LMFDB - Embedded newform 224.2.bd.a.109.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(37,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("224.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.bd (of order $24$, degree $8$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			109.21
Character	$\chi$	$=$	224.109
Dual form			224.2.bd.a.37.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.729975 + 1.21125i) q^{2} +(1.86449 + 2.42985i) q^{3} +(-0.934274 + 1.76837i) q^{4} +(-1.81038 - 1.38916i) q^{5} +(-1.58213 + 4.03209i) q^{6} +(-1.50004 - 2.17942i) q^{7} +(-2.82394 + 0.159222i) q^{8} +(-1.65138 + 6.16305i) q^{9} +O(q^{10})$	\(q+(0.729975 + 1.21125i) q^{2} +(1.86449 + 2.42985i) q^{3} +(-0.934274 + 1.76837i) q^{4} +(-1.81038 - 1.38916i) q^{5} +(-1.58213 + 4.03209i) q^{6} +(-1.50004 - 2.17942i) q^{7} +(-2.82394 + 0.159222i) q^{8} +(-1.65138 + 6.16305i) q^{9} +(0.361087 - 3.20689i) q^{10} +(2.72124 + 0.358257i) q^{11} +(-6.03881 + 1.02696i) q^{12} +(5.37302 + 2.22558i) q^{13} +(1.54484 - 3.40786i) q^{14} -6.98902i q^{15} +(-2.25426 - 3.30428i) q^{16} +(3.84959 + 2.22256i) q^{17} +(-8.67049 + 2.49863i) q^{18} +(-0.502878 - 3.81973i) q^{19} +(4.14794 - 1.90358i) q^{20} +(2.49884 - 7.70837i) q^{21} +(1.55249 + 3.55763i) q^{22} +(0.112813 - 0.421022i) q^{23} +(-5.65209 - 6.56488i) q^{24} +(0.0536402 + 0.200188i) q^{25} +(1.22643 + 8.13271i) q^{26} +(-9.56541 + 3.96212i) q^{27} +(5.25547 - 0.616458i) q^{28} +(-0.123732 + 0.298716i) q^{29} +(8.46548 - 5.10181i) q^{30} +(0.138514 - 0.239913i) q^{31} +(2.35677 - 5.14253i) q^{32} +(4.20320 + 7.28015i) q^{33} +(0.118016 + 6.28525i) q^{34} +(-0.311899 + 6.02938i) q^{35} +(-9.35571 - 8.67824i) q^{36} +(-5.04074 - 3.86790i) q^{37} +(4.25958 - 3.39742i) q^{38} +(4.61011 + 17.2052i) q^{39} +(5.33361 + 3.63465i) q^{40} +(-3.13935 - 3.13935i) q^{41} +(11.1609 - 2.60018i) q^{42} +(-3.00894 - 7.26423i) q^{43} +(-3.17591 + 4.47744i) q^{44} +(11.5511 - 8.86346i) q^{45} +(0.592315 - 0.170691i) q^{46} +(-5.92251 + 3.41936i) q^{47} +(3.82586 - 11.6383i) q^{48} +(-2.49974 + 6.53845i) q^{49} +(-0.203323 + 0.211104i) q^{50} +(1.77703 + 13.4979i) q^{51} +(-8.95552 + 7.42219i) q^{52} +(-5.79272 - 0.762626i) q^{53} +(-11.7816 - 8.69389i) q^{54} +(-4.42881 - 4.42881i) q^{55} +(4.58305 + 5.91571i) q^{56} +(8.34376 - 8.34376i) q^{57} +(-0.452143 + 0.0681839i) q^{58} +(0.148586 - 1.12862i) q^{59} +(12.3592 + 6.52966i) q^{60} +(12.1248 - 1.59625i) q^{61} +(0.391708 - 0.00735495i) q^{62} +(15.9090 - 5.64579i) q^{63} +(7.94930 - 0.899267i) q^{64} +(-6.63556 - 11.4931i) q^{65} +(-5.74989 + 10.4055i) q^{66} +(-8.53108 - 11.1179i) q^{67} +(-7.52689 + 4.73102i) q^{68} +(1.23336 - 0.510873i) q^{69} +(-7.53080 + 4.02351i) q^{70} +(-2.65894 + 2.65894i) q^{71} +(3.68212 - 17.6670i) q^{72} +(4.18372 - 1.12102i) q^{73} +(1.00539 - 8.92909i) q^{74} +(-0.386415 + 0.503586i) q^{75} +(7.22453 + 2.67940i) q^{76} +(-3.30118 - 6.46812i) q^{77} +(-17.4746 + 18.1434i) q^{78} +(-6.14316 + 3.54676i) q^{79} +(-0.509083 + 9.11355i) q^{80} +(-10.8850 - 6.28445i) q^{81} +(1.51090 - 6.09419i) q^{82} +(2.95118 + 1.22242i) q^{83} +(11.2967 + 11.6206i) q^{84} +(-3.88175 - 9.37138i) q^{85} +(6.60238 - 8.94730i) q^{86} +(-0.956531 + 0.256302i) q^{87} +(-7.74165 - 0.578418i) q^{88} +(13.6043 + 3.64526i) q^{89} +(19.1679 + 7.52120i) q^{90} +(-3.20930 - 15.0485i) q^{91} +(0.639125 + 0.592844i) q^{92} +(0.841210 - 0.110747i) q^{93} +(-8.46500 - 4.67762i) q^{94} +(-4.39581 + 7.61376i) q^{95} +(16.8897 - 3.86159i) q^{96} +8.51745 q^{97} +(-9.74447 + 1.74508i) q^{98} +(-6.70177 + 16.1795i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{8}\right)$

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 $

$2$	0.729975	+	1.21125i	0.516170	+	0.856486i
$2$	0.729975	+	1.21125i	0.516170	+	0.856486i
$3$	1.86449	+	2.42985i	1.07646	+	1.40287i	0.908902	+	0.417010i	$0.136922\pi$
$3$	1.86449	+	2.42985i	1.07646	+	1.40287i	0.167560	+	0.985862i	$0.446411\pi$
$4$	−0.934274	+	1.76837i	−0.467137	+	0.884185i
$5$	−1.81038	−	1.38916i	−0.809629	−	0.621250i	0.118734	−	0.992926i	$-0.462116\pi$
$5$	−1.81038	−	1.38916i	−0.809629	−	0.621250i	−0.928362	+	0.371676i	$0.878783\pi$
$6$	−1.58213	+	4.03209i	−0.645903	+	1.64610i
$7$	−1.50004	−	2.17942i	−0.566963	−	0.823743i
$7$	−1.50004	−	2.17942i	−0.566963	−	0.823743i
$8$	−2.82394	+	0.159222i	−0.998414	+	0.0562935i
$9$	−1.65138	+	6.16305i	−0.550462	+	2.05435i
$10$	0.361087	−	3.20689i	0.114186	−	1.01411i
$11$	2.72124	+	0.358257i	0.820483	+	0.108019i	0.529070	−	0.848578i	$-0.322541\pi$
$11$	2.72124	+	0.358257i	0.820483	+	0.108019i	0.291414	+	0.956597i	$0.405874\pi$
$12$	−6.03881	+	1.02696i	−1.74325	+	0.296458i
$13$	5.37302	+	2.22558i	1.49021	+	0.617264i	0.971362	−	0.237604i	$-0.0763619\pi$
$13$	5.37302	+	2.22558i	1.49021	+	0.617264i	0.518846	+	0.854868i	$0.326362\pi$
$14$	1.54484	−	3.40786i	0.412875	−	0.910788i
$15$		−	6.98902i		−	1.80456i
$16$	−2.25426	−	3.30428i	−0.563566	−	0.826071i
$17$	3.84959	+	2.22256i	0.933664	+	0.539051i	0.887968	−	0.459905i	$-0.152116\pi$
$17$	3.84959	+	2.22256i	0.933664	+	0.539051i	0.0456952	+	0.998955i	$0.485450\pi$
$18$	−8.67049	+	2.49863i	−2.04365	+	0.588932i
$19$	−0.502878	−	3.81973i	−0.115368	−	0.876307i	−0.947057	−	0.321065i	$-0.895959\pi$
$19$	−0.502878	−	3.81973i	−0.115368	−	0.876307i	0.831689	−	0.555242i	$-0.187374\pi$
$20$	4.14794	−	1.90358i	0.927507	−	0.425653i
$21$	2.49884	−	7.70837i	0.545292	−	1.68210i
$22$	1.55249	+	3.55763i	0.330992	+	0.758489i
$23$	0.112813	−	0.421022i	0.0235230	−	0.0877892i	−0.953166	−	0.302446i	$-0.902197\pi$
$23$	0.112813	−	0.421022i	0.0235230	−	0.0877892i	0.976689	+	0.214657i	$0.0688634\pi$
$24$	−5.65209	−	6.56488i	−1.15373	−	1.34005i
$25$	0.0536402	+	0.200188i	0.0107280	+	0.0400376i
$26$	1.22643	+	8.13271i	0.240522	+	1.59496i
$27$	−9.56541	+	3.96212i	−1.84086	+	0.762511i
$28$	5.25547	−	0.616458i	0.993191	−	0.116500i
$29$	−0.123732	+	0.298716i	−0.0229765	+	0.0554702i	−0.934951	−	0.354776i	$-0.884557\pi$
$29$	−0.123732	+	0.298716i	−0.0229765	+	0.0554702i	0.911975	+	0.410246i	$0.134557\pi$
$30$	8.46548	−	5.10181i	1.54558	−	0.931458i
$31$	0.138514	−	0.239913i	0.0248779	−	0.0430897i	−0.853318	−	0.521390i	$-0.825414\pi$
$31$	0.138514	−	0.239913i	0.0248779	−	0.0430897i	0.878196	+	0.478300i	$0.158747\pi$
$32$	2.35677	−	5.14253i	0.416622	−	0.909080i
$33$	4.20320	+	7.28015i	0.731683	+	1.26731i
$34$	0.118016	+	6.28525i	0.0202395	+	1.07791i
$35$	−0.311899	+	6.02938i	−0.0527206	+	1.01915i
$36$	−9.35571	−	8.67824i	−1.55929	−	1.44637i
$37$	−5.04074	−	3.86790i	−0.828693	−	0.635878i	0.104793	−	0.994494i	$-0.466582\pi$
$37$	−5.04074	−	3.86790i	−0.828693	−	0.635878i	−0.933485	+	0.358616i	$0.883249\pi$
$38$	4.25958	−	3.39742i	0.690995	−	0.551135i
$39$	4.61011	+	17.2052i	0.738209	+	2.75503i
$40$	5.33361	+	3.63465i	0.843317	+	0.574688i
$41$	−3.13935	−	3.13935i	−0.490284	−	0.490284i	0.418112	−	0.908396i	$-0.362692\pi$
$41$	−3.13935	−	3.13935i	−0.490284	−	0.490284i	−0.908396	+	0.418112i	$0.862692\pi$
$42$	11.1609	−	2.60018i	1.72216	−	0.401217i
$43$	−3.00894	−	7.26423i	−0.458859	−	1.10778i	−0.968860	−	0.247611i	$-0.920355\pi$
$43$	−3.00894	−	7.26423i	−0.458859	−	1.10778i	0.510000	−	0.860174i	$-0.329645\pi$
$44$	−3.17591	+	4.47744i	−0.478787	+	0.675000i
$45$	11.5511	−	8.86346i	1.72193	−	1.32129i
$46$	0.592315	−	0.170691i	0.0873321	−	0.0251670i
$47$	−5.92251	+	3.41936i	−0.863887	+	0.498766i	−0.865312	−	0.501233i	$-0.832880\pi$
$47$	−5.92251	+	3.41936i	−0.863887	+	0.498766i	0.00142483	+	0.999999i	$0.499546\pi$
$48$	3.82586	−	11.6383i	0.552215	−	1.67985i
$49$	−2.49974	+	6.53845i	−0.357105	+	0.934064i
$50$	−0.203323	+	0.211104i	−0.0287542	+	0.0298546i
$51$	1.77703	+	13.4979i	0.248834	+	1.89008i
$52$	−8.95552	+	7.42219i	−1.24191	+	1.02927i
$53$	−5.79272	−	0.762626i	−0.795691	−	0.104755i	−0.278289	−	0.960497i	$-0.589767\pi$
$53$	−5.79272	−	0.762626i	−0.795691	−	0.104755i	−0.517402	+	0.855743i	$0.673101\pi$
$54$	−11.7816	−	8.69389i	−1.60328	−	1.18309i
$55$	−4.42881	−	4.42881i	−0.597180	−	0.597180i
$56$	4.58305	+	5.91571i	0.612436	+	0.790521i
$57$	8.34376	−	8.34376i	1.10516	−	1.10516i
$58$	−0.452143	+	0.0681839i	−0.0593692	+	0.00895299i
$59$	0.148586	−	1.12862i	0.0193443	−	0.146934i	−0.979047	−	0.203635i	$-0.934725\pi$
$59$	0.148586	−	1.12862i	0.0193443	−	0.146934i	0.998391	+	0.0567001i	$0.0180579\pi$
$60$	12.3592	+	6.52966i	1.59556	+	0.842975i
$61$	12.1248	−	1.59625i	1.55242	−	0.204379i	0.695003	−	0.719007i	$-0.255403\pi$
$61$	12.1248	−	1.59625i	1.55242	−	0.204379i	0.857414	+	0.514628i	$0.172070\pi$
$62$	0.391708	−	0.00735495i	0.0497469	−	0.000934079i
$63$	15.9090	−	5.64579i	2.00435	−	0.711302i
$64$	7.94930	−	0.899267i	0.993662	−	0.112408i
$65$	−6.63556	−	11.4931i	−0.823040	−	1.42555i
$66$	−5.74989	+	10.4055i	−0.707762	+	1.28082i
$67$	−8.53108	−	11.1179i	−1.04224	−	1.35827i	−0.931222	−	0.364452i	$-0.881256\pi$
$67$	−8.53108	−	11.1179i	−1.04224	−	1.35827i	−0.111015	−	0.993819i	$-0.535410\pi$
$68$	−7.52689	+	4.73102i	−0.912769	+	0.573721i
$69$	1.23336	−	0.510873i	0.148479	−	0.0615019i
$70$	−7.53080	+	4.02351i	−0.900102	+	0.480901i
$71$	−2.65894	+	2.65894i	−0.315558	+	0.315558i	−0.847058	−	0.531500i	$-0.821628\pi$
$71$	−2.65894	+	2.65894i	−0.315558	+	0.315558i	0.531500	+	0.847058i	$0.321628\pi$
$72$	3.68212	−	17.6670i	0.433942	−	2.08208i
$73$	4.18372	−	1.12102i	0.489667	−	0.131206i	−0.00553336	−	0.999985i	$-0.501761\pi$
$73$	4.18372	−	1.12102i	0.489667	−	0.131206i	0.495200	+	0.868779i	$0.335095\pi$
$74$	1.00539	−	8.92909i	0.116875	−	1.03799i
$75$	−0.386415	+	0.503586i	−0.0446193	+	0.0581491i
$76$	7.22453	+	2.67940i	0.828710	+	0.307349i
$77$	−3.30118	−	6.46812i	−0.376204	−	0.737110i
$78$	−17.4746	+	18.1434i	−1.97861	+	2.05433i
$79$	−6.14316	+	3.54676i	−0.691160	+	0.399041i	−0.804046	−	0.594567i	$-0.797324\pi$
$79$	−6.14316	+	3.54676i	−0.691160	+	0.399041i	0.112887	+	0.993608i	$0.463990\pi$
$80$	−0.509083	+	9.11355i	−0.0569172	+	1.01893i
$81$	−10.8850	−	6.28445i	−1.20944	−	0.698272i
$82$	1.51090	−	6.09419i	0.166851	−	0.672991i
$83$	2.95118	+	1.22242i	0.323934	+	0.134178i	0.538724	−	0.842482i	$-0.318907\pi$
$83$	2.95118	+	1.22242i	0.323934	+	0.134178i	−0.214790	+	0.976660i	$0.568907\pi$
$84$	11.2967	+	11.6206i	1.23257	+	1.26791i
$85$	−3.88175	−	9.37138i	−0.421035	−	1.01647i
$86$	6.60238	−	8.94730i	0.711953	−	0.964812i
$87$	−0.956531	+	0.256302i	−0.102551	+	0.0274784i
$88$	−7.74165	−	0.578418i	−0.825263	−	0.0616595i
$89$	13.6043	+	3.64526i	1.44205	+	0.386397i	0.893252	−	0.449556i	$-0.148418\pi$
$89$	13.6043	+	3.64526i	1.44205	+	0.386397i	0.548801	+	0.835953i	$0.315084\pi$
$90$	19.1679	+	7.52120i	2.02048	+	0.792804i
$91$	−3.20930	−	15.0485i	−0.336426	−	1.57751i
$92$	0.639125	+	0.592844i	0.0666334	+	0.0618083i
$93$	0.841210	−	0.110747i	0.0872294	−	0.0114840i
$94$	−8.46500	−	4.67762i	−0.873099	−	0.482460i
$95$	−4.39581	+	7.61376i	−0.451000	+	0.781156i
$96$	16.8897	−	3.86159i	1.72380	−	0.394121i
$97$	8.51745			0.864816			0.432408	−	0.901678i	$-0.357664\pi$
$97$	8.51745			0.864816			0.432408	+	0.901678i	$0.357664\pi$
$98$	−9.74447	+	1.74508i	−0.984340	+	0.176280i
$99$	−6.70177	+	16.1795i	−0.673553	+	1.62610i
$100$	−0.404121	−	0.0921747i	−0.0404121	−	0.00921747i
$101$	−1.89511	+	14.3948i	−0.188570	+	1.43233i	0.591331	+	0.806429i	$0.298603\pi$
$101$	−1.89511	+	14.3948i	−0.188570	+	1.43233i	−0.779901	+	0.625903i	$0.784731\pi$
$102$	−15.0522	+	12.0055i	−1.49039	+	1.18872i
$103$	5.13223	+	1.37518i	0.505694	+	0.135500i	0.502641	−	0.864495i	$-0.332362\pi$
$103$	5.13223	+	1.37518i	0.505694	+	0.135500i	0.00305252	+	0.999995i	$0.499028\pi$
$104$	−15.5275	−	5.42940i	−1.52259	−	0.532397i
$105$	−15.2320	+	10.4838i	−1.48649	+	1.02312i
$106$	−3.30481	−	7.57316i	−0.320991	−	0.735570i
$107$	−4.74582	+	6.18488i	−0.458796	+	0.597915i	−0.964268	−	0.264928i	$-0.914652\pi$
$107$	−4.74582	+	6.18488i	−0.458796	+	0.597915i	0.505472	+	0.862843i	$0.331318\pi$
$108$	1.93021	−	20.6169i	0.185735	−	1.98386i
$109$	−1.92220	+	1.47496i	−0.184113	+	0.141275i	−0.696706	−	0.717357i	$-0.745352\pi$
$109$	−1.92220	+	1.47496i	−0.184113	+	0.141275i	0.512593	+	0.858632i	$0.328685\pi$
$110$	2.13149	−	8.59733i	0.203230	−	0.819723i
$111$		−	19.4599i		−	1.84705i
$112$	−3.81992	+	9.86956i	−0.360949	+	0.932586i
$113$			16.3928i			1.54211i	0.636770	+	0.771054i	$0.280270\pi$
$113$			16.3928i			1.54211i	−0.636770	+	0.771054i	$0.719730\pi$
$114$	16.1971	+	4.01568i	1.51700	+	0.376103i
$115$	−0.789100	+	0.605498i	−0.0735839	+	0.0564629i
$116$	−0.412641	−	0.497887i	−0.0383127	−	0.0462276i
$117$	−22.5893	+	29.4389i	−2.08838	+	2.72163i
$118$	1.47552	−	0.643892i	0.135832	−	0.0592750i
$119$	−0.930660	−	11.7238i	−0.0853135	−	1.07472i
$120$	1.11281	+	19.7366i	0.101585	+	1.80170i
$121$	−3.34841	−	0.897204i	−0.304401	−	0.0815640i
$122$	10.7842	+	13.5209i	0.976359	+	1.22413i
$123$	1.77486	−	13.4814i	0.160034	−	1.21558i
$124$	0.294846	+	0.469089i	0.0264779	+	0.0421254i
$125$	−4.18532	+	10.1043i	−0.374346	+	0.903752i
$126$	18.4517	+	15.1486i	1.64381	+	1.34954i
$127$	5.00656			0.444260			0.222130	−	0.975017i	$-0.428699\pi$
$127$	5.00656			0.444260			0.222130	+	0.975017i	$0.428699\pi$
$128$	6.89203	+	8.97218i	0.609175	+	0.793036i
$129$	12.0408	−	20.8553i	1.06014	−	1.83621i
$130$	9.07731	−	16.4270i	0.796132	−	1.44075i
$131$	−13.8485	+	1.82319i	−1.20995	+	0.159292i	−0.708383	−	0.705828i	$-0.750575\pi$
$131$	−13.8485	+	1.82319i	−1.20995	+	0.159292i	−0.501563	+	0.865121i	$0.667242\pi$
$132$	−16.8009	+	0.631152i	−1.46233	+	0.0549347i
$133$	−7.57046	+	6.82575i	−0.656442	+	0.591867i
$134$	7.23916	−	18.4491i	0.625368	−	1.59376i
$135$	22.8211	+	6.11489i	1.96413	+	0.526286i
$136$	−11.2249	−	5.66345i	−0.962528	−	0.485637i
$137$	−9.53358	+	2.55452i	−0.814509	+	0.218247i	−0.641944	−	0.766751i	$-0.721872\pi$
$137$	−9.53358	+	2.55452i	−0.814509	+	0.218247i	−0.172565	+	0.984998i	$0.555205\pi$
$138$	1.51912	+	1.12098i	0.129316	+	0.0954245i
$139$	−2.40716	−	5.81140i	−0.204173	−	0.492917i	0.788313	−	0.615274i	$-0.210955\pi$
$139$	−2.40716	−	5.81140i	−0.204173	−	0.492917i	−0.992486	+	0.122357i	$0.960955\pi$
$140$	−10.3708	−	6.18465i	−0.876491	−	0.522698i
$141$	−19.3510	−	8.01544i	−1.62965	−	0.675021i
$142$	−5.16160	−	1.27969i	−0.433152	−	0.107389i
$143$	13.8239	+	7.98125i	1.15601	+	0.667425i
$144$	24.0871	−	8.43651i	2.00726	−	0.703042i
$145$	0.638966	−	0.368907i	0.0530633	−	0.0306361i
$146$	4.41185	+	4.24923i	0.365127	+	0.351668i
$147$	−20.5482	+	6.11687i	−1.69478	+	0.504511i
$148$	11.5493	−	5.30022i	0.949347	−	0.435675i
$149$	8.71519	−	11.3579i	0.713976	−	0.930471i	−0.285636	−	0.958338i	$-0.592205\pi$
$149$	8.71519	−	11.3579i	0.713976	−	0.930471i	0.999612	+	0.0278668i	$0.00887144\pi$
$150$	−0.892043	−	0.100442i	−0.0728350	−	0.00820104i
$151$	2.09402	−	0.561092i	0.170409	−	0.0456610i	−0.172606	−	0.984991i	$-0.555219\pi$
$151$	2.09402	−	0.561092i	0.170409	−	0.0456610i	0.343015	+	0.939330i	$0.388552\pi$
$152$	2.02828	+	10.7066i	0.164515	+	0.868423i
$153$	−20.0549	+	20.0549i	−1.62135	+	1.62135i
$154$	5.42476	−	8.72013i	0.437139	−	0.702688i
$155$	−0.584041	+	0.241918i	−0.0469113	+	0.0194313i
$156$	−34.7322	−	7.92196i	−2.78080	−	0.634265i
$157$	−9.79973	−	12.7713i	−0.782103	−	1.01926i	−0.999072	−	0.0430783i	$-0.986284\pi$
$157$	−9.79973	−	12.7713i	−0.782103	−	1.01926i	0.216968	−	0.976179i	$-0.430383\pi$
$158$	−8.78038	−	4.85189i	−0.698529	−	0.385996i
$159$	−8.94738	−	15.4973i	−0.709574	−	1.22902i
$160$	−11.4104	+	6.03603i	−0.902075	+	0.477190i
$161$	−1.08681	+	0.385686i	−0.0856524	+	0.0303963i
$162$	−0.333698	−	17.7720i	−0.0262178	−	1.39630i
$163$	2.23821	−	0.294666i	0.175310	−	0.0230801i	−0.0423598	−	0.999102i	$-0.513488\pi$
$163$	2.23821	−	0.294666i	0.175310	−	0.0230801i	0.217670	+	0.976022i	$0.430154\pi$
$164$	8.48454	−	2.61852i	0.662531	−	0.204472i
$165$	2.50387	−	19.0188i	0.194926	−	1.48061i
$166$	0.673626	+	4.46696i	0.0522836	+	0.346704i
$167$	−4.79590	+	4.79590i	−0.371118	+	0.371118i	−0.867884	−	0.496767i	$-0.834520\pi$
$167$	−4.79590	+	4.79590i	−0.371118	+	0.371118i	0.496767	+	0.867884i	$0.334520\pi$
$168$	−5.82924	+	22.1659i	−0.449736	+	1.71013i
$169$	14.7238	+	14.7238i	1.13260	+	1.13260i
$170$	8.51755	−	11.5427i	0.653266	−	0.885282i
$171$	24.3717	+	3.20859i	1.86375	+	0.245367i
$172$	15.6570	+	1.46586i	1.19384	+	0.111771i
$173$	0.369457	+	2.80631i	0.0280893	+	0.213360i	0.999733	−	0.0230886i	$-0.00734999\pi$
$173$	0.369457	+	2.80631i	0.0280893	+	0.213360i	−0.971644	+	0.236448i	$0.924017\pi$
$174$	−1.00869	−	0.971509i	−0.0764686	−	0.0736499i
$175$	0.355831	−	0.417196i	0.0268983	−	0.0315370i
$176$	−4.95060	−	9.79934i	−0.373166	−	0.738653i
$177$	3.01942	−	1.74326i	0.226954	−	0.131032i
$178$	5.51546	+	19.1392i	0.413401	+	1.43455i
$179$	4.51834	−	3.46704i	0.337717	−	0.259139i	−0.425954	−	0.904745i	$-0.640062\pi$
$179$	4.51834	−	3.46704i	0.337717	−	0.259139i	0.763671	+	0.645606i	$0.223395\pi$
$180$	4.88200	+	28.7075i	0.363883	+	2.13973i
$181$	−0.247512	−	0.597546i	−0.0183974	−	0.0444152i	0.914414	−	0.404780i	$-0.132652\pi$
$181$	−0.247512	−	0.597546i	−0.0183974	−	0.0444152i	−0.932811	+	0.360365i	$0.882652\pi$
$182$	15.8849	−	14.8723i	1.17747	−	1.10241i
$183$	26.4851	+	26.4851i	1.95784	+	1.95784i
$184$	−0.251540	+	1.20690i	−0.0185438	+	0.0889742i
$185$	3.75256	+	14.0048i	0.275894	+	1.02965i
$186$	0.748205	+	0.938077i	0.0548611	+	0.0687831i
$187$	9.67940	+	7.42726i	0.707828	+	0.543135i
$188$	−0.513452	−	13.6678i	−0.0374473	−	0.996828i
$189$	22.9837	+	14.9037i	1.67181	+	1.08408i
$190$	−12.4310	+	0.233413i	−0.901842	+	0.0169335i
$191$	3.24559	+	5.62153i	0.234843	+	0.406760i	0.959227	−	0.282637i	$-0.0912091\pi$
$191$	3.24559	+	5.62153i	0.234843	+	0.406760i	−0.724384	+	0.689397i	$0.757876\pi$
$192$	17.0064	+	17.6389i	1.22733	+	1.27298i
$193$	−5.46347	+	9.46301i	−0.393269	+	0.681162i	−0.992879	−	0.119130i	$-0.961989\pi$
$193$	−5.46347	+	9.46301i	−0.393269	+	0.681162i	0.599609	+	0.800293i	$0.295323\pi$
$194$	6.21752	+	10.3168i	0.446392	+	0.740703i
$195$	15.5546	−	37.5522i	1.11389	−	2.68917i
$196$	−9.22696	−	10.5292i	−0.659068	−	0.752083i
$197$	18.4557	−	7.64461i	1.31492	−	0.544656i	0.388601	−	0.921406i	$-0.372959\pi$
$197$	18.4557	−	7.64461i	1.31492	−	0.544656i	0.926315	+	0.376751i	$0.122959\pi$
$198$	−24.4896	+	3.69308i	−1.74040	+	0.262456i
$199$	−2.51927	−	9.40206i	−0.178587	−	0.666494i	−0.995913	−	0.0903191i	$-0.971211\pi$
$199$	−2.51927	−	9.40206i	−0.178587	−	0.666494i	0.817326	−	0.576175i	$-0.195455\pi$
$200$	−0.183351	−	0.556779i	−0.0129649	−	0.0393702i
$201$	11.1088	−	41.4584i	0.783551	−	2.92425i
$202$	−18.8191	+	8.21235i	−1.32411	+	0.577819i
$203$	0.836631	−	0.178423i	0.0587200	−	0.0125228i
$204$	−25.5294	−	9.46826i	−1.78742	−	0.662911i
$205$	1.32238	+	10.0445i	0.0923590	+	0.701537i
$206$	2.08071	+	7.22028i	0.144970	+	0.503061i
$207$	2.40848	+	1.39054i	0.167401	+	0.0966492i
$208$	−4.75827	−	22.7710i	−0.329927	−	1.57889i
$209$		−	10.5746i		−	0.731457i
$210$	−23.8176	−	10.7969i	−1.64357	−	0.745057i
$211$	−16.5682	−	6.86279i	−1.14061	−	0.472454i	−0.269232	−	0.963075i	$-0.586770\pi$
$211$	−16.5682	−	6.86279i	−1.14061	−	0.472454i	−0.871373	+	0.490621i	$0.836770\pi$
$212$	6.76059	−	9.53117i	0.464319	−	0.654604i
$213$	−11.4184	−	1.50326i	−0.782373	−	0.103001i
$214$	−10.9558	−	1.23360i	−0.748923	−	0.0843268i
$215$	−4.64381	+	17.3309i	−0.316705	+	1.18196i
$216$	26.3813	−	12.7118i	1.79502	−	0.864930i
$217$	−0.730649	+	0.0580004i	−0.0495997	+	0.00393732i
$218$	−3.18971	−	1.25159i	−0.216034	−	0.0847686i
$219$	10.5244	+	8.07565i	0.711173	+	0.545702i
$220$	11.9695	−	3.69405i	0.806983	−	0.249053i
$221$	15.7375	+	20.5095i	1.05862	+	1.37962i
$222$	23.5708	−	14.2052i	1.58197	−	0.953391i
$223$	−15.9988			−1.07136			−0.535681	−	0.844421i	$-0.679945\pi$
$223$	−15.9988			−1.07136			−0.535681	+	0.844421i	$0.679945\pi$
$224$	−14.7430	+	2.57763i	−0.985058	+	0.172225i
$225$	−1.32235			−0.0881567
$226$	−19.8559	+	11.9664i	−1.32079	+	0.795990i
$227$	−9.59794	−	12.5083i	−0.637038	−	0.830204i	0.357573	−	0.933885i	$-0.383604\pi$
$227$	−9.59794	−	12.5083i	−0.637038	−	0.830204i	−0.994611	+	0.103682i	$0.966938\pi$
$228$	6.95949	+	22.5502i	0.460904	+	1.49342i
$229$	3.72837	+	2.86088i	0.246377	+	0.189052i	0.724566	−	0.689205i	$-0.242040\pi$
$229$	3.72837	+	2.86088i	0.246377	+	0.189052i	−0.478189	+	0.878257i	$0.658707\pi$
$230$	−1.30943	−	0.513803i	−0.0863416	−	0.0338791i
$231$	9.56152	−	20.0811i	0.629102	−	1.32124i
$232$	0.301851	−	0.863258i	0.0198175	−	0.0566756i
$233$	−3.44694	+	12.8641i	−0.225816	+	0.842758i	0.756260	+	0.654272i	$0.227025\pi$
$233$	−3.44694	+	12.8641i	−0.225816	+	0.842758i	−0.982076	+	0.188486i	$0.939642\pi$
$234$	−52.1476	−	5.87169i	−3.40900	−	0.383845i
$235$	15.4721	+	2.03694i	1.00929	+	0.132875i
$236$	1.85701	+	1.31720i	0.120881	+	0.0857424i
$237$	−20.0719	−	8.31406i	−1.30381	−	0.540056i
$238$	13.5212	−	9.68536i	0.876447	−	0.627809i
$239$		−	17.7167i		−	1.14600i	−0.819556	−	0.572998i	$-0.805780\pi$
$239$		−	17.7167i		−	1.14600i	0.819556	−	0.572998i	$-0.194220\pi$
$240$	−23.0937	+	15.7551i	−1.49069	+	1.01699i
$241$	−14.2826	−	8.24609i	−0.920026	−	0.531177i	−0.0363827	−	0.999338i	$-0.511584\pi$
$241$	−14.2826	−	8.24609i	−0.920026	−	0.531177i	−0.883643	+	0.468161i	$0.844917\pi$
$242$	−1.35751	−	4.71071i	−0.0872642	−	0.302816i
$243$	−0.970448	−	7.37128i	−0.0622543	−	0.472868i
$244$	−8.50508	+	22.9324i	−0.544482	+	1.46810i
$245$	13.6084	−	8.36458i	0.869410	−	0.534393i
$246$	17.6250	−	7.69128i	1.12373	−	0.490378i
$247$	5.79915	−	21.6427i	0.368991	−	1.37709i
$248$	−0.352956	+	0.699556i	−0.0224127	+	0.0444218i
$249$	2.53214	+	9.45009i	0.160468	+	0.598875i
$250$	−15.2940	+	2.30636i	−0.967278	+	0.145867i
$251$	21.3468	−	8.84214i	1.34740	−	0.558111i	0.411831	−	0.911260i	$-0.364889\pi$
$251$	21.3468	−	8.84214i	1.34740	−	0.558111i	0.935567	+	0.353149i	$0.114889\pi$
$252$	−4.87955	+	33.4078i	−0.307382	+	2.10449i
$253$	0.457824	−	1.10528i	0.0287831	−	0.0694886i
$254$	3.65466	+	6.06422i	0.229314	+	0.380503i
$255$	15.5335	−	26.9049i	0.972748	−	1.68485i
$256$	−5.83658	+	14.8975i	−0.364786	+	0.931091i
$257$	−7.79869	−	13.5077i	−0.486469	−	0.842588i	0.513410	−	0.858143i	$-0.328382\pi$
$257$	−7.79869	−	13.5077i	−0.486469	−	0.842588i	−0.999879	+	0.0155548i	$0.995049\pi$
$258$	34.0506	−	0.639355i	2.11990	−	0.0398045i
$259$	−0.868437	+	16.7879i	−0.0539620	+	1.04315i
$260$	26.5235	−	0.996395i	1.64492	−	0.0617938i
$261$	−1.63667	−	1.25586i	−0.101308	−	0.0777360i
$262$	−12.3174	−	15.4431i	−0.760970	−	0.954080i
$263$	1.30654	+	4.87607i	0.0805646	+	0.300671i	0.994437	−	0.105329i	$-0.0335897\pi$
$263$	1.30654	+	4.87607i	0.0805646	+	0.300671i	−0.913873	+	0.406001i	$0.866923\pi$
$264$	−13.0287	−	19.8895i	−0.801864	−	1.22411i
$265$	9.42765	+	9.42765i	0.579136	+	0.579136i
$266$	−13.7940	−	4.18713i	−0.845762	−	0.256730i
$267$	16.5076	+	39.8529i	1.01025	+	2.43896i
$268$	27.6310	−	4.69892i	1.68783	−	0.287032i
$269$	17.9608	−	13.7818i	1.09509	−	0.840289i	0.107011	−	0.994258i	$-0.465872\pi$
$269$	17.9608	−	13.7818i	1.09509	−	0.840289i	0.988076	+	0.153969i	$0.0492055\pi$
$270$	9.25212	+	32.1058i	0.563066	+	1.95390i
$271$	−9.57629	+	5.52888i	−0.581718	+	0.335855i	−0.761816	−	0.647793i	$-0.775692\pi$
$271$	−9.57629	+	5.52888i	−0.581718	+	0.335855i	0.180098	+	0.983649i	$0.442359\pi$
$272$	−1.33402	−	17.7304i	−0.0808868	−	1.07506i
$273$	30.5819	−	35.8559i	1.85090	−	2.17010i
$274$	−10.0534	−	9.68286i	−0.607351	−	0.584963i
$275$	0.0742489	+	0.563976i	0.00447737	+	0.0340090i
$276$	−0.248880	+	2.65833i	−0.0149808	+	0.160012i
$277$	−1.36694	−	0.179961i	−0.0821312	−	0.0108128i	0.0893486	−	0.996000i	$-0.471521\pi$
$277$	−1.36694	−	0.179961i	−0.0821312	−	0.0108128i	−0.171480	+	0.985188i	$0.554855\pi$
$278$	5.28192	−	7.15786i	0.316788	−	0.429300i
$279$	1.24986	+	1.24986i	0.0748271	+	0.0748271i
$280$	−0.0792243	−	17.0763i	−0.00473456	−	1.02050i
$281$	−5.07057	+	5.07057i	−0.302485	+	0.302485i	−0.841985	−	0.539501i	$-0.818613\pi$
$281$	−5.07057	+	5.07057i	−0.302485	+	0.302485i	0.539501	+	0.841985i	$0.318613\pi$
$282$	−4.41699	−	29.2900i	−0.263028	−	1.74420i
$283$	−2.53029	+	19.2195i	−0.150410	+	1.14248i	0.735134	+	0.677922i	$0.237119\pi$
$283$	−2.53029	+	19.2195i	−0.150410	+	1.14248i	−0.885544	+	0.464556i	$0.846214\pi$
$284$	−2.21781	−	7.18616i	−0.131603	−	0.426420i
$285$	−26.6962	+	3.51462i	−1.58135	+	0.208188i
$286$	0.423796	+	22.5704i	0.0250596	+	1.33462i
$287$	−2.13280	+	11.5511i	−0.125895	+	0.681841i
$288$	27.8018	+	23.0172i	1.63823	+	1.35630i
$289$	1.37958	+	2.38950i	0.0811517	+	0.140559i
$290$	0.913270	+	0.504658i	0.0536291	+	0.0296345i
$291$	15.8807	+	20.6961i	0.930942	+	1.21323i
$292$	−1.92635	+	8.44570i	−0.112731	+	0.494247i
$293$	−18.5271	+	7.67417i	−1.08236	+	0.448330i	−0.851338	−	0.524618i	$-0.824208\pi$
$293$	−18.5271	+	7.67417i	−1.08236	+	0.448330i	−0.231026	+	0.972948i	$0.574208\pi$
$294$	−22.4087	−	20.4239i	−1.30690	−	1.19114i
$295$	−1.83684	+	1.83684i	−0.106945	+	0.106945i
$296$	14.8506	+	10.1201i	0.863174	+	0.588220i
$297$	−27.4492	+	7.35499i	−1.59276	+	0.426780i
$298$	20.1191	+	2.26536i	1.16547	+	0.131229i
$299$	1.54316	−	2.01109i	0.0892434	−	0.116304i
$300$	−0.529508	−	1.15381i	−0.0305712	−	0.0666153i
$301$	−11.3183	+	17.4544i	−0.652374	+	1.00606i
$302$	2.20821	+	2.12681i	0.127068	+	0.122384i
$303$	−38.5104	+	22.2340i	−2.21237	+	1.27731i
$304$	−11.4879	+	10.2723i	−0.658874	+	0.589159i
$305$	−24.1679	−	13.9534i	−1.38385	−	0.798967i
$306$	−38.9312	−	9.65203i	−2.22555	−	0.551770i
$307$	31.0323	+	12.8540i	1.77111	+	0.733617i	0.994632	+	0.103472i	$0.0329951\pi$
$307$	31.0323	+	12.8540i	1.77111	+	0.733617i	0.776477	+	0.630146i	$0.217005\pi$
$308$	14.5222	+	0.205286i	0.827481	+	0.0116972i
$309$	6.22751	+	15.0345i	0.354270	+	0.855285i
$310$	−0.719359	−	0.530828i	−0.0408568	−	0.0301490i
$311$	−21.2623	+	5.69720i	−1.20567	+	0.323059i	−0.805062	−	0.593190i	$-0.797868\pi$
$311$	−21.2623	+	5.69720i	−1.20567	+	0.323059i	−0.400609	+	0.916249i	$0.631202\pi$
$312$	−15.7581	−	47.8524i	−0.892129	−	2.70911i
$313$	17.8347	+	4.77879i	1.00808	+	0.270113i	0.724825	−	0.688933i	$-0.241920\pi$
$313$	17.8347	+	4.77879i	1.00808	+	0.270113i	0.283251	+	0.959046i	$0.408587\pi$
$314$	8.31568	−	21.1927i	0.469281	−	1.19597i
$315$	−36.6443	−	11.8791i	−2.06467	−	0.669311i
$316$	−0.532581	−	14.1770i	−0.0299600	−	0.797520i
$317$	−8.66699	+	1.14103i	−0.486787	+	0.0640867i	−0.369925	−	0.929062i	$-0.620617\pi$
$317$	−8.66699	+	1.14103i	−0.486787	+	0.0640867i	−0.116862	+	0.993148i	$0.537283\pi$
$318$	12.2398	−	22.1502i	0.686376	−	1.24212i
$319$	−0.443722	+	0.768549i	−0.0248437	+	0.0430305i
$320$	−15.6405	−	9.41480i	−0.874331	−	0.526303i
$321$	−23.8768			−1.33267
$322$	−1.26051	−	1.03486i	−0.0702452	−	0.0576705i
$323$	6.55373	−	15.8221i	0.364659	−	0.880365i
$324$	21.2828	−	13.3773i	1.18238	−	0.743183i
$325$	−0.157324	+	1.19500i	−0.00872677	+	0.0662864i
$326$	1.99076	+	2.49595i	0.110258	+	0.138238i
$327$	−7.16784	−	1.92062i	−0.396382	−	0.106210i
$328$	9.36519	+	8.36548i	0.517106	+	0.461907i
$329$	16.3363	+	7.77844i	0.900647	+	0.428839i
$330$	24.8643	−	10.8504i	1.36874	−	0.597295i
$331$	11.6019	−	15.1199i	0.637698	−	0.831065i	−0.356978	−	0.934113i	$-0.616193\pi$
$331$	11.6019	−	15.1199i	0.637698	−	0.831065i	0.994676	+	0.103048i	$0.0328596\pi$
$332$	−4.91890	+	4.07670i	−0.269960	+	0.223738i
$333$	32.1622	−	24.6790i	1.76248	−	1.35240i
$334$	−9.30993	−	2.30817i	−0.509417	−	0.126297i
$335$			31.9787i			1.74718i
$336$	−31.1037	+	9.11983i	−1.69685	+	0.497527i
$337$			32.6016i			1.77592i	0.459920	+	0.887960i	$0.347878\pi$
$337$			32.6016i			1.77592i	−0.459920	+	0.887960i	$0.652122\pi$
$338$	−7.08625	+	28.5822i	−0.385441	+	1.55467i
$339$	−39.8321	+	30.5642i	−2.16338	+	1.66002i
$340$	20.1987	+	1.89106i	1.09543	+	0.102557i
$341$	0.462880	−	0.603237i	0.0250664	−	0.0326671i
$342$	13.9043	+	31.8625i	0.751857	+	1.72293i
$343$	17.9997	−	4.35998i	0.971894	−	0.235417i
$344$	9.65371	+	20.0347i	0.520493	+	1.08020i
$345$	−2.94253	−	0.788449i	−0.158421	−	0.0424487i
$346$	−3.12946	+	2.49604i	−0.168241	+	0.134188i
$347$	−0.269167	+	2.04452i	−0.0144496	+	0.109756i	−0.997150	−	0.0754482i	$-0.975961\pi$
$347$	−0.269167	+	2.04452i	−0.0144496	+	0.109756i	0.982700	+	0.185204i	$0.0592946\pi$
$348$	0.440426	−	1.93096i	0.0236093	−	0.103510i
$349$	5.81296	−	14.0337i	0.311160	−	0.751208i	−0.688502	−	0.725234i	$-0.741731\pi$
$349$	5.81296	−	14.0337i	0.311160	−	0.751208i	0.999663	−	0.0259735i	$-0.00826857\pi$
$350$	0.765078	+	0.126460i	0.0408951	+	0.00675956i
$351$	−60.2131			−3.21394
$352$	8.25568	−	13.1497i	0.440029	−	0.700882i
$353$	2.35813	−	4.08441i	0.125511	−	0.217391i	−0.796422	−	0.604742i	$-0.793276\pi$
$353$	2.35813	−	4.08441i	0.125511	−	0.217391i	0.921932	+	0.387351i	$0.126610\pi$
$354$	4.31564	+	2.38475i	0.229373	+	0.126748i
$355$	8.50738	−	1.12002i	0.451525	−	0.0594444i
$356$	−19.1563	+	20.6518i	−1.01528	+	1.09454i
$357$	26.7519	−	24.1203i	1.41586	−	1.27658i
$358$	7.49774	+	2.94200i	0.396268	+	0.155490i
$359$	−16.5853	−	4.44401i	−0.875337	−	0.234546i	−0.206943	−	0.978353i	$-0.566351\pi$
$359$	−16.5853	−	4.44401i	−0.875337	−	0.234546i	−0.668394	+	0.743807i	$0.733018\pi$
$360$	−31.2083	+	26.8691i	−1.64482	+	1.41613i
$361$	4.01511	−	1.07585i	0.211322	−	0.0566234i
$362$	0.543103	−	0.735993i	0.0285448	−	0.0386829i
$363$	−4.06300	−	9.80894i	−0.213252	−	0.514836i
$364$	29.6097	+	8.38422i	1.55197	+	0.439453i
$365$	−9.13141	−	3.78236i	−0.477960	−	0.197978i
$366$	−12.7467	+	51.4136i	−0.666283	+	2.68743i
$367$	−6.41818	−	3.70554i	−0.335026	−	0.193427i	0.323044	−	0.946384i	$-0.395294\pi$
$367$	−6.41818	−	3.70554i	−0.335026	−	0.193427i	−0.658070	+	0.752956i	$0.728627\pi$
$368$	−1.64549	+	0.576331i	−0.0857769	+	0.0300433i
$369$	24.5322	−	14.1637i	1.27710	−	0.737332i
$370$	−14.2240	+	14.7684i	−0.739473	+	0.767774i
$371$	7.02725	+	13.7687i	0.364837	+	0.714837i
$372$	−0.590078	+	1.59104i	−0.0305941	+	0.0824915i
$373$	−7.33990	+	9.56554i	−0.380045	+	0.495285i	−0.943735	−	0.330702i	$-0.892715\pi$
$373$	−7.33990	+	9.56554i	−0.380045	+	0.495285i	0.563690	+	0.825986i	$0.309381\pi$
$374$	−1.93059	+	17.1459i	−0.0998284	+	0.886595i
$375$	−32.3553	+	8.66957i	−1.67082	+	0.447694i
$376$	16.1804	−	10.5991i	0.834440	−	0.546606i
$377$	−1.32963	+	1.32963i	−0.0684795	+	0.0684795i
$378$	−1.27466	+	38.7184i	−0.0655614	+	1.99146i
$379$	28.2318	−	11.6940i	1.45017	−	0.600681i	0.487931	−	0.872882i	$-0.337752\pi$
$379$	28.2318	−	11.6940i	1.45017	−	0.600681i	0.962240	+	0.272202i	$0.0877518\pi$
$380$	−9.35706	−	14.8868i	−0.480007	−	0.763674i
$381$	9.33466	+	12.1652i	0.478229	+	0.623240i
$382$	−4.43990	+	8.03481i	−0.227165	+	0.411097i
$383$	11.4861	+	19.8945i	0.586912	+	1.01656i	0.994634	+	0.103456i	$0.0329900\pi$
$383$	11.4861	+	19.8945i	0.586912	+	1.01656i	−0.407722	+	0.913106i	$0.633677\pi$
$384$	−8.95092	+	33.4751i	−0.456775	+	1.70827i
$385$	−3.00882	+	16.2956i	−0.153344	+	0.830502i
$386$	−15.4503	+	0.290105i	−0.786400	+	0.0147659i
$387$	49.7388	−	6.54823i	2.52836	−	0.332865i
$388$	−7.95763	+	15.0620i	−0.403988	+	0.764657i
$389$	0.963031	−	7.31495i	0.0488276	−	0.370883i	−0.949534	−	0.313664i	$-0.898443\pi$
$389$	0.963031	−	7.31495i	0.0488276	−	0.370883i	0.998362	−	0.0572187i	$-0.0182232\pi$
$390$	56.8397	−	8.57153i	2.87819	−	0.434036i
$391$	1.37003	−	1.37003i	0.0692854	−	0.0692854i
$392$	6.01805	−	18.8622i	0.303957	−	0.952686i
$393$	−30.2503	−	30.2503i	−1.52593	−	1.52593i
$394$	22.7318	+	16.7742i	1.14521	+	0.845072i
$395$	16.0485	+	2.11282i	0.807487	+	0.106308i
$396$	−22.3500	−	26.9673i	−1.12313	−	1.35516i
$397$	2.15083	+	16.3372i	0.107947	+	0.819940i	0.956685	+	0.291126i	$0.0940299\pi$
$397$	2.15083	+	16.3372i	0.107947	+	0.819940i	−0.848738	+	0.528814i	$0.822637\pi$
$398$	9.54928	−	9.91475i	0.478662	−	0.496981i
$399$	−30.7005	−	5.66854i	−1.53695	−	0.283782i
$400$	0.540559	−	0.628520i	0.0270280	−	0.0314260i
$401$	−21.3200	+	12.3091i	−1.06467	+	0.614687i	−0.926720	−	0.375752i	$-0.877384\pi$
$401$	−21.3200	+	12.3091i	−1.06467	+	0.614687i	−0.137949	+	0.990439i	$0.544051\pi$
$402$	58.3258	−	16.8081i	2.90903	−	0.838311i
$403$	1.27818	−	0.980786i	0.0636709	−	0.0488564i
$404$	−23.6847	−	16.7999i	−1.17836	−	0.835826i
$405$	10.9759	+	26.4982i	0.545398	+	1.31671i
$406$	0.826835	+	0.883129i	0.0410351	+	0.0438290i
$407$	−12.3313	−	12.3313i	−0.611242	−	0.611242i
$408$	−7.16738	−	37.8342i	−0.354838	−	1.87307i
$409$	2.47200	+	9.22564i	0.122233	+	0.456179i	0.999726	−	0.0234104i	$-0.00745244\pi$
$409$	2.47200	+	9.22564i	0.122233	+	0.456179i	−0.877493	+	0.479589i	$0.840786\pi$
$410$	−11.2011	+	8.93395i	−0.553183	+	0.441216i
$411$	−23.9823	−	18.4023i	−1.18296	−	0.907718i
$412$	−7.22673	+	7.79089i	−0.356036	+	0.383830i
$413$	−2.68263	+	1.36915i	−0.132004	+	0.0673717i
$414$	0.0738362	+	3.93235i	0.00362885	+	0.193264i
$415$	−3.64464	−	6.31270i	−0.178908	−	0.309878i
$416$	24.1081	−	22.3857i	1.18200	−	1.09755i
$417$	9.63269	−	16.6843i	0.471715	−	0.817034i
$418$	12.8085	−	7.71916i	0.626483	−	0.377556i
$419$	−0.968970	+	2.33930i	−0.0473373	+	0.114282i	−0.945779	−	0.324810i	$-0.894700\pi$
$419$	−0.968970	+	2.33930i	−0.0473373	+	0.114282i	0.898442	+	0.439092i	$0.144700\pi$
$420$	−4.30843	−	36.7306i	−0.210230	−	1.79227i
$421$	29.3770	−	12.1684i	1.43175	−	0.593049i	0.473966	−	0.880543i	$-0.342822\pi$
$421$	29.3770	−	12.1684i	1.43175	−	0.593049i	0.957782	+	0.287494i	$0.0928221\pi$
$422$	−3.78181	−	25.0780i	−0.184096	−	1.22078i
$423$	−11.2934	−	42.1474i	−0.549103	−	2.04928i
$424$	16.4797	+	1.23128i	0.800327	+	0.0597964i
$425$	−0.238438	+	0.889862i	−0.0115659	+	0.0431646i
$426$	−6.51429	−	14.9279i	−0.315618	−	0.723258i
$427$	−21.6666	−	24.0305i	−1.04852	−	1.16292i
$428$	−6.50325	−	14.1707i	−0.314347	−	0.684969i
$429$	6.38132	+	48.4709i	0.308093	+	2.34020i
$430$	−24.3820	+	7.02631i	−1.17581	+	0.338839i
$431$	17.0485	+	9.84297i	0.821199	+	0.474119i	0.850830	−	0.525442i	$-0.176100\pi$
$431$	17.0485	+	9.84297i	0.821199	+	0.474119i	−0.0296310	+	0.999561i	$0.509433\pi$
$432$	34.6549	+	22.6751i	1.66734	+	1.09096i
$433$		−	13.7265i		−	0.659651i	−0.944042	−	0.329826i	$-0.893010\pi$
$433$		−	13.7265i		−	0.659651i	0.944042	−	0.329826i	$-0.106990\pi$
$434$	−0.603608	−	0.842663i	−0.0289741	−	0.0404491i
$435$	2.08773	+	0.864767i	0.100099	+	0.0414624i
$436$	−0.812407	−	4.77718i	−0.0389072	−	0.228785i
$437$	−1.66492	−	0.219191i	−0.0796441	−	0.0104853i
$438$	−2.09913	+	18.6427i	−0.100300	+	0.890785i
$439$	3.22629	−	12.0407i	0.153982	−	0.574670i	−0.845208	−	0.534438i	$-0.820523\pi$
$439$	3.22629	−	12.0407i	0.153982	−	0.574670i	0.999190	−	0.0402325i	$-0.0128099\pi$
$440$	13.2119	+	11.8015i	0.629851	+	0.562616i
$441$	−36.1688	−	26.2035i	−1.72232	−	1.24779i
$442$	−13.3542	+	34.0334i	−0.635195	+	1.61881i
$443$	1.31819	+	1.01149i	0.0626293	+	0.0480572i	0.639602	−	0.768707i	$-0.279099\pi$
$443$	1.31819	+	1.01149i	0.0626293	+	0.0480572i	−0.576972	+	0.816764i	$0.695766\pi$
$444$	34.4122	+	18.1808i	1.63313	+	0.862825i
$445$	−19.5652	−	25.4979i	−0.927479	−	1.20871i
$446$	−11.6787	−	19.3787i	−0.553005	−	0.917606i
$447$	43.8472			2.07390
$448$	−13.8842	−	15.9759i	−0.655966	−	0.754791i
$449$	29.5052			1.39244			0.696219	−	0.717829i	$-0.254864\pi$
$449$	29.5052			1.39244			0.696219	+	0.717829i	$0.254864\pi$
$450$	−0.965282	−	1.60170i	−0.0455038	−	0.0755050i
$451$	−7.41821	−	9.66760i	−0.349310	−	0.455230i
$452$	−28.9886	−	15.3154i	−1.36351	−	0.720376i
$453$	5.26764	+	4.04201i	0.247496	+	0.189910i
$454$	8.14445	−	20.7563i	0.382238	−	0.974140i
$455$	−15.0947	+	31.7019i	−0.707651	+	1.48621i
$456$	−22.2338	+	24.8908i	−1.04119	+	1.16562i
$457$	1.12790	−	4.20937i	0.0527608	−	0.196906i	−0.934515	−	0.355924i	$-0.884166\pi$
$457$	1.12790	−	4.20937i	0.0527608	−	0.196906i	0.987276	+	0.159018i	$0.0508328\pi$
$458$	−0.743635	+	6.60436i	−0.0347478	+	0.308602i
$459$	−45.6290	−	6.00717i	−2.12978	−	0.280391i
$460$	−0.333508	−	1.96112i	−0.0155499	−	0.0914378i
$461$	13.9872	+	5.79368i	0.651447	+	0.269838i	0.683835	−	0.729637i	$-0.260311\pi$
$461$	13.9872	+	5.79368i	0.651447	+	0.269838i	−0.0323872	+	0.999475i	$0.510311\pi$
$462$	31.3030	−	3.07724i	1.45635	−	0.143166i
$463$			14.7119i			0.683718i	0.939751	+	0.341859i	$0.111057\pi$
$463$			14.7119i			0.683718i	−0.939751	+	0.341859i	$0.888943\pi$
$464$	1.26597	−	0.264539i	0.0587711	−	0.0122809i
$465$	−1.67676	−	0.968077i	−0.0777579	−	0.0448935i
$466$	−18.0979	+	5.21538i	−0.838370	+	0.241598i
$467$	−3.63198	−	27.5877i	−0.168068	−	1.27660i	−0.842673	−	0.538425i	$-0.819019\pi$
$467$	−3.63198	−	27.5877i	−0.168068	−	1.27660i	0.674605	−	0.738179i	$-0.264314\pi$
$468$	−30.9543	−	67.4502i	−1.43086	−	3.11789i
$469$	−11.4336	+	35.2702i	−0.527955	+	1.62863i
$470$	8.82697	+	20.2275i	0.407158	+	0.933026i
$471$	12.7607	−	47.6237i	0.587983	−	2.19438i
$472$	−0.239897	+	3.21083i	−0.0110422	+	0.147790i
$473$	−5.58558	−	20.8457i	−0.256825	−	0.958484i
$474$	−4.58155	−	30.3812i	−0.210438	−	1.39546i
$475$	0.737691	−	0.305562i	0.0338476	−	0.0140201i
$476$	21.6015	+	9.30751i	0.990105	+	0.426609i
$477$	14.2661	−	34.4415i	0.653201	−	1.57697i
$478$	21.4594	−	12.9327i	0.981530	−	0.591529i
$479$	−3.44262	+	5.96279i	−0.157297	+	0.272447i	−0.933893	−	0.357552i	$-0.883611\pi$
$479$	−3.44262	+	5.96279i	−0.157297	+	0.272447i	0.776596	+	0.629999i	$0.216945\pi$
$480$	−35.9413	−	16.4715i	−1.64049	−	0.751819i
$481$	−18.4757	−	32.0009i	−0.842419	−	1.45911i
$482$	−0.437859	−	23.3194i	−0.0199439	−	1.06217i
$483$	−2.96349	−	1.92167i	−0.134844	−	0.0874390i
$484$	4.71492	−	5.08299i	0.214315	−	0.231045i
$485$	−15.4199	−	11.8321i	−0.700180	−	0.537267i
$486$	8.22010	−	6.55631i	0.372871	−	0.297400i
$487$	9.48833	+	35.4109i	0.429957	+	1.60462i	0.752853	+	0.658188i	$0.228677\pi$
$487$	9.48833	+	35.4109i	0.429957	+	1.60462i	−0.322896	+	0.946434i	$0.604656\pi$
$488$	−33.9855	+	6.43826i	−1.53845	+	0.291446i
$489$	4.88911	+	4.88911i	0.221093	+	0.221093i
$490$	20.0654	+	10.3773i	0.906464	+	0.468800i
$491$	−8.02578	−	19.3759i	−0.362198	−	0.874424i	−0.994978	−	0.100092i	$-0.968086\pi$
$491$	−8.02578	−	19.3759i	−0.362198	−	0.874424i	0.632780	−	0.774332i	$-0.281914\pi$
$492$	22.1819	+	15.7339i	1.00004	+	0.709341i
$493$	−1.14023	+	0.874933i	−0.0513536	+	0.0394050i
$494$	30.4480	−	8.77439i	1.36992	−	0.394778i
$495$	34.6086	−	19.9813i	1.55554	−	0.898093i
$496$	−1.10499	+	0.0831384i	−0.0496155	+	0.00373303i
$497$	9.78346	+	1.80642i	0.438848	+	0.0810288i
$498$	−9.59806	+	9.96540i	−0.430100	+	0.446560i
$499$	−4.48117	−	34.0379i	−0.200605	−	1.52374i	−0.734742	−	0.678347i	$-0.762697\pi$
$499$	−4.48117	−	34.0379i	−0.200605	−	1.52374i	0.534137	−	0.845398i	$-0.320637\pi$
$500$	−13.9578	−	16.8413i	−0.624213	−	0.753167i
$501$	−20.5952	−	2.71141i	−0.920124	−	0.121137i
$502$	26.2927	+	19.4019i	1.17350	+	0.865948i
$503$	8.45095	+	8.45095i	0.376809	+	0.376809i	0.869950	−	0.493141i	$-0.164151\pi$
$503$	8.45095	+	8.45095i	0.376809	+	0.376809i	−0.493141	+	0.869950i	$0.664151\pi$
$504$	−44.0272	+	18.4764i	−1.96113	+	0.823006i
$505$	23.4274	−	23.4274i	1.04251	−	1.04251i
$506$	1.67298	−	0.252289i	0.0743730	−	0.0112156i
$507$	−8.32422	+	63.2288i	−0.369692	+	2.80809i
$508$	−4.67750	+	8.85345i	−0.207530	+	0.392808i
$509$	4.63191	−	0.609802i	0.205306	−	0.0270290i	−0.0271718	−	0.999631i	$-0.508650\pi$
$509$	4.63191	−	0.609802i	0.205306	−	0.0270290i	0.232478	+	0.972602i	$0.425317\pi$
$510$	43.9278	−	0.824815i	1.94515	−	0.0365234i
$511$	−8.71894	−	7.43649i	−0.385703	−	0.328971i
$512$	−22.3052	+	3.80518i	−0.985759	+	0.168167i
$513$	19.9445	+	34.5448i	0.880570	+	1.52519i
$514$	10.6684	−	19.3065i	0.470565	−	0.851573i
$515$	−7.38098	−	9.61907i	−0.325245	−	0.423867i
$516$	25.6305	+	40.7772i	1.12832	+	1.79512i
$517$	−17.3416	+	7.18311i	−0.762681	+	0.315913i
$518$	−20.9684	+	11.2028i	−0.921297	+	0.492225i
$519$	−6.13004	+	6.13004i	−0.269079	+	0.269079i
$520$	20.5684	+	31.3994i	0.901983	+	1.37695i
$521$	−2.27269	+	0.608965i	−0.0995683	+	0.0266792i	−0.308259	−	0.951302i	$-0.599746\pi$
$521$	−2.27269	+	0.608965i	−0.0995683	+	0.0266792i	0.208691	+	0.977982i	$0.433080\pi$
$522$	0.326440	−	2.89918i	0.0142879	−	0.126893i
$523$	10.4095	−	13.5659i	0.455175	−	0.593196i	−0.508238	−	0.861217i	$-0.669703\pi$
$523$	10.4095	−	13.5659i	0.455175	−	0.593196i	0.963413	+	0.268021i	$0.0863697\pi$
$524$	9.71420	−	26.1926i	0.424367	−	1.14423i
$525$	1.67716	+	0.0867595i	0.0731974	+	0.00378650i
$526$	−4.95242	+	5.14196i	−0.215936	+	0.224200i
$527$	1.06645	−	0.615713i	0.0464551	−	0.0268209i
$528$	14.5806	−	30.2999i	0.634538	−	1.31864i
$529$	19.7541	+	11.4050i	0.858872	+	0.495870i
$530$	−4.53733	+	18.3012i	−0.197089	+	0.794954i
$531$	6.71040	+	2.77954i	0.291207	+	0.120622i
$532$	−4.99756	−	19.7645i	−0.216672	−	0.856900i
$533$	−9.88092	−	23.8546i	−0.427990	−	1.03326i
$534$	−36.2219	+	49.0865i	−1.56747	+	2.12418i
$535$	17.1835	−	4.60431i	0.742909	−	0.199062i
$536$	25.8615	+	30.0380i	1.11705	+	1.29745i
$537$	16.8488	+	4.51461i	0.727078	+	0.194820i
$538$	29.8041	+	11.6947i	1.28495	+	0.504194i
$539$	−9.14482	+	16.8971i	−0.393895	+	0.727810i
$540$	−32.1345	+	34.6431i	−1.38285	+	1.49080i
$541$	5.72787	−	0.754088i	0.246260	−	0.0324208i	−0.00638549	−	0.999980i	$-0.502033\pi$
$541$	5.72787	−	0.754088i	0.246260	−	0.0324208i	0.252646	+	0.967559i	$0.418699\pi$
$542$	−13.6873	−	7.56339i	−0.587921	−	0.324875i
$543$	0.990462	−	1.71553i	0.0425048	−	0.0736205i
$544$	20.5022	−	14.5586i	0.879025	−	0.624194i
$545$	5.52887			0.236831
$546$	65.7546	+	10.8686i	2.81404	+	0.465133i
$547$	−16.0579	+	38.7672i	−0.686586	+	1.65756i	0.0649637	+	0.997888i	$0.479307\pi$
$547$	−16.0579	+	38.7672i	−0.686586	+	1.65756i	−0.751549	+	0.659677i	$0.770693\pi$
$548$	4.38965	−	19.2455i	0.187517	−	0.822128i
$549$	−10.1848	+	77.3616i	−0.434678	+	3.30171i
$550$	−0.628919	+	0.501622i	−0.0268172	+	0.0213893i
$551$	1.20324	+	0.322407i	0.0512597	+	0.0137350i
$552$	−3.40158	+	1.63905i	−0.144781	+	0.0697627i
$553$	16.9449	+	8.06824i	0.720570	+	0.343096i
$554$	−0.779851	−	1.78707i	−0.0331327	−	0.0759255i
$555$	−27.0328	+	35.2298i	−1.14748	+	1.49542i
$556$	12.5257	+	1.17269i	0.531206	+	0.0497331i
$557$	−25.0366	+	19.2113i	−1.06083	+	0.814007i	−0.983119	−	0.182969i	$-0.941429\pi$
$557$	−25.0366	+	19.2113i	−1.06083	+	0.814007i	−0.0777159	+	0.996976i	$0.524763\pi$
$558$	−0.601531	+	2.42626i	−0.0254649	+	0.102712i
$559$		−	45.7275i		−	1.93407i
$560$	20.6259	−	12.5612i	0.871603	−	0.530808i
$561$			37.3675i			1.57766i
$562$	−9.84313	−	2.44036i	−0.415207	−	0.102940i
$563$	33.8928	−	26.0069i	1.42841	−	1.09606i	0.449152	−	0.893455i	$-0.351726\pi$
$563$	33.8928	−	26.0069i	1.42841	−	1.09606i	0.979261	−	0.202604i	$-0.0649404\pi$
$564$	32.2534	−	26.7311i	1.35811	−	1.12558i
$565$	22.7722	−	29.6773i	0.958034	−	1.24853i
$566$	−25.1267	+	10.9649i	−1.05615	+	0.460889i
$567$	2.63150	+	33.1499i	0.110513	+	1.39217i
$568$	7.08532	−	7.93204i	0.297293	−	0.332821i
$569$	−18.5302	−	4.96515i	−0.776827	−	0.208150i	−0.151441	−	0.988466i	$-0.548392\pi$
$569$	−18.5302	−	4.96515i	−0.776827	−	0.208150i	−0.625385	+	0.780316i	$0.715058\pi$
$570$	−23.7446	−	29.7703i	−0.994554	−	1.24694i
$571$	−2.45710	+	18.6635i	−0.102826	+	0.781044i	0.859880	+	0.510496i	$0.170538\pi$
$571$	−2.45710	+	18.6635i	−0.102826	+	0.781044i	−0.962707	+	0.270548i	$0.912795\pi$
$572$	−27.0291	+	16.9891i	−1.13014	+	0.710352i
$573$	−7.60809	+	18.3676i	−0.317833	+	0.767316i
$574$	−15.5482	+	5.84866i	−0.648970	+	0.244118i
$575$	0.0903349			0.00376723
$576$	−7.58512	+	50.4770i	−0.316047	+	2.10321i
$577$	−4.23109	+	7.32846i	−0.176142	+	0.305088i	−0.940556	−	0.339639i	$-0.889695\pi$
$577$	−4.23109	+	7.32846i	−0.176142	+	0.305088i	0.764414	+	0.644726i	$0.223029\pi$
$578$	−1.88724	+	3.41530i	−0.0784986	+	0.142058i
$579$	−33.1802	+	4.36826i	−1.37892	+	0.181539i
$580$	0.0553951	+	1.47459i	0.00230016	+	0.0612290i
$581$	−1.76274	−	8.26554i	−0.0731306	−	0.342912i
$582$	−13.4757	+	34.3432i	−0.558588	+	1.42357i
$583$	−15.4901	−	4.15057i	−0.641536	−	0.171899i
$584$	−11.6361	+	3.83184i	−0.481504	+	0.158563i
$585$	81.7906	−	21.9157i	3.38162	−	0.906103i
$586$	−22.8197	−	16.8391i	−0.942672	−	0.695615i
$587$	−1.28471	−	3.10157i	−0.0530258	−	0.128016i	0.895147	−	0.445772i	$-0.147071\pi$
$587$	−1.28471	−	3.10157i	−0.0530258	−	0.128016i	−0.948172	+	0.317756i	$0.897071\pi$
$588$	8.38071	−	42.0516i	0.345615	−	1.73418i
$589$	−0.986061	−	0.408440i	−0.0406299	−	0.0168295i
$590$	−3.56572	−	0.884031i	−0.146798	−	0.0363950i
$591$	52.9857	+	30.5913i	2.17954	+	1.25836i
$592$	−1.41747	+	25.3753i	−0.0582575	+	1.04292i
$593$	0.0566685	−	0.0327176i	0.00232710	−	0.00134355i	−0.498836	−	0.866696i	$-0.666239\pi$
$593$	0.0566685	−	0.0327176i	0.00232710	−	0.00134355i	0.501163	+	0.865353i	$0.332906\pi$
$594$	−28.9460	−	27.8790i	−1.18767	−	1.14389i
$595$	−14.6014	+	22.5175i	−0.598598	+	0.923126i
$596$	11.9425	+	26.0230i	0.489184	+	1.06594i
$597$	18.1484	−	23.6515i	0.742765	−	0.967990i
$598$	3.56241	+	0.401118i	0.145678	+	0.0164029i
$599$	−21.7551	+	5.82927i	−0.888891	+	0.238178i	−0.674239	−	0.738513i	$-0.735528\pi$
$599$	−21.7551	+	5.82927i	−0.888891	+	0.238178i	−0.214652	+	0.976691i	$0.568862\pi$
$600$	1.01103	−	1.48362i	0.0412752	−	0.0605686i
$601$	−5.05178	+	5.05178i	−0.206066	+	0.206066i	−0.802593	−	0.596527i	$-0.796547\pi$
$601$	−5.05178	+	5.05178i	−0.206066	+	0.206066i	0.596527	+	0.802593i	$0.296547\pi$
$602$	−29.4038	−	0.968011i	−1.19841	−	0.0394532i
$603$	82.6084	−	34.2175i	3.36408	−	1.39345i
$604$	−0.964173	+	4.22722i	−0.0392317	+	0.172003i
$605$	4.81555	+	6.27575i	0.195780	+	0.255146i
$606$	−55.0427	−	30.4157i	−2.23596	−	1.23555i
$607$	5.85587	+	10.1427i	0.237683	+	0.411678i	0.960049	−	0.279832i	$-0.0902789\pi$
$607$	5.85587	+	10.1427i	0.237683	+	0.411678i	−0.722366	+	0.691511i	$0.756946\pi$
$608$	−20.8283	−	6.41618i	−0.844698	−	0.260210i
$609$	1.99343	+	1.70022i	0.0807778	+	0.0688963i
$610$	−0.740909	−	39.4591i	−0.0299985	−	1.59765i
$611$	−39.4318	+	5.19130i	−1.59524	+	0.210018i
$612$	−16.7277	−	54.2014i	−0.676179	−	2.19096i
$613$	−3.57324	+	27.1415i	−0.144322	+	1.09623i	0.753993	+	0.656882i	$0.228125\pi$
$613$	−3.57324	+	27.1415i	−0.144322	+	1.09623i	−0.898315	+	0.439352i	$0.855208\pi$
$614$	7.08334	+	46.9712i	0.285860	+	1.89560i
$615$	−21.9410	+	21.9410i	−0.884745	+	0.884745i
$616$	10.3522	+	17.7400i	0.417102	+	0.714763i
$617$	−25.0914	−	25.0914i	−1.01014	−	1.01014i	−0.999948	−	0.0101933i	$-0.996755\pi$
$617$	−25.0914	−	25.0914i	−1.01014	−	1.01014i	−0.0101933	−	0.999948i	$-0.503245\pi$
$618$	−13.6647	+	18.5179i	−0.549676	+	0.744900i
$619$	−25.5861	−	3.36847i	−1.02839	−	0.135390i	−0.402596	−	0.915378i	$-0.631892\pi$
$619$	−25.5861	−	3.36847i	−1.02839	−	0.135390i	−0.625795	+	0.779988i	$0.715225\pi$
$620$	0.117854	−	1.25882i	0.00473314	−	0.0505553i
$621$	0.589043	+	4.47422i	0.0236375	+	0.179544i
$622$	−22.4217	−	21.5952i	−0.899027	−	0.865888i
$623$	−12.4625	−	35.1175i	−0.499300	−	1.40695i
$624$	46.4584	−	54.0181i	1.85982	−	2.16246i
$625$	22.5109	−	12.9966i	0.900434	−	0.519866i
$626$	7.23054	+	25.0907i	0.288990	+	1.00283i
$627$	25.6945	−	19.7161i	1.02614	−	0.787386i
$628$	31.7399	−	5.39769i	1.26656	−	0.215391i
$629$	−10.8082	−	26.0932i	−0.430949	−	1.04040i
$630$	−12.3608	−	53.0570i	−0.492468	−	2.11384i
$631$	−6.88166	−	6.88166i	−0.273954	−	0.273954i	0.556735	−	0.830690i	$-0.312054\pi$
$631$	−6.88166	−	6.88166i	−0.273954	−	0.273954i	−0.830690	+	0.556735i	$0.812054\pi$
$632$	16.7832	−	10.9940i	0.667600	−	0.437316i
$633$	−14.2157	−	53.0539i	−0.565025	−	2.10870i
$634$	−7.70876	−	9.66501i	−0.306154	−	0.383846i
$635$	−9.06380	−	6.95490i	−0.359686	−	0.275997i
$636$	35.7643	−	1.34354i	1.41815	−	0.0532748i
$637$	−27.9830	+	29.5679i	−1.10873	+	1.17152i
$638$	−1.25481	+	0.0235612i	−0.0496785	+	0.000932795i
$639$	−11.9962	−	20.7781i	−0.474564	−	0.821969i
$640$	−0.0134559	−	25.8172i	−0.000531889	−	1.02051i
$641$	1.78549	−	3.09256i	0.0705227	−	0.122149i	−0.828608	−	0.559830i	$-0.810867\pi$
$641$	1.78549	−	3.09256i	0.0705227	−	0.122149i	0.899131	+	0.437681i	$0.144200\pi$
$642$	−17.4295	−	28.9209i	−0.687887	−	1.14142i
$643$	−17.1484	+	41.3999i	−0.676266	+	1.63265i	0.0944933	+	0.995525i	$0.469877\pi$
$643$	−17.1484	+	41.3999i	−0.676266	+	1.63265i	−0.770760	+	0.637126i	$0.780123\pi$
$644$	0.333341	−	2.28221i	0.0131355	−	0.0899318i
$645$	−50.7699	+	21.0296i	−1.99906	+	0.828038i
$646$	23.9486	−	3.61150i	0.942247	−	0.142093i
$647$	5.78919	+	21.6056i	0.227597	+	0.849402i	0.981348	+	0.192242i	$0.0615758\pi$
$647$	5.78919	+	21.6056i	0.227597	+	0.849402i	−0.753751	+	0.657160i	$0.771757\pi$
$648$	31.7392	+	16.0138i	1.24683	+	0.629081i
$649$	0.808676	−	3.01802i	0.0317433	−	0.118468i
$650$	−1.56229	+	0.681757i	−0.0612779	+	0.0267407i
$651$	−1.50322	−	1.66722i	−0.0589157	−	0.0653436i
$652$	−1.57003	+	4.23329i	−0.0614869	+	0.165788i
$653$	−0.467065	−	3.54771i	−0.0182777	−	0.138833i	0.979873	−	0.199622i	$-0.0639715\pi$
$653$	−0.467065	−	3.54771i	−0.0182777	−	0.138833i	−0.998151	+	0.0607896i	$0.980638\pi$
$654$	−2.90598	−	10.0841i	−0.113633	−	0.394318i
$655$	27.6037	+	15.9370i	1.07857	+	0.622711i
$656$	−3.29638	+	17.4502i	−0.128702	+	0.681317i
$657$			27.6357i			1.07817i
$658$	2.50338	+	25.4654i	0.0975920	+	0.992746i
$659$	16.8594	+	6.98340i	0.656749	+	0.272035i	0.686070	−	0.727536i	$-0.259334\pi$
$659$	16.8594	+	6.98340i	0.656749	+	0.272035i	−0.0293206	+	0.999570i	$0.509334\pi$
$660$	31.2929	+	22.1965i	1.21808	+	0.863998i
$661$	9.35165	+	1.23117i	0.363737	+	0.0478869i	0.310180	−	0.950678i	$-0.399611\pi$
$661$	9.35165	+	1.23117i	0.363737	+	0.0478869i	0.0535572	+	0.998565i	$0.482944\pi$
$662$	26.7831	+	3.01572i	1.04096	+	0.117209i
$663$	−20.4925	+	76.4792i	−0.795864	+	2.97021i
$664$	−8.52859	−	2.98215i	−0.330974	−	0.115730i
$665$	23.1875	−	1.84067i	0.899172	−	0.0713781i
$666$	53.3701	+	20.9416i	2.06805	+	0.811472i
$667$	0.111808	+	0.0857929i	0.00432920	+	0.00332192i
$668$	−4.00024	−	12.9616i	−0.154774	−	0.501499i
$669$	−29.8296	−	38.8747i	−1.15328	−	1.50298i
$670$	−38.7344	+	23.3437i	−1.49644	+	0.901844i
$671$	33.5662			1.29581
$672$	−33.7513	−	31.0173i	−1.30199	−	1.19652i
$673$	−38.5787			−1.48710			−0.743550	−	0.668680i	$-0.766860\pi$
$673$	−38.5787			−1.48710			−0.743550	+	0.668680i	$0.766860\pi$
$674$	−39.4888	+	23.7983i	−1.52105	+	0.916677i
$675$	−1.30626	−	1.70235i	−0.0502780	−	0.0655235i
$676$	−39.7931	+	12.2810i	−1.53050	+	0.472348i
$677$	24.5485	+	18.8367i	0.943476	+	0.723955i	0.961190	−	0.275888i	$-0.0889720\pi$
$677$	24.5485	+	18.8367i	0.943476	+	0.723955i	−0.0177135	+	0.999843i	$0.505639\pi$
$678$	−66.0974	−	25.9357i	−2.53846	−	0.996053i
$679$	−12.7766	−	18.5631i	−0.490319	−	0.712386i
$680$	12.4540	+	25.8462i	0.477588	+	0.991156i
$681$	12.4980	−	46.6430i	0.478923	−	1.78737i
$682$	1.06856	+	0.120318i	0.0409174	+	0.00460720i
$683$	11.1518	+	1.46816i	0.426710	+	0.0561774i	0.340823	−	0.940127i	$-0.389294\pi$
$683$	11.1518	+	1.46816i	0.426710	+	0.0561774i	0.0858869	+	0.996305i	$0.472628\pi$
$684$	−28.4438	+	40.1004i	−1.08758	+	1.53328i
$685$	20.8081	+	8.61899i	0.795036	+	0.329315i
$686$	18.4204	+	18.6196i	0.703294	+	0.710899i
$687$			14.3934i			0.549143i
$688$	−17.2201	+	26.3179i	−0.656511	+	1.00336i
$689$	−29.4271	−	16.9898i	−1.12108	−	0.647258i
$690$	−1.19296	−	4.13970i	−0.0454153	−	0.157596i
$691$	6.36465	+	48.3443i	0.242123	+	1.83910i	0.491719	+	0.870754i	$0.336369\pi$
$691$	6.36465	+	48.3443i	0.242123	+	1.83910i	−0.249596	+	0.968350i	$0.580298\pi$
$692$	−5.30776	−	1.96852i	−0.201771	−	0.0748320i
$693$	45.3149	−	9.66399i	1.72137	−	0.367105i
$694$	−2.67292	+	1.16642i	−0.101463	+	0.0442768i
$695$	−3.71506	+	13.8648i	−0.140920	+	0.525922i
$696$	2.66038	−	0.876082i	0.100841	−	0.0332078i
$697$	−5.10781	−	19.0626i	−0.193472	−	0.722048i
$698$	21.2417	−	3.20329i	0.804011	−	0.121246i
$699$	−37.6846	+	15.6095i	−1.42536	+	0.590405i
$700$	0.405312	+	1.01902i	0.0153194	+	0.0385152i
$701$	14.2285	−	34.3507i	0.537404	−	1.29741i	−0.389125	−	0.921185i	$-0.627223\pi$
$701$	14.2285	−	34.3507i	0.537404	−	1.29741i	0.926529	−	0.376223i	$-0.122777\pi$
$702$	−43.9541	−	72.9334i	−1.65894	−	2.75269i
$703$	−12.2395	+	21.1994i	−0.461620	+	0.799549i
$704$	21.9541	+	0.400777i	0.827425	+	0.0151049i
$705$	23.8980	+	41.3926i	0.900051	+	1.55893i
$706$	6.66863	−	0.125214i	0.250977	−	0.00471250i
$707$	34.2149	−	17.4625i	1.28679	−	0.656746i
$708$	0.261768	+	6.96814i	0.00983786	+	0.261879i
$709$	−31.7199	−	24.3396i	−1.19127	−	0.914092i	−0.193515	−	0.981097i	$-0.561989\pi$
$709$	−31.7199	−	24.3396i	−1.19127	−	0.914092i	−0.997753	+	0.0670058i	$0.978655\pi$
$710$	7.56680	+	9.48701i	0.283977	+	0.356041i
$711$	−11.7141	−	43.7177i	−0.439314	−	1.63954i
$712$	−38.9982	−	8.12791i	−1.46152	−	0.304606i
$713$	−0.0853827	−	0.0853827i	−0.00319761	−	0.00319761i
$714$	48.7440	+	14.7961i	1.82420	+	0.553732i
$715$	−13.9394	−	33.6527i	−0.521305	−	1.25854i
$716$	1.90965	+	11.2293i	0.0713669	+	0.419657i
$717$	43.0488	−	33.0325i	1.60769	−	1.23362i
$718$	−6.72400	−	23.3330i	−0.250937	−	0.870779i
$719$	11.9535	−	6.90133i	0.445789	−	0.257376i	−0.260261	−	0.965538i	$-0.583809\pi$
$719$	11.9535	−	6.90133i	0.445789	−	0.257376i	0.706050	+	0.708162i	$0.250475\pi$
$720$	−55.3266	−	18.1875i	−2.06190	−	0.677808i
$721$	−4.70148	−	13.2481i	−0.175092	−	0.493385i
$722$	4.23405	+	4.07798i	0.157575	+	0.151767i
$723$	−6.59307	−	50.0794i	−0.245199	−	1.86247i
$724$	1.28793	+	0.120579i	0.0478654	+	0.00448130i
$725$	−0.0664364	−	0.00874652i	−0.00246739	−	0.000324838i
$726$	8.91524	−	12.0816i	0.330876	−	0.448390i
$727$	−5.93078	−	5.93078i	−0.219960	−	0.219960i	0.588521	−	0.808482i	$-0.299710\pi$
$727$	−5.93078	−	5.93078i	−0.219960	−	0.219960i	−0.808482	+	0.588521i	$0.799710\pi$
$728$	11.4589	+	41.9852i	0.424696	+	1.55607i
$729$	−10.5610	+	10.5610i	−0.391147	+	0.391147i
$730$	−2.08431	−	13.8215i	−0.0771436	−	0.511556i
$731$	4.56201	−	34.6519i	0.168732	−	1.28165i
$732$	−71.5798	+	22.0911i	−2.64567	+	0.816511i
$733$	−49.0790	+	6.46137i	−1.81277	+	0.238656i	−0.959282	−	0.282449i	$-0.908853\pi$
$733$	−49.0790	+	6.46137i	−1.81277	+	0.238656i	−0.853492	+	0.521105i	$0.825520\pi$
$734$	−0.196760	−	10.4790i	−0.00726255	−	0.386787i
$735$	45.6974	+	17.4707i	1.68557	+	0.644417i
$736$	−1.89925	−	1.57240i	−0.0700071	−	0.0579593i
$737$	−19.2320	−	33.3108i	−0.708420	−	1.22702i
$738$	35.0637	+	19.3756i	1.29071	+	0.713227i
$739$	23.4662	+	30.5817i	0.863218	+	1.12497i	0.991092	+	0.133177i	$0.0425179\pi$
$739$	23.4662	+	30.5817i	0.863218	+	1.12497i	−0.127874	+	0.991790i	$0.540815\pi$
$740$	−28.2715	−	6.44836i	−1.03928	−	0.237046i
$741$	63.4009	−	26.2615i	2.32909	−	0.964740i
$742$	−11.5477	+	18.5626i	−0.423930	+	0.681455i
$743$	−11.3823	+	11.3823i	−0.417577	+	0.417577i	−0.884368	−	0.466791i	$-0.845410\pi$
$743$	−11.3823	+	11.3823i	−0.417577	+	0.417577i	0.466791	+	0.884368i	$0.345410\pi$
$744$	−2.35790	+	0.446683i	−0.0864446	+	0.0163762i
$745$	−31.5557	+	8.45532i	−1.15611	+	0.309779i
$746$	−16.9442	−	1.90788i	−0.620373	−	0.0698524i
$747$	−12.4074	+	16.1696i	−0.453962	+	0.591614i
$748$	−22.1774	+	10.1777i	−0.810885	+	0.372132i
$749$	20.5984	+	1.06555i	0.752649	+	0.0389345i
$750$	−34.1196	−	32.8619i	−1.24587	−	1.19995i
$751$	23.7240	−	13.6971i	0.865702	−	0.499813i	−0.000215546	−	1.00000i	$-0.500069\pi$
$751$	23.7240	−	13.6971i	0.865702	−	0.499813i	0.865918	+	0.500187i	$0.166735\pi$
$752$	24.6495	+	11.8615i	0.898873	+	0.432545i
$753$	61.2859	+	35.3834i	2.23338	+	1.28944i
$754$	−2.58112	−	0.639925i	−0.0939988	−	0.0233047i
$755$	−4.57043	−	1.89314i	−0.166335	−	0.0688982i
$756$	−47.8282	+	26.7195i	−1.73950	+	0.971778i
$757$	6.19271	+	14.9505i	0.225078	+	0.543386i	0.995566	−	0.0940689i	$-0.0299874\pi$
$757$	6.19271	+	14.9505i	0.225078	+	0.543386i	−0.770488	+	0.637455i	$0.779987\pi$
$758$	34.7729	+	25.6596i	1.26301	+	0.931998i
$759$	3.53928	−	0.948346i	0.128468	−	0.0344228i
$760$	11.2012	−	22.2007i	0.406311	−	0.805305i
$761$	0.615905	+	0.165031i	0.0223266	+	0.00598238i	0.269965	−	0.962870i	$-0.412988\pi$
$761$	0.615905	+	0.165031i	0.0223266	+	0.00598238i	−0.247638	+	0.968853i	$0.579655\pi$
$762$	−7.92104	+	20.1869i	−0.286949	+	0.731295i
$763$	6.09794	+	1.97678i	0.220760	+	0.0715643i
$764$	−12.9732	+	0.487358i	−0.469355	+	0.0176320i
$765$	64.1666	−	8.44769i	2.31995	−	0.305427i
$766$	−15.7127	+	28.4351i	−0.567725	+	1.02740i
$767$	3.31020	−	5.73343i	0.119524	−	0.207022i
$768$	−47.0808	+	13.5941i	−1.69888	+	0.490535i
$769$	−25.0353			−0.902797			−0.451398	−	0.892323i	$-0.649075\pi$
$769$	−25.0353			−0.902797			−0.451398	+	0.892323i	$0.649075\pi$
$770$	−21.9345	+	8.25095i	−0.790465	+	0.297344i
$771$	18.2811	−	44.1346i	0.658379	−	1.58947i
$772$	−11.6297	−	18.5025i	−0.418563	−	0.665919i
$773$	2.52628	−	19.1890i	0.0908640	−	0.690181i	−0.884017	−	0.467455i	$-0.845171\pi$
$773$	2.52628	−	19.1890i	0.0908640	−	0.690181i	0.974881	−	0.222726i	$-0.0714956\pi$
$774$	44.2396	+	55.4662i	1.59016	+	1.99369i
$775$	0.0554577	+	0.0148599i	0.00199210	+	0.000533782i
$776$	−24.0528	+	1.35617i	−0.863445	+	0.0486835i
$777$	−42.4112	+	29.1906i	−1.52149	+	1.04721i
$778$	9.56325	−	4.17325i	0.342859	−	0.149618i
$779$	−10.4128	+	13.5702i	−0.373076	+	0.486202i
$780$	51.8738	+	62.5903i	1.85738	+	2.24109i
$781$	−8.18818	+	6.28301i	−0.292996	+	0.224824i
$782$	2.65954	+	0.659368i	0.0951051	+	0.0235789i
$783$		−	3.34758i		−	0.119633i
$784$	27.2400	−	6.47955i	0.972856	−	0.231413i
$785$			36.7342i			1.31110i
$786$	14.5589	−	58.7228i	0.519298	−	2.09457i
$787$	17.2486	−	13.2353i	0.614846	−	0.471788i	−0.253776	−	0.967263i	$-0.581673\pi$
$787$	17.2486	−	13.2353i	0.614846	−	0.471788i	0.868622	+	0.495475i	$0.165006\pi$
$788$	−3.72420	+	39.7787i	−0.132669	+	1.41706i
$789$	−9.41207	+	12.2660i	−0.335079	+	0.436683i
$790$	9.15582	+	20.9811i	0.325750	+	0.746474i
$791$	35.7269	−	24.5900i	1.27030	−	0.874319i
$792$	16.3493	−	46.7570i	0.580946	−	1.66144i
$793$	68.6992	+	18.4079i	2.43958	+	0.653683i
$794$	−18.2184	+	14.5309i	−0.646548	+	0.515684i
$795$	−5.33001	+	40.4854i	−0.189036	+	1.43587i
$796$	18.9800	+	4.32909i	0.672729	+	0.153441i
$797$	−9.04663	+	21.8405i	−0.320448	+	0.773630i	0.678780	+	0.734342i	$0.262509\pi$
$797$	−9.04663	+	21.8405i	−0.320448	+	0.773630i	−0.999228	+	0.0392883i	$0.987491\pi$
$798$	−15.5446	−	41.3241i	−0.550272	−	1.46286i
$799$	−30.3990			−1.07544
$800$	1.15589	+	0.195951i	0.0408669	+	0.00692792i
$801$	−44.9319	+	77.8243i	−1.58759	+	2.74979i
$802$	−30.4725	−	16.8386i	−1.07602	−	0.594591i
$803$	11.7865	−	1.55172i	0.415936	−	0.0547591i
$804$	62.9352	+	58.3779i	2.21955	+	2.05883i
$805$	2.50332	+	0.811507i	0.0882304	+	0.0286019i
$806$	2.12102	+	0.832258i	0.0747099	+	0.0293150i
$807$	66.9752	+	17.9459i	2.35764	+	0.631727i
$808$	3.05971	−	40.9517i	0.107640	−	1.44068i
$809$	−49.5935	+	13.2885i	−1.74361	+	0.467200i	−0.983245	−	0.182290i	$-0.941649\pi$
$809$	−49.5935	+	13.2885i	−1.74361	+	0.467200i	−0.760370	+	0.649490i	$0.774982\pi$
$810$	−24.0839	+	32.6377i	−0.846224	+	1.14677i
$811$	−0.850433	−	2.05313i	−0.0298627	−	0.0720950i	0.908245	−	0.418440i	$-0.137423\pi$
$811$	−0.850433	−	2.05313i	−0.0298627	−	0.0720950i	−0.938107	+	0.346345i	$0.887423\pi$
$812$	−0.466125	+	1.64617i	−0.0163578	+	0.0577692i
$813$	−31.2892	−	12.9604i	−1.09736	−	0.454541i
$814$	5.93482	−	23.9380i	0.208015	−	0.839025i
$815$	−4.46137	−	2.57577i	−0.156275	−	0.0902253i
$816$	40.5949	−	36.2995i	1.42110	−	1.27074i
$817$	−26.2343	+	15.1464i	−0.917822	+	0.529905i
$818$	−9.37010	+	9.72871i	−0.327618	+	0.340156i
$819$	98.0447	+	5.07184i	3.42596	+	0.177225i
$820$	−18.9978	−	7.04583i	−0.663432	−	0.246051i
$821$	15.1171	−	19.7010i	0.527591	−	0.687569i	−0.451202	−	0.892422i	$-0.649005\pi$
$821$	15.1171	−	19.7010i	0.527591	−	0.687569i	0.978793	+	0.204852i	$0.0656714\pi$
$822$	4.78336	−	42.4819i	0.166839	−	1.48173i
$823$	49.8309	−	13.3521i	1.73700	−	0.465426i	0.755220	−	0.655472i	$-0.227530\pi$
$823$	49.8309	−	13.3521i	1.73700	−	0.465426i	0.981775	+	0.190045i	$0.0608635\pi$
$824$	−14.7121	−	3.06626i	−0.512520	−	0.106818i
$825$	−1.23194	+	1.23194i	−0.0428906	+	0.0428906i
$826$	−3.61665	−	2.24990i	−0.125839	−	0.0782841i
$827$	0.294533	−	0.122000i	0.0102419	−	0.00424234i	−0.377557	−	0.925987i	$-0.623236\pi$
$827$	0.294533	−	0.122000i	0.0102419	−	0.00424234i	0.387799	+	0.921744i	$0.373236\pi$
$828$	−4.70917	+	2.95995i	−0.163655	+	0.102865i
$829$	2.18540	+	2.84807i	0.0759020	+	0.0989174i	0.829761	−	0.558119i	$-0.188477\pi$
$829$	2.18540	+	2.84807i	0.0759020	+	0.0989174i	−0.753859	+	0.657036i	$0.771810\pi$
$830$	4.98579	−	9.02269i	0.173059	−	0.313182i
$831$	−2.11136	−	3.65698i	−0.0732422	−	0.126859i
$832$	44.7131	+	12.8600i	1.55015	+	0.445840i
$833$	−24.1551	+	19.6145i	−0.836924	+	0.679604i
$834$	27.2406	−	0.511486i	0.943263	−	0.0177113i
$835$	15.3447	−	2.02016i	0.531024	−	0.0699106i
$836$	18.6997	+	9.87953i	0.646744	+	0.341691i
$837$	−0.374377	+	2.84368i	−0.0129404	+	0.0982919i
$838$	−3.54081	+	0.533961i	−0.122315	+	0.0184454i
$839$	32.3250	−	32.3250i	1.11598	−	1.11598i	0.123659	−	0.992325i	$-0.460537\pi$
$839$	32.3250	−	32.3250i	1.11598	−	1.11598i	0.992325	−	0.123659i	$-0.0394628\pi$
$840$	41.3450	−	32.0310i	1.42654	−	1.10518i
$841$	20.4322	+	20.4322i	0.704558	+	0.704558i
$842$	36.1834	+	26.7004i	1.24696	+	0.920158i
$843$	−21.7747	−	2.86669i	−0.749960	−	0.0987342i
$844$	27.6152	−	22.8871i	0.950556	−	0.787805i
$845$	−6.20206	−	47.1093i	−0.213357	−	1.62061i
$846$	42.8074	−	44.4457i	1.47175	−	1.52808i
$847$	3.06738	+	8.64343i	0.105396	+	0.296992i
$848$	10.5384	+	20.8600i	0.361890	+	0.716334i
$849$	−51.4180	+	29.6862i	−1.76466	+	1.01883i
$850$	−1.25190	+	0.360768i	−0.0429399	+	0.0123742i
$851$	−2.19713	+	1.68592i	−0.0753166	+	0.0577925i
$852$	13.3262	−	18.7874i	0.456548	−	0.643647i
$853$	0.706183	+	1.70488i	0.0241792	+	0.0583738i	0.935508	−	0.353306i	$-0.114942\pi$
$853$	0.706183	+	1.70488i	0.0241792	+	0.0583738i	−0.911329	+	0.411679i	$0.864942\pi$
$854$	13.2910	−	43.7854i	0.454808	−	1.49830i
$855$	−39.6649	−	39.6649i	−1.35651	−	1.35651i
$856$	12.4172	−	18.2214i	0.424410	−	0.622794i
$857$	−10.4490	−	38.9962i	−0.356931	−	1.33209i	−0.878037	−	0.478594i	$-0.841147\pi$
$857$	−10.4490	−	38.9962i	−0.356931	−	1.33209i	0.521105	−	0.853493i	$-0.325520\pi$
$858$	−54.0524	+	43.1120i	−1.84532	+	1.47182i
$859$	−12.0105	−	9.21600i	−0.409794	−	0.314446i	0.383211	−	0.923661i	$-0.374818\pi$
$859$	−12.0105	−	9.21600i	−0.409794	−	0.314446i	−0.793005	+	0.609215i	$0.791485\pi$
$860$	−26.3089	−	24.4038i	−0.897127	−	0.832164i
$861$	−32.0440	+	16.3545i	−1.09206	+	0.557361i
$862$	0.522651	+	27.8352i	0.0178016	+	0.948071i
$863$	7.33820	+	12.7101i	0.249795	+	0.432658i	0.963469	−	0.267820i	$-0.0863034\pi$
$863$	7.33820	+	12.7101i	0.249795	+	0.432658i	−0.713674	+	0.700478i	$0.752970\pi$
$864$	−2.16815	+	58.5282i	−0.0737620	+	1.99117i
$865$	3.22954	−	5.59373i	0.109808	−	0.190192i
$866$	16.6262	−	10.0200i	0.564982	−	0.340492i
$867$	−3.23391	+	7.80736i	−0.109829	+	0.265152i
$868$	0.580060	−	1.34625i	0.0196885	−	0.0456946i
$869$	−17.9876	+	7.45073i	−0.610189	+	0.252749i
$870$	0.476539	+	3.16003i	0.0161562	+	0.107135i
$871$	−21.0939	−	78.7234i	−0.714739	−	2.66744i
$872$	5.19334	−	4.47125i	0.175869	−	0.151416i
$873$	−14.0656	+	52.4935i	−0.476048	+	1.77664i
$874$	−0.949855	−	2.17665i	−0.0321293	−	0.0736263i
$875$	28.2996	−	6.03526i	0.956700	−	0.204029i
$876$	−24.1134	+	11.0662i	−0.814717	+	0.373891i
$877$	−1.16672	−	8.86210i	−0.0393973	−	0.299252i	−0.999788	−	0.0205947i	$-0.993444\pi$
$877$	−1.16672	−	8.86210i	−0.0393973	−	0.299252i	0.960391	−	0.278657i	$-0.0898893\pi$
$878$	16.9394	−	4.88153i	0.571678	−	0.164744i
$879$	−53.1905	−	30.7096i	−1.79407	−	1.03581i
$880$	−4.65033	+	24.6177i	−0.156763	+	0.829864i
$881$		−	13.8640i		−	0.467092i	−0.972346	−	0.233546i	$-0.924967\pi$
$881$		−	13.8640i		−	0.467092i	0.972346	−	0.233546i	$-0.0750329\pi$
$882$	5.33682	−	62.9375i	0.179700	−	2.11922i
$883$	−42.1853	−	17.4737i	−1.41965	−	0.588037i	−0.464876	−	0.885376i	$-0.653901\pi$
$883$	−42.1853	−	17.4737i	−1.41965	−	0.588037i	−0.954772	+	0.297339i	$0.903901\pi$
$884$	−50.9714	+	8.66820i	−1.71435	+	0.291543i
$885$	−7.88798	−	1.03847i	−0.265152	−	0.0349079i
$886$	−0.262918	+	2.33503i	−0.00883292	+	0.0784468i
$887$	11.0727	−	41.3240i	0.371786	−	1.38752i	−0.486199	−	0.873848i	$-0.661617\pi$
$887$	11.0727	−	41.3240i	0.371786	−	1.38752i	0.857985	−	0.513675i	$-0.171716\pi$
$888$	3.09844	+	54.9535i	0.103977	+	1.84412i
$889$	−7.51006	−	10.9114i	−0.251879	−	0.365956i
$890$	16.6023	−	42.3112i	0.556510	−	1.41827i
$891$	−27.3692	−	21.0011i	−0.916902	−	0.703563i
$892$	14.9473	−	28.2919i	0.500472	−	0.947281i
$893$	16.0394	+	20.9029i	0.536737	+	0.699489i
$894$	32.0073	+	53.1101i	1.07049	+	1.77627i
$895$	−12.9962			−0.434415
$896$	9.21580	−	28.4793i	0.307878	−	0.951426i
$897$	7.76384			0.259227
$898$	21.5381	+	35.7384i	0.718735	+	1.19260i
$899$	0.0545273	+	0.0710614i	0.00181859	+	0.00237003i
$900$	1.23544	−	2.33840i	0.0411813	−	0.0779468i
$901$	−20.6046	−	15.8105i	−0.686440	−	0.526724i
$902$	6.29482	−	16.0424i	0.209594	−	0.534155i
$903$	−63.5143	+	5.04189i	−2.11362	+	0.167784i
$904$	−2.61010	−	46.2924i	−0.0868106	−	1.53966i
$905$	−0.381994	+	1.42562i	−0.0126979	+	0.0473892i
$906$	−1.05065	+	9.33102i	−0.0349055	+	0.310002i
$907$	9.13019	+	1.20201i	0.303163	+	0.0399122i	0.280573	−	0.959833i	$-0.409475\pi$
$907$	9.13019	+	1.20201i	0.303163	+	0.0399122i	0.0225899	+	0.999745i	$0.492809\pi$
$908$	31.0864	−	5.28655i	1.03164	−	0.175440i
$909$	−85.5861	−	35.4509i	−2.83871	−	1.17583i
$910$	−49.4178	+	4.85802i	−1.63818	+	0.161042i
$911$			11.3129i			0.374812i	0.982283	+	0.187406i	$0.0600080\pi$
$911$			11.3129i			0.374812i	−0.982283	+	0.187406i	$0.939992\pi$
$912$	−46.3792	−	8.76111i	−1.53577	−	0.290109i
$913$	7.59291	+	4.38377i	0.251289	+	0.145082i
$914$	5.92195	−	1.70656i	0.195881	−	0.0564481i
$915$	−11.1563	−	84.7402i	−0.368814	−	2.80142i
$916$	−8.54240	+	3.92029i	−0.282249	+	0.129530i
$917$	24.7468	+	27.4468i	0.817211	+	0.906372i
$918$	−26.0318	−	59.6534i	−0.859177	−	1.96886i
$919$	−10.9970	+	41.0414i	−0.362758	+	1.35383i	0.507678	+	0.861547i	$0.330504\pi$
$919$	−10.9970	+	41.0414i	−0.362758	+	1.35383i	−0.870435	+	0.492283i	$0.836163\pi$
$920$	2.13196	−	1.83553i	0.0702888	−	0.0605157i
$921$	26.6261	+	99.3700i	0.877360	+	3.27435i
$922$	3.19267	+	21.1713i	0.105145	+	0.697238i
$923$	−20.2042	+	8.36885i	−0.665029	+	0.275464i
$924$	26.5777	+	35.6695i	0.874342	+	1.17344i
$925$	0.503920	−	1.21657i	0.0165688	−	0.0400006i
$926$	−17.8198	+	10.7393i	−0.585595	+	0.352915i
$927$	−16.9506	+	29.3593i	−0.556730	+	0.964285i
$928$	1.24455	+	1.34030i	0.0408543	+	0.0439976i
$929$	22.5260	+	39.0162i	0.739055	+	1.28008i	0.952921	+	0.303217i	$0.0980608\pi$
$929$	22.5260	+	39.0162i	0.739055	+	1.28008i	−0.213867	+	0.976863i	$0.568606\pi$
$930$	−0.0514039	−	2.73765i	−0.00168560	−	0.0897712i
$931$	26.2322	+	6.26029i	0.859725	+	0.205173i
$932$	−19.5282	−	18.1141i	−0.639667	−	0.593347i
$933$	−53.4865	−	41.0416i	−1.75107	−	1.34364i
$934$	30.7644	−	24.5375i	1.00664	−	0.802893i
$935$	−7.20580	−	26.8924i	−0.235655	−	0.879476i
$936$	59.1035	−	86.7305i	1.93186	−	2.83488i
$937$	28.8512	+	28.8512i	0.942529	+	0.942529i	0.998436	−	0.0559068i	$-0.0178050\pi$
$937$	28.8512	+	28.8512i	0.942529	+	0.942529i	−0.0559068	+	0.998436i	$0.517805\pi$
$938$	−51.0674	+	11.8973i	−1.66741	+	0.388461i
$939$	21.6408	+	52.2455i	0.706221	+	1.70497i
$940$	−18.0572	+	25.4573i	−0.588961	+	0.830325i
$941$	−3.10852	+	2.38525i	−0.101335	+	0.0777569i	−0.658186	−	0.752855i	$-0.728676\pi$
$941$	−3.10852	+	2.38525i	−0.101335	+	0.0777569i	0.556851	+	0.830612i	$0.312009\pi$
$942$	66.9994	−	19.3076i	2.18296	−	0.629075i
$943$	−1.67589	+	0.967577i	−0.0545746	+	0.0315086i
$944$	−4.06425	+	2.05325i	−0.132280	+	0.0668275i
$945$	−20.9057	−	58.9093i	−0.680063	−	1.91632i
$946$	21.1721	−	21.9824i	0.688363	−	0.714708i
$947$	3.03790	+	23.0751i	0.0987185	+	0.749841i	0.967181	+	0.254087i	$0.0817750\pi$
$947$	3.03790	+	23.0751i	0.0987185	+	0.749841i	−0.868463	+	0.495754i	$0.834892\pi$
$948$	33.4550	−	27.7270i	1.08657	−	0.900530i
$949$	24.9741	+	3.28791i	0.810694	+	0.106730i
$950$	0.908608	+	0.670479i	0.0294791	+	0.0217532i
$951$	−18.9320	−	18.9320i	−0.613913	−	0.613913i
$952$	4.49482	+	32.9592i	0.145678	+	1.06821i
$953$	−3.66728	+	3.66728i	−0.118795	+	0.118795i	−0.764005	−	0.645210i	$-0.776770\pi$
$953$	−3.66728	+	3.66728i	−0.118795	+	0.118795i	0.645210	+	0.764005i	$0.276770\pi$
$954$	52.1313	−	7.86149i	1.68781	−	0.254525i
$955$	1.93342	−	14.6858i	0.0625640	−	0.475220i
$956$	31.3296	+	16.5522i	1.01327	+	0.535337i
$957$	−2.69477	+	0.354773i	−0.0871095	+	0.0114682i
$958$	−9.73549	+	0.182800i	−0.314539	+	0.00590598i
$959$	19.8682	+	16.9458i	0.641576	+	0.547208i
$960$	−6.28500	−	55.5578i	−0.202847	−	1.79312i
$961$	15.4616	+	26.7803i	0.498762	+	0.863881i
$962$	25.2744	−	45.7386i	0.814879	−	1.47467i
$963$	−30.2805	−	39.4624i	−0.975777	−	1.27166i
$964$	27.9260	−	17.5529i	0.899437	−	0.565341i
$965$	23.0366	−	9.54207i	0.741574	−	0.307170i
$966$	0.164354	−	4.99232i	0.00528799	−	0.160625i
$967$	37.3779	−	37.3779i	1.20199	−	1.20199i	0.228432	−	0.973560i	$-0.426640\pi$
$967$	37.3779	−	37.3779i	1.20199	−	1.20199i	0.973560	−	0.228432i	$-0.0733598\pi$
$968$	9.59857	+	2.00051i	0.308510	+	0.0642988i
$969$	50.6646	−	13.5755i	1.62758	−	0.436109i
$970$	3.07554	−	27.3145i	0.0987498	−	0.877016i
$971$	−10.7686	+	14.0339i	−0.345582	+	0.450371i	−0.933515	−	0.358539i	$-0.883275\pi$
$971$	−10.7686	+	14.0339i	−0.345582	+	0.450371i	0.587933	+	0.808910i	$0.299942\pi$
$972$	13.9418	+	5.17069i	0.447184	+	0.165850i
$973$	−9.05463	+	13.9636i	−0.290278	+	0.447651i
$974$	−35.9654	+	37.3419i	−1.15241	+	1.19651i
$975$	−3.19698	+	1.84578i	−0.102385	+	0.0591123i
$976$	−32.6069	−	36.4653i	−1.04372	−	1.16722i
$977$	−39.8044	−	22.9811i	−1.27346	−	0.735230i	−0.297819	−	0.954622i	$-0.596259\pi$
$977$	−39.8044	−	22.9811i	−1.27346	−	0.735230i	−0.975637	+	0.219392i	$0.929593\pi$
$978$	−2.35303	+	9.49089i	−0.0752416	+	0.303485i
$979$	35.7146	+	14.7935i	1.14144	+	0.472801i
$980$	2.07768	+	31.8795i	0.0663691	+	1.01835i
$981$	−5.91594	−	14.2823i	−0.188882	−	0.456000i
$982$	17.6106	−	23.8652i	0.561976	−	0.761569i
$983$	−41.0177	+	10.9906i	−1.30826	+	0.350547i	−0.844568	−	0.535449i	$-0.820142\pi$
$983$	−41.0177	+	10.9906i	−1.30826	+	0.350547i	−0.463693	+	0.885996i	$0.653476\pi$
$984$	−2.86557	+	38.3533i	−0.0913510	+	1.22266i
$985$	−44.0315	−	11.7982i	−1.40296	−	0.375922i
$986$	−1.89211	−	0.742435i	−0.0602570	−	0.0236439i
$987$	11.5583	+	54.1974i	0.367905	+	1.72512i
$988$	32.8543	+	30.4752i	1.04524	+	0.969547i
$989$	−3.39785	+	0.447335i	−0.108045	+	0.0142244i
$990$	49.4659	+	27.3340i	1.57213	+	0.868732i
$991$	6.20485	−	10.7471i	0.197104	−	0.341393i	−0.750485	−	0.660888i	$-0.770180\pi$
$991$	6.20485	−	10.7471i	0.197104	−	0.341393i	0.947588	+	0.319495i	$0.103513\pi$
$992$	−0.907316	−	1.27773i	−0.0288073	−	0.0405681i
$993$	58.3706			1.85234
$994$	4.95365	+	13.1689i	0.157120	+	0.417692i
$995$	−8.50008	+	20.5210i	−0.269471	+	0.650560i
$996$	−19.0770	−	4.35121i	−0.604477	−	0.137873i
$997$	−5.44342	+	41.3469i	−0.172395	+	1.30947i	0.658307	+	0.752750i	$0.271273\pi$
$997$	−5.44342	+	41.3469i	−0.172395	+	1.30947i	−0.830701	+	0.556718i	$0.812060\pi$
$998$	37.9574	−	30.2746i	1.20152	−	0.958326i
$999$	63.5418	+	17.0260i	2.01037	+	0.538678i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.bd.a.109.21	yes	240
4.3	odd	2		896.2.bh.a.529.1		240
7.2	even	3	inner	224.2.bd.a.205.20	yes	240
28.23	odd	6		896.2.bh.a.401.30		240
32.5	even	8	inner	224.2.bd.a.165.20	yes	240
32.27	odd	8		896.2.bh.a.753.30		240
224.37	even	24	inner	224.2.bd.a.37.21	✓	240
224.219	odd	24		896.2.bh.a.625.1		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.21	✓	240	224.37	even	24	inner
224.2.bd.a.109.21	yes	240	1.1	even	1	trivial
224.2.bd.a.165.20	yes	240	32.5	even	8	inner
224.2.bd.a.205.20	yes	240	7.2	even	3	inner
896.2.bh.a.401.30		240	28.23	odd	6
896.2.bh.a.529.1		240	4.3	odd	2
896.2.bh.a.625.1		240	224.219	odd	24
896.2.bh.a.753.30		240	32.27	odd	8

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.bd (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.729975 + 1.21125i) q^{2} +(1.86449 + 2.42985i) q^{3} +(-0.934274 + 1.76837i) q^{4} +(-1.81038 - 1.38916i) q^{5} +(-1.58213 + 4.03209i) q^{6} +(-1.50004 - 2.17942i) q^{7} +(-2.82394 + 0.159222i) q^{8} +(-1.65138 + 6.16305i) q^{9} +O(q^{10})\)	\(q+(0.729975 + 1.21125i) q^{2} +(1.86449 + 2.42985i) q^{3} +(-0.934274 + 1.76837i) q^{4} +(-1.81038 - 1.38916i) q^{5} +(-1.58213 + 4.03209i) q^{6} +(-1.50004 - 2.17942i) q^{7} +(-2.82394 + 0.159222i) q^{8} +(-1.65138 + 6.16305i) q^{9} +(0.361087 - 3.20689i) q^{10} +(2.72124 + 0.358257i) q^{11} +(-6.03881 + 1.02696i) q^{12} +(5.37302 + 2.22558i) q^{13} +(1.54484 - 3.40786i) q^{14} -6.98902i q^{15} +(-2.25426 - 3.30428i) q^{16} +(3.84959 + 2.22256i) q^{17} +(-8.67049 + 2.49863i) q^{18} +(-0.502878 - 3.81973i) q^{19} +(4.14794 - 1.90358i) q^{20} +(2.49884 - 7.70837i) q^{21} +(1.55249 + 3.55763i) q^{22} +(0.112813 - 0.421022i) q^{23} +(-5.65209 - 6.56488i) q^{24} +(0.0536402 + 0.200188i) q^{25} +(1.22643 + 8.13271i) q^{26} +(-9.56541 + 3.96212i) q^{27} +(5.25547 - 0.616458i) q^{28} +(-0.123732 + 0.298716i) q^{29} +(8.46548 - 5.10181i) q^{30} +(0.138514 - 0.239913i) q^{31} +(2.35677 - 5.14253i) q^{32} +(4.20320 + 7.28015i) q^{33} +(0.118016 + 6.28525i) q^{34} +(-0.311899 + 6.02938i) q^{35} +(-9.35571 - 8.67824i) q^{36} +(-5.04074 - 3.86790i) q^{37} +(4.25958 - 3.39742i) q^{38} +(4.61011 + 17.2052i) q^{39} +(5.33361 + 3.63465i) q^{40} +(-3.13935 - 3.13935i) q^{41} +(11.1609 - 2.60018i) q^{42} +(-3.00894 - 7.26423i) q^{43} +(-3.17591 + 4.47744i) q^{44} +(11.5511 - 8.86346i) q^{45} +(0.592315 - 0.170691i) q^{46} +(-5.92251 + 3.41936i) q^{47} +(3.82586 - 11.6383i) q^{48} +(-2.49974 + 6.53845i) q^{49} +(-0.203323 + 0.211104i) q^{50} +(1.77703 + 13.4979i) q^{51} +(-8.95552 + 7.42219i) q^{52} +(-5.79272 - 0.762626i) q^{53} +(-11.7816 - 8.69389i) q^{54} +(-4.42881 - 4.42881i) q^{55} +(4.58305 + 5.91571i) q^{56} +(8.34376 - 8.34376i) q^{57} +(-0.452143 + 0.0681839i) q^{58} +(0.148586 - 1.12862i) q^{59} +(12.3592 + 6.52966i) q^{60} +(12.1248 - 1.59625i) q^{61} +(0.391708 - 0.00735495i) q^{62} +(15.9090 - 5.64579i) q^{63} +(7.94930 - 0.899267i) q^{64} +(-6.63556 - 11.4931i) q^{65} +(-5.74989 + 10.4055i) q^{66} +(-8.53108 - 11.1179i) q^{67} +(-7.52689 + 4.73102i) q^{68} +(1.23336 - 0.510873i) q^{69} +(-7.53080 + 4.02351i) q^{70} +(-2.65894 + 2.65894i) q^{71} +(3.68212 - 17.6670i) q^{72} +(4.18372 - 1.12102i) q^{73} +(1.00539 - 8.92909i) q^{74} +(-0.386415 + 0.503586i) q^{75} +(7.22453 + 2.67940i) q^{76} +(-3.30118 - 6.46812i) q^{77} +(-17.4746 + 18.1434i) q^{78} +(-6.14316 + 3.54676i) q^{79} +(-0.509083 + 9.11355i) q^{80} +(-10.8850 - 6.28445i) q^{81} +(1.51090 - 6.09419i) q^{82} +(2.95118 + 1.22242i) q^{83} +(11.2967 + 11.6206i) q^{84} +(-3.88175 - 9.37138i) q^{85} +(6.60238 - 8.94730i) q^{86} +(-0.956531 + 0.256302i) q^{87} +(-7.74165 - 0.578418i) q^{88} +(13.6043 + 3.64526i) q^{89} +(19.1679 + 7.52120i) q^{90} +(-3.20930 - 15.0485i) q^{91} +(0.639125 + 0.592844i) q^{92} +(0.841210 - 0.110747i) q^{93} +(-8.46500 - 4.67762i) q^{94} +(-4.39581 + 7.61376i) q^{95} +(16.8897 - 3.86159i) q^{96} +8.51745 q^{97} +(-9.74447 + 1.74508i) q^{98} +(-6.70177 + 16.1795i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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