LMFDB - Embedded newform 845.2.f.d.437.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(408,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("845.408");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			437.10
Root			$2.25081i$ of defining polynomial
Character	$\chi$	$=$	845.437
Dual form			845.2.f.d.408.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.25081i q^{2} +(1.40490 - 1.40490i) q^{3} -3.06613 q^{4} +(-0.247944 + 2.22228i) q^{5} +(3.16216 + 3.16216i) q^{6} +1.27718 q^{7} -2.39966i q^{8} -0.947480i q^{9} +(-5.00192 - 0.558075i) q^{10} +(-3.86239 + 3.86239i) q^{11} +(-4.30760 + 4.30760i) q^{12} +2.87469i q^{14} +(2.77374 + 3.47041i) q^{15} -0.731101 q^{16} +(2.27799 - 2.27799i) q^{17} +2.13259 q^{18} +(0.861676 - 0.861676i) q^{19} +(0.760230 - 6.81380i) q^{20} +(1.79431 - 1.79431i) q^{21} +(-8.69350 - 8.69350i) q^{22} +(0.117133 + 0.117133i) q^{23} +(-3.37127 - 3.37127i) q^{24} +(-4.87705 - 1.10200i) q^{25} +(2.88358 + 2.88358i) q^{27} -3.91601 q^{28} +9.71181i q^{29} +(-7.81123 + 6.24315i) q^{30} +(-0.233305 - 0.233305i) q^{31} -6.44488i q^{32} +10.8525i q^{33} +(5.12732 + 5.12732i) q^{34} +(-0.316670 + 2.83826i) q^{35} +2.90510i q^{36} -1.32163 q^{37} +(1.93947 + 1.93947i) q^{38} +(5.33270 + 0.594981i) q^{40} +(-0.354016 - 0.354016i) q^{41} +(4.03865 + 4.03865i) q^{42} +(4.71126 + 4.71126i) q^{43} +(11.8426 - 11.8426i) q^{44} +(2.10556 + 0.234922i) q^{45} +(-0.263643 + 0.263643i) q^{46} -3.20027 q^{47} +(-1.02712 + 1.02712i) q^{48} -5.36880 q^{49} +(2.48039 - 10.9773i) q^{50} -6.40069i q^{51} +(4.49845 - 4.49845i) q^{53} +(-6.49039 + 6.49039i) q^{54} +(-7.62565 - 9.54097i) q^{55} -3.06480i q^{56} -2.42113i q^{57} -21.8594 q^{58} +(0.00162606 + 0.00162606i) q^{59} +(-8.50465 - 10.6407i) q^{60} +1.39199 q^{61} +(0.525123 - 0.525123i) q^{62} -1.21011i q^{63} +13.0440 q^{64} -24.4270 q^{66} -6.07436i q^{67} +(-6.98462 + 6.98462i) q^{68} +0.329120 q^{69} +(-6.38837 - 0.712764i) q^{70} +(8.59633 + 8.59633i) q^{71} -2.27363 q^{72} +7.34614i q^{73} -2.97474i q^{74} +(-8.39996 + 5.30355i) q^{75} +(-2.64201 + 2.64201i) q^{76} +(-4.93298 + 4.93298i) q^{77} -11.1774i q^{79} +(0.181272 - 1.62471i) q^{80} +10.9447 q^{81} +(0.796822 - 0.796822i) q^{82} -2.65539 q^{83} +(-5.50160 + 5.50160i) q^{84} +(4.49752 + 5.62715i) q^{85} +(-10.6041 + 10.6041i) q^{86} +(13.6441 + 13.6441i) q^{87} +(9.26841 + 9.26841i) q^{88} +(5.09904 + 5.09904i) q^{89} +(-0.528764 + 4.73922i) q^{90} +(-0.359145 - 0.359145i) q^{92} -0.655538 q^{93} -7.20320i q^{94} +(1.70124 + 2.12853i) q^{95} +(-9.05440 - 9.05440i) q^{96} -4.18070i q^{97} -12.0841i q^{98} +(3.65954 + 3.65954i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{3} - 12 q^{4} - 4 q^{6} - 4 q^{7} - 8 q^{10} - 8 q^{11} - 24 q^{12} - 28 q^{15} + 4 q^{16} - 14 q^{17} - 4 q^{19} + 12 q^{20} - 4 q^{21} - 32 q^{22} + 8 q^{23} + 4 q^{24} + 18 q^{25} + 4 q^{27}+ \cdots - 60 q^{99}+O(q^{100}) $ 20 * q + 4 * q^3 - 12 * q^4 - 4 * q^6 - 4 * q^7 - 8 * q^10 - 8 * q^11 - 24 * q^12 - 28 * q^15 + 4 * q^16 - 14 * q^17 - 4 * q^19 + 12 * q^20 - 4 * q^21 - 32 * q^22 + 8 * q^23 + 4 * q^24 + 18 * q^25 + 4 * q^27 + 36 * q^28 + 40 * q^30 - 2 * q^34 - 20 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^40 + 38 * q^41 + 16 * q^42 - 32 * q^43 + 36 * q^44 + 6 * q^45 - 4 * q^46 + 40 * q^47 + 28 * q^48 - 36 * q^49 - 42 * q^50 - 10 * q^53 - 36 * q^54 - 16 * q^55 - 8 * q^59 - 28 * q^60 + 32 * q^61 + 4 * q^62 + 20 * q^64 - 32 * q^66 - 50 * q^68 + 32 * q^69 + 12 * q^70 + 40 * q^71 + 8 * q^72 + 4 * q^75 + 16 * q^76 - 28 * q^77 - 112 * q^80 + 28 * q^81 - 34 * q^82 - 48 * q^83 - 8 * q^84 + 2 * q^85 - 60 * q^86 - 28 * q^87 - 32 * q^88 - 12 * q^89 + 46 * q^90 - 8 * q^92 + 64 * q^93 + 40 * q^95 - 56 * q^96 - 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$			2.25081i			1.59156i	0.605585	+	0.795780i	$0.292939\pi$
$2$			2.25081i			1.59156i	−0.605585	+	0.795780i	$0.707061\pi$
$3$	1.40490	−	1.40490i	0.811119	−	0.811119i	−0.173683	−	0.984802i	$-0.555567\pi$
$3$	1.40490	−	1.40490i	0.811119	−	0.811119i	0.984802	+	0.173683i	$0.0555668\pi$
$4$	−3.06613			−1.53307
$5$	−0.247944	+	2.22228i	−0.110884	+	0.993833i
$5$	−0.247944	+	2.22228i	−0.110884	+	0.993833i
$6$	3.16216	+	3.16216i	1.29094	+	1.29094i
$7$	1.27718			0.482730			0.241365	−	0.970434i	$-0.422405\pi$
$7$	1.27718			0.482730			0.241365	+	0.970434i	$0.422405\pi$
$8$		−	2.39966i		−	0.848406i
$9$		−	0.947480i		−	0.315827i
$10$	−5.00192	−	0.558075i	−1.58175	−	0.176479i
$11$	−3.86239	+	3.86239i	−1.16455	+	1.16455i	−0.181088	+	0.983467i	$0.557962\pi$
$11$	−3.86239	+	3.86239i	−1.16455	+	1.16455i	−0.983467	+	0.181088i	$0.942038\pi$
$12$	−4.30760	+	4.30760i	−1.24350	+	1.24350i
$13$		0			0
$13$		0			0
$14$			2.87469i			0.768294i
$15$	2.77374	+	3.47041i	0.716177	+	0.896057i
$16$	−0.731101			−0.182775
$17$	2.27799	−	2.27799i	0.552494	−	0.552494i	−0.374666	−	0.927160i	$-0.622243\pi$
$17$	2.27799	−	2.27799i	0.552494	−	0.552494i	0.927160	+	0.374666i	$0.122243\pi$
$18$	2.13259			0.502657
$19$	0.861676	−	0.861676i	0.197682	−	0.197682i	−0.601324	−	0.799006i	$-0.705360\pi$
$19$	0.861676	−	0.861676i	0.197682	−	0.197682i	0.799006	+	0.601324i	$0.205360\pi$
$20$	0.760230	−	6.81380i	0.169993	−	1.52361i
$21$	1.79431	−	1.79431i	0.391551	−	0.391551i
$22$	−8.69350	−	8.69350i	−1.85346	−	1.85346i
$23$	0.117133	+	0.117133i	0.0244239	+	0.0244239i	0.719213	−	0.694789i	$-0.244502\pi$
$23$	0.117133	+	0.117133i	0.0244239	+	0.0244239i	−0.694789	+	0.719213i	$0.744502\pi$
$24$	−3.37127	−	3.37127i	−0.688158	−	0.688158i
$25$	−4.87705	−	1.10200i	−0.975409	−	0.220401i
$26$		0			0
$27$	2.88358	+	2.88358i	0.554946	+	0.554946i
$28$	−3.91601			−0.740057
$29$			9.71181i			1.80344i	0.432322	+	0.901719i	$0.357694\pi$
$29$			9.71181i			1.80344i	−0.432322	+	0.901719i	$0.642306\pi$
$30$	−7.81123	+	6.24315i	−1.42613	+	1.13984i
$31$	−0.233305	−	0.233305i	−0.0419027	−	0.0419027i	0.685845	−	0.727748i	$-0.259433\pi$
$31$	−0.233305	−	0.233305i	−0.0419027	−	0.0419027i	−0.727748	+	0.685845i	$0.759433\pi$
$32$		−	6.44488i		−	1.13930i
$33$			10.8525i			1.88918i
$34$	5.12732	+	5.12732i	0.879328	+	0.879328i
$35$	−0.316670	+	2.83826i	−0.0535271	+	0.479753i
$36$			2.90510i			0.484183i
$37$	−1.32163			−0.217275			−0.108638	−	0.994081i	$-0.534649\pi$
$37$	−1.32163			−0.217275			−0.108638	+	0.994081i	$0.534649\pi$
$38$	1.93947	+	1.93947i	0.314623	+	0.314623i
$39$		0			0
$40$	5.33270	+	0.594981i	0.843175	+	0.0940747i
$41$	−0.354016	−	0.354016i	−0.0552880	−	0.0552880i	0.678922	−	0.734210i	$-0.262447\pi$
$41$	−0.354016	−	0.354016i	−0.0552880	−	0.0552880i	−0.734210	+	0.678922i	$0.762447\pi$
$42$	4.03865	+	4.03865i	0.623178	+	0.623178i
$43$	4.71126	+	4.71126i	0.718460	+	0.718460i	0.968290	−	0.249830i	$-0.0803747\pi$
$43$	4.71126	+	4.71126i	0.718460	+	0.718460i	−0.249830	+	0.968290i	$0.580375\pi$
$44$	11.8426	−	11.8426i	1.78534	−	1.78534i
$45$	2.10556	+	0.234922i	0.313879	+	0.0350201i
$46$	−0.263643	+	0.263643i	−0.0388721	+	0.0388721i
$47$	−3.20027			−0.466808			−0.233404	−	0.972380i	$-0.574986\pi$
$47$	−3.20027			−0.466808			−0.233404	+	0.972380i	$0.574986\pi$
$48$	−1.02712	+	1.02712i	−0.148252	+	0.148252i
$49$	−5.36880			−0.766972
$50$	2.48039	−	10.9773i	0.350781	−	1.55242i
$51$		−	6.40069i		−	0.896276i
$52$		0			0
$53$	4.49845	−	4.49845i	0.617909	−	0.617909i	−0.327086	−	0.944995i	$-0.606067\pi$
$53$	4.49845	−	4.49845i	0.617909	−	0.617909i	0.944995	+	0.327086i	$0.106067\pi$
$54$	−6.49039	+	6.49039i	−0.883230	+	0.883230i
$55$	−7.62565	−	9.54097i	−1.02824	−	1.28650i
$56$		−	3.06480i		−	0.409551i
$57$		−	2.42113i		−	0.320687i
$58$	−21.8594			−2.87028
$59$	0.00162606	+	0.00162606i	0.000211694	+	0.000211694i	0.707213	−	0.707001i	$-0.249952\pi$
$59$	0.00162606	+	0.00162606i	0.000211694	+	0.000211694i	−0.707001	+	0.707213i	$0.749952\pi$
$60$	−8.50465	−	10.6407i	−1.09795	−	1.37371i
$61$	1.39199			0.178226			0.0891128	−	0.996022i	$-0.471597\pi$
$61$	1.39199			0.178226			0.0891128	+	0.996022i	$0.471597\pi$
$62$	0.525123	−	0.525123i	0.0666907	−	0.0666907i
$63$		−	1.21011i		−	0.152459i
$64$	13.0440			1.63050
$65$		0			0
$66$	−24.4270			−3.00675
$67$		−	6.07436i		−	0.742101i	−0.928613	−	0.371050i	$-0.878998\pi$
$67$		−	6.07436i		−	0.742101i	0.928613	−	0.371050i	$-0.121002\pi$
$68$	−6.98462	+	6.98462i	−0.847009	+	0.847009i
$69$	0.329120			0.0396213
$70$	−6.38837	−	0.712764i	−0.763557	−	0.0851916i
$71$	8.59633	+	8.59633i	1.02020	+	1.02020i	0.999792	+	0.0204050i	$0.00649556\pi$
$71$	8.59633	+	8.59633i	1.02020	+	1.02020i	0.0204050	+	0.999792i	$0.493504\pi$
$72$	−2.27363			−0.267949
$73$			7.34614i			0.859801i	0.902876	+	0.429901i	$0.141451\pi$
$73$			7.34614i			0.859801i	−0.902876	+	0.429901i	$0.858549\pi$
$74$		−	2.97474i		−	0.345806i
$75$	−8.39996	+	5.30355i	−0.969944	+	0.612402i
$76$	−2.64201	+	2.64201i	−0.303060	+	0.303060i
$77$	−4.93298	+	4.93298i	−0.562166	+	0.562166i
$78$		0			0
$79$		−	11.1774i		−	1.25756i	−0.777584	−	0.628779i	$-0.783555\pi$
$79$		−	11.1774i		−	1.25756i	0.777584	−	0.628779i	$-0.216445\pi$
$80$	0.181272	−	1.62471i	0.0202669	−	0.181648i
$81$	10.9447			1.21608
$82$	0.796822	−	0.796822i	0.0879943	−	0.0879943i
$83$	−2.65539			−0.291467			−0.145733	−	0.989324i	$-0.546554\pi$
$83$	−2.65539			−0.291467			−0.145733	+	0.989324i	$0.546554\pi$
$84$	−5.50160	+	5.50160i	−0.600274	+	0.600274i
$85$	4.49752	+	5.62715i	0.487824	+	0.610350i
$86$	−10.6041	+	10.6041i	−1.14347	+	1.14347i
$87$	13.6441	+	13.6441i	1.46280	+	1.46280i
$88$	9.26841	+	9.26841i	0.988016	+	0.988016i
$89$	5.09904	+	5.09904i	0.540497	+	0.540497i	0.923675	−	0.383178i	$-0.125170\pi$
$89$	5.09904	+	5.09904i	0.540497	+	0.540497i	−0.383178	+	0.923675i	$0.625170\pi$
$90$	−0.528764	+	4.73922i	−0.0557367	+	0.499558i
$91$		0			0
$92$	−0.359145	−	0.359145i	−0.0374434	−	0.0374434i
$93$	−0.655538			−0.0679762
$94$		−	7.20320i		−	0.742953i
$95$	1.70124	+	2.12853i	0.174543	+	0.218383i
$96$	−9.05440	−	9.05440i	−0.924111	−	0.924111i
$97$		−	4.18070i		−	0.424486i	−0.977217	−	0.212243i	$-0.931923\pi$
$97$		−	4.18070i		−	0.424486i	0.977217	−	0.212243i	$-0.0680768\pi$
$98$		−	12.0841i		−	1.22068i
$99$	3.65954	+	3.65954i	0.367797	+	0.367797i
$100$	14.9537	+	3.37888i	1.49537	+	0.337888i
$101$		−	8.62930i		−	0.858647i	−0.903151	−	0.429323i	$-0.858752\pi$
$101$		−	8.62930i		−	0.858647i	0.903151	−	0.429323i	$-0.141248\pi$
$102$	14.4067			1.42648
$103$	1.07603	+	1.07603i	0.106025	+	0.106025i	0.758129	−	0.652104i	$-0.226114\pi$
$103$	1.07603	+	1.07603i	0.106025	+	0.106025i	−0.652104	+	0.758129i	$0.726114\pi$
$104$		0			0
$105$	3.54258	+	4.43236i	0.345720	+	0.432554i
$106$	10.1251	+	10.1251i	0.983440	+	0.983440i
$107$	10.2713	+	10.2713i	0.992966	+	0.992966i	0.999975	−	0.00700981i	$-0.00223131\pi$
$107$	10.2713	+	10.2713i	0.992966	+	0.992966i	−0.00700981	+	0.999975i	$0.502231\pi$
$108$	−8.84144	−	8.84144i	−0.850768	−	0.850768i
$109$	4.72405	−	4.72405i	0.452481	−	0.452481i	−0.443696	−	0.896177i	$-0.646333\pi$
$109$	4.72405	−	4.72405i	0.452481	−	0.452481i	0.896177	+	0.443696i	$0.146333\pi$
$110$	21.4749	−	17.1639i	2.04755	−	1.63651i
$111$	−1.85676	+	1.85676i	−0.176236	+	0.176236i
$112$	−0.933751			−0.0882311
$113$	8.05734	−	8.05734i	0.757971	−	0.757971i	−0.217982	−	0.975953i	$-0.569947\pi$
$113$	8.05734	−	8.05734i	0.757971	−	0.757971i	0.975953	+	0.217982i	$0.0699474\pi$
$114$	5.44951			0.510393
$115$	−0.289344	+	0.231259i	−0.0269815	+	0.0215651i
$116$		−	29.7777i		−	2.76479i
$117$		0			0
$118$	−0.00365994	+	0.00365994i	−0.000336925	+	0.000336925i
$119$	2.90941	−	2.90941i	0.266705	−	0.266705i
$120$	8.32780	−	6.65602i	0.760220	−	0.607609i
$121$		−	18.8361i		−	1.71238i
$122$			3.13309i			0.283657i
$123$	−0.994714			−0.0896903
$124$	0.715342	+	0.715342i	0.0642396	+	0.0642396i
$125$	3.65819	−	10.5649i	0.327199	−	0.944956i
$126$	2.72372			0.242648
$127$	0.370894	−	0.370894i	0.0329115	−	0.0329115i	−0.690460	−	0.723371i	$-0.742592\pi$
$127$	0.370894	−	0.370894i	0.0329115	−	0.0329115i	0.723371	+	0.690460i	$0.242592\pi$
$128$			16.4697i			1.45573i
$129$	13.2377			1.16551
$130$		0			0
$131$	5.09883			0.445486			0.222743	−	0.974877i	$-0.428499\pi$
$131$	5.09883			0.445486			0.222743	+	0.974877i	$0.428499\pi$
$132$		−	33.2753i		−	2.89624i
$133$	1.10052	−	1.10052i	0.0954271	−	0.0954271i
$134$	13.6722			1.18110
$135$	−7.12309	+	5.69316i	−0.613058	+	0.489989i
$136$	−5.46639	−	5.46639i	−0.468739	−	0.468739i
$137$	−3.80346			−0.324952			−0.162476	−	0.986713i	$-0.551948\pi$
$137$	−3.80346			−0.324952			−0.162476	+	0.986713i	$0.551948\pi$
$138$			0.740785i			0.0630598i
$139$			1.47821i			0.125380i	0.998033	+	0.0626902i	$0.0199680\pi$
$139$			1.47821i			0.125380i	−0.998033	+	0.0626902i	$0.980032\pi$
$140$	0.970953	−	8.70248i	0.0820605	−	0.735493i
$141$	−4.49606	+	4.49606i	−0.378637	+	0.378637i
$142$	−19.3487	+	19.3487i	−1.62371	+	1.62371i
$143$		0			0
$144$			0.692704i			0.0577253i
$145$	−21.5824	−	2.40799i	−1.79232	−	0.199973i
$146$	−16.5347			−1.36843
$147$	−7.54262	+	7.54262i	−0.622105	+	0.622105i
$148$	4.05230			0.333097
$149$	12.1736	−	12.1736i	0.997302	−	0.997302i	−0.00269418	−	0.999996i	$-0.500858\pi$
$149$	12.1736	−	12.1736i	0.997302	−	0.997302i	0.999996	+	0.00269418i	$0.000857587\pi$
$150$	−11.9373	−	18.9067i	−0.974675	−	1.54372i
$151$	10.0539	−	10.0539i	0.818178	−	0.818178i	−0.167666	−	0.985844i	$-0.553623\pi$
$151$	10.0539	−	10.0539i	0.818178	−	0.818178i	0.985844	+	0.167666i	$0.0536230\pi$
$152$	−2.06773	−	2.06773i	−0.167715	−	0.167715i
$153$	−2.15835	−	2.15835i	−0.174492	−	0.174492i
$154$	−11.1032	−	11.1032i	−0.894721	−	0.894721i
$155$	0.576314	−	0.460621i	0.0462907	−	0.0369980i
$156$		0			0
$157$	3.07230	+	3.07230i	0.245196	+	0.245196i	0.818996	−	0.573799i	$-0.194531\pi$
$157$	3.07230	+	3.07230i	0.245196	+	0.245196i	−0.573799	+	0.818996i	$0.694531\pi$
$158$	25.1582			2.00148
$159$		−	12.6397i		−	1.00240i
$160$	14.3223	+	1.59797i	1.13228	+	0.126331i
$161$	0.149600	+	0.149600i	0.0117902	+	0.0117902i
$162$			24.6345i			1.93547i
$163$			9.20501i			0.720992i	0.932761	+	0.360496i	$0.117393\pi$
$163$			9.20501i			0.720992i	−0.932761	+	0.360496i	$0.882607\pi$
$164$	1.08546	+	1.08546i	0.0847602	+	0.0847602i
$165$	−24.1174	−	2.69082i	−1.87753	−	0.209480i
$166$		−	5.97677i		−	0.463887i
$167$	12.6387			0.978014			0.489007	−	0.872280i	$-0.337359\pi$
$167$	12.6387			0.978014			0.489007	+	0.872280i	$0.337359\pi$
$168$	−4.30574	−	4.30574i	−0.332195	−	0.332195i
$169$		0			0
$170$	−12.6656	+	10.1230i	−0.971409	+	0.776402i
$171$	−0.816421	−	0.816421i	−0.0624333	−	0.0624333i
$172$	−14.4453	−	14.4453i	−1.10145	−	1.10145i
$173$	9.69831	+	9.69831i	0.737349	+	0.737349i	0.972064	−	0.234716i	$-0.0754159\pi$
$173$	9.69831	+	9.69831i	0.737349	+	0.737349i	−0.234716	+	0.972064i	$0.575416\pi$
$174$	−30.7103	+	30.7103i	−2.32814	+	2.32814i
$175$	−6.22889	−	1.40746i	−0.470860	−	0.106394i
$176$	2.82380	−	2.82380i	0.212852	−	0.212852i
$177$	0.00456889			0.000343419
$178$	−11.4770	+	11.4770i	−0.860234	+	0.860234i
$179$	12.6425			0.944946			0.472473	−	0.881345i	$-0.343361\pi$
$179$	12.6425			0.944946			0.472473	+	0.881345i	$0.343361\pi$
$180$	−6.45594	−	0.720302i	−0.481197	−	0.0536882i
$181$		−	8.16619i		−	0.606988i	−0.952833	−	0.303494i	$-0.901847\pi$
$181$		−	8.16619i		−	0.606988i	0.952833	−	0.303494i	$-0.0981533\pi$
$182$		0			0
$183$	1.95560	−	1.95560i	0.144562	−	0.144562i
$184$	0.281079	−	0.281079i	0.0207214	−	0.0207214i
$185$	0.327691	−	2.93704i	0.0240923	−	0.215935i
$186$		−	1.47549i		−	0.108188i
$187$			17.5970i			1.28682i
$188$	9.81246			0.715647
$189$	3.68287	+	3.68287i	0.267889	+	0.267889i
$190$	−4.79091	+	3.82916i	−0.347569	+	0.277796i
$191$	−14.7538			−1.06755			−0.533775	−	0.845626i	$-0.679227\pi$
$191$	−14.7538			−1.06755			−0.533775	+	0.845626i	$0.679227\pi$
$192$	18.3255	−	18.3255i	1.32253	−	1.32253i
$193$		−	15.0969i		−	1.08670i	−0.839507	−	0.543349i	$-0.817156\pi$
$193$		−	15.0969i		−	1.08670i	0.839507	−	0.543349i	$-0.182844\pi$
$194$	9.40995			0.675595
$195$		0			0
$196$	16.4614			1.17582
$197$			15.3715i			1.09518i	0.836748	+	0.547588i	$0.184454\pi$
$197$			15.3715i			1.09518i	−0.836748	+	0.547588i	$0.815546\pi$
$198$	−8.23691	+	8.23691i	−0.585372	+	0.585372i
$199$	−11.4562			−0.812109			−0.406054	−	0.913849i	$-0.633096\pi$
$199$	−11.4562			−0.812109			−0.406054	+	0.913849i	$0.633096\pi$
$200$	−2.64443	+	11.7032i	−0.186989	+	0.827544i
$201$	−8.53385	−	8.53385i	−0.601932	−	0.601932i
$202$	19.4229			1.36659
$203$			12.4038i			0.870574i
$204$			19.6254i			1.37405i
$205$	0.874499	−	0.698946i	0.0610777	−	0.0488165i
$206$	−2.42194	+	2.42194i	−0.168745	+	0.168745i
$207$	0.110981	−	0.110981i	0.00771372	−	0.00771372i
$208$		0			0
$209$			6.65626i			0.460423i
$210$	−9.97638	+	7.97366i	−0.688435	+	0.550234i
$211$	3.18391			0.219189			0.109595	−	0.993976i	$-0.465045\pi$
$211$	3.18391			0.219189			0.109595	+	0.993976i	$0.465045\pi$
$212$	−13.7928	+	13.7928i	−0.947295	+	0.947295i
$213$	24.1539			1.65500
$214$	−23.1187	+	23.1187i	−1.58037	+	1.58037i
$215$	−11.6379	+	9.30159i	−0.793695	+	0.634363i
$216$	6.91961	−	6.91961i	0.470820	−	0.470820i
$217$	−0.297973	−	0.297973i	−0.0202277	−	0.0202277i
$218$	10.6329	+	10.6329i	0.720152	+	0.720152i
$219$	10.3206	+	10.3206i	0.697401	+	0.697401i
$220$	23.3813	+	29.2539i	1.57636	+	1.97230i
$221$		0			0
$222$	−4.17921	−	4.17921i	−0.280490	−	0.280490i
$223$	11.8775			0.795375			0.397688	−	0.917521i	$-0.369813\pi$
$223$	11.8775			0.795375			0.397688	+	0.917521i	$0.369813\pi$
$224$		−	8.23130i		−	0.549977i
$225$	−1.04413	+	4.62090i	−0.0696084	+	0.308060i
$226$	18.1355	+	18.1355i	1.20636	+	1.20636i
$227$			27.6666i			1.83630i	0.396236	+	0.918149i	$0.370316\pi$
$227$			27.6666i			1.83630i	−0.396236	+	0.918149i	$0.629684\pi$
$228$			7.42352i			0.491634i
$229$	−12.9000	−	12.9000i	−0.852455	−	0.852455i	0.137980	−	0.990435i	$-0.455939\pi$
$229$	−12.9000	−	12.9000i	−0.852455	−	0.852455i	−0.990435	+	0.137980i	$0.955939\pi$
$230$	−0.520520	−	0.651258i	−0.0343221	−	0.0429427i
$231$			13.8607i			0.911966i
$232$	23.3050			1.53005
$233$	−16.3545	−	16.3545i	−1.07142	−	1.07142i	−0.997246	−	0.0741712i	$-0.976369\pi$
$233$	−16.3545	−	16.3545i	−1.07142	−	1.07142i	−0.0741712	−	0.997246i	$-0.523631\pi$
$234$		0			0
$235$	0.793489	−	7.11190i	0.0517615	−	0.463929i
$236$	−0.00498570	−	0.00498570i	−0.000324541	−	0.000324541i
$237$	−15.7031	−	15.7031i	−1.02003	−	1.02003i
$238$	6.54853	+	6.54853i	0.424478	+	0.424478i
$239$	2.61794	−	2.61794i	0.169341	−	0.169341i	−0.617349	−	0.786690i	$-0.711793\pi$
$239$	2.61794	−	2.61794i	0.169341	−	0.169341i	0.786690	+	0.617349i	$0.211793\pi$
$240$	−2.02788	−	2.53722i	−0.130899	−	0.163777i
$241$	−14.7152	+	14.7152i	−0.947888	+	0.947888i	−0.998708	−	0.0508198i	$-0.983817\pi$
$241$	−14.7152	+	14.7152i	−0.947888	+	0.947888i	0.0508198	+	0.998708i	$0.483817\pi$
$242$	42.3965			2.72535
$243$	6.72548	−	6.72548i	0.431439	−	0.431439i
$244$	−4.26801			−0.273232
$245$	1.33116	−	11.9310i	0.0850449	−	0.762242i
$246$		−	2.23891i		−	0.142748i
$247$		0			0
$248$	−0.559851	+	0.559851i	−0.0355505	+	0.0355505i
$249$	−3.73055	+	3.73055i	−0.236414	+	0.236414i
$250$	23.7796	+	8.23389i	1.50395	+	0.520757i
$251$			2.36772i			0.149449i	0.997204	+	0.0747245i	$0.0238078\pi$
$251$			2.36772i			0.149449i	−0.997204	+	0.0747245i	$0.976192\pi$
$252$			3.71034i			0.233730i
$253$	−0.904826			−0.0568859
$254$	0.834811	+	0.834811i	0.0523807	+	0.0523807i
$255$	14.2241	+	1.58701i	0.890749	+	0.0993827i
$256$	−10.9822			−0.686387
$257$	−0.615209	+	0.615209i	−0.0383757	+	0.0383757i	−0.726034	−	0.687659i	$-0.758639\pi$
$257$	−0.615209	+	0.615209i	−0.0383757	+	0.0383757i	0.687659	+	0.726034i	$0.258639\pi$
$258$			29.7954i			1.85498i
$259$	−1.68797			−0.104885
$260$		0			0
$261$	9.20175			0.569574
$262$			11.4765i			0.709019i
$263$	−10.7397	+	10.7397i	−0.662236	+	0.662236i	−0.955907	−	0.293670i	$-0.905123\pi$
$263$	−10.7397	+	10.7397i	−0.662236	+	0.662236i	0.293670	+	0.955907i	$0.405123\pi$
$264$	26.0424			1.60280
$265$	8.88144	+	11.1122i	0.545582	+	0.682615i
$266$	2.47706	+	2.47706i	0.151878	+	0.151878i
$267$	14.3273			0.876814
$268$			18.6248i			1.13769i
$269$		−	24.3816i		−	1.48657i	−0.668975	−	0.743285i	$-0.733267\pi$
$269$		−	24.3816i		−	1.48657i	0.668975	−	0.743285i	$-0.266733\pi$
$270$	−12.8142	−	16.0327i	−0.779847	−	0.975719i
$271$	−9.27487	+	9.27487i	−0.563408	+	0.563408i	−0.930274	−	0.366866i	$-0.880431\pi$
$271$	−9.27487	+	9.27487i	−0.563408	+	0.563408i	0.366866	+	0.930274i	$0.380431\pi$
$272$	−1.66544	+	1.66544i	−0.100982	+	0.100982i
$273$		0			0
$274$		−	8.56086i		−	0.517181i
$275$	23.0934	−	14.5807i	1.39259	−	0.879249i
$276$	−1.00912			−0.0607421
$277$	8.64616	−	8.64616i	0.519498	−	0.519498i	−0.397922	−	0.917419i	$-0.630268\pi$
$277$	8.64616	−	8.64616i	0.519498	−	0.519498i	0.917419	+	0.397922i	$0.130268\pi$
$278$	−3.32717			−0.199550
$279$	−0.221051	+	0.221051i	−0.0132340	+	0.0132340i
$280$	6.81085	+	0.759900i	0.407026	+	0.0454127i
$281$	6.43529	−	6.43529i	0.383897	−	0.383897i	−0.488607	−	0.872504i	$-0.662495\pi$
$281$	6.43529	−	6.43529i	0.383897	−	0.383897i	0.872504	+	0.488607i	$0.162495\pi$
$282$	−10.1198	−	10.1198i	−0.602623	−	0.602623i
$283$	19.3416	+	19.3416i	1.14974	+	1.14974i	0.986603	+	0.163137i	$0.0521613\pi$
$283$	19.3416	+	19.3416i	1.14974	+	1.14974i	0.163137	+	0.986603i	$0.447839\pi$
$284$	−26.3575	−	26.3575i	−1.56403	−	1.56403i
$285$	5.38044	+	0.600307i	0.318710	+	0.0355591i
$286$		0			0
$287$	−0.452144	−	0.452144i	−0.0266892	−	0.0266892i
$288$	−6.10639			−0.359823
$289$			6.62152i			0.389501i
$290$	5.41992	−	48.5777i	0.318268	−	2.85258i
$291$	−5.87346	−	5.87346i	−0.344308	−	0.344308i
$292$		−	22.5242i		−	1.31813i
$293$		−	26.1241i		−	1.52618i	−0.646289	−	0.763092i	$-0.723680\pi$
$293$		−	26.1241i		−	1.52618i	0.646289	−	0.763092i	$-0.276320\pi$
$294$	−16.9770	−	16.9770i	−0.990118	−	0.990118i
$295$	−0.00401672	+	0.00321038i	−0.000233863	+	0.000186915i
$296$			3.17146i			0.184338i
$297$	−22.2750			−1.29253
$298$	27.4005	+	27.4005i	1.58727	+	1.58727i
$299$		0			0
$300$	25.7554	−	16.2614i	1.48699	−	0.938852i
$301$	6.01714	+	6.01714i	0.346822	+	0.346822i
$302$	22.6295	+	22.6295i	1.30218	+	1.30218i
$303$	−12.1233	−	12.1233i	−0.696464	−	0.696464i
$304$	−0.629972	+	0.629972i	−0.0361314	+	0.0361314i
$305$	−0.345135	+	3.09338i	−0.0197624	+	0.177127i
$306$	4.85803	−	4.85803i	0.277715	−	0.277715i
$307$	−14.7038			−0.839189			−0.419595	−	0.907712i	$-0.637828\pi$
$307$	−14.7038			−0.839189			−0.419595	+	0.907712i	$0.637828\pi$
$308$	15.1252	−	15.1252i	0.861837	−	0.861837i
$309$	3.02343			0.171997
$310$	1.03677	+	1.29717i	0.0588845	+	0.0736744i
$311$			31.8525i			1.80619i	0.429440	+	0.903095i	$0.358711\pi$
$311$			31.8525i			1.80619i	−0.429440	+	0.903095i	$0.641289\pi$
$312$		0			0
$313$	−11.9865	+	11.9865i	−0.677519	+	0.677519i	−0.959438	−	0.281919i	$-0.909029\pi$
$313$	−11.9865	+	11.9865i	−0.677519	+	0.677519i	0.281919	+	0.959438i	$0.409029\pi$
$314$	−6.91516	+	6.91516i	−0.390245	+	0.390245i
$315$	2.68919	+	0.300039i	0.151519	+	0.0169053i
$316$			34.2714i			1.92792i
$317$		−	15.5627i		−	0.874088i	−0.899440	−	0.437044i	$-0.856025\pi$
$317$		−	15.5627i		−	0.874088i	0.899440	−	0.437044i	$-0.143975\pi$
$318$	28.4496			1.59537
$319$	−37.5108	−	37.5108i	−2.10020	−	2.10020i
$320$	−3.23418	+	28.9874i	−0.180796	+	1.62044i
$321$	28.8603			1.61083
$322$	−0.336721	+	0.336721i	−0.0187647	+	0.0187647i
$323$		−	3.92578i		−	0.218436i
$324$	−33.5580			−1.86433
$325$		0			0
$326$	−20.7187			−1.14750
$327$		−	13.2736i		−	0.734032i
$328$	−0.849517	+	0.849517i	−0.0469067	+	0.0469067i
$329$	−4.08734			−0.225342
$330$	6.05653	−	54.2835i	0.333401	−	2.98821i
$331$	−12.0656	−	12.0656i	−0.663187	−	0.663187i	0.292943	−	0.956130i	$-0.405365\pi$
$331$	−12.0656	−	12.0656i	−0.663187	−	0.663187i	−0.956130	+	0.292943i	$0.905365\pi$
$332$	8.14177			0.446838
$333$			1.25222i			0.0686212i
$334$			28.4473i			1.55657i
$335$	13.4989	+	1.50610i	0.737524	+	0.0822871i
$336$	−1.31182	+	1.31182i	−0.0715659	+	0.0715659i
$337$	25.0560	−	25.0560i	1.36489	−	1.36489i	0.497319	−	0.867568i	$-0.334318\pi$
$337$	25.0560	−	25.0560i	1.36489	−	1.36489i	0.867568	−	0.497319i	$-0.165682\pi$
$338$		0			0
$339$		−	22.6395i		−	1.22961i
$340$	−13.7900	−	17.2536i	−0.747866	−	0.935706i
$341$	1.80223			0.0975961
$342$	1.83761	−	1.83761i	0.0993663	−	0.0993663i
$343$	−15.7972			−0.852971
$344$	11.3054	−	11.3054i	0.609546	−	0.609546i
$345$	−0.0816033	+	0.731396i	−0.00439337	+	0.0393770i
$346$	−21.8290	+	21.8290i	−1.17354	+	1.17354i
$347$	9.12161	+	9.12161i	0.489674	+	0.489674i	0.908203	−	0.418529i	$-0.137454\pi$
$347$	9.12161	+	9.12161i	0.489674	+	0.489674i	−0.418529	+	0.908203i	$0.637454\pi$
$348$	−41.8346	−	41.8346i	−2.24257	−	2.24257i
$349$	18.9866	+	18.9866i	1.01633	+	1.01633i	0.999864	+	0.0164642i	$0.00524094\pi$
$349$	18.9866	+	18.9866i	1.01633	+	1.01633i	0.0164642	+	0.999864i	$0.494759\pi$
$350$	3.16792	−	14.0200i	0.169332	−	0.749402i
$351$		0			0
$352$	24.8926	+	24.8926i	1.32678	+	1.32678i
$353$	−23.3117			−1.24076			−0.620378	−	0.784303i	$-0.713021\pi$
$353$	−23.3117			−1.24076			−0.620378	+	0.784303i	$0.713021\pi$
$354$			0.0102837i			0.000546571i
$355$	−21.2349	+	16.9720i	−1.12703	+	0.900782i
$356$	−15.6343	−	15.6343i	−0.828617	−	0.828617i
$357$		−	8.17486i		−	0.432660i
$358$			28.4559i			1.50394i
$359$	−9.17222	−	9.17222i	−0.484091	−	0.484091i	0.422344	−	0.906435i	$-0.361207\pi$
$359$	−9.17222	−	9.17222i	−0.484091	−	0.484091i	−0.906435	+	0.422344i	$0.861207\pi$
$360$	0.563732	−	5.05263i	0.0297113	−	0.266297i
$361$			17.5150i			0.921844i
$362$	18.3805			0.966059
$363$	−26.4629	−	26.4629i	−1.38894	−	1.38894i
$364$		0			0
$365$	−16.3252	−	1.82143i	−0.854499	−	0.0953382i
$366$	4.40168	+	4.40168i	0.230079	+	0.230079i
$367$	10.5124	+	10.5124i	0.548741	+	0.548741i	0.926077	−	0.377335i	$-0.123160\pi$
$367$	10.5124	+	10.5124i	0.548741	+	0.548741i	−0.377335	+	0.926077i	$0.623160\pi$
$368$	−0.0856360	−	0.0856360i	−0.00446408	−	0.00446408i
$369$	−0.335423	+	0.335423i	−0.0174614	+	0.0174614i
$370$	6.61070	+	0.737570i	0.343674	+	0.0383444i
$371$	5.74534	−	5.74534i	0.298283	−	0.298283i
$372$	2.00997			0.104212
$373$	4.37075	−	4.37075i	0.226309	−	0.226309i	−0.584840	−	0.811149i	$-0.698843\pi$
$373$	4.37075	−	4.37075i	0.226309	−	0.226309i	0.811149	+	0.584840i	$0.198843\pi$
$374$	−39.6074			−2.04805
$375$	−9.70326	−	19.9820i	−0.501074	−	1.03187i
$376$			7.67955i			0.396043i
$377$		0			0
$378$	−8.28942	+	8.28942i	−0.426362	+	0.426362i
$379$	12.9181	−	12.9181i	0.663556	−	0.663556i	−0.292660	−	0.956216i	$-0.594540\pi$
$379$	12.9181	−	12.9181i	0.663556	−	0.663556i	0.956216	+	0.292660i	$0.0945405\pi$
$380$	−5.21622	−	6.52636i	−0.267586	−	0.334795i
$381$		−	1.04214i		−	0.0533903i
$382$		−	33.2081i		−	1.69907i
$383$	−10.2434			−0.523414			−0.261707	−	0.965147i	$-0.584285\pi$
$383$	−10.2434			−0.523414			−0.261707	+	0.965147i	$0.584285\pi$
$384$	23.1383	+	23.1383i	1.18077	+	1.18077i
$385$	−9.73936	−	12.1856i	−0.496364	−	0.621034i
$386$	33.9802			1.72955
$387$	4.46382	−	4.46382i	0.226909	−	0.226909i
$388$			12.8186i			0.650765i
$389$	−3.41200			−0.172995			−0.0864977	−	0.996252i	$-0.527568\pi$
$389$	−3.41200			−0.172995			−0.0864977	+	0.996252i	$0.527568\pi$
$390$		0			0
$391$	0.533655			0.0269881
$392$			12.8833i			0.650704i
$393$	7.16333	−	7.16333i	0.361342	−	0.361342i
$394$	−34.5983			−1.74304
$395$	24.8393	+	2.77138i	1.24980	+	0.139443i
$396$	−11.2206	−	11.2206i	−0.563858	−	0.563858i
$397$	11.9321			0.598853			0.299426	−	0.954119i	$-0.403205\pi$
$397$	11.9321			0.598853			0.299426	+	0.954119i	$0.403205\pi$
$398$		−	25.7857i		−	1.29252i
$399$		−	3.09223i		−	0.154805i
$400$	3.56561	+	0.805675i	0.178281	+	0.0402838i
$401$	2.88224	−	2.88224i	0.143932	−	0.143932i	−0.631469	−	0.775401i	$-0.717548\pi$
$401$	2.88224	−	2.88224i	0.143932	−	0.143932i	0.775401	+	0.631469i	$0.217548\pi$
$402$	19.2081	−	19.2081i	0.958011	−	0.958011i
$403$		0			0
$404$			26.4586i			1.31636i
$405$	−2.71368	+	24.3222i	−0.134844	+	1.20858i
$406$	−27.9185			−1.38557
$407$	5.10466	−	5.10466i	0.253029	−	0.253029i
$408$	−15.3595			−0.760406
$409$	4.90669	−	4.90669i	0.242620	−	0.242620i	−0.575313	−	0.817933i	$-0.695120\pi$
$409$	4.90669	−	4.90669i	0.242620	−	0.242620i	0.817933	+	0.575313i	$0.195120\pi$
$410$	1.57319	+	1.96833i	0.0776945	+	0.0972088i
$411$	−5.34348	+	5.34348i	−0.263574	+	0.263574i
$412$	−3.29926	−	3.29926i	−0.162543	−	0.162543i
$413$	0.00207677	+	0.00207677i	0.000102191	+	0.000102191i
$414$	0.249797	+	0.249797i	0.0122768	+	0.0122768i
$415$	0.658389	−	5.90102i	0.0323190	−	0.289670i
$416$		0			0
$417$	2.07674	+	2.07674i	0.101698	+	0.101698i
$418$	−14.9820			−0.732791
$419$		−	21.2287i		−	1.03709i	−0.855050	−	0.518546i	$-0.826474\pi$
$419$		−	21.2287i		−	1.03709i	0.855050	−	0.518546i	$-0.173526\pi$
$420$	−10.8620	−	13.5902i	−0.530012	−	0.663133i
$421$	3.15727	+	3.15727i	0.153876	+	0.153876i	0.779847	−	0.625971i	$-0.215297\pi$
$421$	3.15727	+	3.15727i	0.153876	+	0.153876i	−0.625971	+	0.779847i	$0.715297\pi$
$422$			7.16636i			0.348853i
$423$			3.03219i			0.147430i
$424$	−10.7947	−	10.7947i	−0.524238	−	0.524238i
$425$	−13.6202	+	8.59952i	−0.660678	+	0.417138i
$426$			54.3659i			2.63403i
$427$	1.77782			0.0860349
$428$	−31.4932	−	31.4932i	−1.52228	−	1.52228i
$429$		0			0
$430$	−20.9361	−	26.1946i	−1.00963	−	1.26321i
$431$	−25.3455	−	25.3455i	−1.22085	−	1.22085i	−0.967330	−	0.253522i	$-0.918411\pi$
$431$	−25.3455	−	25.3455i	−1.22085	−	1.22085i	−0.253522	−	0.967330i	$-0.581589\pi$
$432$	−2.10819	−	2.10819i	−0.101430	−	0.101430i
$433$	−5.72268	−	5.72268i	−0.275014	−	0.275014i	0.556101	−	0.831115i	$-0.312297\pi$
$433$	−5.72268	−	5.72268i	−0.275014	−	0.275014i	−0.831115	+	0.556101i	$0.812297\pi$
$434$	0.670679	−	0.670679i	0.0321936	−	0.0321936i
$435$	−33.7040	+	26.9380i	−1.61598	+	1.29158i
$436$	−14.4845	+	14.4845i	−0.693684	+	0.693684i
$437$	0.201861			0.00965633
$438$	−23.2296	+	23.2296i	−1.10996	+	1.10996i
$439$	−28.6671			−1.36821			−0.684104	−	0.729384i	$-0.739807\pi$
$439$	−28.6671			−1.36821			−0.684104	+	0.729384i	$0.739807\pi$
$440$	−22.8950	+	18.2989i	−1.09148	+	0.872368i
$441$			5.08683i			0.242230i
$442$		0			0
$443$	−17.1586	+	17.1586i	−0.815229	+	0.815229i	−0.985412	−	0.170184i	$-0.945564\pi$
$443$	−17.1586	+	17.1586i	−0.815229	+	0.815229i	0.170184	+	0.985412i	$0.445564\pi$
$444$	5.69307	−	5.69307i	0.270181	−	0.270181i
$445$	−12.5958	+	10.0672i	−0.597096	+	0.477231i
$446$			26.7339i			1.26589i
$447$		−	34.2054i		−	1.61786i
$448$	16.6596			0.787090
$449$	6.48150	+	6.48150i	0.305881	+	0.305881i	0.843309	−	0.537428i	$-0.180604\pi$
$449$	6.48150	+	6.48150i	0.305881	+	0.305881i	−0.537428	+	0.843309i	$0.680604\pi$
$450$	−10.4008	−	2.35012i	−0.490297	−	0.110786i
$451$	2.73470			0.128772
$452$	−24.7049	+	24.7049i	−1.16202	+	1.16202i
$453$		−	28.2495i		−	1.32728i
$454$	−62.2722			−2.92258
$455$		0			0
$456$	−5.80989			−0.272073
$457$			21.4798i			1.00478i	0.864640	+	0.502391i	$0.167546\pi$
$457$			21.4798i			1.00478i	−0.864640	+	0.502391i	$0.832454\pi$
$458$	29.0354	−	29.0354i	1.35673	−	1.35673i
$459$	13.1375			0.613208
$460$	0.887168	−	0.709072i	0.0413644	−	0.0330607i
$461$	−3.59137	−	3.59137i	−0.167267	−	0.167267i	0.618510	−	0.785777i	$-0.287737\pi$
$461$	−3.59137	−	3.59137i	−0.167267	−	0.167267i	−0.785777	+	0.618510i	$0.787737\pi$
$462$	−31.1977			−1.45145
$463$		−	20.0793i		−	0.933163i	−0.884478	−	0.466581i	$-0.845485\pi$
$463$		−	20.0793i		−	0.933163i	0.884478	−	0.466581i	$-0.154515\pi$
$464$		−	7.10032i		−	0.329624i
$465$	0.162537	−	1.45679i	0.00753747	−	0.0675570i
$466$	36.8107	−	36.8107i	1.70522	−	1.70522i
$467$	−21.4507	+	21.4507i	−0.992618	+	0.992618i	−0.999973	−	0.00735447i	$-0.997659\pi$
$467$	−21.4507	+	21.4507i	−0.992618	+	0.992618i	0.00735447	+	0.999973i	$0.497659\pi$
$468$		0			0
$469$		−	7.75807i		−	0.358234i
$470$	16.0075	+	1.78599i	0.738372	+	0.0823816i
$471$	8.63254			0.397767
$472$	0.00390197	−	0.00390197i	0.000179603	−	0.000179603i
$473$	−36.3934			−1.67337
$474$	35.3447	−	35.3447i	1.62344	−	1.62344i
$475$	−5.15200	+	3.25287i	−0.236390	+	0.149252i
$476$	−8.92064	+	8.92064i	−0.408877	+	0.408877i
$477$	−4.26219	−	4.26219i	−0.195152	−	0.195152i
$478$	5.89248	+	5.89248i	0.269516	+	0.269516i
$479$	−21.9979	−	21.9979i	−1.00511	−	1.00511i	−0.999987	−	0.00512249i	$-0.998369\pi$
$479$	−21.9979	−	21.9979i	−1.00511	−	1.00511i	−0.00512249	−	0.999987i	$-0.501631\pi$
$480$	22.3664	−	17.8764i	1.02088	−	0.815943i
$481$		0			0
$482$	−33.1210	−	33.1210i	−1.50862	−	1.50862i
$483$	0.420346			0.0191264
$484$			57.7541i			2.62518i
$485$	9.29068	+	1.03658i	0.421868	+	0.0470687i
$486$	15.1377	+	15.1377i	0.686662	+	0.686662i
$487$		−	19.4316i		−	0.880529i	−0.897868	−	0.440264i	$-0.854885\pi$
$487$		−	19.4316i		−	0.880529i	0.897868	−	0.440264i	$-0.145115\pi$
$488$		−	3.34029i		−	0.151208i
$489$	12.9321	+	12.9321i	0.584810	+	0.584810i
$490$	26.8543	+	2.99619i	1.21315	+	0.135354i
$491$		−	35.3136i		−	1.59368i	−0.604191	−	0.796839i	$-0.706504\pi$
$491$		−	35.3136i		−	1.59368i	0.604191	−	0.796839i	$-0.293496\pi$
$492$	3.04992			0.137501
$493$	22.1234	+	22.1234i	0.996389	+	0.996389i
$494$		0			0
$495$	−9.03988	+	7.22515i	−0.406312	+	0.324746i
$496$	0.170569	+	0.170569i	0.00765878	+	0.00765878i
$497$	10.9791	+	10.9791i	0.492480	+	0.492480i
$498$	−8.39676	−	8.39676i	−0.376268	−	0.376268i
$499$	9.44430	−	9.44430i	0.422785	−	0.422785i	−0.463377	−	0.886161i	$-0.653362\pi$
$499$	9.44430	−	9.44430i	0.422785	−	0.422785i	0.886161	+	0.463377i	$0.153362\pi$
$500$	−11.2165	+	32.3934i	−0.501617	+	1.44868i
$501$	17.7561	−	17.7561i	0.793285	−	0.793285i
$502$	−5.32928			−0.237857
$503$	−17.0606	+	17.0606i	−0.760693	+	0.760693i	−0.976448	−	0.215754i	$-0.930779\pi$
$503$	−17.0606	+	17.0606i	−0.760693	+	0.760693i	0.215754	+	0.976448i	$0.430779\pi$
$504$	−2.90384			−0.129347
$505$	19.1767	+	2.13958i	0.853352	+	0.0952102i
$506$		−	2.03659i		−	0.0905374i
$507$		0			0
$508$	−1.13721	+	1.13721i	−0.0504555	+	0.0504555i
$509$	2.63199	−	2.63199i	0.116661	−	0.116661i	−0.646366	−	0.763027i	$-0.723712\pi$
$509$	2.63199	−	2.63199i	0.116661	−	0.116661i	0.763027	+	0.646366i	$0.223712\pi$
$510$	−3.57206	+	32.0158i	−0.158174	+	1.41768i
$511$			9.38238i			0.415052i
$512$			8.22064i			0.363304i
$513$	4.96943			0.219406
$514$	−1.38472	−	1.38472i	−0.0610772	−	0.0610772i
$515$	−2.65804	+	2.12445i	−0.117127	+	0.0936144i
$516$	−40.5884			−1.78681
$517$	12.3607	−	12.3607i	0.543623	−	0.543623i
$518$		−	3.79929i		−	0.166931i
$519$	27.2503			1.19615
$520$		0			0
$521$	45.2323			1.98166			0.990832	−	0.135103i	$-0.0431364\pi$
$521$	45.2323			1.98166			0.990832	+	0.135103i	$0.0431364\pi$
$522$			20.7114i			0.906511i
$523$	0.807155	−	0.807155i	0.0352944	−	0.0352944i	−0.689239	−	0.724534i	$-0.742055\pi$
$523$	0.807155	−	0.807155i	0.0352944	−	0.0352944i	0.724534	+	0.689239i	$0.242055\pi$
$524$	−15.6337			−0.682960
$525$	−10.7283	+	6.77362i	−0.468221	+	0.295625i
$526$	−24.1729	−	24.1729i	−1.05399	−	1.05399i
$527$	−1.06293			−0.0463020
$528$		−	7.93430i		−	0.345296i
$529$		−	22.9726i		−	0.998807i
$530$	−25.0113	+	19.9904i	−1.08642	+	0.868328i
$531$	0.00154066	−	0.00154066i	6.68587e−5	−	6.68587e-5i
$532$	−3.37434	+	3.37434i	−0.146296	+	0.146296i
$533$		0			0
$534$			32.2479i			1.39550i
$535$	−25.3724	+	20.2790i	−1.09695	+	0.876738i
$536$	−14.5764			−0.629603
$537$	17.7615	−	17.7615i	0.766463	−	0.766463i
$538$	54.8782			2.36597
$539$	20.7364	−	20.7364i	0.893180	−	0.893180i
$540$	21.8403	−	17.4560i	0.939858	−	0.751185i
$541$	−22.3573	+	22.3573i	−0.961218	+	0.961218i	−0.999276	−	0.0380580i	$-0.987883\pi$
$541$	−22.3573	+	22.3573i	−0.961218	+	0.961218i	0.0380580	+	0.999276i	$0.487883\pi$
$542$	−20.8759	−	20.8759i	−0.896698	−	0.896698i
$543$	−11.4727	−	11.4727i	−0.492339	−	0.492339i
$544$	−14.6814	−	14.6814i	−0.629459	−	0.629459i
$545$	9.32685	+	11.6694i	0.399518	+	0.499864i
$546$		0			0
$547$	−5.20384	−	5.20384i	−0.222500	−	0.222500i	0.587050	−	0.809550i	$-0.300289\pi$
$547$	−5.20384	−	5.20384i	−0.222500	−	0.222500i	−0.809550	+	0.587050i	$0.800289\pi$
$548$	11.6619			0.498173
$549$		−	1.31888i		−	0.0562884i
$550$	32.8183	+	51.9789i	1.39938	+	2.21639i
$551$	8.36844	+	8.36844i	0.356507	+	0.356507i
$552$		−	0.789774i		−	0.0336150i
$553$		−	14.2756i		−	0.607061i
$554$	19.4608	+	19.4608i	0.826812	+	0.826812i
$555$	−3.66586	−	4.58661i	−0.155607	−	0.194691i
$556$		−	4.53239i		−	0.192216i
$557$	−6.58643			−0.279076			−0.139538	−	0.990217i	$-0.544562\pi$
$557$	−6.58643			−0.279076			−0.139538	+	0.990217i	$0.544562\pi$
$558$	−0.497544	−	0.497544i	−0.0210627	−	0.0210627i
$559$		0			0
$560$	0.231518	−	2.07505i	0.00978343	−	0.0876871i
$561$	24.7220	+	24.7220i	1.04376	+	1.04376i
$562$	14.4846	+	14.4846i	0.610996	+	0.610996i
$563$	−20.7568	−	20.7568i	−0.874794	−	0.874794i	0.118197	−	0.992990i	$-0.462289\pi$
$563$	−20.7568	−	20.7568i	−0.874794	−	0.874794i	−0.992990	+	0.118197i	$0.962289\pi$
$564$	13.7855	−	13.7855i	0.580475	−	0.580475i
$565$	15.9079	+	19.9034i	0.669250	+	0.837344i
$566$	−43.5343	+	43.5343i	−1.82988	+	1.82988i
$567$	13.9784			0.587039
$568$	20.6282	−	20.6282i	0.865542	−	0.865542i
$569$	33.9087			1.42153			0.710763	−	0.703432i	$-0.248350\pi$
$569$	33.9087			1.42153			0.710763	+	0.703432i	$0.248350\pi$
$570$	−1.35117	+	12.1103i	−0.0565945	+	0.507246i
$571$			33.5525i			1.40413i	0.712113	+	0.702065i	$0.247738\pi$
$571$			33.5525i			1.40413i	−0.712113	+	0.702065i	$0.752262\pi$
$572$		0			0
$573$	−20.7277	+	20.7277i	−0.865910	+	0.865910i
$574$	1.01769	−	1.01769i	0.0424775	−	0.0424775i
$575$	−0.442182	−	0.700343i	−0.0184403	−	0.0292063i
$576$		−	12.3589i		−	0.514954i
$577$		−	11.0413i		−	0.459654i	−0.973232	−	0.229827i	$-0.926184\pi$
$577$		−	11.0413i		−	0.459654i	0.973232	−	0.229827i	$-0.0738160\pi$
$578$	−14.9038			−0.619914
$579$	−21.2096	−	21.2096i	−0.881442	−	0.881442i
$580$	66.1743	+	7.38321i	2.74774	+	0.306571i
$581$	−3.39142			−0.140700
$582$	13.2200	−	13.2200i	0.547988	−	0.547988i
$583$			34.7495i			1.43918i
$584$	17.6282			0.729461
$585$		0			0
$586$	58.8002			2.42902
$587$		−	23.5058i		−	0.970190i	−0.874461	−	0.485095i	$-0.838785\pi$
$587$		−	23.5058i		−	0.970190i	0.874461	−	0.485095i	$-0.161215\pi$
$588$	23.1267	−	23.1267i	0.953728	−	0.953728i
$589$	−0.402066			−0.0165668
$590$	−0.00722594	−	0.00904086i	−0.000297487	−	0.000372206i
$591$	21.5954	+	21.5954i	0.888317	+	0.888317i
$592$	0.966247			0.0397125
$593$		−	30.6582i		−	1.25898i	−0.777007	−	0.629491i	$-0.783263\pi$
$593$		−	30.6582i		−	1.25898i	0.777007	−	0.629491i	$-0.216737\pi$
$594$		−	50.1368i		−	2.05714i
$595$	5.74416	+	7.18690i	0.235487	+	0.294634i
$596$	−37.3259	+	37.3259i	−1.52893	+	1.52893i
$597$	−16.0948	+	16.0948i	−0.658717	+	0.658717i
$598$		0			0
$599$			7.49378i			0.306188i	0.988212	+	0.153094i	$0.0489237\pi$
$599$			7.49378i			0.306188i	−0.988212	+	0.153094i	$0.951076\pi$
$600$	12.7267	+	20.1570i	0.519566	+	0.822906i
$601$	−14.0931			−0.574868			−0.287434	−	0.957801i	$-0.592802\pi$
$601$	−14.0931			−0.574868			−0.287434	+	0.957801i	$0.592802\pi$
$602$	−13.5434	+	13.5434i	−0.551989	+	0.551989i
$603$	−5.75533			−0.234375
$604$	−30.8267	+	30.8267i	−1.25432	+	1.25432i
$605$	41.8591	+	4.67031i	1.70182	+	0.189875i
$606$	27.2872	−	27.2872i	1.10847	−	1.10847i
$607$	10.6631	+	10.6631i	0.432801	+	0.432801i	0.889580	−	0.456779i	$-0.150997\pi$
$607$	10.6631	+	10.6631i	0.432801	+	0.432801i	−0.456779	+	0.889580i	$0.650997\pi$
$608$	−5.55340	−	5.55340i	−0.225220	−	0.225220i
$609$	17.4260	+	17.4260i	0.706139	+	0.706139i
$610$	−6.96260	−	0.776832i	−0.281908	−	0.0314530i
$611$		0			0
$612$	6.61779	+	6.61779i	0.267508	+	0.267508i
$613$	−11.9161			−0.481288			−0.240644	−	0.970613i	$-0.577359\pi$
$613$	−11.9161			−0.481288			−0.240644	+	0.970613i	$0.577359\pi$
$614$		−	33.0954i		−	1.33562i
$615$	0.246634	−	2.21053i	0.00994522	−	0.0891372i
$616$	11.8375	+	11.8375i	0.476945	+	0.476945i
$617$			38.8317i			1.56330i	0.623714	+	0.781652i	$0.285623\pi$
$617$			38.8317i			1.56330i	−0.623714	+	0.781652i	$0.714377\pi$
$618$			6.80516i			0.273744i
$619$	14.9567	+	14.9567i	0.601159	+	0.601159i	0.940620	−	0.339461i	$-0.110245\pi$
$619$	14.9567	+	14.9567i	0.601159	+	0.601159i	−0.339461	+	0.940620i	$0.610245\pi$
$620$	−1.76706	+	1.41233i	−0.0709667	+	0.0567203i
$621$			0.675525i			0.0271079i
$622$	−71.6939			−2.87466
$623$	6.51241	+	6.51241i	0.260914	+	0.260914i
$624$		0			0
$625$	22.5712	+	10.7490i	0.902847	+	0.429961i
$626$	−26.9794	−	26.9794i	−1.07831	−	1.07831i
$627$	9.35137	+	9.35137i	0.373458	+	0.373458i
$628$	−9.42008	−	9.42008i	−0.375902	−	0.375902i
$629$	−3.01067	+	3.01067i	−0.120043	+	0.120043i
$630$	−0.675330	+	6.05286i	−0.0269058	+	0.241152i
$631$	27.6170	−	27.6170i	1.09942	−	1.09942i	0.104938	−	0.994479i	$-0.466535\pi$
$631$	27.6170	−	27.6170i	1.09942	−	1.09942i	0.994479	−	0.104938i	$-0.0334646\pi$
$632$	−26.8219			−1.06692
$633$	4.47307	−	4.47307i	0.177788	−	0.177788i
$634$	35.0286			1.39116
$635$	0.732269	+	0.916191i	0.0290592	+	0.0363579i
$636$			38.7550i			1.53674i
$637$		0			0
$638$	84.4296	−	84.4296i	3.34260	−	3.34260i
$639$	8.14485	−	8.14485i	0.322205	−	0.322205i
$640$	−36.6003	−	4.08357i	−1.44675	−	0.161417i
$641$			8.72499i			0.344617i	0.985043	+	0.172308i	$0.0551225\pi$
$641$			8.72499i			0.344617i	−0.985043	+	0.172308i	$0.944877\pi$
$642$			64.9590i			2.56373i
$643$	−14.7970			−0.583538			−0.291769	−	0.956489i	$-0.594244\pi$
$643$	−14.7970			−0.583538			−0.291769	+	0.956489i	$0.594244\pi$
$644$	−0.458694	−	0.458694i	−0.0180751	−	0.0180751i
$645$	−3.28220	+	29.4178i	−0.129237	+	1.15832i
$646$	8.83617			0.347655
$647$	−23.9537	+	23.9537i	−0.941716	+	0.941716i	−0.998393	−	0.0566765i	$-0.981950\pi$
$647$	−23.9537	+	23.9537i	−0.941716	+	0.941716i	0.0566765	+	0.998393i	$0.481950\pi$
$648$		−	26.2636i		−	1.03173i
$649$	−0.0125609			−0.000493060
$650$		0			0
$651$	−0.837243			−0.0328141
$652$		−	28.2238i		−	1.10533i
$653$	−14.3176	+	14.3176i	−0.560289	+	0.560289i	−0.929390	−	0.369100i	$-0.879666\pi$
$653$	−14.3176	+	14.3176i	−0.560289	+	0.560289i	0.369100	+	0.929390i	$0.379666\pi$
$654$	29.8763			1.16826
$655$	−1.26422	+	11.3310i	−0.0493973	+	0.442739i
$656$	0.258822	+	0.258822i	0.0101053	+	0.0101053i
$657$	6.96032			0.271548
$658$		−	9.19981i		−	0.358646i
$659$			30.2898i			1.17992i	0.807432	+	0.589961i	$0.200857\pi$
$659$			30.2898i			1.17992i	−0.807432	+	0.589961i	$0.799143\pi$
$660$	73.9470	+	8.25042i	2.87838	+	0.321147i
$661$	−15.4711	+	15.4711i	−0.601754	+	0.601754i	−0.940778	−	0.339024i	$-0.889903\pi$
$661$	−15.4711	+	15.4711i	−0.601754	+	0.601754i	0.339024	+	0.940778i	$0.389903\pi$
$662$	27.1574	−	27.1574i	1.05550	−	1.05550i
$663$		0			0
$664$			6.37202i			0.247282i
$665$	2.17279	+	2.71853i	0.0842573	+	0.105420i
$666$	−2.81851			−0.109215
$667$	−1.13757	+	1.13757i	−0.0440470	+	0.0440470i
$668$	−38.7520			−1.49936
$669$	16.6867	−	16.6867i	0.645143	−	0.645143i
$670$	−3.38994	+	30.3834i	−0.130965	+	1.17381i
$671$	−5.37640	+	5.37640i	−0.207553	+	0.207553i
$672$	−11.5641	−	11.5641i	−0.446096	−	0.446096i
$673$	0.406042	+	0.406042i	0.0156518	+	0.0156518i	0.714889	−	0.699238i	$-0.246477\pi$
$673$	0.406042	+	0.406042i	0.0156518	+	0.0156518i	−0.699238	+	0.714889i	$0.746477\pi$
$674$	56.3962	+	56.3962i	2.17230	+	2.17230i
$675$	−10.8857	−	17.2411i	−0.418989	−	0.663610i
$676$		0			0
$677$	−11.5229	−	11.5229i	−0.442862	−	0.442862i	0.450111	−	0.892973i	$-0.351385\pi$
$677$	−11.5229	−	11.5229i	−0.442862	−	0.442862i	−0.892973	+	0.450111i	$0.851385\pi$
$678$	50.9571			1.95700
$679$		−	5.33952i		−	0.204912i
$680$	13.5032	−	10.7925i	0.517825	−	0.413873i
$681$	38.8688	+	38.8688i	1.48946	+	1.48946i
$682$			4.05646i			0.155330i
$683$			20.1058i			0.769326i	0.923057	+	0.384663i	$0.125682\pi$
$683$			20.1058i			0.769326i	−0.923057	+	0.384663i	$0.874318\pi$
$684$	2.50325	+	2.50325i	0.0957143	+	0.0957143i
$685$	0.943047	−	8.45236i	0.0360320	−	0.322948i
$686$		−	35.5565i		−	1.35755i
$687$	−36.2463			−1.38288
$688$	−3.44440	−	3.44440i	−0.131317	−	0.131317i
$689$		0			0
$690$	−1.64623	−	0.183673i	−0.0626709	−	0.00699232i
$691$	30.6415	+	30.6415i	1.16566	+	1.16566i	0.983216	+	0.182443i	$0.0584005\pi$
$691$	30.6415	+	30.6415i	1.16566	+	1.16566i	0.182443	+	0.983216i	$0.441600\pi$
$692$	−29.7363	−	29.7363i	−1.13040	−	1.13040i
$693$	4.67390	+	4.67390i	0.177547	+	0.177547i
$694$	−20.5310	+	20.5310i	−0.779346	+	0.779346i
$695$	−3.28500	−	0.366514i	−0.124607	−	0.0139027i
$696$	32.7412	−	32.7412i	1.24105	−	1.24105i
$697$	−1.61289			−0.0610926
$698$	−42.7351	+	42.7351i	−1.61755	+	1.61755i
$699$	−45.9527			−1.73809
$700$	19.0986	+	4.31546i	0.721859	+	0.163109i
$701$			8.03468i			0.303466i	0.988422	+	0.151733i	$0.0484853\pi$
$701$			8.03468i			0.303466i	−0.988422	+	0.151733i	$0.951515\pi$
$702$		0			0
$703$	−1.13882	+	1.13882i	−0.0429514	+	0.0429514i
$704$	−50.3809	+	50.3809i	−1.89880	+	1.89880i
$705$	−8.87673	−	11.1063i	−0.334317	−	0.418286i
$706$		−	52.4701i		−	1.97474i
$707$		−	11.0212i		−	0.414495i
$708$	−0.0140088			−0.000526483
$709$	16.0704	+	16.0704i	0.603536	+	0.603536i	0.941249	−	0.337713i	$-0.109653\pi$
$709$	16.0704	+	16.0704i	0.603536	+	0.603536i	−0.337713	+	0.941249i	$0.609653\pi$
$710$	−38.2008	−	47.7956i	−1.43365	−	1.79374i
$711$	−10.5904			−0.397170
$712$	12.2359	−	12.2359i	0.458561	−	0.458561i
$713$		−	0.0546553i		−	0.00204686i
$714$	18.4000			0.688604
$715$		0			0
$716$	−38.7636			−1.44866
$717$		−	7.35589i		−	0.274711i
$718$	20.6449	−	20.6449i	0.770460	−	0.770460i
$719$	−42.9573			−1.60204			−0.801018	−	0.598640i	$-0.795708\pi$
$719$	−42.9573			−1.60204			−0.801018	+	0.598640i	$0.795708\pi$
$720$	−1.53938	−	0.171752i	−0.0573693	−	0.00640081i
$721$	1.37429	+	1.37429i	0.0511813	+	0.0511813i
$722$	−39.4229			−1.46717
$723$			41.3467i			1.53770i
$724$			25.0386i			0.930553i
$725$	10.7024	−	47.3650i	0.397479	−	1.75909i
$726$	59.5628	−	59.5628i	2.21058	−	2.21058i
$727$	−1.42786	+	1.42786i	−0.0529563	+	0.0529563i	−0.733089	−	0.680133i	$-0.761922\pi$
$727$	−1.42786	+	1.42786i	−0.0529563	+	0.0529563i	0.680133	+	0.733089i	$0.261922\pi$
$728$		0			0
$729$			13.9369i			0.516183i
$730$	4.09970	−	36.7448i	0.151737	−	1.35999i
$731$	21.4644			0.793889
$732$	−5.99613	+	5.99613i	−0.221623	+	0.221623i
$733$	−32.1064			−1.18588			−0.592939	−	0.805247i	$-0.702033\pi$
$733$	−32.1064			−1.18588			−0.592939	+	0.805247i	$0.702033\pi$
$734$	−23.6613	+	23.6613i	−0.873355	+	0.873355i
$735$	−14.8917	−	18.6320i	−0.549287	−	0.687250i
$736$	0.754907	−	0.754907i	0.0278262	−	0.0278262i
$737$	23.4615	+	23.4615i	0.864217	+	0.864217i
$738$	−0.754973	−	0.754973i	−0.0277909	−	0.0277909i
$739$	−14.5283	−	14.5283i	−0.534431	−	0.534431i	0.387457	−	0.921888i	$-0.373354\pi$
$739$	−14.5283	−	14.5283i	−0.534431	−	0.534431i	−0.921888	+	0.387457i	$0.873354\pi$
$740$	−1.00474	+	9.00534i	−0.0369351	+	0.331043i
$741$		0			0
$742$	12.9317	+	12.9317i	0.474736	+	0.474736i
$743$	−22.5040			−0.825593			−0.412797	−	0.910823i	$-0.635448\pi$
$743$	−22.5040			−0.825593			−0.412797	+	0.910823i	$0.635448\pi$
$744$			1.57307i			0.0576714i
$745$	24.0348	+	30.0716i	0.880567	+	1.10174i
$746$	9.83771	+	9.83771i	0.360184	+	0.360184i
$747$			2.51593i			0.0920530i
$748$		−	53.9547i		−	1.97278i
$749$	13.1184	+	13.1184i	0.479334	+	0.479334i
$750$	44.9757	−	21.8402i	1.64228	−	0.797490i
$751$			1.66512i			0.0607611i	0.999538	+	0.0303806i	$0.00967192\pi$
$751$			1.66512i			0.0607611i	−0.999538	+	0.0303806i	$0.990328\pi$
$752$	2.33972			0.0853209
$753$	3.32640	+	3.32640i	0.121221	+	0.121221i
$754$		0			0
$755$	19.8498	+	24.8355i	0.722410	+	0.903855i
$756$	−11.2921	−	11.2921i	−0.410692	−	0.410692i
$757$	−27.5976	−	27.5976i	−1.00305	−	1.00305i	−0.999995	−	0.00305681i	$-0.999027\pi$
$757$	−27.5976	−	27.5976i	−1.00305	−	1.00305i	−0.00305681	−	0.999995i	$-0.500973\pi$
$758$	29.0761	+	29.0761i	1.05609	+	1.05609i
$759$	−1.27119	+	1.27119i	−0.0461412	+	0.0461412i
$760$	5.10774	−	4.08238i	0.185277	−	0.148084i
$761$	11.5012	−	11.5012i	0.416918	−	0.416918i	−0.467222	−	0.884140i	$-0.654745\pi$
$761$	11.5012	−	11.5012i	0.416918	−	0.416918i	0.884140	+	0.467222i	$0.154745\pi$
$762$	2.34565			0.0849739
$763$	6.03348	−	6.03348i	0.218426	−	0.218426i
$764$	45.2372			1.63663
$765$	5.33161	−	4.26131i	0.192765	−	0.154068i
$766$		−	23.0560i		−	0.833045i
$767$		0			0
$768$	−15.4289	+	15.4289i	−0.556741	+	0.556741i
$769$	28.2209	−	28.2209i	1.01767	−	1.01767i	0.0178298	−	0.999841i	$-0.494324\pi$
$769$	28.2209	−	28.2209i	1.01767	−	1.01767i	0.999841	−	0.0178298i	$-0.00567570\pi$
$770$	27.4274	−	21.9214i	0.988414	−	0.789993i
$771$			1.72861i			0.0622544i
$772$			46.2891i			1.66598i
$773$	−20.5887			−0.740525			−0.370262	−	0.928927i	$-0.620732\pi$
$773$	−20.5887			−0.740525			−0.370262	+	0.928927i	$0.620732\pi$
$774$	10.0472	+	10.0472i	0.361139	+	0.361139i
$775$	0.880735	+	1.39494i	0.0316369	+	0.0501077i
$776$	−10.0322			−0.360137
$777$	−2.37142	+	2.37142i	−0.0850744	+	0.0850744i
$778$		−	7.67976i		−	0.275333i
$779$	−0.610095			−0.0218589
$780$		0			0
$781$	−66.4048			−2.37615
$782$			1.20115i			0.0429532i
$783$	−28.0048	+	28.0048i	−1.00081	+	1.00081i
$784$	3.92514			0.140183
$785$	−7.58927	+	6.06575i	−0.270873	+	0.216496i
$786$	16.1233	+	16.1233i	0.575098	+	0.575098i
$787$	−28.6489			−1.02122			−0.510611	−	0.859812i	$-0.670581\pi$
$787$	−28.6489			−1.02122			−0.510611	+	0.859812i	$0.670581\pi$
$788$		−	47.1311i		−	1.67898i
$789$			30.1763i			1.07430i
$790$	−6.23783	+	55.9085i	−0.221932	+	1.98914i
$791$	10.2907	−	10.2907i	0.365895	−	0.365895i
$792$	8.78163	−	8.78163i	0.312042	−	0.312042i
$793$		0			0
$794$			26.8568i			0.953111i
$795$	28.0890	+	3.13395i	0.996214	+	0.111150i
$796$	35.1262			1.24502
$797$	−6.21167	+	6.21167i	−0.220029	+	0.220029i	−0.808510	−	0.588482i	$-0.799726\pi$
$797$	−6.21167	+	6.21167i	−0.220029	+	0.220029i	0.588482	+	0.808510i	$0.299726\pi$
$798$	6.96002			0.246382
$799$	−7.29019	+	7.29019i	−0.257909	+	0.257909i
$800$	−7.10227	+	31.4320i	−0.251103	+	1.11129i
$801$	4.83124	−	4.83124i	0.170703	−	0.170703i
$802$	6.48736	+	6.48736i	0.229077	+	0.229077i
$803$	−28.3737	−	28.3737i	−1.00129	−	1.00129i
$804$	26.1659	+	26.1659i	0.922801	+	0.922801i
$805$	−0.369546	+	0.295361i	−0.0130248	+	0.0104101i
$806$		0			0
$807$	−34.2536	−	34.2536i	−1.20578	−	1.20578i
$808$	−20.7073			−0.728482
$809$		−	0.947514i		−	0.0333128i	−0.999861	−	0.0166564i	$-0.994698\pi$
$809$		−	0.947514i		−	0.0333128i	0.999861	−	0.0166564i	$-0.00530214\pi$
$810$	−54.7446	−	6.10797i	−1.92353	−	0.214612i
$811$	−28.8041	−	28.8041i	−1.01145	−	1.01145i	−0.999934	−	0.0115151i	$-0.996335\pi$
$811$	−28.8041	−	28.8041i	−1.01145	−	1.01145i	−0.0115151	−	0.999934i	$-0.503665\pi$
$812$		−	38.0316i		−	1.33465i
$813$			26.0605i			0.913981i
$814$	11.4896	+	11.4896i	0.402711	+	0.402711i
$815$	−20.4561	−	2.28233i	−0.716546	−	0.0799465i
$816$			4.67955i			0.163817i
$817$	8.11915			0.284053
$818$	11.0440	+	11.0440i	0.386145	+	0.386145i
$819$		0			0
$820$	−2.68133	+	2.14306i	−0.0936361	+	0.0748390i
$821$	−0.951434	−	0.951434i	−0.0332053	−	0.0332053i	0.690309	−	0.723514i	$-0.257474\pi$
$821$	−0.951434	−	0.951434i	−0.0332053	−	0.0332053i	−0.723514	+	0.690309i	$0.757474\pi$
$822$	−12.0271	−	12.0271i	−0.419495	−	0.419495i
$823$	23.3838	+	23.3838i	0.815109	+	0.815109i	0.985395	−	0.170286i	$-0.0544692\pi$
$823$	23.3838	+	23.3838i	0.815109	+	0.815109i	−0.170286	+	0.985395i	$0.554469\pi$
$824$	2.58211	−	2.58211i	0.0899520	−	0.0899520i
$825$	11.9595	−	52.9283i	0.416377	−	1.84273i
$826$	−0.00467441	+	0.00467441i	−0.000162644	+	0.000162644i
$827$	26.4195			0.918697			0.459349	−	0.888256i	$-0.348083\pi$
$827$	26.4195			0.918697			0.459349	+	0.888256i	$0.348083\pi$
$828$	−0.340282	+	0.340282i	−0.0118256	+	0.0118256i
$829$	−2.46068			−0.0854629			−0.0427314	−	0.999087i	$-0.513606\pi$
$829$	−2.46068			−0.0854629			−0.0427314	+	0.999087i	$0.513606\pi$
$830$	13.2820	+	1.48191i	0.461027	+	0.0514377i
$831$		−	24.2940i		−	0.842748i
$832$		0			0
$833$	−12.2301	+	12.2301i	−0.423747	+	0.423747i
$834$	−4.67434	+	4.67434i	−0.161859	+	0.161859i
$835$	−3.13370	+	28.0868i	−0.108446	+	0.971983i
$836$		−	20.4090i		−	0.705859i
$837$		−	1.34551i		−	0.0465075i
$838$	47.7818			1.65059
$839$	35.6002	+	35.6002i	1.22906	+	1.22906i	0.964321	+	0.264736i	$0.0852847\pi$
$839$	35.6002	+	35.6002i	1.22906	+	1.22906i	0.264736	+	0.964321i	$0.414715\pi$
$840$	10.6361	−	8.50096i	0.366981	−	0.293311i
$841$	−65.3193			−2.25239
$842$	−7.10641	+	7.10641i	−0.244903	+	0.244903i
$843$		−	18.0819i		−	0.622773i
$844$	−9.76228			−0.336032
$845$		0			0
$846$	−6.82488			−0.234644
$847$		−	24.0572i		−	0.826616i
$848$	−3.28882	+	3.28882i	−0.112939	+	0.112939i
$849$	54.3461			1.86515
$850$	−19.3559	−	30.6565i	−0.663900	−	1.05151i
$851$	−0.154807	−	0.154807i	−0.00530670	−	0.00530670i
$852$	−74.0592			−2.53723
$853$			42.9612i			1.47096i	0.677545	+	0.735481i	$0.263044\pi$
$853$			42.9612i			1.47096i	−0.677545	+	0.735481i	$0.736956\pi$
$854$			4.00154i			0.136930i
$855$	2.01674	−	1.61189i	0.0689711	−	0.0551254i
$856$	24.6476	−	24.6476i	0.842438	−	0.842438i
$857$	29.0789	−	29.0789i	0.993316	−	0.993316i	−0.00666151	−	0.999978i	$-0.502120\pi$
$857$	29.0789	−	29.0789i	0.993316	−	0.993316i	0.999978	+	0.00666151i	$0.00212044\pi$
$858$		0			0
$859$		−	42.1283i		−	1.43740i	−0.695321	−	0.718700i	$-0.744738\pi$
$859$		−	42.1283i		−	1.43740i	0.695321	−	0.718700i	$-0.255262\pi$
$860$	35.6832	−	28.5199i	1.21679	−	0.972521i
$861$	−1.27043			−0.0432962
$862$	57.0479	−	57.0479i	1.94306	−	1.94306i
$863$	−6.80768			−0.231736			−0.115868	−	0.993265i	$-0.536965\pi$
$863$	−6.80768			−0.231736			−0.115868	+	0.993265i	$0.536965\pi$
$864$	18.5843	−	18.5843i	0.632252	−	0.632252i
$865$	−23.9570	+	19.1477i	−0.814562	+	0.651041i
$866$	12.8806	−	12.8806i	0.437702	−	0.437702i
$867$	9.30256	+	9.30256i	0.315931	+	0.315931i
$868$	0.913624	+	0.913624i	0.0310104	+	0.0310104i
$869$	43.1715	+	43.1715i	1.46449	+	1.46449i
$870$	−60.6323	−	75.8612i	−2.05563	−	2.57194i
$871$		0			0
$872$	−11.3361	−	11.3361i	−0.383888	−	0.383888i
$873$	−3.96113			−0.134064
$874$			0.454351i			0.0153686i
$875$	4.67219	−	13.4934i	0.157949	−	0.456159i
$876$	−31.6443	−	31.6443i	−1.06916	−	1.06916i
$877$		−	47.6814i		−	1.61009i	−0.593217	−	0.805043i	$-0.702142\pi$
$877$		−	47.6814i		−	1.61009i	0.593217	−	0.805043i	$-0.297858\pi$
$878$		−	64.5242i		−	2.17759i
$879$	−36.7017	−	36.7017i	−1.23792	−	1.23792i
$880$	5.57512	+	6.97541i	0.187937	+	0.235141i
$881$			5.12384i			0.172627i	0.996268	+	0.0863133i	$0.0275086\pi$
$881$			5.12384i			0.172627i	−0.996268	+	0.0863133i	$0.972491\pi$
$882$	−11.4495			−0.385524
$883$	−14.8283	−	14.8283i	−0.499014	−	0.499014i	0.412117	−	0.911131i	$-0.364789\pi$
$883$	−14.8283	−	14.8283i	−0.499014	−	0.499014i	−0.911131	+	0.412117i	$0.864789\pi$
$884$		0			0
$885$	−0.00113283	+	0.0101533i	−3.80796e−5	+	0.000341301i
$886$	−38.6206	−	38.6206i	−1.29749	−	1.29749i
$887$	−7.44750	−	7.44750i	−0.250063	−	0.250063i	0.570934	−	0.820996i	$-0.306581\pi$
$887$	−7.44750	−	7.44750i	−0.250063	−	0.250063i	−0.820996	+	0.570934i	$0.806581\pi$
$888$	4.45558	+	4.45558i	0.149520	+	0.149520i
$889$	0.473700	−	0.473700i	0.0158874	−	0.0158874i
$890$	−22.6593	−	28.3506i	−0.759543	−	0.950315i
$891$	−42.2728	+	42.2728i	−1.41619	+	1.41619i
$892$	−36.4179			−1.21936
$893$	−2.75760	+	2.75760i	−0.0922795	+	0.0922795i
$894$	76.9898			2.57492
$895$	−3.13464	+	28.0952i	−0.104779	+	0.939119i
$896$			21.0349i			0.702725i
$897$		0			0
$898$	−14.5886	+	14.5886i	−0.486828	+	0.486828i
$899$	2.26581	−	2.26581i	0.0755690	−	0.0755690i
$900$	3.20143	−	14.1683i	0.106714	−	0.472277i
$901$		−	20.4948i		−	0.682782i
$902$			6.15528i			0.204948i
$903$	16.9069			0.562628
$904$	−19.3348	−	19.3348i	−0.643067	−	0.643067i
$905$	18.1476	+	2.02476i	0.603245	+	0.0673053i
$906$	63.5842			2.11244
$907$	−15.2289	+	15.2289i	−0.505668	+	0.505668i	−0.913194	−	0.407526i	$-0.866392\pi$
$907$	−15.2289	+	15.2289i	−0.505668	+	0.505668i	0.407526	+	0.913194i	$0.366392\pi$
$908$		−	84.8295i		−	2.81517i
$909$	−8.17608			−0.271184
$910$		0			0
$911$	−16.6400			−0.551309			−0.275654	−	0.961257i	$-0.588895\pi$
$911$	−16.6400			−0.551309			−0.275654	+	0.961257i	$0.588895\pi$
$912$			1.77009i			0.0586137i
$913$	10.2562	−	10.2562i	0.339429	−	0.339429i
$914$	−48.3469			−1.59917
$915$	3.86101	+	4.83077i	0.127641	+	0.159700i
$916$	39.5530	+	39.5530i	1.30687	+	1.30687i
$917$	6.51214			0.215050
$918$			29.5701i			0.975958i
$919$		−	6.87460i		−	0.226772i	−0.993551	−	0.113386i	$-0.963830\pi$
$919$		−	6.87460i		−	0.226772i	0.993551	−	0.113386i	$-0.0361697\pi$
$920$	0.554943	+	0.694327i	0.0182959	+	0.0228913i
$921$	−20.6573	+	20.6573i	−0.680682	+	0.680682i
$922$	8.08349	−	8.08349i	0.266216	−	0.266216i
$923$		0			0
$924$		−	42.4987i		−	1.39810i
$925$	6.44566	+	1.45644i	0.211932	+	0.0478875i
$926$	45.1946			1.48519
$927$	1.01952	−	1.01952i	0.0334854	−	0.0334854i
$928$	62.5915			2.05467
$929$	−31.4342	+	31.4342i	−1.03132	+	1.03132i	−0.0318293	+	0.999493i	$0.510133\pi$
$929$	−31.4342	+	31.4342i	−1.03132	+	1.03132i	−0.999493	+	0.0318293i	$0.989867\pi$
$930$	3.27895	+	0.365839i	0.107521	+	0.0119963i
$931$	−4.62617	+	4.62617i	−0.151617	+	0.151617i
$932$	50.1449	+	50.1449i	1.64255	+	1.64255i
$933$	44.7495	+	44.7495i	1.46503	+	1.46503i
$934$	−48.2813	−	48.2813i	−1.57981	−	1.57981i
$935$	−39.1054	−	4.36307i	−1.27888	−	0.142688i
$936$		0			0
$937$	13.1724	+	13.1724i	0.430323	+	0.430323i	0.888738	−	0.458415i	$-0.151583\pi$
$937$	13.1724	+	13.1724i	0.430323	+	0.430323i	−0.458415	+	0.888738i	$0.651583\pi$
$938$	17.4619			0.570152
$939$			33.6797i			1.09910i
$940$	−2.43294	+	21.8060i	−0.0793538	+	0.711234i
$941$	−40.0251	−	40.0251i	−1.30478	−	1.30478i	−0.925130	−	0.379650i	$-0.876045\pi$
$941$	−40.0251	−	40.0251i	−1.30478	−	1.30478i	−0.379650	−	0.925130i	$-0.623955\pi$
$942$			19.4302i			0.633070i
$943$		−	0.0829339i		−	0.00270070i
$944$	−0.00118881	−	0.00118881i	−3.86925e−5	−	3.86925e-5i
$945$	−9.09750	+	7.27121i	−0.295942	+	0.236532i
$946$		−	81.9146i		−	2.66327i
$947$	58.8943			1.91381			0.956904	−	0.290404i	$-0.0937896\pi$
$947$	58.8943			1.91381			0.956904	+	0.290404i	$0.0937896\pi$
$948$	48.1479	+	48.1479i	1.56377	+	1.56377i
$949$		0			0
$950$	−7.32157	−	11.5962i	−0.237543	−	0.376229i
$951$	−21.8640	−	21.8640i	−0.708989	−	0.708989i
$952$	−6.98159	−	6.98159i	−0.226275	−	0.226275i
$953$	12.6246	+	12.6246i	0.408953	+	0.408953i	0.881373	−	0.472421i	$-0.156620\pi$
$953$	12.6246	+	12.6246i	0.408953	+	0.408953i	−0.472421	+	0.881373i	$0.656620\pi$
$954$	9.59336	−	9.59336i	0.310596	−	0.310596i
$955$	3.65813	−	32.7872i	0.118374	−	1.06097i
$956$	−8.02696	+	8.02696i	−0.259610	+	0.259610i
$957$	−105.398			−3.40703
$958$	49.5130	−	49.5130i	1.59969	−	1.59969i
$959$	−4.85772			−0.156864
$960$	36.1806	+	45.2680i	1.16772	+	1.46102i
$961$		−	30.8911i		−	0.996488i
$962$		0			0
$963$	9.73187	−	9.73187i	0.313605	−	0.313605i
$964$	45.1187	−	45.1187i	1.45317	−	1.45317i
$965$	33.5495	+	3.74319i	1.08000	+	0.120498i
$966$			0.946118i			0.0304409i
$967$			23.2093i			0.746360i	0.927759	+	0.373180i	$0.121733\pi$
$967$			23.2093i			0.746360i	−0.927759	+	0.373180i	$0.878267\pi$
$968$	−45.2002			−1.45279
$969$	−5.51532	−	5.51532i	−0.177178	−	0.177178i
$970$	−2.33314	+	20.9115i	−0.0749127	+	0.671429i
$971$	42.3865			1.36025			0.680123	−	0.733098i	$-0.261926\pi$
$971$	42.3865			1.36025			0.680123	+	0.733098i	$0.261926\pi$
$972$	−20.6212	+	20.6212i	−0.661425	+	0.661425i
$973$			1.88795i			0.0605249i
$974$	43.7367			1.40141
$975$		0			0
$976$	−1.01768			−0.0325752
$977$			24.4098i			0.780938i	0.920616	+	0.390469i	$0.127687\pi$
$977$			24.4098i			0.780938i	−0.920616	+	0.390469i	$0.872313\pi$
$978$	−29.1077	+	29.1077i	−0.930761	+	0.930761i
$979$	−39.3890			−1.25888
$980$	−4.08152	+	36.5819i	−0.130379	+	1.16857i
$981$	−4.47594	−	4.47594i	−0.142906	−	0.142906i
$982$	79.4840			2.53644
$983$		−	4.47004i		−	0.142572i	−0.997456	−	0.0712860i	$-0.977290\pi$
$983$		−	4.47004i		−	0.142572i	0.997456	−	0.0712860i	$-0.0227103\pi$
$984$			2.38697i			0.0760938i
$985$	−34.1598	−	3.81128i	−1.08842	−	0.121438i
$986$	−49.7955	+	49.7955i	−1.58581	+	1.58581i
$987$	−5.74230	+	5.74230i	−0.182779	+	0.182779i
$988$		0			0
$989$			1.10369i			0.0350952i
$990$	−16.2624	−	20.3470i	−0.516854	−	0.646671i
$991$	−49.5350			−1.57353			−0.786766	−	0.617251i	$-0.788246\pi$
$991$	−49.5350			−1.57353			−0.786766	+	0.617251i	$0.788246\pi$
$992$	−1.50362	+	1.50362i	−0.0477400	+	0.0477400i
$993$	−33.9020			−1.07585
$994$	−24.7118	+	24.7118i	−0.783812	+	0.783812i
$995$	2.84050	−	25.4589i	0.0900499	−	0.807101i
$996$	11.4384	−	11.4384i	0.362439	−	0.362439i
$997$	−24.7788	−	24.7788i	−0.784753	−	0.784753i	0.195876	−	0.980629i	$-0.437245\pi$
$997$	−24.7788	−	24.7788i	−0.784753	−	0.784753i	−0.980629	+	0.195876i	$0.937245\pi$
$998$	21.2573	+	21.2573i	0.672888	+	0.672888i
$999$	−3.81104	−	3.81104i	−0.120576	−	0.120576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.f.d.437.10		20
5.3	odd	4		845.2.k.d.268.10		20
13.2	odd	12		845.2.o.g.357.1		20
13.3	even	3		845.2.t.e.657.1		20
13.4	even	6		65.2.t.a.37.1	yes	20
13.5	odd	4		845.2.k.d.577.10		20
13.6	odd	12		845.2.o.f.587.1		20
13.7	odd	12		845.2.o.e.587.5		20
13.8	odd	4		845.2.k.e.577.1		20
13.9	even	3		845.2.t.g.427.5		20
13.10	even	6		845.2.t.f.657.5		20
13.11	odd	12		65.2.o.a.32.5	✓	20
13.12	even	2		845.2.f.e.437.1		20
39.11	even	12		585.2.cf.a.487.1		20
39.17	odd	6		585.2.dp.a.37.5		20
65.3	odd	12		845.2.o.f.488.1		20
65.4	even	6		325.2.x.b.232.5		20
65.8	even	4		845.2.f.e.408.10		20
65.17	odd	12		325.2.s.b.193.1		20
65.18	even	4	inner	845.2.f.d.408.1		20
65.23	odd	12		845.2.o.e.488.5		20
65.24	odd	12		325.2.s.b.32.1		20
65.28	even	12		845.2.t.g.188.5		20
65.33	even	12		845.2.t.f.418.5		20
65.37	even	12		325.2.x.b.318.5		20
65.38	odd	4		845.2.k.e.268.1		20
65.43	odd	12		65.2.o.a.63.5	yes	20
65.48	odd	12		845.2.o.g.258.1		20
65.58	even	12		845.2.t.e.418.1		20
65.63	even	12		65.2.t.a.58.1	yes	20
195.128	odd	12		585.2.dp.a.253.5		20
195.173	even	12		585.2.cf.a.388.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.5	✓	20	13.11	odd	12
65.2.o.a.63.5	yes	20	65.43	odd	12
65.2.t.a.37.1	yes	20	13.4	even	6
65.2.t.a.58.1	yes	20	65.63	even	12
325.2.s.b.32.1		20	65.24	odd	12
325.2.s.b.193.1		20	65.17	odd	12
325.2.x.b.232.5		20	65.4	even	6
325.2.x.b.318.5		20	65.37	even	12
585.2.cf.a.388.1		20	195.173	even	12
585.2.cf.a.487.1		20	39.11	even	12
585.2.dp.a.37.5		20	39.17	odd	6
585.2.dp.a.253.5		20	195.128	odd	12
845.2.f.d.408.1		20	65.18	even	4	inner
845.2.f.d.437.10		20	1.1	even	1	trivial
845.2.f.e.408.10		20	65.8	even	4
845.2.f.e.437.1		20	13.12	even	2
845.2.k.d.268.10		20	5.3	odd	4
845.2.k.d.577.10		20	13.5	odd	4
845.2.k.e.268.1		20	65.38	odd	4
845.2.k.e.577.1		20	13.8	odd	4
845.2.o.e.488.5		20	65.23	odd	12
845.2.o.e.587.5		20	13.7	odd	12
845.2.o.f.488.1		20	65.3	odd	12
845.2.o.f.587.1		20	13.6	odd	12
845.2.o.g.258.1		20	65.48	odd	12
845.2.o.g.357.1		20	13.2	odd	12
845.2.t.e.418.1		20	65.58	even	12
845.2.t.e.657.1		20	13.3	even	3
845.2.t.f.418.5		20	65.33	even	12
845.2.t.f.657.5		20	13.10	even	6
845.2.t.g.188.5		20	65.28	even	12
845.2.t.g.427.5		20	13.9	even	3

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.25081i q^{2} +(1.40490 - 1.40490i) q^{3} -3.06613 q^{4} +(-0.247944 + 2.22228i) q^{5} +(3.16216 + 3.16216i) q^{6} +1.27718 q^{7} -2.39966i q^{8} -0.947480i q^{9} +(-5.00192 - 0.558075i) q^{10} +(-3.86239 + 3.86239i) q^{11} +(-4.30760 + 4.30760i) q^{12} +2.87469i q^{14} +(2.77374 + 3.47041i) q^{15} -0.731101 q^{16} +(2.27799 - 2.27799i) q^{17} +2.13259 q^{18} +(0.861676 - 0.861676i) q^{19} +(0.760230 - 6.81380i) q^{20} +(1.79431 - 1.79431i) q^{21} +(-8.69350 - 8.69350i) q^{22} +(0.117133 + 0.117133i) q^{23} +(-3.37127 - 3.37127i) q^{24} +(-4.87705 - 1.10200i) q^{25} +(2.88358 + 2.88358i) q^{27} -3.91601 q^{28} +9.71181i q^{29} +(-7.81123 + 6.24315i) q^{30} +(-0.233305 - 0.233305i) q^{31} -6.44488i q^{32} +10.8525i q^{33} +(5.12732 + 5.12732i) q^{34} +(-0.316670 + 2.83826i) q^{35} +2.90510i q^{36} -1.32163 q^{37} +(1.93947 + 1.93947i) q^{38} +(5.33270 + 0.594981i) q^{40} +(-0.354016 - 0.354016i) q^{41} +(4.03865 + 4.03865i) q^{42} +(4.71126 + 4.71126i) q^{43} +(11.8426 - 11.8426i) q^{44} +(2.10556 + 0.234922i) q^{45} +(-0.263643 + 0.263643i) q^{46} -3.20027 q^{47} +(-1.02712 + 1.02712i) q^{48} -5.36880 q^{49} +(2.48039 - 10.9773i) q^{50} -6.40069i q^{51} +(4.49845 - 4.49845i) q^{53} +(-6.49039 + 6.49039i) q^{54} +(-7.62565 - 9.54097i) q^{55} -3.06480i q^{56} -2.42113i q^{57} -21.8594 q^{58} +(0.00162606 + 0.00162606i) q^{59} +(-8.50465 - 10.6407i) q^{60} +1.39199 q^{61} +(0.525123 - 0.525123i) q^{62} -1.21011i q^{63} +13.0440 q^{64} -24.4270 q^{66} -6.07436i q^{67} +(-6.98462 + 6.98462i) q^{68} +0.329120 q^{69} +(-6.38837 - 0.712764i) q^{70} +(8.59633 + 8.59633i) q^{71} -2.27363 q^{72} +7.34614i q^{73} -2.97474i q^{74} +(-8.39996 + 5.30355i) q^{75} +(-2.64201 + 2.64201i) q^{76} +(-4.93298 + 4.93298i) q^{77} -11.1774i q^{79} +(0.181272 - 1.62471i) q^{80} +10.9447 q^{81} +(0.796822 - 0.796822i) q^{82} -2.65539 q^{83} +(-5.50160 + 5.50160i) q^{84} +(4.49752 + 5.62715i) q^{85} +(-10.6041 + 10.6041i) q^{86} +(13.6441 + 13.6441i) q^{87} +(9.26841 + 9.26841i) q^{88} +(5.09904 + 5.09904i) q^{89} +(-0.528764 + 4.73922i) q^{90} +(-0.359145 - 0.359145i) q^{92} -0.655538 q^{93} -7.20320i q^{94} +(1.70124 + 2.12853i) q^{95} +(-9.05440 - 9.05440i) q^{96} -4.18070i q^{97} -12.0841i q^{98} +(3.65954 + 3.65954i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{3} - 12 q^{4} - 4 q^{6} - 4 q^{7} - 8 q^{10} - 8 q^{11} - 24 q^{12} - 28 q^{15} + 4 q^{16} - 14 q^{17} - 4 q^{19} + 12 q^{20} - 4 q^{21} - 32 q^{22} + 8 q^{23} + 4 q^{24} + 18 q^{25} + 4 q^{27}+ \cdots - 60 q^{99}+O(q^{100}) \) 20 * q + 4 * q^3 - 12 * q^4 - 4 * q^6 - 4 * q^7 - 8 * q^10 - 8 * q^11 - 24 * q^12 - 28 * q^15 + 4 * q^16 - 14 * q^17 - 4 * q^19 + 12 * q^20 - 4 * q^21 - 32 * q^22 + 8 * q^23 + 4 * q^24 + 18 * q^25 + 4 * q^27 + 36 * q^28 + 40 * q^30 - 2 * q^34 - 20 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^40 + 38 * q^41 + 16 * q^42 - 32 * q^43 + 36 * q^44 + 6 * q^45 - 4 * q^46 + 40 * q^47 + 28 * q^48 - 36 * q^49 - 42 * q^50 - 10 * q^53 - 36 * q^54 - 16 * q^55 - 8 * q^59 - 28 * q^60 + 32 * q^61 + 4 * q^62 + 20 * q^64 - 32 * q^66 - 50 * q^68 + 32 * q^69 + 12 * q^70 + 40 * q^71 + 8 * q^72 + 4 * q^75 + 16 * q^76 - 28 * q^77 - 112 * q^80 + 28 * q^81 - 34 * q^82 - 48 * q^83 - 8 * q^84 + 2 * q^85 - 60 * q^86 - 28 * q^87 - 32 * q^88 - 12 * q^89 + 46 * q^90 - 8 * q^92 + 64 * q^93 + 40 * q^95 - 56 * q^96 - 60 * q^99

Introduction

L-functions

Modular forms

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