LMFDB - Embedded newform 414.2.i.f.397.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(55,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("414.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.i (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 46)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			397.1
Root			$0.959493 - 0.281733i$ of defining polynomial
Character	$\chi$	$=$	414.397
Dual form			414.2.i.f.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 + 0.909632i) q^{2} +(-0.654861 - 0.755750i) q^{4} +(-0.767092 + 0.492980i) q^{5} +(-0.601808 + 4.18567i) q^{7} +(0.959493 - 0.281733i) q^{8} +O(q^{10})$	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.654861 - 0.755750i) q^{4} +(-0.767092 + 0.492980i) q^{5} +(-0.601808 + 4.18567i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.129769 - 0.902563i) q^{10} +(-0.630972 - 1.38164i) q^{11} +(-0.0694846 - 0.483276i) q^{13} +(-3.55742 - 2.28621i) q^{14} +(-0.142315 + 0.989821i) q^{16} +(-2.10926 + 2.43422i) q^{17} +(-3.48325 - 4.01989i) q^{19} +(0.874908 + 0.256896i) q^{20} +1.51890 q^{22} +(-2.89510 + 3.82340i) q^{23} +(-1.73167 + 3.79184i) q^{25} +(0.468468 + 0.137555i) q^{26} +(3.55742 - 2.28621i) q^{28} +(-5.24460 + 6.05259i) q^{29} +(-7.89071 + 2.31692i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(-1.33803 - 2.92987i) q^{34} +(-1.60181 - 3.50747i) q^{35} +(6.47324 + 4.16010i) q^{37} +(5.10362 - 1.49856i) q^{38} +(-0.597131 + 0.689126i) q^{40} +(7.73806 - 4.97295i) q^{41} +(4.30093 + 1.26287i) q^{43} +(-0.630972 + 1.38164i) q^{44} +(-2.27522 - 4.22177i) q^{46} +0.273137 q^{47} +(-10.4412 - 3.06580i) q^{49} +(-2.72981 - 3.15037i) q^{50} +(-0.319733 + 0.368991i) q^{52} +(1.04432 - 7.26339i) q^{53} +(1.16513 + 0.748786i) q^{55} +(0.601808 + 4.18567i) q^{56} +(-3.32694 - 7.28499i) q^{58} +(-0.161473 - 1.12307i) q^{59} +(13.8768 - 4.07459i) q^{61} +(1.17037 - 8.14013i) q^{62} +(0.841254 - 0.540641i) q^{64} +(0.291546 + 0.336462i) q^{65} +(0.851175 - 1.86381i) q^{67} +3.22094 q^{68} +3.85592 q^{70} +(-4.40736 + 9.65077i) q^{71} +(-0.420749 - 0.485571i) q^{73} +(-6.47324 + 4.16010i) q^{74} +(-0.756983 + 5.26493i) q^{76} +(6.16279 - 1.80956i) q^{77} +(0.230973 + 1.60645i) q^{79} +(-0.378794 - 0.829443i) q^{80} +(1.30905 + 9.10463i) q^{82} +(10.0793 + 6.47759i) q^{83} +(0.417977 - 2.90710i) q^{85} +(-2.93542 + 3.38765i) q^{86} +(-0.994666 - 1.14791i) q^{88} +(8.97609 + 2.63562i) q^{89} +2.06465 q^{91} +(4.78542 - 0.315828i) q^{92} +(-0.113465 + 0.248454i) q^{94} +(4.65370 + 1.36645i) q^{95} +(-3.83870 + 2.46698i) q^{97} +(7.12617 - 8.22404i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} - q^{4} + 6 q^{5} + 3 q^{7} + q^{8}+O(q^{10}) $ 10 * q + q^2 - q^4 + 6 * q^5 + 3 * q^7 + q^8	$ 10 q + q^{2} - q^{4} + 6 q^{5} + 3 q^{7} + q^{8} - 6 q^{10} + 12 q^{11} - 14 q^{13} - 3 q^{14} - q^{16} - 15 q^{17} + 2 q^{19} - 5 q^{20} + 10 q^{22} + q^{23} + 13 q^{25} + 3 q^{26} + 3 q^{28} + 8 q^{29} - 21 q^{31} + q^{32} - 7 q^{34} - 7 q^{35} + 28 q^{37} + 9 q^{38} - 6 q^{40} + 31 q^{41} + 11 q^{43} + 12 q^{44} - 12 q^{46} - 18 q^{47} - 24 q^{49} - 2 q^{50} + 8 q^{52} + 21 q^{53} + 5 q^{55} - 3 q^{56} - 8 q^{58} + 5 q^{59} + 37 q^{61} - q^{62} - q^{64} - 37 q^{65} - 13 q^{67} - 26 q^{68} + 18 q^{70} - 49 q^{71} - 8 q^{73} - 28 q^{74} - 20 q^{76} + 8 q^{77} + 8 q^{79} - 5 q^{80} + 2 q^{82} + 7 q^{83} - 42 q^{85} - 22 q^{86} - q^{88} + 13 q^{89} - 24 q^{91} + 23 q^{92} - 37 q^{94} + 10 q^{95} - 32 q^{97} + 24 q^{98}+O(q^{100}) $ 10 * q + q^2 - q^4 + 6 * q^5 + 3 * q^7 + q^8 - 6 * q^10 + 12 * q^11 - 14 * q^13 - 3 * q^14 - q^16 - 15 * q^17 + 2 * q^19 - 5 * q^20 + 10 * q^22 + q^23 + 13 * q^25 + 3 * q^26 + 3 * q^28 + 8 * q^29 - 21 * q^31 + q^32 - 7 * q^34 - 7 * q^35 + 28 * q^37 + 9 * q^38 - 6 * q^40 + 31 * q^41 + 11 * q^43 + 12 * q^44 - 12 * q^46 - 18 * q^47 - 24 * q^49 - 2 * q^50 + 8 * q^52 + 21 * q^53 + 5 * q^55 - 3 * q^56 - 8 * q^58 + 5 * q^59 + 37 * q^61 - q^62 - q^64 - 37 * q^65 - 13 * q^67 - 26 * q^68 + 18 * q^70 - 49 * q^71 - 8 * q^73 - 28 * q^74 - 20 * q^76 + 8 * q^77 + 8 * q^79 - 5 * q^80 + 2 * q^82 + 7 * q^83 - 42 * q^85 - 22 * q^86 - q^88 + 13 * q^89 - 24 * q^91 + 23 * q^92 - 37 * q^94 + 10 * q^95 - 32 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

Coefficient data

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

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

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

$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$3$		0			0
$3$		0			0
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	−0.767092	+	0.492980i	−0.343054	+	0.220467i	−0.700810	−	0.713347i	$-0.747178\pi$
$5$	−0.767092	+	0.492980i	−0.343054	+	0.220467i	0.357757	+	0.933815i	$0.383542\pi$
$6$		0			0
$7$	−0.601808	+	4.18567i	−0.227462	+	1.58203i	0.481281	+	0.876566i	$0.340172\pi$
$7$	−0.601808	+	4.18567i	−0.227462	+	1.58203i	−0.708743	+	0.705467i	$0.750738\pi$
$8$	0.959493	−	0.281733i	0.339232	−	0.0996075i
$9$		0			0
$10$	−0.129769	−	0.902563i	−0.0410365	−	0.285415i
$11$	−0.630972	−	1.38164i	−0.190245	−	0.416579i	0.790341	−	0.612667i	$-0.209903\pi$
$11$	−0.630972	−	1.38164i	−0.190245	−	0.416579i	−0.980586	+	0.196088i	$0.937176\pi$
$12$		0			0
$13$	−0.0694846	−	0.483276i	−0.0192715	−	0.134037i	0.977914	−	0.209007i	$-0.0670230\pi$
$13$	−0.0694846	−	0.483276i	−0.0192715	−	0.134037i	−0.997186	+	0.0749700i	$0.976114\pi$
$14$	−3.55742	−	2.28621i	−0.950759	−	0.611016i
$15$		0			0
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	−2.10926	+	2.43422i	−0.511572	+	0.590385i	−0.951500	−	0.307647i	$-0.900458\pi$
$17$	−2.10926	+	2.43422i	−0.511572	+	0.590385i	0.439929	+	0.898033i	$0.355004\pi$
$18$		0			0
$19$	−3.48325	−	4.01989i	−0.799113	−	0.922226i	0.199219	−	0.979955i	$-0.436159\pi$
$19$	−3.48325	−	4.01989i	−0.799113	−	0.922226i	−0.998332	+	0.0577292i	$0.981614\pi$
$20$	0.874908	+	0.256896i	0.195635	+	0.0574437i
$21$		0			0
$22$	1.51890			0.323830
$23$	−2.89510	+	3.82340i	−0.603670	+	0.797235i
$23$	−2.89510	+	3.82340i	−0.603670	+	0.797235i
$24$		0			0
$25$	−1.73167	+	3.79184i	−0.346335	+	0.758368i
$26$	0.468468	+	0.137555i	0.0918741	+	0.0269767i
$27$		0			0
$28$	3.55742	−	2.28621i	0.672288	−	0.432053i
$29$	−5.24460	+	6.05259i	−0.973898	+	1.12394i	0.0183713	+	0.999831i	$0.494152\pi$
$29$	−5.24460	+	6.05259i	−0.973898	+	1.12394i	−0.992269	+	0.124107i	$0.960394\pi$
$30$		0			0
$31$	−7.89071	+	2.31692i	−1.41721	+	0.416131i	−0.898559	−	0.438853i	$-0.855385\pi$
$31$	−7.89071	+	2.31692i	−1.41721	+	0.416131i	−0.518654	+	0.854984i	$0.673567\pi$
$32$	−0.841254	−	0.540641i	−0.148714	−	0.0955727i
$33$		0			0
$34$	−1.33803	−	2.92987i	−0.229469	−	0.502468i
$35$	−1.60181	−	3.50747i	−0.270755	−	0.592871i
$36$		0			0
$37$	6.47324	+	4.16010i	1.06419	+	0.683916i	0.950854	−	0.309640i	$-0.100209\pi$
$37$	6.47324	+	4.16010i	1.06419	+	0.683916i	0.113341	+	0.993556i	$0.463845\pi$
$38$	5.10362	−	1.49856i	0.827916	−	0.243098i
$39$		0			0
$40$	−0.597131	+	0.689126i	−0.0944147	+	0.108960i
$41$	7.73806	−	4.97295i	1.20848	−	0.776644i	0.228078	−	0.973643i	$-0.426756\pi$
$41$	7.73806	−	4.97295i	1.20848	−	0.776644i	0.980404	+	0.196998i	$0.0631194\pi$
$42$		0			0
$43$	4.30093	+	1.26287i	0.655886	+	0.192586i	0.592709	−	0.805417i	$-0.298058\pi$
$43$	4.30093	+	1.26287i	0.655886	+	0.192586i	0.0631773	+	0.998002i	$0.479877\pi$
$44$	−0.630972	+	1.38164i	−0.0951227	+	0.208290i
$45$		0			0
$46$	−2.27522	−	4.22177i	−0.335463	−	0.622466i
$47$	0.273137			0.0398411			0.0199205	−	0.999802i	$-0.493659\pi$
$47$	0.273137			0.0398411			0.0199205	+	0.999802i	$0.493659\pi$
$48$		0			0
$49$	−10.4412	−	3.06580i	−1.49160	−	0.437972i
$50$	−2.72981	−	3.15037i	−0.386054	−	0.445530i
$51$		0			0
$52$	−0.319733	+	0.368991i	−0.0443389	+	0.0511699i
$53$	1.04432	−	7.26339i	0.143448	−	0.997704i	−0.783199	−	0.621771i	$-0.786413\pi$
$53$	1.04432	−	7.26339i	0.143448	−	0.997704i	0.926647	−	0.375933i	$-0.122678\pi$
$54$		0			0
$55$	1.16513	+	0.748786i	0.157107	+	0.100966i
$56$	0.601808	+	4.18567i	0.0804200	+	0.559333i
$57$		0			0
$58$	−3.32694	−	7.28499i	−0.436849	−	0.956566i
$59$	−0.161473	−	1.12307i	−0.0210220	−	0.146211i	0.976607	−	0.215032i	$-0.0689855\pi$
$59$	−0.161473	−	1.12307i	−0.0210220	−	0.146211i	−0.997629	+	0.0688206i	$0.978076\pi$
$60$		0			0
$61$	13.8768	−	4.07459i	1.77674	−	0.521698i	0.781922	−	0.623377i	$-0.214240\pi$
$61$	13.8768	−	4.07459i	1.77674	−	0.521698i	0.994817	+	0.101679i	$0.0324215\pi$
$62$	1.17037	−	8.14013i	0.148638	−	1.03380i
$63$		0			0
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	0.291546	+	0.336462i	0.0361619	+	0.0417330i
$66$		0			0
$67$	0.851175	−	1.86381i	0.103988	−	0.227701i	−0.850485	−	0.525999i	$-0.823692\pi$
$67$	0.851175	−	1.86381i	0.103988	−	0.227701i	0.954473	+	0.298298i	$0.0964189\pi$
$68$	3.22094			0.390596
$69$		0			0
$70$	3.85592			0.460871
$71$	−4.40736	+	9.65077i	−0.523057	+	1.14534i	0.445212	+	0.895425i	$0.353128\pi$
$71$	−4.40736	+	9.65077i	−0.523057	+	1.14534i	−0.968269	+	0.249910i	$0.919599\pi$
$72$		0			0
$73$	−0.420749	−	0.485571i	−0.0492450	−	0.0568317i	0.730593	−	0.682814i	$-0.239244\pi$
$73$	−0.420749	−	0.485571i	−0.0492450	−	0.0568317i	−0.779838	+	0.625982i	$0.784698\pi$
$74$	−6.47324	+	4.16010i	−0.752499	+	0.483602i
$75$		0			0
$76$	−0.756983	+	5.26493i	−0.0868319	+	0.603929i
$77$	6.16279	−	1.80956i	0.702316	−	0.206218i
$78$		0			0
$79$	0.230973	+	1.60645i	0.0259865	+	0.180740i	0.998681	−	0.0513506i	$-0.0163526\pi$
$79$	0.230973	+	1.60645i	0.0259865	+	0.180740i	−0.972694	+	0.232090i	$0.925443\pi$
$80$	−0.378794	−	0.829443i	−0.0423504	−	0.0927345i
$81$		0			0
$82$	1.30905	+	9.10463i	0.144560	+	1.00544i
$83$	10.0793	+	6.47759i	1.10635	+	0.711008i	0.960495	−	0.278298i	$-0.0897704\pi$
$83$	10.0793	+	6.47759i	1.10635	+	0.711008i	0.145855	+	0.989306i	$0.453407\pi$
$84$		0			0
$85$	0.417977	−	2.90710i	0.0453360	−	0.315319i
$86$	−2.93542	+	3.38765i	−0.316534	+	0.365300i
$87$		0			0
$88$	−0.994666	−	1.14791i	−0.106032	−	0.122367i
$89$	8.97609	+	2.63562i	0.951463	+	0.279375i	0.720396	−	0.693563i	$-0.243960\pi$
$89$	8.97609	+	2.63562i	0.951463	+	0.279375i	0.231067	+	0.972938i	$0.425778\pi$
$90$		0			0
$91$	2.06465			0.216434
$92$	4.78542	−	0.315828i	0.498915	−	0.0329273i
$93$		0			0
$94$	−0.113465	+	0.248454i	−0.0117030	+	0.0256260i
$95$	4.65370	+	1.36645i	0.477460	+	0.140195i
$96$		0			0
$97$	−3.83870	+	2.46698i	−0.389761	+	0.250484i	−0.720815	−	0.693128i	$-0.756232\pi$
$97$	−3.83870	+	2.46698i	−0.389761	+	0.250484i	0.331054	+	0.943612i	$0.392596\pi$
$98$	7.12617	−	8.22404i	0.719852	−	0.830754i
$99$		0			0
$100$	3.99969	−	1.17441i	0.399969	−	0.117441i
$101$	0.793605	+	0.510019i	0.0789666	+	0.0507488i	0.579528	−	0.814952i	$-0.303237\pi$
$101$	0.793605	+	0.510019i	0.0789666	+	0.0507488i	−0.500562	+	0.865701i	$0.666873\pi$
$102$		0			0
$103$	3.83595	+	8.39955i	0.377967	+	0.827632i	0.999037	+	0.0438773i	$0.0139710\pi$
$103$	3.83595	+	8.39955i	0.377967	+	0.827632i	−0.621070	+	0.783755i	$0.713302\pi$
$104$	−0.202824	−	0.444124i	−0.0198886	−	0.0435499i
$105$		0			0
$106$	6.17319	+	3.96727i	0.599593	+	0.385335i
$107$	−3.67940	+	1.08037i	−0.355701	+	0.104443i	−0.454701	−	0.890644i	$-0.650254\pi$
$107$	−3.67940	+	1.08037i	−0.355701	+	0.104443i	0.0990000	+	0.995087i	$0.468436\pi$
$108$		0			0
$109$	−5.92480	+	6.83758i	−0.567493	+	0.654921i	−0.964868	−	0.262735i	$-0.915376\pi$
$109$	−5.92480	+	6.83758i	−0.567493	+	0.654921i	0.397376	+	0.917656i	$0.369921\pi$
$110$	−1.16513	+	0.748786i	−0.111091	+	0.0713939i
$111$		0			0
$112$	−4.05742	−	1.19136i	−0.383390	−	0.112573i
$113$	4.66678	−	10.2188i	0.439013	−	0.961305i	−0.552765	−	0.833337i	$-0.686427\pi$
$113$	4.66678	−	10.2188i	0.439013	−	0.961305i	0.991778	−	0.127968i	$-0.0408455\pi$
$114$		0			0
$115$	0.335945	−	4.36013i	0.0313270	−	0.406584i
$116$	8.00872			0.743591
$117$		0			0
$118$	1.08866	+	0.319659i	0.100219	+	0.0294270i
$119$	−8.91946	−	10.2936i	−0.817646	−	0.943614i
$120$		0			0
$121$	5.69267	−	6.56970i	0.517516	−	0.597245i
$122$	−2.05824	+	14.3154i	−0.186345	+	1.29606i
$123$		0			0
$124$	6.91833	+	4.44614i	0.621284	+	0.399275i
$125$	−1.18979	−	8.27518i	−0.106418	−	0.740155i
$126$		0			0
$127$	1.86599	+	4.08594i	0.165580	+	0.362569i	0.974174	−	0.225797i	$-0.0724987\pi$
$127$	1.86599	+	4.08594i	0.165580	+	0.362569i	−0.808595	+	0.588366i	$0.799771\pi$
$128$	0.142315	+	0.989821i	0.0125790	+	0.0874887i
$129$		0			0
$130$	−0.427170	+	0.125428i	−0.0374653	+	0.0110008i
$131$	−1.14934	+	7.99383i	−0.100418	+	0.698424i	0.875964	+	0.482376i	$0.160226\pi$
$131$	−1.14934	+	7.99383i	−0.100418	+	0.698424i	−0.976383	+	0.216048i	$0.930683\pi$
$132$		0			0
$133$	18.9222	−	12.1605i	1.64076	−	1.05445i
$134$	1.34179	+	1.54851i	0.115913	+	0.133771i
$135$		0			0
$136$	−1.33803	+	2.92987i	−0.114735	+	0.251234i
$137$	0.602808			0.0515013			0.0257507	−	0.999668i	$-0.491802\pi$
$137$	0.602808			0.0515013			0.0257507	+	0.999668i	$0.491802\pi$
$138$		0			0
$139$	−15.6895			−1.33077			−0.665384	−	0.746501i	$-0.731732\pi$
$139$	−15.6895			−1.33077			−0.665384	+	0.746501i	$0.731732\pi$
$140$	−1.60181	+	3.50747i	−0.135377	+	0.296435i
$141$		0			0
$142$	−6.94777	−	8.01815i	−0.583044	−	0.672868i
$143$	−0.623869	+	0.400936i	−0.0521705	+	0.0335280i
$144$		0			0
$145$	1.03928	−	7.22838i	0.0863078	−	0.600284i
$146$	0.616476	−	0.181014i	0.0510199	−	0.0149808i
$147$		0			0
$148$	−1.09508	−	7.61644i	−0.0900149	−	0.626067i
$149$	1.68160	+	3.68220i	0.137762	+	0.301658i	0.965921	−	0.258836i	$-0.0833388\pi$
$149$	1.68160	+	3.68220i	0.137762	+	0.301658i	−0.828159	+	0.560493i	$0.810612\pi$
$150$		0			0
$151$	0.0103213	+	0.0717863i	0.000839936	+	0.00584189i	0.990237	−	0.139393i	$-0.0445152\pi$
$151$	0.0103213	+	0.0717863i	0.000839936	+	0.00584189i	−0.989397	+	0.145235i	$0.953606\pi$
$152$	−4.47469	−	2.87571i	−0.362945	−	0.233251i
$153$		0			0
$154$	−0.914084	+	6.35759i	−0.0736590	+	0.512309i
$155$	4.91070	−	5.66726i	0.394437	−	0.455205i
$156$		0			0
$157$	−0.0235791	−	0.0272118i	−0.00188182	−	0.00217174i	0.754808	−	0.655946i	$-0.227730\pi$
$157$	−0.0235791	−	0.0272118i	−0.00188182	−	0.00217174i	−0.756690	+	0.653774i	$0.773185\pi$
$158$	−1.55723	−	0.457243i	−0.123886	−	0.0363763i
$159$		0			0
$160$	0.911844			0.0720876
$161$	−14.2612	−	14.4189i	−1.12394	−	1.13637i
$162$		0			0
$163$	−6.64774	+	14.5565i	−0.520691	+	1.14015i	0.448486	+	0.893790i	$0.351963\pi$
$163$	−6.64774	+	14.5565i	−0.520691	+	1.14015i	−0.969177	+	0.246365i	$0.920764\pi$
$164$	−8.82566	−	2.59145i	−0.689168	−	0.202358i
$165$		0			0
$166$	−10.0793	+	6.47759i	−0.782307	+	0.502758i
$167$	3.00660	−	3.46980i	0.232657	−	0.268501i	−0.627401	−	0.778696i	$-0.715881\pi$
$167$	3.00660	−	3.46980i	0.232657	−	0.268501i	0.860059	+	0.510195i	$0.170427\pi$
$168$		0			0
$169$	12.2447	−	3.59536i	0.941899	−	0.276566i
$170$	2.47075	+	1.58786i	0.189498	+	0.121783i
$171$		0			0
$172$	−1.86210	−	4.07743i	−0.141984	−	0.310901i
$173$	8.60729	+	18.8473i	0.654400	+	1.43294i	0.887650	+	0.460519i	$0.152337\pi$
$173$	8.60729	+	18.8473i	0.654400	+	1.43294i	−0.233250	+	0.972417i	$0.574936\pi$
$174$		0			0
$175$	−14.8292	−	9.53017i	−1.12098	−	0.720413i
$176$	1.45737	−	0.427923i	0.109853	−	0.0322559i
$177$		0			0
$178$	−6.12624	+	7.07006i	−0.459181	+	0.529923i
$179$	0.458738	−	0.294813i	0.0342877	−	0.0220354i	−0.523385	−	0.852097i	$-0.675331\pi$
$179$	0.458738	−	0.294813i	0.0342877	−	0.0220354i	0.557672	+	0.830061i	$0.311695\pi$
$180$		0			0
$181$	2.45842	+	0.721857i	0.182733	+	0.0536552i	0.371819	−	0.928305i	$-0.378734\pi$
$181$	2.45842	+	0.721857i	0.182733	+	0.0536552i	−0.189086	+	0.981961i	$0.560552\pi$
$182$	−0.857685	+	1.87807i	−0.0635759	+	0.139212i
$183$		0			0
$184$	−1.70065	+	4.48417i	−0.125373	+	0.330578i
$185$	−7.01642			−0.515857
$186$		0			0
$187$	4.69410	+	1.37831i	0.343266	+	0.100792i
$188$	−0.178866	−	0.206423i	−0.0130452	−	0.0150549i
$189$		0			0
$190$	−3.17618	+	3.66551i	−0.230425	+	0.265924i
$191$	−0.554917	+	3.85953i	−0.0401524	+	0.279266i	−0.999999	−	0.00125875i	$-0.999599\pi$
$191$	−0.554917	+	3.85953i	−0.0401524	+	0.279266i	0.959847	+	0.280525i	$0.0905084\pi$
$192$		0			0
$193$	−11.2055	−	7.20135i	−0.806590	−	0.518364i	0.0711699	−	0.997464i	$-0.477327\pi$
$193$	−11.2055	−	7.20135i	−0.806590	−	0.518364i	−0.877760	+	0.479100i	$0.840963\pi$
$194$	−0.649393	−	4.51662i	−0.0466237	−	0.324275i
$195$		0			0
$196$	4.52053	+	9.89858i	0.322895	+	0.707042i
$197$	2.37532	+	16.5207i	0.169235	+	1.17705i	0.880471	+	0.474100i	$0.157226\pi$
$197$	2.37532	+	16.5207i	0.169235	+	1.17705i	−0.711237	+	0.702953i	$0.751865\pi$
$198$		0			0
$199$	2.86040	−	0.839888i	0.202768	−	0.0595381i	−0.178771	−	0.983891i	$-0.557212\pi$
$199$	2.86040	−	0.839888i	0.202768	−	0.0595381i	0.381539	+	0.924353i	$0.375394\pi$
$200$	−0.593245	+	4.12611i	−0.0419488	+	0.291760i
$201$		0			0
$202$	−0.793605	+	0.510019i	−0.0558378	+	0.0358848i
$203$	−22.1779	−	25.5946i	−1.55658	−	1.79639i
$204$		0			0
$205$	−3.48424	+	7.62942i	−0.243350	+	0.532862i
$206$	−9.23401			−0.643364
$207$		0			0
$208$	0.488245			0.0338537
$209$	−3.35619	+	7.34903i	−0.232153	+	0.508343i
$210$		0			0
$211$	−16.0787	−	18.5558i	−1.10690	−	1.27743i	−0.957430	−	0.288664i	$-0.906789\pi$
$211$	−16.0787	−	18.5558i	−1.10690	−	1.27743i	−0.149470	−	0.988766i	$-0.547757\pi$
$212$	−6.17319	+	3.96727i	−0.423976	+	0.272473i
$213$		0			0
$214$	0.545739	−	3.79570i	0.0373060	−	0.259469i
$215$	−3.92178	+	1.15154i	−0.267463	+	0.0785343i
$216$		0			0
$217$	−4.94917	−	34.4222i	−0.335971	−	2.33673i
$218$	−3.75843	−	8.22982i	−0.254553	−	0.557394i
$219$		0			0
$220$	−0.197106	−	1.37090i	−0.0132889	−	0.0924260i
$221$	1.32296	+	0.850215i	0.0889920	+	0.0571917i
$222$		0			0
$223$	0.840553	−	5.84618i	0.0562876	−	0.391489i	−0.942130	−	0.335249i	$-0.891180\pi$
$223$	0.840553	−	5.84618i	0.0562876	−	0.391489i	0.998417	−	0.0562402i	$-0.0179113\pi$
$224$	2.76921	−	3.19584i	0.185026	−	0.213531i
$225$		0			0
$226$	7.35671	+	8.49010i	0.489361	+	0.564753i
$227$	−5.19631	−	1.52578i	−0.344892	−	0.101269i	0.104699	−	0.994504i	$-0.466612\pi$
$227$	−5.19631	−	1.52578i	−0.344892	−	0.101269i	−0.449591	+	0.893235i	$0.648430\pi$
$228$		0			0
$229$	14.7114			0.972154			0.486077	−	0.873916i	$-0.338427\pi$
$229$	14.7114			0.972154			0.486077	+	0.873916i	$0.338427\pi$
$230$	3.82656	+	2.11685i	0.252316	+	0.139581i
$231$		0			0
$232$	−3.32694	+	7.28499i	−0.218425	+	0.478283i
$233$	−24.5668	−	7.21346i	−1.60942	−	0.472569i	−0.651275	−	0.758842i	$-0.725766\pi$
$233$	−24.5668	−	7.21346i	−1.60942	−	0.472569i	−0.958148	+	0.286272i	$0.907584\pi$
$234$		0			0
$235$	−0.209521	+	0.134651i	−0.0136676	+	0.00878365i
$236$	−0.743017	+	0.857487i	−0.0483663	+	0.0558176i
$237$		0			0
$238$	13.0687	−	3.83731i	0.847116	−	0.248736i
$239$	−1.70531	−	1.09594i	−0.110307	−	0.0708903i	0.484324	−	0.874889i	$-0.339066\pi$
$239$	−1.70531	−	1.09594i	−0.110307	−	0.0708903i	−0.594631	+	0.803998i	$0.702702\pi$
$240$		0			0
$241$	7.69901	+	16.8585i	0.495937	+	1.08595i	0.977769	+	0.209687i	$0.0672444\pi$
$241$	7.69901	+	16.8585i	0.495937	+	1.08595i	−0.481832	+	0.876264i	$0.660028\pi$
$242$	3.61118	+	7.90739i	0.232136	+	0.508306i
$243$		0			0
$244$	−12.1667	−	7.81908i	−0.778895	−	0.500565i
$245$	9.52072	−	2.79554i	0.608256	−	0.178600i
$246$		0			0
$247$	−1.70068	+	1.96269i	−0.108212	+	0.124883i
$248$	−6.91833	+	4.44614i	−0.439314	+	0.282330i
$249$		0			0
$250$	8.02163	+	2.35536i	0.507332	+	0.148966i
$251$	−9.74401	+	21.3364i	−0.615036	+	1.34674i	0.304039	+	0.952660i	$0.401665\pi$
$251$	−9.74401	+	21.3364i	−0.615036	+	1.34674i	−0.919075	+	0.394082i	$0.871063\pi$
$252$		0			0
$253$	7.10928	+	1.58751i	0.446957	+	0.0998060i
$254$	−4.49186			−0.281844
$255$		0			0
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	6.80351	+	7.85166i	0.424391	+	0.489773i	0.927170	−	0.374642i	$-0.122234\pi$
$257$	6.80351	+	7.85166i	0.424391	+	0.489773i	−0.502779	+	0.864415i	$0.667689\pi$
$258$		0			0
$259$	−21.3084	+	24.5912i	−1.32404	+	1.52803i
$260$	0.0633591	−	0.440672i	0.00392936	−	0.0273293i
$261$		0			0
$262$	−6.79399	−	4.36623i	−0.419734	−	0.269747i
$263$	−3.68520	−	25.6312i	−0.227239	−	1.58049i	−0.709659	−	0.704545i	$-0.751151\pi$
$263$	−3.68520	−	25.6312i	−0.227239	−	1.58049i	0.482420	−	0.875940i	$-0.339758\pi$
$264$		0			0
$265$	2.77962	+	6.08652i	0.170751	+	0.373892i
$266$	3.20106	+	22.2639i	0.196270	+	1.36509i
$267$		0			0
$268$	−1.96598	+	0.577263i	−0.120091	+	0.0352620i
$269$	1.83374	−	12.7540i	0.111805	−	0.777623i	−0.854357	−	0.519687i	$-0.826049\pi$
$269$	1.83374	−	12.7540i	0.111805	−	0.777623i	0.966162	−	0.257936i	$-0.0830423\pi$
$270$		0			0
$271$	−13.5616	+	8.71552i	−0.823809	+	0.529430i	−0.883305	−	0.468799i	$-0.844687\pi$
$271$	−13.5616	+	8.71552i	−0.823809	+	0.529430i	0.0594961	+	0.998229i	$0.481051\pi$
$272$	−2.10926	−	2.43422i	−0.127893	−	0.147596i
$273$		0			0
$274$	−0.250415	+	0.548333i	−0.0151281	+	0.0331260i
$275$	6.33158			0.381809
$276$		0			0
$277$	−4.14896			−0.249287			−0.124643	−	0.992202i	$-0.539779\pi$
$277$	−4.14896			−0.249287			−0.124643	+	0.992202i	$0.539779\pi$
$278$	6.51767	−	14.2717i	0.390904	−	0.855960i
$279$		0			0
$280$	−2.52509	−	2.91411i	−0.150903	−	0.174151i
$281$	4.37371	−	2.81081i	0.260914	−	0.167679i	−0.403644	−	0.914916i	$-0.632256\pi$
$281$	4.37371	−	2.81081i	0.260914	−	0.167679i	0.664557	+	0.747237i	$0.268620\pi$
$282$		0			0
$283$	1.98080	−	13.7768i	0.117746	−	0.818944i	−0.842281	−	0.539038i	$-0.818788\pi$
$283$	1.98080	−	13.7768i	0.117746	−	0.818944i	0.960028	−	0.279905i	$-0.0903031\pi$
$284$	10.1798	−	2.98905i	0.604058	−	0.177368i
$285$		0			0
$286$	−0.105540	−	0.734046i	−0.00624070	−	0.0434050i
$287$	16.1583	+	35.3817i	0.953793	+	2.08852i
$288$		0			0
$289$	0.942917	+	6.55813i	0.0554657	+	0.385773i
$290$	6.14343	+	3.94814i	0.360755	+	0.231843i
$291$		0			0
$292$	−0.0914376	+	0.635962i	−0.00535098	+	0.0372169i
$293$	16.9201	−	19.5268i	0.988481	−	1.14077i	−0.00156123	−	0.999999i	$-0.500497\pi$
$293$	16.9201	−	19.5268i	0.988481	−	1.14077i	0.990042	−	0.140769i	$-0.0449576\pi$
$294$		0			0
$295$	0.677515	+	0.781894i	0.0394465	+	0.0455237i
$296$	7.38307	+	2.16786i	0.429132	+	0.126005i
$297$		0			0
$298$	−4.04801			−0.234495
$299$	2.04892	+	1.13346i	0.118492	+	0.0655498i
$300$		0			0
$301$	−7.87428	+	17.2423i	−0.453866	+	0.993828i
$302$	−0.0695867	−	0.0204325i	−0.00400427	−	0.00117576i
$303$		0			0
$304$	4.47469	−	2.87571i	0.256641	−	0.164933i
$305$	−8.63607	+	9.96656i	−0.494500	+	0.570684i
$306$		0			0
$307$	31.6662	−	9.29803i	1.80728	−	0.530667i	0.808924	−	0.587913i	$-0.200050\pi$
$307$	31.6662	−	9.29803i	1.80728	−	0.530667i	0.998360	+	0.0572466i	$0.0182321\pi$
$308$	−5.40335	−	3.47252i	−0.307884	−	0.197865i
$309$		0			0
$310$	3.11514	+	6.82120i	0.176928	+	0.387418i
$311$	−6.17137	−	13.5134i	−0.349946	−	0.766276i	−0.999980	−	0.00637009i	$-0.997972\pi$
$311$	−6.17137	−	13.5134i	−0.349946	−	0.766276i	0.650033	−	0.759906i	$-0.274755\pi$
$312$		0			0
$313$	5.85184	+	3.76075i	0.330765	+	0.212570i	0.695473	−	0.718552i	$-0.255195\pi$
$313$	5.85184	+	3.76075i	0.330765	+	0.212570i	−0.364708	+	0.931122i	$0.618831\pi$
$314$	0.0345478	−	0.0101442i	0.00194965	−	0.000572468i
$315$		0			0
$316$	1.06282	−	1.22656i	0.0597882	−	0.0689993i
$317$	−3.72494	+	2.39388i	−0.209214	+	0.134453i	−0.641052	−	0.767498i	$-0.721502\pi$
$317$	−3.72494	+	2.39388i	−0.209214	+	0.134453i	0.431838	+	0.901951i	$0.357865\pi$
$318$		0			0
$319$	11.6717	+	3.42711i	0.653489	+	0.191882i
$320$	−0.378794	+	0.829443i	−0.0211752	+	0.0463672i
$321$		0			0
$322$	19.0402	−	6.98262i	1.06107	−	0.389126i
$323$	17.1324			0.953272
$324$		0			0
$325$	1.95283	+	0.573402i	0.108323	+	0.0318066i
$326$	−10.4795	−	12.0940i	−0.580406	−	0.669824i
$327$		0			0
$328$	6.02357	−	6.95157i	0.332596	−	0.383836i
$329$	−0.164376	+	1.14326i	−0.00906233	+	0.0630299i
$330$		0			0
$331$	4.30350	+	2.76569i	0.236542	+	0.152016i	0.653542	−	0.756890i	$-0.273282\pi$
$331$	4.30350	+	2.76569i	0.236542	+	0.152016i	−0.417000	+	0.908906i	$0.636919\pi$
$332$	−1.70512	−	11.8594i	−0.0935805	−	0.650867i
$333$		0			0
$334$	1.90725	+	4.17630i	0.104360	+	0.228517i
$335$	0.265893	+	1.84933i	0.0145273	+	0.101040i
$336$		0			0
$337$	−11.5860	+	3.40195i	−0.631129	+	0.185316i	−0.581624	−	0.813458i	$-0.697583\pi$
$337$	−11.5860	+	3.40195i	−0.631129	+	0.185316i	−0.0495050	+	0.998774i	$0.515764\pi$
$338$	−1.81617	+	12.6317i	−0.0987865	+	0.687075i
$339$		0			0
$340$	−2.47075	+	1.58786i	−0.133995	+	0.0861137i
$341$	8.17996	+	9.44018i	0.442970	+	0.511215i
$342$		0			0
$343$	6.81933	−	14.9322i	0.368209	−	0.806266i
$344$	4.48251			0.241681
$345$		0			0
$346$	−20.7197			−1.11390
$347$	−8.34765	+	18.2788i	−0.448125	+	0.981257i	0.541910	+	0.840437i	$0.317701\pi$
$347$	−8.34765	+	18.2788i	−0.448125	+	0.981257i	−0.990035	+	0.140821i	$0.955026\pi$
$348$		0			0
$349$	−5.83909	−	6.73867i	−0.312559	−	0.360713i	0.577634	−	0.816296i	$-0.303976\pi$
$349$	−5.83909	−	6.73867i	−0.312559	−	0.360713i	−0.890193	+	0.455583i	$0.849431\pi$
$350$	14.8292	−	9.53017i	0.792656	−	0.509409i
$351$		0			0
$352$	−0.216162	+	1.50344i	−0.0115214	+	0.0801334i
$353$	−12.1485	+	3.56713i	−0.646601	+	0.189859i	−0.588558	−	0.808455i	$-0.700304\pi$
$353$	−12.1485	+	3.56713i	−0.646601	+	0.189859i	−0.0580428	+	0.998314i	$0.518486\pi$
$354$		0			0
$355$	−1.37679	−	9.57577i	−0.0730723	−	0.508229i
$356$	−3.88622	−	8.50964i	−0.205969	−	0.451010i
$357$		0			0
$358$	0.0776047	+	0.539753i	0.00410154	+	0.0285268i
$359$	−8.24006	−	5.29557i	−0.434894	−	0.279489i	0.304821	−	0.952410i	$-0.401403\pi$
$359$	−8.24006	−	5.29557i	−0.434894	−	0.279489i	−0.739715	+	0.672920i	$0.765040\pi$
$360$		0			0
$361$	−1.32247	+	9.19798i	−0.0696037	+	0.484104i
$362$	−1.67789	+	1.93639i	−0.0881878	+	0.101774i
$363$		0			0
$364$	−1.35206	−	1.56036i	−0.0708670	−	0.0817849i
$365$	0.562130	+	0.165056i	0.0294232	+	0.00863944i
$366$		0			0
$367$	10.9305			0.570568			0.285284	−	0.958443i	$-0.407912\pi$
$367$	10.9305			0.570568			0.285284	+	0.958443i	$0.407912\pi$
$368$	−3.37247	−	3.40976i	−0.175802	−	0.177746i
$369$		0			0
$370$	2.91473	−	6.38236i	0.151529	−	0.331803i
$371$	29.7737	+	8.74233i	1.54577	+	0.453879i
$372$		0			0
$373$	7.62102	−	4.89773i	0.394601	−	0.253595i	−0.328261	−	0.944587i	$-0.606463\pi$
$373$	7.62102	−	4.89773i	0.394601	−	0.253595i	0.722862	+	0.690992i	$0.242826\pi$
$374$	−3.20375	+	3.69733i	−0.165662	+	0.191184i
$375$		0			0
$376$	0.262073	−	0.0769515i	0.0135154	−	0.00396847i
$377$	3.28949	+	2.11403i	0.169417	+	0.108878i
$378$		0			0
$379$	6.75852	+	14.7991i	0.347162	+	0.760179i	0.999996	+	0.00267820i	$0.000852497\pi$
$379$	6.75852	+	14.7991i	0.347162	+	0.760179i	−0.652834	+	0.757501i	$0.726420\pi$
$380$	−2.01483	−	4.41187i	−0.103359	−	0.226324i
$381$		0			0
$382$	−3.28023	−	2.10808i	−0.167831	−	0.107859i
$383$	28.0369	−	8.23237i	1.43262	−	0.420655i	0.528864	−	0.848707i	$-0.322618\pi$
$383$	28.0369	−	8.23237i	1.43262	−	0.420655i	0.903754	+	0.428052i	$0.140800\pi$
$384$		0			0
$385$	−3.83535	+	4.42623i	−0.195468	+	0.225582i
$386$	11.2055	−	7.20135i	0.570346	−	0.366539i
$387$		0			0
$388$	4.37823	+	1.28557i	0.222271	+	0.0652647i
$389$	11.3460	−	24.8442i	0.575264	−	1.25965i	−0.368682	−	0.929555i	$-0.620191\pi$
$389$	11.3460	−	24.8442i	0.575264	−	1.25965i	0.943947	−	0.330098i	$-0.107082\pi$
$390$		0			0
$391$	−3.20048	−	15.1119i	−0.161855	−	0.764240i
$392$	−10.8820			−0.549622
$393$		0			0
$394$	−16.0145	−	4.70229i	−0.806800	−	0.236898i
$395$	−0.969125	−	1.11843i	−0.0487620	−	0.0562743i
$396$		0			0
$397$	−7.92826	+	9.14970i	−0.397908	+	0.459210i	−0.918981	−	0.394302i	$-0.870986\pi$
$397$	−7.92826	+	9.14970i	−0.397908	+	0.459210i	0.521073	+	0.853512i	$0.325532\pi$
$398$	−0.424262	+	2.95081i	−0.0212663	+	0.147911i
$399$		0			0
$400$	−3.50680	−	2.25368i	−0.175340	−	0.112684i
$401$	−0.192189	−	1.33671i	−0.00959747	−	0.0667519i	0.984460	−	0.175610i	$-0.0561897\pi$
$401$	−0.192189	−	1.33671i	−0.00959747	−	0.0667519i	−0.994057	+	0.108858i	$0.965281\pi$
$402$		0			0
$403$	1.66799	+	3.65240i	0.0830887	+	0.181939i
$404$	−0.134254	−	0.933758i	−0.00667939	−	0.0464562i
$405$		0			0
$406$	32.4947	−	9.54131i	1.61269	−	0.473527i
$407$	1.66331	−	11.5686i	0.0824472	−	0.573433i
$408$		0			0
$409$	8.13725	−	5.22949i	0.402361	−	0.258582i	−0.323773	−	0.946135i	$-0.604951\pi$
$409$	8.13725	−	5.22949i	0.402361	−	0.258582i	0.726134	+	0.687553i	$0.241315\pi$
$410$	−5.49256	−	6.33875i	−0.271258	−	0.313049i
$411$		0			0
$412$	3.83595	−	8.39955i	0.188984	−	0.413816i
$413$	4.79797			0.236093
$414$		0			0
$415$	−10.9251			−0.536292
$416$	−0.202824	+	0.444124i	−0.00994429	+	0.0217749i
$417$		0			0
$418$	−5.29070	−	6.10580i	−0.258777	−	0.298644i
$419$	−21.6263	+	13.8984i	−1.05652	+	0.678981i	−0.949017	−	0.315224i	$-0.897920\pi$
$419$	−21.6263	+	13.8984i	−1.05652	+	0.678981i	−0.107498	+	0.994205i	$0.534284\pi$
$420$		0			0
$421$	−2.25678	+	15.6963i	−0.109989	+	0.764989i	0.857937	+	0.513754i	$0.171746\pi$
$421$	−2.25678	+	15.6963i	−0.109989	+	0.764989i	−0.967926	+	0.251235i	$0.919163\pi$
$422$	23.5582	−	6.91732i	1.14680	−	0.336730i
$423$		0			0
$424$	−1.04432	−	7.26339i	−0.0507166	−	0.352742i
$425$	−5.57761	−	12.2133i	−0.270554	−	0.592430i
$426$		0			0
$427$	8.70371	+	60.5357i	0.421202	+	2.92953i
$428$	3.22598	+	2.07321i	0.155934	+	0.100212i
$429$		0			0
$430$	0.581690	−	4.04574i	0.0280516	−	0.195103i
$431$	−25.0732	+	28.9361i	−1.20774	+	1.39380i	−0.311486	+	0.950251i	$0.600827\pi$
$431$	−25.0732	+	28.9361i	−1.20774	+	1.39380i	−0.896249	+	0.443550i	$0.853719\pi$
$432$		0			0
$433$	−7.92749	−	9.14881i	−0.380971	−	0.439664i	0.532585	−	0.846376i	$-0.321221\pi$
$433$	−7.92749	−	9.14881i	−0.380971	−	0.439664i	−0.913556	+	0.406712i	$0.866675\pi$
$434$	33.3675	+	9.79758i	1.60169	+	0.470299i
$435$		0			0
$436$	9.04741			0.433293
$437$	25.4540	−	1.67991i	1.21763	−	0.0803610i
$438$		0			0
$439$	9.63515	−	21.0980i	0.459861	−	1.00695i	−0.527658	−	0.849457i	$-0.676930\pi$
$439$	9.63515	−	21.0980i	0.459861	−	1.00695i	0.987519	−	0.157498i	$-0.0503428\pi$
$440$	1.32889	+	0.390199i	0.0633526	+	0.0186020i
$441$		0			0
$442$	−1.32296	+	0.850215i	−0.0629268	+	0.0404406i
$443$	6.10576	−	7.04642i	0.290093	−	0.334786i	−0.591932	−	0.805988i	$-0.701634\pi$
$443$	6.10576	−	7.04642i	0.290093	−	0.334786i	0.882025	+	0.471203i	$0.156180\pi$
$444$		0			0
$445$	−8.18479	+	2.40327i	−0.387996	+	0.113926i
$446$	4.96869	+	3.19318i	0.235274	+	0.151202i
$447$		0			0
$448$	1.75667	+	3.84657i	0.0829948	+	0.181733i
$449$	17.3174	+	37.9197i	0.817256	+	1.78954i	0.572382	+	0.819987i	$0.306020\pi$
$449$	17.3174	+	37.9197i	0.817256	+	1.78954i	0.244875	+	0.969555i	$0.421253\pi$
$450$		0			0
$451$	−11.7533	−	7.55340i	−0.553442	−	0.355676i
$452$	−10.7790	+	3.16499i	−0.506999	+	0.148868i
$453$		0			0
$454$	3.54652	−	4.09290i	0.166446	−	0.192089i
$455$	−1.58377	+	1.01783i	−0.0742485	+	0.0477166i
$456$		0			0
$457$	−26.1393	−	7.67519i	−1.22274	−	0.359030i	−0.394237	−	0.919009i	$-0.628991\pi$
$457$	−26.1393	−	7.67519i	−1.22274	−	0.359030i	−0.828507	+	0.559979i	$0.810809\pi$
$458$	−6.11132	+	13.3819i	−0.285563	+	0.625296i
$459$		0			0
$460$	−3.51516	+	2.60139i	−0.163895	+	0.121290i
$461$	−29.0881			−1.35477			−0.677384	−	0.735629i	$-0.736886\pi$
$461$	−29.0881			−1.35477			−0.677384	+	0.735629i	$0.736886\pi$
$462$		0			0
$463$	−1.99904	−	0.586970i	−0.0929031	−	0.0272788i	0.234951	−	0.972007i	$-0.424507\pi$
$463$	−1.99904	−	0.586970i	−0.0929031	−	0.0272788i	−0.327854	+	0.944728i	$0.606325\pi$
$464$	−5.24460	−	6.05259i	−0.243474	−	0.280984i
$465$		0			0
$466$	16.7670	−	19.3502i	0.776716	−	0.896379i
$467$	3.78800	−	26.3461i	0.175288	−	1.21915i	−0.692205	−	0.721701i	$-0.743360\pi$
$467$	3.78800	−	26.3461i	0.175288	−	1.21915i	0.867492	−	0.497451i	$-0.165730\pi$
$468$		0			0
$469$	7.28906	+	4.68439i	0.336577	+	0.216305i
$470$	−0.0354446	−	0.246523i	−0.00163494	−	0.0113713i
$471$		0			0
$472$	−0.471337	−	1.03208i	−0.0216951	−	0.0475055i
$473$	−0.968945	−	6.73916i	−0.0445522	−	0.309867i
$474$		0			0
$475$	21.2746	−	6.24679i	0.976147	−	0.286623i
$476$	−1.93838	+	13.4818i	−0.0888457	+	0.617935i
$477$		0			0
$478$	1.70531	−	1.09594i	0.0779992	−	0.0501270i
$479$	2.98599	+	3.44602i	0.136434	+	0.157453i	0.819855	−	0.572572i	$-0.194054\pi$
$479$	2.98599	+	3.44602i	0.136434	+	0.157453i	−0.683421	+	0.730024i	$0.739509\pi$
$480$		0			0
$481$	1.56068	−	3.41742i	0.0711611	−	0.155821i
$482$	−18.5333			−0.844169
$483$		0			0
$484$	−8.69295			−0.395134
$485$	1.72846	−	3.78480i	0.0784854	−	0.171859i
$486$		0			0
$487$	7.71086	+	8.89881i	0.349413	+	0.403244i	0.903065	−	0.429504i	$-0.141312\pi$
$487$	7.71086	+	8.89881i	0.349413	+	0.403244i	−0.553652	+	0.832748i	$0.686766\pi$
$488$	12.1667	−	7.81908i	0.550762	−	0.353953i
$489$		0			0
$490$	−1.41214	+	9.82166i	−0.0637940	+	0.443697i
$491$	8.20130	−	2.40812i	0.370119	−	0.108677i	−0.0913831	−	0.995816i	$-0.529129\pi$
$491$	8.20130	−	2.40812i	0.370119	−	0.108677i	0.461502	+	0.887139i	$0.347311\pi$
$492$		0			0
$493$	−3.67109	−	25.5330i	−0.165338	−	1.14995i
$494$	−1.07884	−	2.36233i	−0.0485392	−	0.106286i
$495$		0			0
$496$	−1.17037	−	8.14013i	−0.0525513	−	0.365502i
$497$	−37.7425	−	24.2556i	−1.69298	−	1.08801i
$498$		0			0
$499$	−1.71847	+	11.9522i	−0.0769291	+	0.535054i	0.914518	+	0.404545i	$0.132570\pi$
$499$	−1.71847	+	11.9522i	−0.0769291	+	0.535054i	−0.991447	+	0.130509i	$0.958339\pi$
$500$	−5.47482	+	6.31828i	−0.244841	+	0.282562i
$501$		0			0
$502$	−15.3605	−	17.7269i	−0.685571	−	0.791191i
$503$	−6.26872	−	1.84066i	−0.279508	−	0.0820711i	0.138974	−	0.990296i	$-0.455620\pi$
$503$	−6.26872	−	1.84066i	−0.279508	−	0.0820711i	−0.418482	+	0.908225i	$0.637438\pi$
$504$		0			0
$505$	−0.860197			−0.0382783
$506$	−4.39735	+	5.80735i	−0.195486	+	0.258168i
$507$		0			0
$508$	1.86599	−	4.08594i	0.0827898	−	0.181284i
$509$	21.6949	+	6.37019i	0.961608	+	0.282354i	0.724612	−	0.689157i	$-0.242019\pi$
$509$	21.6949	+	6.37019i	0.961608	+	0.282354i	0.236996	+	0.971511i	$0.423837\pi$
$510$		0			0
$511$	2.28565	−	1.46890i	0.101111	−	0.0649801i
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$		0			0
$514$	−9.96840	+	2.92699i	−0.439687	+	0.129104i
$515$	−7.08334	−	4.55218i	−0.312129	−	0.200593i
$516$		0			0
$517$	−0.172342	−	0.377376i	−0.00757958	−	0.0165970i
$518$	−13.5171	−	29.5984i	−0.593909	−	1.30048i
$519$		0			0
$520$	0.374529	+	0.240695i	0.0164242	+	0.0105552i
$521$	−15.6623	+	4.59886i	−0.686176	+	0.201480i	−0.606194	−	0.795317i	$-0.707305\pi$
$521$	−15.6623	+	4.59886i	−0.686176	+	0.201480i	−0.0799822	+	0.996796i	$0.525486\pi$
$522$		0			0
$523$	−12.8909	+	14.8769i	−0.563680	+	0.650522i	−0.964015	−	0.265847i	$-0.914348\pi$
$523$	−12.8909	+	14.8769i	−0.563680	+	0.650522i	0.400335	+	0.916369i	$0.368894\pi$
$524$	6.79399	−	4.36623i	0.296797	−	0.190740i
$525$		0			0
$526$	24.8458	+	7.29539i	1.08333	+	0.318094i
$527$	11.0037	−	24.0947i	0.479329	−	1.04958i
$528$		0			0
$529$	−6.23682	−	22.1382i	−0.271166	−	0.962533i
$530$	−6.69119			−0.290647
$531$		0			0
$532$	−21.5817	−	6.33696i	−0.935685	−	0.274742i
$533$	−2.94098	−	3.39407i	−0.127388	−	0.147014i
$534$		0			0
$535$	2.28984	−	2.64261i	0.0989983	−	0.114250i
$536$	0.291600	−	2.02812i	0.0125952	−	0.0876014i
$537$		0			0
$538$	10.8396	+	6.96622i	0.467330	+	0.300335i
$539$	2.35226	+	16.3603i	0.101319	+	0.704690i
$540$		0			0
$541$	1.09643	+	2.40084i	0.0471390	+	0.103220i	0.931736	−	0.363136i	$-0.118294\pi$
$541$	1.09643	+	2.40084i	0.0471390	+	0.103220i	−0.884597	+	0.466356i	$0.845567\pi$
$542$	−2.29422	−	15.9566i	−0.0985450	−	0.685396i
$543$		0			0
$544$	3.09047	−	0.907443i	0.132503	−	0.0389063i
$545$	1.17407	−	8.16586i	0.0502918	−	0.349787i
$546$		0			0
$547$	−13.8142	+	8.87783i	−0.590651	+	0.379589i	−0.801558	−	0.597918i	$-0.795995\pi$
$547$	−13.8142	+	8.87783i	−0.590651	+	0.379589i	0.210906	+	0.977506i	$0.432359\pi$
$548$	−0.394755	−	0.455572i	−0.0168631	−	0.0194611i
$549$		0			0
$550$	−2.63023	+	5.75941i	−0.112154	+	0.245582i
$551$	42.5990			1.81478
$552$		0			0
$553$	−6.86306			−0.291847
$554$	1.72354	−	3.77402i	0.0732262	−	0.160343i
$555$		0			0
$556$	10.2745	+	11.8574i	0.435734	+	0.502864i
$557$	−27.4471	+	17.6391i	−1.16297	+	0.747395i	−0.972180	−	0.234236i	$-0.924741\pi$
$557$	−27.4471	+	17.6391i	−1.16297	+	0.747395i	−0.190789	+	0.981631i	$0.561105\pi$
$558$		0			0
$559$	0.311465	−	2.16629i	0.0131736	−	0.0916242i
$560$	3.69973	−	1.08634i	0.156342	−	0.0459062i
$561$		0			0
$562$	0.739901	+	5.14612i	0.0312108	+	0.217076i
$563$	9.24940	+	20.2534i	0.389816	+	0.853577i	0.998202	+	0.0599365i	$0.0190898\pi$
$563$	9.24940	+	20.2534i	0.389816	+	0.853577i	−0.608386	+	0.793641i	$0.708183\pi$
$564$		0			0
$565$	1.45783	+	10.1394i	0.0613312	+	0.426568i
$566$	11.7089	+	7.52487i	0.492163	+	0.316294i
$567$		0			0
$568$	−1.50989	+	10.5015i	−0.0633537	+	0.440635i
$569$	−8.55133	+	9.86876i	−0.358490	+	0.413720i	−0.906133	−	0.422992i	$-0.860980\pi$
$569$	−8.55133	+	9.86876i	−0.358490	+	0.413720i	0.547643	+	0.836712i	$0.315525\pi$
$570$		0			0
$571$	−26.3070	−	30.3599i	−1.10092	−	1.27052i	−0.959847	−	0.280525i	$-0.909492\pi$
$571$	−26.3070	−	30.3599i	−1.10092	−	1.27052i	−0.141069	−	0.990000i	$-0.545054\pi$
$572$	0.711554	+	0.208931i	0.0297516	+	0.00873585i
$573$		0			0
$574$	−38.8967			−1.62352
$575$	−9.48436	−	17.5986i	−0.395525	−	0.733914i
$576$		0			0
$577$	−9.65310	+	21.1373i	−0.401864	+	0.879959i	0.595214	+	0.803567i	$0.297067\pi$
$577$	−9.65310	+	21.1373i	−0.401864	+	0.879959i	−0.997078	+	0.0763918i	$0.975660\pi$
$578$	−6.35719	−	1.86664i	−0.264424	−	0.0776420i
$579$		0			0
$580$	−6.14343	+	3.94814i	−0.255092	+	0.163938i
$581$	−33.1788	+	38.2904i	−1.37649	+	1.58855i
$582$		0			0
$583$	−10.6943	+	3.14013i	−0.442913	+	0.130051i
$584$	−0.540507	−	0.347363i	−0.0223663	−	0.0143740i
$585$		0			0
$586$	10.7334	+	23.5028i	0.443391	+	0.970890i
$587$	−3.17611	−	6.95471i	−0.131092	−	0.287051i	0.832692	−	0.553737i	$-0.186799\pi$
$587$	−3.17611	−	6.95471i	−0.131092	−	0.287051i	−0.963784	+	0.266686i	$0.914071\pi$
$588$		0			0
$589$	36.7991	+	23.6494i	1.51628	+	0.974455i
$590$	−0.992686	+	0.291479i	−0.0408682	+	0.0120000i
$591$		0			0
$592$	−5.03899	+	5.81531i	−0.207101	+	0.239008i
$593$	25.5201	−	16.4007i	1.04798	−	0.673498i	0.101035	−	0.994883i	$-0.467785\pi$
$593$	25.5201	−	16.4007i	1.04798	−	0.673498i	0.946949	+	0.321385i	$0.104148\pi$
$594$		0			0
$595$	11.9166	+	3.49903i	0.488533	+	0.143446i
$596$	1.68160	−	3.68220i	0.0688812	−	0.150829i
$597$		0			0
$598$	−1.88219	+	1.39291i	−0.0769684	+	0.0569602i
$599$	−4.69418			−0.191799			−0.0958995	−	0.995391i	$-0.530573\pi$
$599$	−4.69418			−0.191799			−0.0958995	+	0.995391i	$0.530573\pi$
$600$		0			0
$601$	−37.4716	−	11.0026i	−1.52850	−	0.448807i	−0.593907	−	0.804533i	$-0.702415\pi$
$601$	−37.4716	−	11.0026i	−1.52850	−	0.448807i	−0.934590	+	0.355726i	$0.884234\pi$
$602$	−12.4130	−	14.3254i	−0.505917	−	0.583859i
$603$		0			0
$604$	0.0474934	−	0.0548104i	0.00193248	−	0.00223020i
$605$	−1.12808	+	7.84594i	−0.0458628	+	0.318983i
$606$		0			0
$607$	39.3317	+	25.2769i	1.59642	+	1.02596i	0.968929	+	0.247338i	$0.0795558\pi$
$607$	39.3317	+	25.2769i	1.59642	+	1.02596i	0.627494	+	0.778621i	$0.284081\pi$
$608$	0.756983	+	5.26493i	0.0306997	+	0.213521i
$609$		0			0
$610$	−5.47835	−	11.9959i	−0.221812	−	0.485700i
$611$	−0.0189788	−	0.132000i	−0.000767799	−	0.00534016i
$612$		0			0
$613$	21.3373	−	6.26519i	0.861804	−	0.253049i	0.179178	−	0.983817i	$-0.442656\pi$
$613$	21.3373	−	6.26519i	0.861804	−	0.253049i	0.682626	+	0.730768i	$0.260838\pi$
$614$	−4.69682	+	32.6671i	−0.189548	+	1.31834i
$615$		0			0
$616$	5.40335	−	3.47252i	0.217707	−	0.139912i
$617$	16.6962	+	19.2685i	0.672165	+	0.775719i	0.984713	−	0.174182i	$-0.0557282\pi$
$617$	16.6962	+	19.2685i	0.672165	+	0.775719i	−0.312549	+	0.949902i	$0.601183\pi$
$618$		0			0
$619$	7.07356	−	15.4889i	0.284310	−	0.622553i	−0.712560	−	0.701612i	$-0.752464\pi$
$619$	7.07356	−	15.4889i	0.284310	−	0.622553i	0.996870	+	0.0790587i	$0.0251915\pi$
$620$	−7.49885			−0.301161
$621$		0			0
$622$	14.8559			0.595668
$623$	−16.4337	+	35.9848i	−0.658402	+	1.44170i
$624$		0			0
$625$	−8.65689	−	9.99058i	−0.346275	−	0.399623i
$626$	−5.85184	+	3.76075i	−0.233887	+	0.150310i
$627$		0			0
$628$	−0.00512424	+	0.0356399i	−0.000204479	+	0.00142219i
$629$	−23.7804	+	6.98255i	−0.948186	+	0.278413i
$630$		0			0
$631$	3.24308	+	22.5561i	0.129105	+	0.897945i	0.946692	+	0.322140i	$0.104402\pi$
$631$	3.24308	+	22.5561i	0.129105	+	0.897945i	−0.817587	+	0.575805i	$0.804689\pi$
$632$	0.674206	+	1.47631i	0.0268185	+	0.0587243i
$633$		0			0
$634$	−0.630148	−	4.38278i	−0.0250264	−	0.174062i
$635$	−3.44567	−	2.21440i	−0.136737	−	0.0878757i
$636$		0			0
$637$	−0.756129	+	5.25899i	−0.0299589	+	0.208369i
$638$	−7.96600	+	9.19326i	−0.315377	+	0.363965i
$639$		0			0
$640$	−0.597131	−	0.689126i	−0.0236037	−	0.0272401i
$641$	−2.51720	−	0.739116i	−0.0994234	−	0.0291933i	0.231642	−	0.972801i	$-0.425590\pi$
$641$	−2.51720	−	0.739116i	−0.0994234	−	0.0291933i	−0.331066	+	0.943608i	$0.607408\pi$
$642$		0			0
$643$	44.5362			1.75634			0.878168	−	0.478352i	$-0.158766\pi$
$643$	44.5362			1.75634			0.878168	+	0.478352i	$0.158766\pi$
$644$	−1.55796	+	20.2202i	−0.0613920	+	0.796789i
$645$		0			0
$646$	−7.11706	+	15.5842i	−0.280017	+	0.613151i
$647$	−35.6308	−	10.4622i	−1.40079	−	0.411310i	−0.507836	−	0.861454i	$-0.669554\pi$
$647$	−35.6308	−	10.4622i	−1.40079	−	0.411310i	−0.892956	+	0.450144i	$0.851373\pi$
$648$		0			0
$649$	−1.44979	+	0.931723i	−0.0569092	+	0.0365733i
$650$	−1.33282	+	1.53815i	−0.0522774	+	0.0603314i
$651$		0			0
$652$	15.3544	−	4.50847i	0.601326	−	0.176565i
$653$	21.8542	+	14.0448i	0.855221	+	0.549617i	0.893199	−	0.449661i	$-0.148455\pi$
$653$	21.8542	+	14.0448i	0.855221	+	0.549617i	−0.0379778	+	0.999279i	$0.512092\pi$
$654$		0			0
$655$	−3.05915	−	6.69861i	−0.119531	−	0.261736i
$656$	3.82109	+	8.36702i	0.149189	+	0.326677i
$657$		0			0
$658$	−0.971660	−	0.624448i	−0.0378792	−	0.0243435i
$659$	−8.36443	+	2.45602i	−0.325832	+	0.0956728i	−0.440558	−	0.897724i	$-0.645219\pi$
$659$	−8.36443	+	2.45602i	−0.325832	+	0.0956728i	0.114726	+	0.993397i	$0.463401\pi$
$660$		0			0
$661$	−2.00404	+	2.31278i	−0.0779480	+	0.0899568i	−0.793384	−	0.608722i	$-0.791683\pi$
$661$	−2.00404	+	2.31278i	−0.0779480	+	0.0899568i	0.715436	+	0.698678i	$0.246228\pi$
$662$	−4.30350	+	2.76569i	−0.167260	+	0.107492i
$663$		0			0
$664$	11.4960	+	3.37553i	0.446131	+	0.130996i
$665$	−8.52014	+	18.6565i	−0.330397	+	0.723468i
$666$		0			0
$667$	−7.95786	−	37.5751i	−0.308130	−	1.45491i
$668$	−4.59120			−0.177639
$669$		0			0
$670$	−1.79266	−	0.526374i	−0.0692567	−	0.0203356i
$671$	−14.3855	−	16.6017i	−0.555345	−	0.640902i
$672$		0			0
$673$	−22.7134	+	26.2126i	−0.875536	+	1.01042i	0.124298	+	0.992245i	$0.460332\pi$
$673$	−22.7134	+	26.2126i	−0.875536	+	1.01042i	−0.999835	+	0.0181779i	$0.994213\pi$
$674$	1.71847	−	11.9522i	0.0661929	−	0.460382i
$675$		0			0
$676$	−10.7358	−	6.89945i	−0.412914	−	0.265363i
$677$	2.16688	+	15.0710i	0.0832801	+	0.579226i	0.988145	+	0.153526i	$0.0490629\pi$
$677$	2.16688	+	15.0710i	0.0832801	+	0.579226i	−0.904864	+	0.425700i	$0.860028\pi$
$678$		0			0
$679$	−8.01580	−	17.5522i	−0.307618	−	0.673590i
$680$	−0.417977	−	2.90710i	−0.0160287	−	0.111482i
$681$		0			0
$682$	−11.9852	+	3.51916i	−0.458936	+	0.134756i
$683$	5.32744	−	37.0532i	0.203849	−	1.41780i	−0.588877	−	0.808222i	$-0.700430\pi$
$683$	5.32744	−	37.0532i	0.203849	−	1.41780i	0.792726	−	0.609578i	$-0.208661\pi$
$684$		0			0
$685$	−0.462409	+	0.297172i	−0.0176677	+	0.0113544i
$686$	10.7500	+	12.4062i	0.410437	+	0.473669i
$687$		0			0
$688$	−1.86210	+	4.07743i	−0.0709919	+	0.155451i
$689$	−3.58279			−0.136493
$690$		0			0
$691$	−6.04705			−0.230041			−0.115020	−	0.993363i	$-0.536693\pi$
$691$	−6.04705			−0.230041			−0.115020	+	0.993363i	$0.536693\pi$
$692$	8.60729	−	18.8473i	0.327200	−	0.716468i
$693$		0			0
$694$	−13.1592	−	15.1866i	−0.499518	−	0.576474i
$695$	12.0353	−	7.73463i	0.456526	−	0.293391i
$696$		0			0
$697$	−4.21636	+	29.3254i	−0.159706	+	1.11078i
$698$	8.55535	−	2.51208i	0.323825	−	0.0950836i
$699$		0			0
$700$	2.50866	+	17.4481i	0.0948184	+	0.659477i
$701$	−12.4636	−	27.2915i	−0.470744	−	1.03079i	−0.984906	−	0.173093i	$-0.944624\pi$
$701$	−12.4636	−	27.2915i	−0.470744	−	1.03079i	0.514161	−	0.857694i	$-0.328103\pi$
$702$		0			0
$703$	−5.82480	−	40.5124i	−0.219687	−	1.52795i
$704$	−1.27778	−	0.821177i	−0.0481580	−	0.0309493i
$705$		0			0
$706$	1.80191	−	12.5325i	0.0678156	−	0.471668i
$707$	−2.61237	+	3.01483i	−0.0982481	+	0.113384i
$708$		0			0
$709$	15.8016	+	18.2361i	0.593443	+	0.684869i	0.970439	−	0.241345i	$-0.0775887\pi$
$709$	15.8016	+	18.2361i	0.593443	+	0.684869i	−0.376997	+	0.926215i	$0.623043\pi$
$710$	9.28236	+	2.72555i	0.348361	+	0.102288i
$711$		0			0
$712$	9.35503			0.350595
$713$	13.9859	−	36.8771i	0.523774	−	1.38106i
$714$		0			0
$715$	0.280911	−	0.615110i	0.0105055	−	0.0230038i
$716$	−0.523214	−	0.153630i	−0.0195534	−	0.00574141i
$717$		0			0
$718$	8.24006	−	5.29557i	0.307516	−	0.197629i
$719$	14.6435	−	16.8995i	0.546110	−	0.630245i	−0.413862	−	0.910340i	$-0.635820\pi$
$719$	14.6435	−	16.8995i	0.546110	−	0.630245i	0.959972	+	0.280095i	$0.0903659\pi$
$720$		0			0
$721$	−37.4662	+	11.0011i	−1.39531	+	0.409701i
$722$	−7.81740	−	5.02394i	−0.290934	−	0.186972i
$723$		0			0
$724$	−1.06438	−	2.33066i	−0.0395573	−	0.0866185i
$725$	−13.8685	−	30.3678i	−0.515063	−	1.12783i
$726$		0			0
$727$	−8.62131	−	5.54058i	−0.319747	−	0.205489i	0.370915	−	0.928667i	$-0.379044\pi$
$727$	−8.62131	−	5.54058i	−0.319747	−	0.205489i	−0.690661	+	0.723178i	$0.742681\pi$
$728$	1.98101	−	0.581678i	0.0734213	−	0.0215584i
$729$		0			0
$730$	−0.383658	+	0.442765i	−0.0141998	+	0.0163875i
$731$	−12.1459	+	7.80570i	−0.449233	+	0.288704i
$732$		0			0
$733$	−5.50513	−	1.61645i	−0.203337	−	0.0597050i	0.178478	−	0.983944i	$-0.442883\pi$
$733$	−5.50513	−	1.61645i	−0.203337	−	0.0597050i	−0.381815	+	0.924239i	$0.624701\pi$
$734$	−4.54070	+	9.94275i	−0.167600	+	0.366994i
$735$		0			0
$736$	4.50260	−	1.65124i	0.165968	−	0.0608656i
$737$	−3.11218			−0.114639
$738$		0			0
$739$	−16.3476	−	4.80010i	−0.601357	−	0.176574i	−0.0331367	−	0.999451i	$-0.510550\pi$
$739$	−16.3476	−	4.80010i	−0.601357	−	0.176574i	−0.568220	+	0.822876i	$0.692368\pi$
$740$	4.59478	+	5.30266i	0.168907	+	0.194930i
$741$		0			0
$742$	−20.3207	+	23.4514i	−0.745997	+	0.860927i
$743$	−0.877334	+	6.10199i	−0.0321863	+	0.223860i	−0.999566	−	0.0294718i	$-0.990617\pi$
$743$	−0.877334	+	6.10199i	−0.0321863	+	0.223860i	0.967379	+	0.253332i	$0.0815266\pi$
$744$		0			0
$745$	−3.10520	−	1.99559i	−0.113766	−	0.0731127i
$746$	1.28925	+	8.96691i	0.0472027	+	0.328302i
$747$		0			0
$748$	−2.03232	−	4.45016i	−0.0743090	−	0.162714i
$749$	−2.30777	−	16.0509i	−0.0843241	−	0.586487i
$750$		0			0
$751$	1.66332	−	0.488395i	0.0606955	−	0.0178218i	−0.251244	−	0.967924i	$-0.580840\pi$
$751$	1.66332	−	0.488395i	0.0606955	−	0.0178218i	0.311939	+	0.950102i	$0.399021\pi$
$752$	−0.0388714	+	0.270356i	−0.00141749	+	0.00985888i
$753$		0			0
$754$	−3.28949	+	2.11403i	−0.119796	+	0.0769883i
$755$	−0.0433066	−	0.0499785i	−0.00157609	−	0.00181890i
$756$		0			0
$757$	9.81588	−	21.4938i	0.356764	−	0.781204i	−0.643117	−	0.765768i	$-0.722359\pi$
$757$	9.81588	−	21.4938i	0.356764	−	0.781204i	0.999881	−	0.0154362i	$-0.00491370\pi$
$758$	−16.2693			−0.590929
$759$		0			0
$760$	4.85017			0.175934
$761$	−1.02392	+	2.24208i	−0.0371172	+	0.0812752i	−0.927282	−	0.374363i	$-0.877862\pi$
$761$	−1.02392	+	2.24208i	−0.0371172	+	0.0812752i	0.890165	+	0.455638i	$0.150589\pi$
$762$		0			0
$763$	−25.0542	−	28.9141i	−0.907024	−	1.04676i
$764$	3.28023	−	2.10808i	0.118675	−	0.0762675i
$765$		0			0
$766$	−4.15851	+	28.9231i	−0.150253	+	1.04503i
$767$	−0.531532	+	0.156072i	−0.0191925	+	0.00563543i
$768$		0			0
$769$	2.83570	+	19.7227i	0.102258	+	0.711220i	0.974865	+	0.222797i	$0.0715186\pi$
$769$	2.83570	+	19.7227i	0.102258	+	0.711220i	−0.872607	+	0.488423i	$0.837572\pi$
$770$	−2.43298	−	5.32748i	−0.0876785	−	0.191989i
$771$		0			0
$772$	1.89564	+	13.1844i	0.0682254	+	0.474518i
$773$	12.1822	+	7.82904i	0.438164	+	0.281591i	0.741068	−	0.671430i	$-0.234320\pi$
$773$	12.1822	+	7.82904i	0.438164	+	0.281591i	−0.302904	+	0.953021i	$0.597956\pi$
$774$		0			0
$775$	4.87875	−	33.9324i	0.175250	−	1.21889i
$776$	−2.98818	+	3.44854i	−0.107269	+	0.123795i
$777$		0			0
$778$	17.8858	+	20.6413i	0.641238	+	0.740028i
$779$	−46.9443	−	13.7841i	−1.68196	−	0.493867i
$780$		0			0
$781$	16.1148			0.576632
$782$	15.0758	+	3.36644i	0.539109	+	0.120384i
$783$		0			0
$784$	4.52053	−	9.89858i	0.161448	−	0.353521i
$785$	0.0315022	+	0.00924989i	0.00112436	+	0.000330143i
$786$		0			0
$787$	26.6603	−	17.1336i	0.950338	−	0.610745i	0.0290302	−	0.999579i	$-0.490758\pi$
$787$	26.6603	−	17.1336i	0.950338	−	0.610745i	0.921308	+	0.388833i	$0.127122\pi$
$788$	10.9300	−	12.6139i	0.389366	−	0.449352i
$789$		0			0
$790$	1.41995	−	0.416935i	0.0505195	−	0.0148339i
$791$	39.9640	+	25.6833i	1.42096	+	0.913194i
$792$		0			0
$793$	−2.93337	−	6.42319i	−0.104167	−	0.228094i
$794$	−5.02934	−	11.0127i	−0.178485	−	0.390827i
$795$		0			0
$796$	−2.50791	−	1.61173i	−0.0888903	−	0.0571264i
$797$	46.4770	−	13.6469i	1.64630	−	0.483398i	0.678393	−	0.734700i	$-0.262677\pi$
$797$	46.4770	−	13.6469i	1.64630	−	0.483398i	0.967909	+	0.251302i	$0.0808587\pi$
$798$		0			0
$799$	−0.576117	+	0.664875i	−0.0203816	+	0.0235216i
$800$	3.50680	−	2.25368i	0.123984	−	0.0796797i
$801$		0			0
$802$	1.29575	+	0.380466i	0.0457545	+	0.0134347i
$803$	−0.405401	+	0.887704i	−0.0143063	+	0.0313264i
$804$		0			0
$805$	18.0479	+	4.03011i	0.636103	+	0.142043i
$806$	−4.01525			−0.141431
$807$		0			0
$808$	0.905147	+	0.265775i	0.0318430	+	0.00934994i
$809$	16.6402	+	19.2039i	0.585040	+	0.675172i	0.968681	−	0.248310i	$-0.0798753\pi$
$809$	16.6402	+	19.2039i	0.585040	+	0.675172i	−0.383641	+	0.923483i	$0.625330\pi$
$810$		0			0
$811$	18.9473	−	21.8663i	0.665329	−	0.767830i	−0.318309	−	0.947987i	$-0.603115\pi$
$811$	18.9473	−	21.8663i	0.665329	−	0.767830i	0.983638	+	0.180157i	$0.0576605\pi$
$812$	−4.81971	+	33.5218i	−0.169139	+	1.17639i
$813$		0			0
$814$	9.83219	+	6.31876i	0.344618	+	0.221472i
$815$	−2.07665	−	14.4434i	−0.0727417	−	0.505930i
$816$		0			0
$817$	−9.90465	−	21.6882i	−0.346520	−	0.758773i
$818$	1.37658	+	9.57431i	0.0481309	+	0.334758i
$819$		0			0
$820$	8.04762	−	2.36300i	0.281035	−	0.0825194i
$821$	−4.14106	+	28.8017i	−0.144524	+	1.00519i	0.780467	+	0.625197i	$0.214981\pi$
$821$	−4.14106	+	28.8017i	−0.144524	+	1.00519i	−0.924991	+	0.379989i	$0.875928\pi$
$822$		0			0
$823$	11.7641	−	7.56035i	0.410072	−	0.263537i	−0.319301	−	0.947653i	$-0.603448\pi$
$823$	11.7641	−	7.56035i	0.410072	−	0.263537i	0.729373	+	0.684116i	$0.239812\pi$
$824$	6.04699	+	6.97860i	0.210657	+	0.243111i
$825$		0			0
$826$	−1.99315	+	4.36438i	−0.0693505	+	0.151856i
$827$	36.4585			1.26779			0.633894	−	0.773420i	$-0.281456\pi$
$827$	36.4585			1.26779			0.633894	+	0.773420i	$0.281456\pi$
$828$		0			0
$829$	−19.6791			−0.683482			−0.341741	−	0.939794i	$-0.611017\pi$
$829$	−19.6791			−0.683482			−0.341741	+	0.939794i	$0.611017\pi$
$830$	4.53845	−	9.93781i	0.157532	−	0.344946i
$831$		0			0
$832$	−0.319733	−	0.368991i	−0.0110847	−	0.0127925i
$833$	29.4860	−	18.9495i	1.02163	−	0.656562i
$834$		0			0
$835$	−0.595795	+	4.14385i	−0.0206183	+	0.143404i
$836$	7.75186	−	2.27615i	0.268104	−	0.0787224i
$837$		0			0
$838$	−3.65852	−	25.4456i	−0.126382	−	0.879004i
$839$	15.3408	+	33.5917i	0.529624	+	1.15971i	0.965666	+	0.259788i	$0.0836526\pi$
$839$	15.3408	+	33.5917i	0.529624	+	1.15971i	−0.436042	+	0.899926i	$0.643620\pi$
$840$		0			0
$841$	−5.00090	−	34.7820i	−0.172445	−	1.19938i
$842$	−13.3403	−	8.57330i	−0.459738	−	0.295456i
$843$		0			0
$844$	−3.49422	+	24.3029i	−0.120276	+	0.836539i
$845$	−7.62036	+	8.79436i	−0.262148	+	0.302535i
$846$		0			0
$847$	24.0727	+	27.7813i	0.827146	+	0.954577i
$848$	7.04084	+	2.06738i	0.241783	+	0.0709940i
$849$		0			0
$850$	13.4266			0.460529
$851$	−34.6464	+	12.7059i	−1.18766	+	0.435553i
$852$		0			0
$853$	−0.861454	+	1.88632i	−0.0294956	+	0.0645864i	−0.923806	−	0.382860i	$-0.874939\pi$
$853$	−0.861454	+	1.88632i	−0.0294956	+	0.0645864i	0.894311	+	0.447446i	$0.147666\pi$
$854$	−58.6808	−	17.2302i	−2.00802	−	0.589607i
$855$		0			0
$856$	−3.22598	+	2.07321i	−0.110262	+	0.0708609i
$857$	0.262276	−	0.302682i	0.00895916	−	0.0103394i	−0.751252	−	0.660015i	$-0.770550\pi$
$857$	0.262276	−	0.302682i	0.00895916	−	0.0103394i	0.760211	+	0.649676i	$0.225095\pi$
$858$		0			0
$859$	38.8368	−	11.4035i	1.32509	−	0.389083i	0.458765	−	0.888557i	$-0.348292\pi$
$859$	38.8368	−	11.4035i	1.32509	−	0.389083i	0.866328	+	0.499475i	$0.166474\pi$
$860$	3.43850	+	2.20979i	0.117252	+	0.0753531i
$861$		0			0
$862$	−15.9054	−	34.8279i	−0.541739	−	1.18624i
$863$	−1.77473	−	3.88613i	−0.0604127	−	0.132285i	0.877018	−	0.480458i	$-0.159530\pi$
$863$	−1.77473	−	3.88613i	−0.0604127	−	0.132285i	−0.937430	+	0.348173i	$0.886802\pi$
$864$		0			0
$865$	−15.8939	−	10.2144i	−0.540410	−	0.347301i
$866$	11.6153	−	3.41055i	0.394702	−	0.115895i
$867$		0			0
$868$	−22.7736	+	26.2821i	−0.772985	+	0.892072i
$869$	2.07379	−	1.33275i	0.0703486	−	0.0452103i
$870$		0			0
$871$	−0.959879	−	0.281846i	−0.0325243	−	0.00954999i
$872$	−3.75843	+	8.22982i	−0.127277	+	0.278697i
$873$		0			0
$874$	−9.04588	+	23.8516i	−0.305981	+	0.806794i
$875$	35.3532			1.19516
$876$		0			0
$877$	32.9543	+	9.67625i	1.11279	+	0.326744i	0.785921	−	0.618327i	$-0.212189\pi$
$877$	32.9543	+	9.67625i	1.11279	+	0.326744i	0.326866	+	0.945071i	$0.394007\pi$
$878$	15.1889	+	17.5289i	0.512600	+	0.591571i
$879$		0			0
$880$	−0.906980	+	1.04671i	−0.0305743	+	0.0352846i
$881$	4.50512	−	31.3338i	0.151781	−	1.05566i	−0.761450	−	0.648223i	$-0.775512\pi$
$881$	4.50512	−	31.3338i	0.151781	−	1.05566i	0.913232	−	0.407440i	$-0.133579\pi$
$882$		0			0
$883$	26.9690	+	17.3319i	0.907578	+	0.583265i	0.909028	−	0.416734i	$-0.136825\pi$
$883$	26.9690	+	17.3319i	0.907578	+	0.583265i	−0.00145064	+	0.999999i	$0.500462\pi$
$884$	−0.223805	−	1.55660i	−0.00752739	−	0.0523541i
$885$		0			0
$886$	3.87323	+	8.48118i	0.130124	+	0.284931i
$887$	0.175049	+	1.21749i	0.00587757	+	0.0408794i	0.992549	−	0.121845i	$-0.0388810\pi$
$887$	0.175049	+	1.21749i	0.00587757	+	0.0408794i	−0.986672	+	0.162724i	$0.947972\pi$
$888$		0			0
$889$	−18.2253	+	5.35144i	−0.611258	+	0.179482i
$890$	1.21399	−	8.44350i	0.0406931	−	0.283027i
$891$		0			0
$892$	−4.96869	+	3.19318i	−0.166364	+	0.106916i
$893$	−0.951404	−	1.09798i	−0.0318375	−	0.0367424i
$894$		0			0
$895$	−0.206557	+	0.452298i	−0.00690445	+	0.0151186i
$896$	−4.22871			−0.141271
$897$		0			0
$898$	−41.6869			−1.39111
$899$	27.3602	−	59.9106i	0.912515	−	1.99813i
$900$		0			0
$901$	15.4780	+	17.8625i	0.515646	+	0.595087i
$902$	11.7533	−	7.55340i	0.391343	−	0.251501i
$903$		0			0
$904$	1.59877	−	11.1197i	0.0531742	−	0.369835i
$905$	−2.24169	+	0.658221i	−0.0745164	+	0.0218800i
$906$		0			0
$907$	−4.30921	−	29.9712i	−0.143085	−	0.995178i	−0.927201	−	0.374564i	$-0.877792\pi$
$907$	−4.30921	−	29.9712i	−0.143085	−	0.995178i	0.784116	−	0.620614i	$-0.213117\pi$
$908$	2.24976	+	4.92628i	0.0746608	+	0.163484i
$909$		0			0
$910$	−0.267927	−	1.86347i	−0.00888169	−	0.0617735i
$911$	41.7100	+	26.8054i	1.38192	+	0.888103i	0.999358	−	0.0358289i	$-0.0114071\pi$
$911$	41.7100	+	26.8054i	1.38192	+	0.888103i	0.382557	+	0.923932i	$0.375043\pi$
$912$		0			0
$913$	2.58990	−	18.0131i	0.0857131	−	0.596148i
$914$	17.8402	−	20.5887i	0.590103	−	0.681015i
$915$		0			0
$916$	−9.63389	−	11.1181i	−0.318313	−	0.367353i
$917$	−32.7678	−	9.62150i	−1.08209	−	0.317730i
$918$		0			0
$919$	−30.4532			−1.00456			−0.502279	−	0.864705i	$-0.667505\pi$
$919$	−30.4532			−1.00456			−0.502279	+	0.864705i	$0.667505\pi$
$920$	−0.906053	−	4.27816i	−0.0298717	−	0.141047i
$921$		0			0
$922$	12.0836	−	26.4595i	0.397953	−	0.871396i
$923$	4.97023	+	1.45939i	0.163597	+	0.0480364i
$924$		0			0
$925$	−26.9840	+	17.3415i	−0.887228	+	0.570187i
$926$	1.36436	−	1.57455i	0.0448355	−	0.0517430i
$927$		0			0
$928$	7.68431	−	2.25632i	0.252250	−	0.0740673i
$929$	−48.6422	−	31.2604i	−1.59590	−	1.02562i	−0.969173	−	0.246382i	$-0.920758\pi$
$929$	−48.6422	−	31.2604i	−1.59590	−	1.02562i	−0.626726	−	0.779240i	$-0.715606\pi$
$930$		0			0
$931$	24.0451	+	52.6513i	0.788045	+	1.72558i
$932$	10.6363	+	23.2901i	0.348402	+	0.762894i
$933$		0			0
$934$	22.3917	+	14.3902i	0.732678	+	0.470863i
$935$	−4.28028	+	1.25681i	−0.139980	+	0.0411019i
$936$		0			0
$937$	−29.9525	+	34.5670i	−0.978505	+	1.12926i	0.0130948	+	0.999914i	$0.495832\pi$
$937$	−29.9525	+	34.5670i	−0.978505	+	1.12926i	−0.991600	+	0.129341i	$0.958714\pi$
$938$	−7.28906	+	4.68439i	−0.237996	+	0.152951i
$939$		0			0
$940$	0.238969	+	0.0701677i	0.00779432	+	0.00228862i
$941$	13.1150	−	28.7179i	0.427538	−	0.936178i	−0.566182	−	0.824280i	$-0.691580\pi$
$941$	13.1150	−	28.7179i	0.427538	−	0.936178i	0.993720	−	0.111897i	$-0.0356928\pi$
$942$		0			0
$943$	−3.38885	+	43.9829i	−0.110356	+	1.43228i
$944$	1.13462			0.0369287
$945$		0			0
$946$	6.53267	+	1.91817i	0.212396	+	0.0623650i
$947$	19.0440	+	21.9780i	0.618848	+	0.714188i	0.975488	−	0.220054i	$-0.0706232\pi$
$947$	19.0440	+	21.9780i	0.618848	+	0.714188i	−0.356640	+	0.934242i	$0.616078\pi$
$948$		0			0
$949$	−0.205429	+	0.237078i	−0.00666850	+	0.00769586i
$950$	−3.15552	+	21.9471i	−0.102378	+	0.712058i
$951$		0			0
$952$	−11.4582	−	7.36374i	−0.371363	−	0.238660i
$953$	−2.79626	−	19.4484i	−0.0905797	−	0.629996i	−0.983652	−	0.180082i	$-0.942364\pi$
$953$	−2.79626	−	19.4484i	−0.0905797	−	0.629996i	0.893072	−	0.449914i	$-0.148545\pi$
$954$		0			0
$955$	−1.47700	−	3.23418i	−0.0477946	−	0.104656i
$956$	0.288488	+	2.00648i	0.00933036	+	0.0648941i
$957$		0			0
$958$	−4.37504	+	1.28463i	−0.141351	+	0.0415044i
$959$	−0.362774	+	2.52315i	−0.0117146	+	0.0814768i
$960$		0			0
$961$	30.8163	−	19.8044i	0.994075	−	0.638853i
$962$	2.46027	+	2.83930i	0.0793221	+	0.0915426i
$963$		0			0
$964$	7.69901	−	16.8585i	0.247968	−	0.542975i
$965$	12.1458			0.390986
$966$		0			0
$967$	26.2117			0.842911			0.421455	−	0.906849i	$-0.361519\pi$
$967$	26.2117			0.842911			0.421455	+	0.906849i	$0.361519\pi$
$968$	3.61118	−	7.90739i	0.116068	−	0.254153i
$969$		0			0
$970$	2.72475	+	3.14453i	0.0874865	+	0.100965i
$971$	49.8758	−	32.0532i	1.60059	−	1.02864i	0.633656	−	0.773615i	$-0.281553\pi$
$971$	49.8758	−	32.0532i	1.60059	−	1.02864i	0.966935	−	0.255023i	$-0.0820830\pi$
$972$		0			0
$973$	9.44208	−	65.6711i	0.302699	−	2.10532i
$974$	−11.2979	+	3.31735i	−0.362007	+	0.106295i
$975$		0			0
$976$	2.05824	+	14.3154i	0.0658828	+	0.458225i
$977$	12.0987	+	26.4926i	0.387073	+	0.847572i	0.998419	+	0.0562085i	$0.0179011\pi$
$977$	12.0987	+	26.4926i	0.387073	+	0.847572i	−0.611346	+	0.791363i	$0.709372\pi$
$978$		0			0
$979$	−2.02220	−	14.0647i	−0.0646297	−	0.449510i
$980$	−8.34747	−	5.36459i	−0.266650	−	0.171366i
$981$		0			0
$982$	−1.21644	+	8.46053i	−0.0388182	+	0.269986i
$983$	1.37496	−	1.58678i	0.0438543	−	0.0506105i	−0.733399	−	0.679799i	$-0.762067\pi$
$983$	1.37496	−	1.58678i	0.0438543	−	0.0506105i	0.777253	+	0.629188i	$0.216613\pi$
$984$		0			0
$985$	−9.96647	−	11.5019i	−0.317558	−	0.366482i
$986$	24.7507	+	7.26746i	0.788222	+	0.231443i
$987$		0			0
$988$	2.59701			0.0826220
$989$	−17.2801	+	12.7881i	−0.549474	+	0.406637i
$990$		0			0
$991$	−17.3984	+	38.0972i	−0.552679	+	1.21020i	0.402841	+	0.915270i	$0.368023\pi$
$991$	−17.3984	+	38.0972i	−0.552679	+	1.21020i	−0.955520	+	0.294928i	$0.904704\pi$
$992$	7.89071	+	2.31692i	0.250530	+	0.0735623i
$993$		0			0
$994$	37.7425	−	24.2556i	1.19712	−	0.769342i
$995$	−1.78014	+	2.05439i	−0.0564342	+	0.0651285i
$996$		0			0
$997$	5.06282	−	1.48658i	0.160341	−	0.0470804i	−0.200577	−	0.979678i	$-0.564282\pi$
$997$	5.06282	−	1.48658i	0.160341	−	0.0470804i	0.360918	+	0.932598i	$0.382463\pi$
$998$	−10.1582	−	6.52829i	−0.321553	−	0.206650i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.f.397.1		10
3.2	odd	2		46.2.c.a.29.1	yes	10
12.11	even	2		368.2.m.b.305.1		10
23.2	even	11		9522.2.a.bp.1.4		5
23.4	even	11	inner	414.2.i.f.73.1		10
23.21	odd	22		9522.2.a.bu.1.2		5
69.2	odd	22		1058.2.a.m.1.4		5
69.44	even	22		1058.2.a.l.1.4		5
69.50	odd	22		46.2.c.a.27.1	✓	10
276.71	even	22		8464.2.a.bx.1.2		5
276.119	even	22		368.2.m.b.257.1		10
276.251	odd	22		8464.2.a.bw.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.2.c.a.27.1	✓	10	69.50	odd	22
46.2.c.a.29.1	yes	10	3.2	odd	2
368.2.m.b.257.1		10	276.119	even	22
368.2.m.b.305.1		10	12.11	even	2
414.2.i.f.73.1		10	23.4	even	11	inner
414.2.i.f.397.1		10	1.1	even	1	trivial
1058.2.a.l.1.4		5	69.44	even	22
1058.2.a.m.1.4		5	69.2	odd	22
8464.2.a.bw.1.2		5	276.251	odd	22
8464.2.a.bx.1.2		5	276.71	even	22
9522.2.a.bp.1.4		5	23.2	even	11
9522.2.a.bu.1.2		5	23.21	odd	22

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.654861 - 0.755750i) q^{4} +(-0.767092 + 0.492980i) q^{5} +(-0.601808 + 4.18567i) q^{7} +(0.959493 - 0.281733i) q^{8} +O(q^{10})\)	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.654861 - 0.755750i) q^{4} +(-0.767092 + 0.492980i) q^{5} +(-0.601808 + 4.18567i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.129769 - 0.902563i) q^{10} +(-0.630972 - 1.38164i) q^{11} +(-0.0694846 - 0.483276i) q^{13} +(-3.55742 - 2.28621i) q^{14} +(-0.142315 + 0.989821i) q^{16} +(-2.10926 + 2.43422i) q^{17} +(-3.48325 - 4.01989i) q^{19} +(0.874908 + 0.256896i) q^{20} +1.51890 q^{22} +(-2.89510 + 3.82340i) q^{23} +(-1.73167 + 3.79184i) q^{25} +(0.468468 + 0.137555i) q^{26} +(3.55742 - 2.28621i) q^{28} +(-5.24460 + 6.05259i) q^{29} +(-7.89071 + 2.31692i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(-1.33803 - 2.92987i) q^{34} +(-1.60181 - 3.50747i) q^{35} +(6.47324 + 4.16010i) q^{37} +(5.10362 - 1.49856i) q^{38} +(-0.597131 + 0.689126i) q^{40} +(7.73806 - 4.97295i) q^{41} +(4.30093 + 1.26287i) q^{43} +(-0.630972 + 1.38164i) q^{44} +(-2.27522 - 4.22177i) q^{46} +0.273137 q^{47} +(-10.4412 - 3.06580i) q^{49} +(-2.72981 - 3.15037i) q^{50} +(-0.319733 + 0.368991i) q^{52} +(1.04432 - 7.26339i) q^{53} +(1.16513 + 0.748786i) q^{55} +(0.601808 + 4.18567i) q^{56} +(-3.32694 - 7.28499i) q^{58} +(-0.161473 - 1.12307i) q^{59} +(13.8768 - 4.07459i) q^{61} +(1.17037 - 8.14013i) q^{62} +(0.841254 - 0.540641i) q^{64} +(0.291546 + 0.336462i) q^{65} +(0.851175 - 1.86381i) q^{67} +3.22094 q^{68} +3.85592 q^{70} +(-4.40736 + 9.65077i) q^{71} +(-0.420749 - 0.485571i) q^{73} +(-6.47324 + 4.16010i) q^{74} +(-0.756983 + 5.26493i) q^{76} +(6.16279 - 1.80956i) q^{77} +(0.230973 + 1.60645i) q^{79} +(-0.378794 - 0.829443i) q^{80} +(1.30905 + 9.10463i) q^{82} +(10.0793 + 6.47759i) q^{83} +(0.417977 - 2.90710i) q^{85} +(-2.93542 + 3.38765i) q^{86} +(-0.994666 - 1.14791i) q^{88} +(8.97609 + 2.63562i) q^{89} +2.06465 q^{91} +(4.78542 - 0.315828i) q^{92} +(-0.113465 + 0.248454i) q^{94} +(4.65370 + 1.36645i) q^{95} +(-3.83870 + 2.46698i) q^{97} +(7.12617 - 8.22404i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - q^{4} + 6 q^{5} + 3 q^{7} + q^{8}+O(q^{10}) \) 10 * q + q^2 - q^4 + 6 * q^5 + 3 * q^7 + q^8	\( 10 q + q^{2} - q^{4} + 6 q^{5} + 3 q^{7} + q^{8} - 6 q^{10} + 12 q^{11} - 14 q^{13} - 3 q^{14} - q^{16} - 15 q^{17} + 2 q^{19} - 5 q^{20} + 10 q^{22} + q^{23} + 13 q^{25} + 3 q^{26} + 3 q^{28} + 8 q^{29} - 21 q^{31} + q^{32} - 7 q^{34} - 7 q^{35} + 28 q^{37} + 9 q^{38} - 6 q^{40} + 31 q^{41} + 11 q^{43} + 12 q^{44} - 12 q^{46} - 18 q^{47} - 24 q^{49} - 2 q^{50} + 8 q^{52} + 21 q^{53} + 5 q^{55} - 3 q^{56} - 8 q^{58} + 5 q^{59} + 37 q^{61} - q^{62} - q^{64} - 37 q^{65} - 13 q^{67} - 26 q^{68} + 18 q^{70} - 49 q^{71} - 8 q^{73} - 28 q^{74} - 20 q^{76} + 8 q^{77} + 8 q^{79} - 5 q^{80} + 2 q^{82} + 7 q^{83} - 42 q^{85} - 22 q^{86} - q^{88} + 13 q^{89} - 24 q^{91} + 23 q^{92} - 37 q^{94} + 10 q^{95} - 32 q^{97} + 24 q^{98}+O(q^{100}) \) 10 * q + q^2 - q^4 + 6 * q^5 + 3 * q^7 + q^8 - 6 * q^10 + 12 * q^11 - 14 * q^13 - 3 * q^14 - q^16 - 15 * q^17 + 2 * q^19 - 5 * q^20 + 10 * q^22 + q^23 + 13 * q^25 + 3 * q^26 + 3 * q^28 + 8 * q^29 - 21 * q^31 + q^32 - 7 * q^34 - 7 * q^35 + 28 * q^37 + 9 * q^38 - 6 * q^40 + 31 * q^41 + 11 * q^43 + 12 * q^44 - 12 * q^46 - 18 * q^47 - 24 * q^49 - 2 * q^50 + 8 * q^52 + 21 * q^53 + 5 * q^55 - 3 * q^56 - 8 * q^58 + 5 * q^59 + 37 * q^61 - q^62 - q^64 - 37 * q^65 - 13 * q^67 - 26 * q^68 + 18 * q^70 - 49 * q^71 - 8 * q^73 - 28 * q^74 - 20 * q^76 + 8 * q^77 + 8 * q^79 - 5 * q^80 + 2 * q^82 + 7 * q^83 - 42 * q^85 - 22 * q^86 - q^88 + 13 * q^89 - 24 * q^91 + 23 * q^92 - 37 * q^94 + 10 * q^95 - 32 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

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Database

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