489352\pi$
$812$	3.45153	+	3.45153i	0.121125	+	0.121125i
$813$		0			0
$814$			4.28869i			0.150318i
$815$	−17.2592	−	22.6895i	−0.604565	−	0.794779i
$816$		0			0
$817$	9.14000	−	9.14000i	0.319768	−	0.319768i
$818$	−6.07126	+	6.07126i	−0.212277	+	0.212277i
$819$		0			0
$820$	14.2903	+	1.94250i	0.499038	+	0.0678349i
$821$		−	38.6250i		−	1.34802i	−0.738721	−	0.674012i	$-0.764570\pi$
$821$		−	38.6250i		−	1.34802i	0.738721	−	0.674012i	$-0.235430\pi$
$822$		0			0
$823$	−15.1323	−	15.1323i	−0.527478	−	0.527478i	0.392342	−	0.919819i	$-0.371665\pi$
$823$	−15.1323	−	15.1323i	−0.527478	−	0.527478i	−0.919819	+	0.392342i	$0.871665\pi$
$824$	−10.7726			−0.375282
$825$		0			0
$826$	0.342391			0.0119133
$827$	23.1603	+	23.1603i	0.805364	+	0.805364i	0.983928	−	0.178564i	$-0.0571453\pi$
$827$	23.1603	+	23.1603i	0.805364	+	0.805364i	−0.178564	+	0.983928i	$0.557145\pi$
$828$		0			0
$829$		−	34.1116i		−	1.18475i	−0.805664	−	0.592373i	$-0.798191\pi$
$829$		−	34.1116i		−	1.18475i	0.805664	−	0.592373i	$-0.201809\pi$
$830$	25.4842	+	3.46410i	0.884570	+	0.120241i
$831$		0			0
$832$	−0.425935	+	0.425935i	−0.0147666	+	0.0147666i
$833$	0.151824	−	0.151824i	0.00526041	−	0.00526041i
$834$		0			0
$835$	−0.0120298	−	0.0158148i	−0.000416309	−	0.000547293i
$836$		−	24.9082i		−	0.861468i
$837$		0			0
$838$	−10.9283	−	10.9283i	−0.377512	−	0.377512i
$839$	−37.6116			−1.29850			−0.649249	−	0.760576i	$-0.724917\pi$
$839$	−37.6116			−1.29850			−0.649249	+	0.760576i	$0.724917\pi$
$840$		0			0
$841$	−25.6129			−0.883204
$842$	−13.3661	−	13.3661i	−0.460628	−	0.460628i
$843$		0			0
$844$		−	1.30893i		−	0.0450552i
$845$	−3.80608	+	28.0000i	−0.130933	+	0.963231i
$846$		0			0
$847$	−22.5427	+	22.5427i	−0.774577	+	0.774577i
$848$	1.31215	−	1.31215i	0.0450593	−	0.0450593i
$849$		0			0
$850$	−8.32126	+	30.0428i	−0.285417	+	1.03046i
$851$			2.35270i			0.0806495i
$852$		0			0
$853$	−5.42972	−	5.42972i	−0.185910	−	0.185910i	0.608015	−	0.793925i	$-0.291966\pi$
$853$	−5.42972	−	5.42972i	−0.185910	−	0.185910i	−0.793925	+	0.608015i	$0.791966\pi$
$854$	−33.2726			−1.13856
$855$		0			0
$856$	−6.15702			−0.210442
$857$	5.12629	+	5.12629i	0.175111	+	0.175111i	0.789221	−	0.614110i	$-0.210485\pi$
$857$	5.12629	+	5.12629i	0.175111	+	0.175111i	−0.614110	+	0.789221i	$0.710485\pi$
$858$		0			0
$859$			1.73720i			0.0592726i	0.999561	+	0.0296363i	$0.00943490\pi$
$859$			1.73720i			0.0592726i	−0.999561	+	0.0296363i	$0.990565\pi$
$860$	−4.43117	+	3.37066i	−0.151102	+	0.114939i
$861$		0			0
$862$	−2.76781	+	2.76781i	−0.0942720	+	0.0942720i
$863$	−36.4612	+	36.4612i	−1.24115	+	1.24115i	−0.281630	+	0.959523i	$0.590875\pi$
$863$	−36.4612	+	36.4612i	−1.24115	+	1.24115i	−0.959523	+	0.281630i	$0.909125\pi$
$864$		0			0
$865$	−18.4784	+	14.0560i	−0.628286	+	0.477918i
$866$		−	38.4735i		−	1.30738i
$867$		0			0
$868$	7.64754	+	7.64754i	0.259574	+	0.259574i
$869$	−20.0993			−0.681821
$870$		0			0
$871$	−6.65115			−0.225365
$872$	10.9280	+	10.9280i	0.370070	+	0.370070i
$873$		0			0
$874$		−	13.6642i		−	0.462199i
$875$	−27.5368	+	11.0014i	−0.930913	+	0.371914i
$876$		0			0
$877$	7.32721	−	7.32721i	0.247422	−	0.247422i	−0.572490	−	0.819912i	$-0.694022\pi$
$877$	7.32721	−	7.32721i	0.247422	−	0.247422i	0.819912	+	0.572490i	$0.194022\pi$
$878$	10.8369	−	10.8369i	0.365728	−	0.365728i
$879$		0			0
$880$	−1.44505	+	10.6307i	−0.0487125	+	0.358361i
$881$			1.17719i			0.0396604i	0.999803	+	0.0198302i	$0.00631257\pi$
$881$			1.17719i			0.0396604i	−0.999803	+	0.0198302i	$0.993687\pi$
$882$		0			0
$883$	−22.1929	−	22.1929i	−0.746850	−	0.746850i	0.227036	−	0.973886i	$-0.427097\pi$
$883$	−22.1929	−	22.1929i	−0.746850	−	0.746850i	−0.973886	+	0.227036i	$0.927097\pi$
$884$	3.75560			0.126315
$885$		0			0
$886$	27.8199			0.934626
$887$	−6.44565	−	6.44565i	−0.216424	−	0.216424i	0.590566	−	0.806989i	$-0.298905\pi$
$887$	−6.44565	−	6.44565i	−0.216424	−	0.216424i	−0.806989	+	0.590566i	$0.798905\pi$
$888$		0			0
$889$		−	9.44601i		−	0.316809i
$890$	−2.77506	−	3.64818i	−0.0930203	−	0.122287i
$891$		0			0
$892$	−14.8324	+	14.8324i	−0.496625	+	0.496625i
$893$	14.5433	−	14.5433i	0.486674	−	0.486674i
$894$		0			0
$895$	−3.24137	−	0.440604i	−0.108347	−	0.0147278i
$896$		−	2.65225i		−	0.0886055i
$897$		0			0
$898$	−17.2270	−	17.2270i	−0.574874	−	0.574874i
$899$	7.50472			0.250296
$900$		0			0
$901$	−11.5696			−0.385439
$902$	−21.8811	−	21.8811i	−0.728562	−	0.728562i
$903$		0			0
$904$			5.93342i			0.197343i
$905$	19.2450	+	2.61599i	0.639724	+	0.0869585i
$906$		0			0
$907$	−5.38206	+	5.38206i	−0.178708	+	0.178708i	−0.790793	−	0.612084i	$-0.790331\pi$
$907$	−5.38206	+	5.38206i	−0.178708	+	0.178708i	0.612084	+	0.790793i	$0.290331\pi$
$908$	−4.21080	+	4.21080i	−0.139740	+	0.139740i
$909$		0			0
$910$	2.16280	+	2.84328i	0.0716960	+	0.0942538i
$911$			45.3246i			1.50167i	0.660490	+	0.750835i	$0.270349\pi$
$911$			45.3246i			1.50167i	−0.660490	+	0.750835i	$0.729651\pi$
$912$		0			0
$913$	−39.0212	−	39.0212i	−1.29141	−	1.29141i
$914$	13.1175			0.433888
$915$		0			0
$916$	11.7574			0.388477
$917$	−24.4930	−	24.4930i	−0.808829	−	0.808829i
$918$		0			0
$919$		−	19.9726i		−	0.658836i	−0.944184	−	0.329418i	$-0.893148\pi$
$919$		−	19.9726i		−	0.658836i	0.944184	−	0.329418i	$-0.106852\pi$
$920$	−0.792727	+	5.83183i	−0.0261354	+	0.192270i
$921$		0			0
$922$	−28.3883	+	28.3883i	−0.934919	+	0.934919i
$923$	−4.43836	+	4.43836i	−0.146090	+	0.146090i
$924$		0			0
$925$	3.88919	−	2.20204i	0.127876	−	0.0724027i
$926$			11.9769i			0.393586i
$927$		0			0
$928$	−1.30136	−	1.30136i	−0.0427192	−	0.0427192i
$929$	49.7840			1.63336			0.816681	−	0.577090i	$-0.195812\pi$
$929$	49.7840			1.63336			0.816681	+	0.577090i	$0.195812\pi$
$930$		0			0
$931$	0.178782			0.00585936
$932$	13.4322	+	13.4322i	0.439986	+	0.439986i
$933$		0			0
$934$			12.2064i			0.399406i
$935$	53.2379	−	40.4964i	1.74106	−	1.32438i
$936$		0			0
$937$	28.6750	−	28.6750i	0.936771	−	0.936771i	−0.0613453	−	0.998117i	$-0.519539\pi$
$937$	28.6750	−	28.6750i	0.936771	−	0.936771i	0.998117	+	0.0613453i	$0.0195391\pi$
$938$	20.7080	−	20.7080i	0.676139	−	0.676139i
$939$		0			0
$940$	−7.05077	+	5.36331i	−0.229971	+	0.174932i
$941$			49.0268i			1.59823i	0.601178	+	0.799115i	$0.294698\pi$
$941$			49.0268i			1.59823i	−0.601178	+	0.799115i	$0.705302\pi$
$942$		0			0
$943$	−12.0036	−	12.0036i	−0.390891	−	0.390891i
$944$	−0.129095			−0.00420167
$945$		0			0
$946$	11.9461			0.388401
$947$	31.8740	+	31.8740i	1.03577	+	1.03577i	0.999336	+	0.0364298i	$0.0115985\pi$
$947$	31.8740	+	31.8740i	1.03577	+	1.03577i	0.0364298	+	0.999336i	$0.488401\pi$
$948$		0			0
$949$		−	2.81135i		−	0.0912604i
$950$	−22.5880	+	12.7892i	−0.732850	+	0.414936i
$951$		0			0
$952$	−11.6929	+	11.6929i	−0.378968	+	0.378968i
$953$	−2.71971	+	2.71971i	−0.0881001	+	0.0881001i	−0.749783	−	0.661683i	$-0.769842\pi$
$953$	−2.71971	+	2.71971i	−0.0881001	+	0.0881001i	0.661683	+	0.749783i	$0.269842\pi$
$954$		0			0
$955$	−1.50863	+	11.0985i	−0.0488181	+	0.359138i
$956$			4.55886i			0.147444i
$957$		0			0
$958$	−7.26182	−	7.26182i	−0.234619	−	0.234619i
$959$	8.61756			0.278276
$960$		0			0
$961$	−14.3719			−0.463608
$962$	−0.380728	−	0.380728i	−0.0122752	−	0.0122752i
$963$		0			0
$964$		−	16.0621i		−	0.517325i
$965$	−4.55990	−	5.99459i	−0.146789	−	0.192973i
$966$		0			0
$967$	22.1538	−	22.1538i	0.712419	−	0.712419i	−0.254622	−	0.967041i	$-0.581951\pi$
$967$	22.1538	−	22.1538i	0.712419	−	0.712419i	0.967041	+	0.254622i	$0.0819510\pi$
$968$	8.49947	−	8.49947i	0.273183	−	0.273183i
$969$		0			0
$970$	−38.3336	−	5.21073i	−1.23082	−	0.167307i
$971$		−	31.9680i		−	1.02590i	−0.858418	−	0.512951i	$-0.828552\pi$
$971$		−	31.9680i		−	1.02590i	0.858418	−	0.512951i	$-0.171448\pi$
$972$		0			0
$973$	41.2491	+	41.2491i	1.32238	+	1.32238i
$974$	24.7795			0.793987
$975$		0			0
$976$	12.5450			0.401556
$977$	6.19265	+	6.19265i	0.198120	+	0.198120i	0.799194	−	0.601073i	$-0.205260\pi$
$977$	6.19265	+	6.19265i	0.198120	+	0.198120i	−0.601073	+	0.799194i	$0.705260\pi$
$978$		0			0
$979$			9.83521i			0.314335i
$980$	−0.0763036	−	0.0103720i	−0.00243743	−	0.000331323i
$981$		0			0
$982$	−6.28784	+	6.28784i	−0.200653	+	0.200653i
$983$	−29.8236	+	29.8236i	−0.951224	+	0.951224i	−0.998865	−	0.0476409i	$-0.984830\pi$
$983$	−29.8236	+	29.8236i	−0.951224	+	0.951224i	0.0476409	+	0.998865i	$0.484830\pi$
$984$		0			0
$985$	29.6801	+	39.0184i	0.945687	+	1.24323i
$986$			11.4745i			0.365422i
$987$		0			0
$988$	2.21122	+	2.21122i	0.0703484	+	0.0703484i
$989$	6.55342			0.208387
$990$		0			0
$991$	−13.9120			−0.441929			−0.220964	−	0.975282i	$-0.570920\pi$
$991$	−13.9120			−0.441929			−0.220964	+	0.975282i	$0.570920\pi$
$992$	−2.88341	−	2.88341i	−0.0915485	−	0.0915485i
$993$		0			0
$994$		−	27.6372i		−	0.876597i
$995$	5.56002	−	40.9032i	0.176264	−	1.29672i
$996$		0			0
$997$	−21.4033	+	21.4033i	−0.677848	+	0.677848i	−0.959513	−	0.281665i	$-0.909113\pi$
$997$	−21.4033	+	21.4033i	−0.677848	+	0.677848i	0.281665	+	0.959513i	$0.409113\pi$
$998$	20.7542	−	20.7542i	0.656963	−	0.656963i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.f.c.323.5		16
3.2	odd	2	inner	810.2.f.c.323.4		16
5.2	odd	4	inner	810.2.f.c.647.4		16
9.2	odd	6		270.2.m.b.233.1		16
9.4	even	3		270.2.m.b.143.1		16
9.5	odd	6		90.2.l.b.83.3	yes	16
9.7	even	3		90.2.l.b.23.3	✓	16
15.2	even	4	inner	810.2.f.c.647.5		16
36.7	odd	6		720.2.cu.b.113.4		16
36.23	even	6		720.2.cu.b.353.3		16
45.2	even	12		270.2.m.b.17.1		16
45.4	even	6		1350.2.q.h.143.3		16
45.7	odd	12		90.2.l.b.77.3	yes	16
45.13	odd	12		1350.2.q.h.1007.4		16
45.14	odd	6		450.2.p.h.443.2		16
45.22	odd	12		270.2.m.b.197.1		16
45.23	even	12		450.2.p.h.407.2		16
45.29	odd	6		1350.2.q.h.1043.4		16
45.32	even	12		90.2.l.b.47.3	yes	16
45.34	even	6		450.2.p.h.293.2		16
45.38	even	12		1350.2.q.h.557.3		16
45.43	odd	12		450.2.p.h.257.2		16
180.7	even	12		720.2.cu.b.257.3		16
180.167	odd	12		720.2.cu.b.497.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.3	✓	16	9.7	even	3
90.2.l.b.47.3	yes	16	45.32	even	12
90.2.l.b.77.3	yes	16	45.7	odd	12
90.2.l.b.83.3	yes	16	9.5	odd	6
270.2.m.b.17.1		16	45.2	even	12
270.2.m.b.143.1		16	9.4	even	3
270.2.m.b.197.1		16	45.22	odd	12
270.2.m.b.233.1		16	9.2	odd	6
450.2.p.h.257.2		16	45.43	odd	12
450.2.p.h.293.2		16	45.34	even	6
450.2.p.h.407.2		16	45.23	even	12
450.2.p.h.443.2		16	45.14	odd	6
720.2.cu.b.113.4		16	36.7	odd	6
720.2.cu.b.257.3		16	180.7	even	12
720.2.cu.b.353.3		16	36.23	even	6
720.2.cu.b.497.4		16	180.167	odd	12
810.2.f.c.323.4		16	3.2	odd	2	inner
810.2.f.c.323.5		16	1.1	even	1	trivial
810.2.f.c.647.4		16	5.2	odd	4	inner
810.2.f.c.647.5		16	15.2	even	4	inner
1350.2.q.h.143.3		16	45.4	even	6
1350.2.q.h.557.3		16	45.38	even	12
1350.2.q.h.1007.4		16	45.13	odd	12
1350.2.q.h.1043.4		16	45.29	odd	6

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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-2.21569 - 0.301182i) q^{5} +(1.87542 - 1.87542i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.35376 - 1.77970i) q^{10} +4.79792i q^{11} +(-0.425935 - 0.425935i) q^{13} +2.65225 q^{14} -1.00000 q^{16} +(4.40865 + 4.40865i) q^{17} +5.19145i q^{19} +(0.301182 - 2.21569i) q^{20} +(-3.39264 + 3.39264i) q^{22} +(-1.86115 + 1.86115i) q^{23} +(4.81858 + 1.33465i) q^{25} -0.602363i q^{26} +(1.87542 + 1.87542i) q^{28} +1.84040 q^{29} +4.07776 q^{31} +(-0.707107 - 0.707107i) q^{32} +6.23478i q^{34} +(-4.72021 + 3.59052i) q^{35} +(0.632057 - 0.632057i) q^{37} +(-3.67091 + 3.67091i) q^{38} +(1.77970 - 1.35376i) q^{40} +6.44958i q^{41} +(-1.76059 - 1.76059i) q^{43} -4.79792 q^{44} -2.63206 q^{46} +(-2.80140 - 2.80140i) q^{47} -0.0344378i q^{49} +(2.46351 + 4.35099i) q^{50} +(0.425935 - 0.425935i) q^{52} +(-1.31215 + 1.31215i) q^{53} +(1.44505 - 10.6307i) q^{55} +2.65225i q^{56} +(1.30136 + 1.30136i) q^{58} +0.129095 q^{59} -12.5450 q^{61} +(2.88341 + 2.88341i) q^{62} -1.00000i q^{64} +(0.815457 + 1.07203i) q^{65} +(7.80770 - 7.80770i) q^{67} +(-4.40865 + 4.40865i) q^{68} +(-5.87657 - 0.798810i) q^{70} -10.4203i q^{71} +(3.30021 + 3.30021i) q^{73} +0.893864 q^{74} -5.19145 q^{76} +(8.99814 + 8.99814i) q^{77} +4.18916i q^{79} +(2.21569 + 0.301182i) q^{80} +(-4.56054 + 4.56054i) q^{82} +(-8.13293 + 8.13293i) q^{83} +(-8.44041 - 11.0960i) q^{85} -2.48985i q^{86} +(-3.39264 - 3.39264i) q^{88} +2.04989 q^{89} -1.59762 q^{91} +(-1.86115 - 1.86115i) q^{92} -3.96178i q^{94} +(1.56357 - 11.5027i) q^{95} +(12.2336 - 12.2336i) q^{97} +(0.0243512 - 0.0243512i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{7} - 8 q^{10} - 16 q^{16} - 16 q^{22} + 32 q^{25} - 16 q^{28} + 16 q^{31} + 8 q^{40} - 32 q^{46} + 24 q^{55} - 32 q^{58} + 48 q^{61} + 32 q^{67} - 32 q^{70} + 16 q^{73} - 32 q^{76} - 16 q^{82}+ \cdots + 96 q^{97}+O(q^{100}) \) 16 * q - 16 * q^7 - 8 * q^10 - 16 * q^16 - 16 * q^22 + 32 * q^25 - 16 * q^28 + 16 * q^31 + 8 * q^40 - 32 * q^46 + 24 * q^55 - 32 * q^58 + 48 * q^61 + 32 * q^67 - 32 * q^70 + 16 * q^73 - 32 * q^76 - 16 * q^82 + 8 * q^85 - 16 * q^88 + 96 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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