LMFDB - Embedded newform 1110.2.o.a.487.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(253,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1110.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.o (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			487.8
Character	$\chi$	$=$	1110.487
Dual form			1110.2.o.a.253.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(2.23596 - 0.0221544i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-0.281427 - 0.281427i) q^{7} -1.00000 q^{8} +1.00000i q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(2.23596 - 0.0221544i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-0.281427 - 0.281427i) q^{7} -1.00000 q^{8} +1.00000i q^{9} +(-2.23596 + 0.0221544i) q^{10} +1.64708i q^{11} +(-0.707107 - 0.707107i) q^{12} +3.15714 q^{13} +(0.281427 + 0.281427i) q^{14} +(-1.59673 - 1.56540i) q^{15} +1.00000 q^{16} +3.44561i q^{17} -1.00000i q^{18} +(-1.85024 + 1.85024i) q^{19} +(2.23596 - 0.0221544i) q^{20} +0.397998i q^{21} -1.64708i q^{22} +3.91265 q^{23} +(0.707107 + 0.707107i) q^{24} +(4.99902 - 0.0990726i) q^{25} -3.15714 q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.281427 - 0.281427i) q^{28} +(2.67202 + 2.67202i) q^{29} +(1.59673 + 1.56540i) q^{30} +(-6.77259 + 6.77259i) q^{31} -1.00000 q^{32} +(1.16466 - 1.16466i) q^{33} -3.44561i q^{34} +(-0.635494 - 0.623024i) q^{35} +1.00000i q^{36} +(0.925435 - 6.01195i) q^{37} +(1.85024 - 1.85024i) q^{38} +(-2.23244 - 2.23244i) q^{39} +(-2.23596 + 0.0221544i) q^{40} +8.72049i q^{41} -0.397998i q^{42} +1.27639 q^{43} +1.64708i q^{44} +(0.0221544 + 2.23596i) q^{45} -3.91265 q^{46} +(-0.752821 - 0.752821i) q^{47} +(-0.707107 - 0.707107i) q^{48} -6.84160i q^{49} +(-4.99902 + 0.0990726i) q^{50} +(2.43642 - 2.43642i) q^{51} +3.15714 q^{52} +(3.88760 - 3.88760i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(0.0364901 + 3.68281i) q^{55} +(0.281427 + 0.281427i) q^{56} +2.61664 q^{57} +(-2.67202 - 2.67202i) q^{58} +(-6.53793 + 6.53793i) q^{59} +(-1.59673 - 1.56540i) q^{60} +(-0.144746 + 0.144746i) q^{61} +(6.77259 - 6.77259i) q^{62} +(0.281427 - 0.281427i) q^{63} +1.00000 q^{64} +(7.05924 - 0.0699446i) q^{65} +(-1.16466 + 1.16466i) q^{66} +(-0.492575 + 0.492575i) q^{67} +3.44561i q^{68} +(-2.76666 - 2.76666i) q^{69} +(0.635494 + 0.623024i) q^{70} +11.2201 q^{71} -1.00000i q^{72} +(0.804916 + 0.804916i) q^{73} +(-0.925435 + 6.01195i) q^{74} +(-3.60489 - 3.46478i) q^{75} +(-1.85024 + 1.85024i) q^{76} +(0.463534 - 0.463534i) q^{77} +(2.23244 + 2.23244i) q^{78} +(2.86326 - 2.86326i) q^{79} +(2.23596 - 0.0221544i) q^{80} -1.00000 q^{81} -8.72049i q^{82} +(3.45461 - 3.45461i) q^{83} +0.397998i q^{84} +(0.0763355 + 7.70424i) q^{85} -1.27639 q^{86} -3.77880i q^{87} -1.64708i q^{88} +(12.5832 + 12.5832i) q^{89} +(-0.0221544 - 2.23596i) q^{90} +(-0.888506 - 0.888506i) q^{91} +3.91265 q^{92} +9.57788 q^{93} +(0.752821 + 0.752821i) q^{94} +(-4.09608 + 4.17806i) q^{95} +(0.707107 + 0.707107i) q^{96} -6.92746i q^{97} +6.84160i q^{98} -1.64708 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8}+O(q^{10}) $ 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8	$ 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8} - 4 q^{10} - 8 q^{13} - 4 q^{14} + 36 q^{16} - 4 q^{19} + 4 q^{20} + 4 q^{25} + 8 q^{26} + 4 q^{28} - 36 q^{29} - 4 q^{31} - 36 q^{32} + 4 q^{33} + 28 q^{35} + 28 q^{37} + 4 q^{38} - 4 q^{39} - 4 q^{40} - 32 q^{43} + 16 q^{47} - 4 q^{50} - 8 q^{52} - 8 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 36 q^{58} + 4 q^{59} - 4 q^{61} + 4 q^{62} - 4 q^{63} + 36 q^{64} - 52 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} - 28 q^{70} - 8 q^{71} + 4 q^{73} - 28 q^{74} + 16 q^{75} - 4 q^{76} - 8 q^{77} + 4 q^{78} + 12 q^{79} + 4 q^{80} - 36 q^{81} + 8 q^{83} - 8 q^{85} + 32 q^{86} + 24 q^{89} + 56 q^{91} - 8 q^{93} - 16 q^{94} + 20 q^{95} + 8 q^{99}+O(q^{100}) $ 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8 - 4 * q^10 - 8 * q^13 - 4 * q^14 + 36 * q^16 - 4 * q^19 + 4 * q^20 + 4 * q^25 + 8 * q^26 + 4 * q^28 - 36 * q^29 - 4 * q^31 - 36 * q^32 + 4 * q^33 + 28 * q^35 + 28 * q^37 + 4 * q^38 - 4 * q^39 - 4 * q^40 - 32 * q^43 + 16 * q^47 - 4 * q^50 - 8 * q^52 - 8 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 36 * q^58 + 4 * q^59 - 4 * q^61 + 4 * q^62 - 4 * q^63 + 36 * q^64 - 52 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 - 28 * q^70 - 8 * q^71 + 4 * q^73 - 28 * q^74 + 16 * q^75 - 4 * q^76 - 8 * q^77 + 4 * q^78 + 12 * q^79 + 4 * q^80 - 36 * q^81 + 8 * q^83 - 8 * q^85 + 32 * q^86 + 24 * q^89 + 56 * q^91 - 8 * q^93 - 16 * q^94 + 20 * q^95 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	1.00000			0.500000
$5$	2.23596	−	0.0221544i	0.999951	−	0.00990775i
$5$	2.23596	−	0.0221544i	0.999951	−	0.00990775i
$6$	0.707107	+	0.707107i	0.288675	+	0.288675i
$7$	−0.281427	−	0.281427i	−0.106369	−	0.106369i	0.651919	−	0.758289i	$-0.273964\pi$
$7$	−0.281427	−	0.281427i	−0.106369	−	0.106369i	−0.758289	+	0.651919i	$0.773964\pi$
$8$	−1.00000			−0.353553
$9$			1.00000i			0.333333i
$10$	−2.23596	+	0.0221544i	−0.707072	+	0.00700584i
$11$			1.64708i			0.496614i	0.968681	+	0.248307i	$0.0798742\pi$
$11$			1.64708i			0.496614i	−0.968681	+	0.248307i	$0.920126\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	3.15714			0.875634			0.437817	−	0.899064i	$-0.355752\pi$
$13$	3.15714			0.875634			0.437817	+	0.899064i	$0.355752\pi$
$14$	0.281427	+	0.281427i	0.0752146	+	0.0752146i
$15$	−1.59673	−	1.56540i	−0.412273	−	0.404183i
$16$	1.00000			0.250000
$17$			3.44561i			0.835684i	0.908520	+	0.417842i	$0.137213\pi$
$17$			3.44561i			0.835684i	−0.908520	+	0.417842i	$0.862787\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−1.85024	+	1.85024i	−0.424475	+	0.424475i	−0.886741	−	0.462266i	$-0.847036\pi$
$19$	−1.85024	+	1.85024i	−0.424475	+	0.424475i	0.462266	+	0.886741i	$0.347036\pi$
$20$	2.23596	−	0.0221544i	0.499975	−	0.00495387i
$21$			0.397998i			0.0868503i
$22$		−	1.64708i		−	0.351159i
$23$	3.91265			0.815844			0.407922	−	0.913017i	$-0.366253\pi$
$23$	3.91265			0.815844			0.407922	+	0.913017i	$0.366253\pi$
$24$	0.707107	+	0.707107i	0.144338	+	0.144338i
$25$	4.99902	−	0.0990726i	0.999804	−	0.0198145i
$26$	−3.15714			−0.619167
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−0.281427	−	0.281427i	−0.0531847	−	0.0531847i
$29$	2.67202	+	2.67202i	0.496181	+	0.496181i	0.910247	−	0.414066i	$-0.135892\pi$
$29$	2.67202	+	2.67202i	0.496181	+	0.496181i	−0.414066	+	0.910247i	$0.635892\pi$
$30$	1.59673	+	1.56540i	0.291521	+	0.285801i
$31$	−6.77259	+	6.77259i	−1.21639	+	1.21639i	−0.247506	+	0.968886i	$0.579611\pi$
$31$	−6.77259	+	6.77259i	−1.21639	+	1.21639i	−0.968886	+	0.247506i	$0.920389\pi$
$32$	−1.00000			−0.176777
$33$	1.16466	−	1.16466i	0.202742	−	0.202742i
$34$		−	3.44561i		−	0.590917i
$35$	−0.635494	−	0.623024i	−0.107418	−	0.105310i
$36$			1.00000i			0.166667i
$37$	0.925435	−	6.01195i	0.152141	−	0.988359i
$37$	0.925435	−	6.01195i	0.152141	−	0.988359i
$38$	1.85024	−	1.85024i	0.300149	−	0.300149i
$39$	−2.23244	−	2.23244i	−0.357476	−	0.357476i
$40$	−2.23596	+	0.0221544i	−0.353536	+	0.00350292i
$41$			8.72049i			1.36191i	0.732325	+	0.680956i	$0.238435\pi$
$41$			8.72049i			1.36191i	−0.732325	+	0.680956i	$0.761565\pi$
$42$		−	0.397998i		−	0.0614124i
$43$	1.27639			0.194647			0.0973237	−	0.995253i	$-0.468972\pi$
$43$	1.27639			0.194647			0.0973237	+	0.995253i	$0.468972\pi$
$44$			1.64708i			0.248307i
$45$	0.0221544	+	2.23596i	0.00330258	+	0.333317i
$46$	−3.91265			−0.576889
$47$	−0.752821	−	0.752821i	−0.109810	−	0.109810i	0.650067	−	0.759877i	$-0.274741\pi$
$47$	−0.752821	−	0.752821i	−0.109810	−	0.109810i	−0.759877	+	0.650067i	$0.774741\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$		−	6.84160i		−	0.977371i
$50$	−4.99902	+	0.0990726i	−0.706968	+	0.0140110i
$51$	2.43642	−	2.43642i	0.341166	−	0.341166i
$52$	3.15714			0.437817
$53$	3.88760	−	3.88760i	0.534003	−	0.534003i	−0.387758	−	0.921761i	$-0.626750\pi$
$53$	3.88760	−	3.88760i	0.534003	−	0.534003i	0.921761	+	0.387758i	$0.126750\pi$
$54$	−0.707107	+	0.707107i	−0.0962250	+	0.0962250i
$55$	0.0364901	+	3.68281i	0.00492033	+	0.496590i
$56$	0.281427	+	0.281427i	0.0376073	+	0.0376073i
$57$	2.61664			0.346582
$58$	−2.67202	−	2.67202i	−0.350853	−	0.350853i
$59$	−6.53793	+	6.53793i	−0.851166	+	0.851166i	−0.990277	−	0.139111i	$-0.955576\pi$
$59$	−6.53793	+	6.53793i	−0.851166	+	0.851166i	0.139111	+	0.990277i	$0.455576\pi$
$60$	−1.59673	−	1.56540i	−0.206137	−	0.202092i
$61$	−0.144746	+	0.144746i	−0.0185328	+	0.0185328i	−0.716312	−	0.697780i	$-0.754171\pi$
$61$	−0.144746	+	0.144746i	−0.0185328	+	0.0185328i	0.697780	+	0.716312i	$0.254171\pi$
$62$	6.77259	−	6.77259i	0.860119	−	0.860119i
$63$	0.281427	−	0.281427i	0.0354565	−	0.0354565i
$64$	1.00000			0.125000
$65$	7.05924	−	0.0699446i	0.875591	−	0.00867556i
$66$	−1.16466	+	1.16466i	−0.143360	+	0.143360i
$67$	−0.492575	+	0.492575i	−0.0601777	+	0.0601777i	−0.736555	−	0.676377i	$-0.763549\pi$
$67$	−0.492575	+	0.492575i	−0.0601777	+	0.0601777i	0.676377	+	0.736555i	$0.263549\pi$
$68$			3.44561i			0.417842i
$69$	−2.76666	−	2.76666i	−0.333067	−	0.333067i
$70$	0.635494	+	0.623024i	0.0759561	+	0.0744657i
$71$	11.2201			1.33158			0.665790	−	0.746140i	$-0.268095\pi$
$71$	11.2201			1.33158			0.665790	+	0.746140i	$0.268095\pi$
$72$		−	1.00000i		−	0.117851i
$73$	0.804916	+	0.804916i	0.0942083	+	0.0942083i	0.752640	−	0.658432i	$-0.228780\pi$
$73$	0.804916	+	0.804916i	0.0942083	+	0.0942083i	−0.658432	+	0.752640i	$0.728780\pi$
$74$	−0.925435	+	6.01195i	−0.107580	+	0.698875i
$75$	−3.60489	−	3.46478i	−0.416257	−	0.400079i
$76$	−1.85024	+	1.85024i	−0.212237	+	0.212237i
$77$	0.463534	−	0.463534i	0.0528246	−	0.0528246i
$78$	2.23244	+	2.23244i	0.252774	+	0.252774i
$79$	2.86326	−	2.86326i	0.322142	−	0.322142i	−0.527446	−	0.849588i	$-0.676850\pi$
$79$	2.86326	−	2.86326i	0.322142	−	0.322142i	0.849588	+	0.527446i	$0.176850\pi$
$80$	2.23596	−	0.0221544i	0.249988	−	0.00247694i
$81$	−1.00000			−0.111111
$82$		−	8.72049i		−	0.963017i
$83$	3.45461	−	3.45461i	0.379192	−	0.379192i	−0.491618	−	0.870811i	$-0.663594\pi$
$83$	3.45461	−	3.45461i	0.379192	−	0.379192i	0.870811	+	0.491618i	$0.163594\pi$
$84$			0.397998i			0.0434251i
$85$	0.0763355	+	7.70424i	0.00827974	+	0.835643i
$86$	−1.27639			−0.137636
$87$		−	3.77880i		−	0.405130i
$88$		−	1.64708i		−	0.175580i
$89$	12.5832	+	12.5832i	1.33381	+	1.33381i	0.901929	+	0.431885i	$0.142151\pi$
$89$	12.5832	+	12.5832i	1.33381	+	1.33381i	0.431885	+	0.901929i	$0.357849\pi$
$90$	−0.0221544	−	2.23596i	−0.00233528	−	0.235691i
$91$	−0.888506	−	0.888506i	−0.0931407	−	0.0931407i
$92$	3.91265			0.407922
$93$	9.57788			0.993180
$94$	0.752821	+	0.752821i	0.0776476	+	0.0776476i
$95$	−4.09608	+	4.17806i	−0.420248	+	0.428660i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$		−	6.92746i		−	0.703377i	−0.936117	−	0.351689i	$-0.885608\pi$
$97$		−	6.92746i		−	0.703377i	0.936117	−	0.351689i	$-0.114392\pi$
$98$			6.84160i			0.691106i
$99$	−1.64708			−0.165538
$100$	4.99902	−	0.0990726i	0.499902	−	0.00990726i
$101$			6.04485i			0.601486i	0.953705	+	0.300743i	$0.0972346\pi$
$101$			6.04485i			0.601486i	−0.953705	+	0.300743i	$0.902765\pi$
$102$	−2.43642	+	2.43642i	−0.241241	+	0.241241i
$103$		−	11.2563i		−	1.10912i	−0.832144	−	0.554560i	$-0.812887\pi$
$103$		−	11.2563i		−	1.10912i	0.832144	−	0.554560i	$-0.187113\pi$
$104$	−3.15714			−0.309583
$105$	0.00881741	+	0.889907i	0.000860491	+	0.0868460i
$106$	−3.88760	+	3.88760i	−0.377597	+	0.377597i
$107$	8.88960	+	8.88960i	0.859390	+	0.859390i	0.991266	−	0.131876i	$-0.0421001\pi$
$107$	8.88960	+	8.88960i	0.859390	+	0.859390i	−0.131876	+	0.991266i	$0.542100\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	8.94425	−	8.94425i	0.856704	−	0.856704i	−0.134244	−	0.990948i	$-0.542861\pi$
$109$	8.94425	−	8.94425i	0.856704	−	0.856704i	0.990948	+	0.134244i	$0.0428607\pi$
$110$	−0.0364901	−	3.68281i	−0.00347920	−	0.351142i
$111$	−4.90547	+	3.59671i	−0.465607	+	0.341385i
$112$	−0.281427	−	0.281427i	−0.0265924	−	0.0265924i
$113$			0.196751i			0.0185088i	0.999957	+	0.00925440i	$0.00294581\pi$
$113$			0.196751i			0.0185088i	−0.999957	+	0.00925440i	$0.997054\pi$
$114$	−2.61664			−0.245071
$115$	8.74853	−	0.0866825i	0.815804	−	0.00808318i
$116$	2.67202	+	2.67202i	0.248090	+	0.248090i
$117$			3.15714i			0.291878i
$118$	6.53793	−	6.53793i	0.601865	−	0.601865i
$119$	0.969688	−	0.969688i	0.0888912	−	0.0888912i
$120$	1.59673	+	1.56540i	0.145761	+	0.142900i
$121$	8.28712			0.753375
$122$	0.144746	−	0.144746i	0.0131047	−	0.0131047i
$123$	6.16632	−	6.16632i	0.555998	−	0.555998i
$124$	−6.77259	+	6.77259i	−0.608196	+	0.608196i
$125$	11.1754	−	0.332273i	0.999558	−	0.0297194i
$126$	−0.281427	+	0.281427i	−0.0250715	+	0.0250715i
$127$	6.37075	+	6.37075i	0.565313	+	0.565313i	0.930812	−	0.365499i	$-0.119102\pi$
$127$	6.37075	+	6.37075i	0.565313	+	0.565313i	−0.365499	+	0.930812i	$0.619102\pi$
$128$	−1.00000			−0.0883883
$129$	−0.902543	−	0.902543i	−0.0794644	−	0.0794644i
$130$	−7.05924	+	0.0699446i	−0.619136	+	0.00613455i
$131$	−2.48554	+	2.48554i	−0.217162	+	0.217162i	−0.807302	−	0.590139i	$-0.799073\pi$
$131$	−2.48554	+	2.48554i	−0.217162	+	0.217162i	0.590139	+	0.807302i	$0.299073\pi$
$132$	1.16466	−	1.16466i	0.101371	−	0.101371i
$133$	1.04142			0.0903023
$134$	0.492575	−	0.492575i	0.0425520	−	0.0425520i
$135$	1.56540	−	1.59673i	0.134728	−	0.137424i
$136$		−	3.44561i		−	0.295459i
$137$	15.3866	+	15.3866i	1.31456	+	1.31456i	0.918012	+	0.396553i	$0.129794\pi$
$137$	15.3866	+	15.3866i	1.31456	+	1.31456i	0.396553	+	0.918012i	$0.370206\pi$
$138$	2.76666	+	2.76666i	0.235514	+	0.235514i
$139$	−2.99885			−0.254359			−0.127180	−	0.991880i	$-0.540592\pi$
$139$	−2.99885			−0.254359			−0.127180	+	0.991880i	$0.540592\pi$
$140$	−0.635494	−	0.623024i	−0.0537091	−	0.0526552i
$141$			1.06465i			0.0896597i
$142$	−11.2201			−0.941569
$143$			5.20007i			0.434852i
$144$			1.00000i			0.0833333i
$145$	6.03371	+	5.91532i	0.501073	+	0.491240i
$146$	−0.804916	−	0.804916i	−0.0666153	−	0.0666153i
$147$	−4.83774	+	4.83774i	−0.399010	+	0.399010i
$148$	0.925435	−	6.01195i	0.0760703	−	0.494179i
$149$		−	8.60756i		−	0.705159i	−0.935782	−	0.352579i	$-0.885305\pi$
$149$		−	8.60756i		−	0.705159i	0.935782	−	0.352579i	$-0.114695\pi$
$150$	3.60489	+	3.46478i	0.294338	+	0.282898i
$151$		−	2.73615i		−	0.222665i	−0.993783	−	0.111332i	$-0.964488\pi$
$151$		−	2.73615i		−	0.222665i	0.993783	−	0.111332i	$-0.0355118\pi$
$152$	1.85024	−	1.85024i	0.150075	−	0.150075i
$153$	−3.44561			−0.278561
$154$	−0.463534	+	0.463534i	−0.0373526	+	0.0373526i
$155$	−14.9932	+	15.2933i	−1.20428	+	1.22838i
$156$	−2.23244	−	2.23244i	−0.178738	−	0.178738i
$157$	−4.40198	−	4.40198i	−0.351317	−	0.351317i	0.509283	−	0.860599i	$-0.329911\pi$
$157$	−4.40198	−	4.40198i	−0.351317	−	0.351317i	−0.860599	+	0.509283i	$0.829911\pi$
$158$	−2.86326	+	2.86326i	−0.227789	+	0.227789i
$159$	−5.49790			−0.436011
$160$	−2.23596	+	0.0221544i	−0.176768	+	0.00175146i
$161$	−1.10113	−	1.10113i	−0.0867809	−	0.0867809i
$162$	1.00000			0.0785674
$163$		−	10.2487i		−	0.802740i	−0.915916	−	0.401370i	$-0.868534\pi$
$163$		−	10.2487i		−	0.802740i	0.915916	−	0.401370i	$-0.131466\pi$
$164$			8.72049i			0.680956i
$165$	2.57834	−	2.62994i	0.200723	−	0.204741i
$166$	−3.45461	+	3.45461i	−0.268130	+	0.268130i
$167$		−	2.97278i		−	0.230040i	−0.993363	−	0.115020i	$-0.963307\pi$
$167$		−	2.97278i		−	0.230040i	0.993363	−	0.115020i	$-0.0366933\pi$
$168$		−	0.397998i		−	0.0307062i
$169$	−3.03245			−0.233265
$170$	−0.0763355	−	7.70424i	−0.00585466	−	0.590888i
$171$	−1.85024	−	1.85024i	−0.141492	−	0.141492i
$172$	1.27639			0.0973237
$173$	−5.83257	−	5.83257i	−0.443442	−	0.443442i	0.449725	−	0.893167i	$-0.351522\pi$
$173$	−5.83257	−	5.83257i	−0.443442	−	0.443442i	−0.893167	+	0.449725i	$0.851522\pi$
$174$			3.77880i			0.286470i
$175$	−1.43474	−	1.37898i	−0.108456	−	0.104241i
$176$			1.64708i			0.124153i
$177$	9.24603			0.694974
$178$	−12.5832	−	12.5832i	−0.943149	−	0.943149i
$179$	−4.52269	−	4.52269i	−0.338042	−	0.338042i	0.517588	−	0.855630i	$-0.326830\pi$
$179$	−4.52269	−	4.52269i	−0.338042	−	0.338042i	−0.855630	+	0.517588i	$0.826830\pi$
$180$	0.0221544	+	2.23596i	0.00165129	+	0.166658i
$181$	−16.8840			−1.25497			−0.627487	−	0.778627i	$-0.715917\pi$
$181$	−16.8840			−1.25497			−0.627487	+	0.778627i	$0.715917\pi$
$182$	0.888506	+	0.888506i	0.0658604	+	0.0658604i
$183$	0.204701			0.0151320
$184$	−3.91265			−0.288445
$185$	1.93604	−	13.4630i	0.142341	−	0.989818i
$186$	−9.57788			−0.702284
$187$	−5.67521			−0.415012
$188$	−0.752821	−	0.752821i	−0.0549051	−	0.0549051i
$189$	−0.397998			−0.0289501
$190$	4.09608	−	4.17806i	0.297161	−	0.303108i
$191$	−18.5005	−	18.5005i	−1.33865	−	1.33865i	−0.897372	−	0.441274i	$-0.854527\pi$
$191$	−18.5005	−	18.5005i	−1.33865	−	1.33865i	−0.441274	−	0.897372i	$-0.645473\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	−17.1049			−1.23124			−0.615620	−	0.788043i	$-0.711094\pi$
$193$	−17.1049			−1.23124			−0.615620	+	0.788043i	$0.711094\pi$
$194$			6.92746i			0.497363i
$195$	−5.04109	−	4.94218i	−0.361000	−	0.353917i
$196$		−	6.84160i		−	0.488686i
$197$	−0.556751	−	0.556751i	−0.0396669	−	0.0396669i	0.686995	−	0.726662i	$-0.258929\pi$
$197$	−0.556751	−	0.556751i	−0.0396669	−	0.0396669i	−0.726662	+	0.686995i	$0.758929\pi$
$198$	1.64708			0.117053
$199$	−7.91159	−	7.91159i	−0.560838	−	0.560838i	0.368707	−	0.929546i	$-0.379800\pi$
$199$	−7.91159	−	7.91159i	−0.560838	−	0.560838i	−0.929546	+	0.368707i	$0.879800\pi$
$200$	−4.99902	+	0.0990726i	−0.353484	+	0.00700549i
$201$	0.696607			0.0491349
$202$		−	6.04485i		−	0.425314i
$203$		−	1.50396i		−	0.105557i
$204$	2.43642	−	2.43642i	0.170583	−	0.170583i
$205$	0.193197	+	19.4986i	0.0134935	+	1.36184i
$206$			11.2563i			0.784266i
$207$			3.91265i			0.271948i
$208$	3.15714			0.218908
$209$	−3.04750	−	3.04750i	−0.210800	−	0.210800i
$210$	−0.00881741	−	0.889907i	−0.000608459	−	0.0614094i
$211$	−1.32938			−0.0915183			−0.0457592	−	0.998953i	$-0.514571\pi$
$211$	−1.32938			−0.0915183			−0.0457592	+	0.998953i	$0.514571\pi$
$212$	3.88760	−	3.88760i	0.267001	−	0.267001i
$213$	−7.93380	−	7.93380i	−0.543615	−	0.543615i
$214$	−8.88960	−	8.88960i	−0.607681	−	0.607681i
$215$	2.85395	−	0.0282776i	0.194638	−	0.00192852i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	3.81198			0.258774
$218$	−8.94425	+	8.94425i	−0.605781	+	0.605781i
$219$		−	1.13832i		−	0.0769207i
$220$	0.0364901	+	3.68281i	0.00246016	+	0.248295i
$221$			10.8783i			0.731753i
$222$	4.90547	−	3.59671i	0.329234	−	0.241395i
$223$	−3.07126	+	3.07126i	−0.205667	+	0.205667i	−0.802423	−	0.596756i	$-0.796456\pi$
$223$	−3.07126	+	3.07126i	−0.205667	+	0.205667i	0.596756	+	0.802423i	$0.296456\pi$
$224$	0.281427	+	0.281427i	0.0188036	+	0.0188036i
$225$	0.0990726	+	4.99902i	0.00660484	+	0.333268i
$226$		−	0.196751i		−	0.0130877i
$227$			24.6591i			1.63668i	0.574732	+	0.818342i	$0.305106\pi$
$227$			24.6591i			1.63668i	−0.574732	+	0.818342i	$0.694894\pi$
$228$	2.61664			0.173291
$229$			14.8812i			0.983377i	0.870771	+	0.491689i	$0.163620\pi$
$229$			14.8812i			0.983377i	−0.870771	+	0.491689i	$0.836380\pi$
$230$	−8.74853	+	0.0866825i	−0.576861	+	0.00571567i
$231$	−0.655535			−0.0431311
$232$	−2.67202	−	2.67202i	−0.175426	−	0.175426i
$233$	−14.6836	−	14.6836i	−0.961952	−	0.961952i	0.0373500	−	0.999302i	$-0.488108\pi$
$233$	−14.6836	−	14.6836i	−0.961952	−	0.961952i	−0.999302	+	0.0373500i	$0.988108\pi$
$234$		−	3.15714i		−	0.206389i
$235$	−1.69995	−	1.66660i	−0.110893	−	0.108717i
$236$	−6.53793	+	6.53793i	−0.425583	+	0.425583i
$237$	−4.04926			−0.263028
$238$	−0.969688	+	0.969688i	−0.0628556	+	0.0628556i
$239$	−11.8998	+	11.8998i	−0.769736	+	0.769736i	−0.978060	−	0.208324i	$-0.933199\pi$
$239$	−11.8998	+	11.8998i	−0.769736	+	0.769736i	0.208324	+	0.978060i	$0.433199\pi$
$240$	−1.59673	−	1.56540i	−0.103068	−	0.101046i
$241$	15.6655	+	15.6655i	1.00910	+	1.00910i	0.999958	+	0.00914615i	$0.00291135\pi$
$241$	15.6655	+	15.6655i	1.00910	+	1.00910i	0.00914615	+	0.999958i	$0.497089\pi$
$242$	−8.28712			−0.532716
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−0.144746	+	0.144746i	−0.00926640	+	0.00926640i
$245$	−0.151571	−	15.2975i	−0.00968355	−	0.977323i
$246$	−6.16632	+	6.16632i	−0.393150	+	0.393150i
$247$	−5.84148	+	5.84148i	−0.371685	+	0.371685i
$248$	6.77259	−	6.77259i	0.430060	−	0.430060i
$249$	−4.88555			−0.309609
$250$	−11.1754	+	0.332273i	−0.706794	+	0.0210148i
$251$	8.27735	−	8.27735i	0.522462	−	0.522462i	−0.395852	−	0.918314i	$-0.629551\pi$
$251$	8.27735	−	8.27735i	0.522462	−	0.522462i	0.918314	+	0.395852i	$0.129551\pi$
$252$	0.281427	−	0.281427i	0.0177282	−	0.0177282i
$253$			6.44446i			0.405160i
$254$	−6.37075	−	6.37075i	−0.399737	−	0.399737i
$255$	5.39375	−	5.50170i	0.337769	−	0.344530i
$256$	1.00000			0.0625000
$257$			4.24215i			0.264618i	0.991209	+	0.132309i	$0.0422391\pi$
$257$			4.24215i			0.264618i	−0.991209	+	0.132309i	$0.957761\pi$
$258$	0.902543	+	0.902543i	0.0561898	+	0.0561898i
$259$	−1.95237	+	1.43148i	−0.121314	+	0.0889481i
$260$	7.05924	−	0.0699446i	0.437795	−	0.00433778i
$261$	−2.67202	+	2.67202i	−0.165394	+	0.165394i
$262$	2.48554	−	2.48554i	0.153557	−	0.153557i
$263$	−22.4018	−	22.4018i	−1.38135	−	1.38135i	−0.842223	−	0.539129i	$-0.818754\pi$
$263$	−22.4018	−	22.4018i	−1.38135	−	1.38135i	−0.539129	−	0.842223i	$-0.681246\pi$
$264$	−1.16466	+	1.16466i	−0.0716801	+	0.0716801i
$265$	8.60638	−	8.77864i	0.528686	−	0.539267i
$266$	−1.04142			−0.0638534
$267$		−	17.7953i		−	1.08905i
$268$	−0.492575	+	0.492575i	−0.0300888	+	0.0300888i
$269$		−	15.2647i		−	0.930706i	−0.885125	−	0.465353i	$-0.845927\pi$
$269$		−	15.2647i		−	0.930706i	0.885125	−	0.465353i	$-0.154073\pi$
$270$	−1.56540	+	1.59673i	−0.0952669	+	0.0971737i
$271$	14.7969			0.898849			0.449424	−	0.893318i	$-0.351629\pi$
$271$	14.7969			0.898849			0.449424	+	0.893318i	$0.351629\pi$
$272$			3.44561i			0.208921i
$273$			1.25654i			0.0760491i
$274$	−15.3866	−	15.3866i	−0.929538	−	0.929538i
$275$	0.163181	+	8.23379i	0.00984017	+	0.496516i
$276$	−2.76666	−	2.76666i	−0.166534	−	0.166534i
$277$	3.00385			0.180484			0.0902420	−	0.995920i	$-0.471236\pi$
$277$	3.00385			0.180484			0.0902420	+	0.995920i	$0.471236\pi$
$278$	2.99885			0.179859
$279$	−6.77259	−	6.77259i	−0.405464	−	0.405464i
$280$	0.635494	+	0.623024i	0.0379780	+	0.0372328i
$281$	−8.35723	−	8.35723i	−0.498551	−	0.498551i	0.412436	−	0.910987i	$-0.364678\pi$
$281$	−8.35723	−	8.35723i	−0.498551	−	0.498551i	−0.910987	+	0.412436i	$0.864678\pi$
$282$		−	1.06465i		−	0.0633990i
$283$		−	3.86949i		−	0.230018i	−0.993364	−	0.115009i	$-0.963310\pi$
$283$		−	3.86949i		−	0.230018i	0.993364	−	0.115009i	$-0.0366896\pi$
$284$	11.2201			0.665790
$285$	5.85070	−	0.0579701i	0.346565	−	0.00343385i
$286$		−	5.20007i		−	0.307487i
$287$	2.45418	−	2.45418i	0.144866	−	0.144866i
$288$		−	1.00000i		−	0.0589256i
$289$	5.12776			0.301633
$290$	−6.03371	−	5.91532i	−0.354312	−	0.347359i
$291$	−4.89845	+	4.89845i	−0.287152	+	0.287152i
$292$	0.804916	+	0.804916i	0.0471041	+	0.0471041i
$293$	10.7523	−	10.7523i	0.628156	−	0.628156i	−0.319448	−	0.947604i	$-0.603498\pi$
$293$	10.7523	−	10.7523i	0.628156	−	0.628156i	0.947604	+	0.319448i	$0.103498\pi$
$294$	4.83774	−	4.83774i	0.282143	−	0.282143i
$295$	−14.4737	+	14.7634i	−0.842691	+	0.859557i
$296$	−0.925435	+	6.01195i	−0.0537898	+	0.349438i
$297$	1.16466	+	1.16466i	0.0675806	+	0.0675806i
$298$			8.60756i			0.498622i
$299$	12.3528			0.714381
$300$	−3.60489	−	3.46478i	−0.208129	−	0.200039i
$301$	−0.359210	−	0.359210i	−0.0207045	−	0.0207045i
$302$			2.73615i			0.157448i
$303$	4.27436	−	4.27436i	0.245555	−	0.245555i
$304$	−1.85024	+	1.85024i	−0.106119	+	0.106119i
$305$	−0.320439	+	0.326852i	−0.0183483	+	0.0187155i
$306$	3.44561			0.196972
$307$	−19.3837	+	19.3837i	−1.10629	+	1.10629i	−0.112652	+	0.993634i	$0.535935\pi$
$307$	−19.3837	+	19.3837i	−1.10629	+	1.10629i	−0.993634	+	0.112652i	$0.964065\pi$
$308$	0.463534	−	0.463534i	0.0264123	−	0.0264123i
$309$	−7.95943	+	7.95943i	−0.452796	+	0.452796i
$310$	14.9932	−	15.2933i	0.851555	−	0.868599i
$311$	−9.43851	+	9.43851i	−0.535209	+	0.535209i	−0.922118	−	0.386909i	$-0.873543\pi$
$311$	−9.43851	+	9.43851i	−0.535209	+	0.535209i	0.386909	+	0.922118i	$0.373543\pi$
$312$	2.23244	+	2.23244i	0.126387	+	0.126387i
$313$	−20.7779			−1.17444			−0.587218	−	0.809429i	$-0.699777\pi$
$313$	−20.7779			−1.17444			−0.587218	+	0.809429i	$0.699777\pi$
$314$	4.40198	+	4.40198i	0.248418	+	0.248418i
$315$	0.623024	−	0.635494i	0.0351034	−	0.0358060i
$316$	2.86326	−	2.86326i	0.161071	−	0.161071i
$317$	−3.25873	+	3.25873i	−0.183029	+	0.183029i	−0.792674	−	0.609646i	$-0.791312\pi$
$317$	−3.25873	+	3.25873i	−0.183029	+	0.183029i	0.609646	+	0.792674i	$0.291312\pi$
$318$	5.49790			0.308307
$319$	−4.40103	+	4.40103i	−0.246410	+	0.246410i
$320$	2.23596	−	0.0221544i	0.124994	−	0.00123847i
$321$		−	12.5718i		−	0.701689i
$322$	1.10113	+	1.10113i	0.0613634	+	0.0613634i
$323$	−6.37522	−	6.37522i	−0.354727	−	0.354727i
$324$	−1.00000			−0.0555556
$325$	15.7826	−	0.312786i	0.875462	−	0.0173503i
$326$			10.2487i			0.567623i
$327$	−12.6491			−0.699496
$328$		−	8.72049i		−	0.481508i
$329$			0.423728i			0.0233609i
$330$	−2.57834	+	2.62994i	−0.141933	+	0.144773i
$331$	2.00568	+	2.00568i	0.110242	+	0.110242i	0.760076	−	0.649834i	$-0.225162\pi$
$331$	2.00568	+	2.00568i	0.110242	+	0.110242i	−0.649834	+	0.760076i	$0.725162\pi$
$332$	3.45461	−	3.45461i	0.189596	−	0.189596i
$333$	6.01195	+	0.925435i	0.329453	+	0.0507135i
$334$			2.97278i			0.162663i
$335$	−1.09047	+	1.11229i	−0.0595785	+	0.0607709i
$336$			0.397998i			0.0217126i
$337$	8.49643	−	8.49643i	0.462830	−	0.462830i	−0.436752	−	0.899582i	$-0.643871\pi$
$337$	8.49643	−	8.49643i	0.462830	−	0.462830i	0.899582	+	0.436752i	$0.143871\pi$
$338$	3.03245			0.164944
$339$	0.139124	−	0.139124i	0.00755619	−	0.00755619i
$340$	0.0763355	+	7.70424i	0.00413987	+	0.417821i
$341$	−11.1550	−	11.1550i	−0.604077	−	0.604077i
$342$	1.85024	+	1.85024i	0.100050	+	0.100050i
$343$	−3.89540	+	3.89540i	−0.210332	+	0.210332i
$344$	−1.27639			−0.0688182
$345$	−6.24744	−	6.12485i	−0.336351	−	0.329751i
$346$	5.83257	+	5.83257i	0.313561	+	0.313561i
$347$	−0.455842			−0.0244709			−0.0122354	−	0.999925i	$-0.503895\pi$
$347$	−0.455842			−0.0244709			−0.0122354	+	0.999925i	$0.503895\pi$
$348$		−	3.77880i		−	0.202565i
$349$		−	18.0258i		−	0.964899i	−0.875924	−	0.482450i	$-0.839747\pi$
$349$		−	18.0258i		−	0.964899i	0.875924	−	0.482450i	$-0.160253\pi$
$350$	1.43474	+	1.37898i	0.0766901	+	0.0737095i
$351$	2.23244	−	2.23244i	0.119159	−	0.119159i
$352$		−	1.64708i		−	0.0877898i
$353$		−	16.2235i		−	0.863489i	−0.901996	−	0.431745i	$-0.857898\pi$
$353$		−	16.2235i		−	0.863489i	0.901996	−	0.431745i	$-0.142102\pi$
$354$	−9.24603			−0.491421
$355$	25.0876	−	0.248574i	1.33151	−	0.0131930i
$356$	12.5832	+	12.5832i	0.666907	+	0.666907i
$357$	−1.37135			−0.0725794
$358$	4.52269	+	4.52269i	0.239031	+	0.239031i
$359$		−	19.2940i		−	1.01830i	−0.860678	−	0.509149i	$-0.829960\pi$
$359$		−	19.2940i		−	1.01830i	0.860678	−	0.509149i	$-0.170040\pi$
$360$	−0.0221544	−	2.23596i	−0.00116764	−	0.117845i
$361$			12.1532i			0.639642i
$362$	16.8840			0.887401
$363$	−5.85988	−	5.85988i	−0.307564	−	0.307564i
$364$	−0.888506	−	0.888506i	−0.0465703	−	0.0465703i
$365$	1.81759	+	1.78193i	0.0951370	+	0.0932703i
$366$	−0.204701			−0.0106999
$367$	−3.21053	−	3.21053i	−0.167588	−	0.167588i	0.618330	−	0.785919i	$-0.287810\pi$
$367$	−3.21053	−	3.21053i	−0.167588	−	0.167588i	−0.785919	+	0.618330i	$0.787810\pi$
$368$	3.91265			0.203961
$369$	−8.72049			−0.453970
$370$	−1.93604	+	13.4630i	−0.100650	+	0.699907i
$371$	−2.18815			−0.113603
$372$	9.57788			0.496590
$373$	−2.94440	−	2.94440i	−0.152455	−	0.152455i	0.626759	−	0.779214i	$-0.284381\pi$
$373$	−2.94440	−	2.94440i	−0.152455	−	0.152455i	−0.779214	+	0.626759i	$0.784381\pi$
$374$	5.67521			0.293458
$375$	−8.13715	−	7.66725i	−0.420201	−	0.395935i
$376$	0.752821	+	0.752821i	0.0388238	+	0.0388238i
$377$	8.43593	+	8.43593i	0.434473	+	0.434473i
$378$	0.397998			0.0204708
$379$		−	25.1637i		−	1.29257i	−0.763094	−	0.646287i	$-0.776321\pi$
$379$		−	25.1637i		−	1.29257i	0.763094	−	0.646287i	$-0.223679\pi$
$380$	−4.09608	+	4.17806i	−0.210124	+	0.214330i
$381$		−	9.00960i		−	0.461576i
$382$	18.5005	+	18.5005i	0.946566	+	0.946566i
$383$	−0.995617			−0.0508736			−0.0254368	−	0.999676i	$-0.508098\pi$
$383$	−0.995617			−0.0508736			−0.0254368	+	0.999676i	$0.508098\pi$
$384$	0.707107	+	0.707107i	0.0360844	+	0.0360844i
$385$	1.02617	−	1.04671i	0.0522986	−	0.0533453i
$386$	17.1049			0.870618
$387$			1.27639i			0.0648824i
$388$		−	6.92746i		−	0.351689i
$389$	−19.4231	+	19.4231i	−0.984788	+	0.984788i	−0.999886	−	0.0150980i	$-0.995194\pi$
$389$	−19.4231	+	19.4231i	−0.984788	+	0.984788i	0.0150980	+	0.999886i	$0.495194\pi$
$390$	5.04109	+	4.94218i	0.255266	+	0.250257i
$391$			13.4815i			0.681788i
$392$			6.84160i			0.345553i
$393$	3.51508			0.177312
$394$	0.556751	+	0.556751i	0.0280487	+	0.0280487i
$395$	6.33870	−	6.46557i	0.318935	−	0.325318i
$396$	−1.64708			−0.0827690
$397$	6.49757	−	6.49757i	0.326104	−	0.326104i	−0.524999	−	0.851103i	$-0.675934\pi$
$397$	6.49757	−	6.49757i	0.326104	−	0.326104i	0.851103	+	0.524999i	$0.175934\pi$
$398$	7.91159	+	7.91159i	0.396572	+	0.396572i
$399$	−0.736393	−	0.736393i	−0.0368658	−	0.0368658i
$400$	4.99902	−	0.0990726i	0.249951	−	0.00495363i
$401$	−24.2700	+	24.2700i	−1.21199	+	1.21199i	−0.241616	+	0.970372i	$0.577678\pi$
$401$	−24.2700	+	24.2700i	−1.21199	+	1.21199i	−0.970372	+	0.241616i	$0.922322\pi$
$402$	−0.696607			−0.0347436
$403$	−21.3820	+	21.3820i	−1.06511	+	1.06511i
$404$			6.04485i			0.300743i
$405$	−2.23596	+	0.0221544i	−0.111106	+	0.00110086i
$406$			1.50396i			0.0746401i
$407$	9.90218	+	1.52427i	0.490833	+	0.0755551i
$408$	−2.43642	+	2.43642i	−0.120621	+	0.120621i
$409$	24.0003	+	24.0003i	1.18674	+	1.18674i	0.977963	+	0.208776i	$0.0669481\pi$
$409$	24.0003	+	24.0003i	1.18674	+	1.18674i	0.208776	+	0.977963i	$0.433052\pi$
$410$	−0.193197	−	19.4986i	−0.00954133	−	0.962969i
$411$		−	21.7599i		−	1.07334i
$412$		−	11.2563i		−	0.554560i
$413$	3.67990			0.181076
$414$		−	3.91265i		−	0.192296i
$415$	7.64782	−	7.80089i	0.375417	−	0.382931i
$416$	−3.15714			−0.154792
$417$	2.12051	+	2.12051i	0.103842	+	0.103842i
$418$	3.04750	+	3.04750i	0.149058	+	0.149058i
$419$		−	32.2473i		−	1.57538i	−0.616070	−	0.787692i	$-0.711276\pi$
$419$		−	32.2473i		−	1.57538i	0.616070	−	0.787692i	$-0.288724\pi$
$420$	0.00881741	+	0.889907i	0.000430245	+	0.0434230i
$421$	−3.85720	+	3.85720i	−0.187988	+	0.187988i	−0.794826	−	0.606838i	$-0.792438\pi$
$421$	−3.85720	+	3.85720i	−0.187988	+	0.187988i	0.606838	+	0.794826i	$0.292438\pi$
$422$	1.32938			0.0647132
$423$	0.752821	−	0.752821i	0.0366034	−	0.0366034i
$424$	−3.88760	+	3.88760i	−0.188798	+	0.188798i
$425$	0.341366	+	17.2247i	0.0165587	+	0.835519i
$426$	7.93380	+	7.93380i	0.384394	+	0.384394i
$427$	0.0814708			0.00394265
$428$	8.88960	+	8.88960i	0.429695	+	0.429695i
$429$	3.67701	−	3.67701i	0.177528	−	0.177528i
$430$	−2.85395	+	0.0282776i	−0.137630	+	0.00136367i
$431$	−15.1362	+	15.1362i	−0.729087	+	0.729087i	−0.970438	−	0.241351i	$-0.922410\pi$
$431$	−15.1362	+	15.1362i	−0.729087	+	0.729087i	0.241351	+	0.970438i	$0.422410\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	−27.7575	+	27.7575i	−1.33394	+	1.33394i	−0.432130	+	0.901811i	$0.642238\pi$
$433$	−27.7575	+	27.7575i	−1.33394	+	1.33394i	−0.901811	+	0.432130i	$0.857762\pi$
$434$	−3.81198			−0.182981
$435$	−0.0837171	−	8.44924i	−0.00401393	−	0.405110i
$436$	8.94425	−	8.94425i	0.428352	−	0.428352i
$437$	−7.23936	+	7.23936i	−0.346306	+	0.346306i
$438$			1.13832i			0.0543912i
$439$	17.1813	+	17.1813i	0.820020	+	0.820020i	0.986110	−	0.166091i	$-0.0531145\pi$
$439$	17.1813	+	17.1813i	0.820020	+	0.820020i	−0.166091	+	0.986110i	$0.553115\pi$
$440$	−0.0364901	−	3.68281i	−0.00173960	−	0.175571i
$441$	6.84160			0.325790
$442$		−	10.8783i		−	0.517427i
$443$	−7.22878	−	7.22878i	−0.343450	−	0.343450i	0.514213	−	0.857663i	$-0.328084\pi$
$443$	−7.22878	−	7.22878i	−0.343450	−	0.343450i	−0.857663	+	0.514213i	$0.828084\pi$
$444$	−4.90547	+	3.59671i	−0.232803	+	0.170692i
$445$	28.4142	+	27.8567i	1.34696	+	1.32053i
$446$	3.07126	−	3.07126i	0.145429	−	0.145429i
$447$	−6.08646	+	6.08646i	−0.287880	+	0.287880i
$448$	−0.281427	−	0.281427i	−0.0132962	−	0.0132962i
$449$	9.76421	−	9.76421i	0.460802	−	0.460802i	−0.438116	−	0.898918i	$-0.644354\pi$
$449$	9.76421	−	9.76421i	0.460802	−	0.460802i	0.898918	+	0.438116i	$0.144354\pi$
$450$	−0.0990726	−	4.99902i	−0.00467033	−	0.235656i
$451$	−14.3634			−0.676344
$452$			0.196751i			0.00925440i
$453$	−1.93475	+	1.93475i	−0.0909024	+	0.0909024i
$454$		−	24.6591i		−	1.15731i
$455$	−2.00635	−	1.96698i	−0.0940589	−	0.0922133i
$456$	−2.61664			−0.122535
$457$		−	20.5176i		−	0.959771i	−0.877331	−	0.479886i	$-0.840678\pi$
$457$		−	20.5176i		−	0.959771i	0.877331	−	0.479886i	$-0.159322\pi$
$458$		−	14.8812i		−	0.695353i
$459$	2.43642	+	2.43642i	0.113722	+	0.113722i
$460$	8.74853	−	0.0866825i	0.407902	−	0.00404159i
$461$	21.6195	+	21.6195i	1.00692	+	1.00692i	0.999976	+	0.00694687i	$0.00221127\pi$
$461$	21.6195	+	21.6195i	1.00692	+	1.00692i	0.00694687	+	0.999976i	$0.497789\pi$
$462$	0.655535			0.0304983
$463$	1.38040			0.0641527			0.0320764	−	0.999485i	$-0.489788\pi$
$463$	1.38040			0.0641527			0.0320764	+	0.999485i	$0.489788\pi$
$464$	2.67202	+	2.67202i	0.124045	+	0.124045i
$465$	21.4157	−	0.212192i	0.993131	−	0.00984018i
$466$	14.6836	+	14.6836i	0.680203	+	0.680203i
$467$			0.453871i			0.0210026i	0.999945	+	0.0105013i	$0.00334274\pi$
$467$			0.453871i			0.0210026i	−0.999945	+	0.0105013i	$0.996657\pi$
$468$			3.15714i			0.145939i
$469$	0.277248			0.0128021
$470$	1.69995	+	1.66660i	0.0784131	+	0.0768744i
$471$			6.22534i			0.286849i
$472$	6.53793	−	6.53793i	0.300933	−	0.300933i
$473$			2.10232i			0.0966646i
$474$	4.04926			0.185989
$475$	−9.06609	+	9.43271i	−0.415981	+	0.432802i
$476$	0.969688	−	0.969688i	0.0444456	−	0.0444456i
$477$	3.88760	+	3.88760i	0.178001	+	0.178001i
$478$	11.8998	−	11.8998i	0.544285	−	0.544285i
$479$	10.7493	−	10.7493i	0.491147	−	0.491147i	−0.417521	−	0.908667i	$-0.637101\pi$
$479$	10.7493	−	10.7493i	0.491147	−	0.491147i	0.908667	+	0.417521i	$0.137101\pi$
$480$	1.59673	+	1.56540i	0.0728803	+	0.0714502i
$481$	2.92173	−	18.9806i	0.133219	−	0.865440i
$482$	−15.6655	−	15.6655i	−0.713545	−	0.713545i
$483$			1.55723i			0.0708563i
$484$	8.28712			0.376687
$485$	−0.153474	−	15.4895i	−0.00696888	−	0.703343i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$			13.2268i			0.599365i	0.954039	+	0.299682i	$0.0968807\pi$
$487$			13.2268i			0.599365i	−0.954039	+	0.299682i	$0.903119\pi$
$488$	0.144746	−	0.144746i	0.00655233	−	0.00655233i
$489$	−7.24692	+	7.24692i	−0.327717	+	0.327717i
$490$	0.151571	+	15.2975i	0.00684730	+	0.691072i
$491$	−30.4522			−1.37429			−0.687145	−	0.726520i	$-0.741136\pi$
$491$	−30.4522			−1.37429			−0.687145	+	0.726520i	$0.741136\pi$
$492$	6.16632	−	6.16632i	0.277999	−	0.277999i
$493$	−9.20673	+	9.20673i	−0.414650	+	0.414650i
$494$	5.84148	−	5.84148i	0.262821	−	0.262821i
$495$	−3.68281	+	0.0364901i	−0.165530	+	0.00164011i
$496$	−6.77259	+	6.77259i	−0.304098	+	0.304098i
$497$	−3.15764	−	3.15764i	−0.141639	−	0.141639i
$498$	4.88555			0.218927
$499$	−6.74452	−	6.74452i	−0.301926	−	0.301926i	0.539841	−	0.841767i	$-0.318484\pi$
$499$	−6.74452	−	6.74452i	−0.301926	−	0.301926i	−0.841767	+	0.539841i	$0.818484\pi$
$500$	11.1754	−	0.332273i	0.499779	−	0.0148597i
$501$	−2.10207	+	2.10207i	−0.0939136	+	0.0939136i
$502$	−8.27735	+	8.27735i	−0.369436	+	0.369436i
$503$	31.0691			1.38530			0.692652	−	0.721272i	$-0.256442\pi$
$503$	31.0691			1.38530			0.692652	+	0.721272i	$0.256442\pi$
$504$	−0.281427	+	0.281427i	−0.0125358	+	0.0125358i
$505$	0.133920	+	13.5160i	0.00595937	+	0.601456i
$506$		−	6.44446i		−	0.286491i
$507$	2.14427	+	2.14427i	0.0952302	+	0.0952302i
$508$	6.37075	+	6.37075i	0.282656	+	0.282656i
$509$	−11.0860			−0.491377			−0.245688	−	0.969349i	$-0.579014\pi$
$509$	−11.0860			−0.491377			−0.245688	+	0.969349i	$0.579014\pi$
$510$	−5.39375	+	5.50170i	−0.238839	+	0.243619i
$511$		−	0.453050i		−	0.0200418i
$512$	−1.00000			−0.0441942
$513$			2.61664i			0.115527i
$514$		−	4.24215i		−	0.187113i
$515$	−0.249377	−	25.1687i	−0.0109889	−	1.10907i
$516$	−0.902543	−	0.902543i	−0.0397322	−	0.0397322i
$517$	1.23996	−	1.23996i	0.0545333	−	0.0545333i
$518$	1.95237	−	1.43148i	0.0857822	−	0.0628958i
$519$			8.24851i			0.362069i
$520$	−7.05924	+	0.0699446i	−0.309568	+	0.00306727i
$521$		−	32.8476i		−	1.43908i	−0.694451	−	0.719540i	$-0.744353\pi$
$521$		−	32.8476i		−	1.43908i	0.694451	−	0.719540i	$-0.255647\pi$
$522$	2.67202	−	2.67202i	0.116951	−	0.116951i
$523$	−9.72492			−0.425241			−0.212620	−	0.977135i	$-0.568200\pi$
$523$	−9.72492			−0.425241			−0.212620	+	0.977135i	$0.568200\pi$
$524$	−2.48554	+	2.48554i	−0.108581	+	0.108581i
$525$	0.0394307	+	1.98960i	0.00172090	+	0.0868332i
$526$	22.4018	+	22.4018i	0.976763	+	0.976763i
$527$	−23.3357	−	23.3357i	−1.01652	−	1.01652i
$528$	1.16466	−	1.16466i	0.0506854	−	0.0506854i
$529$	−7.69115			−0.334398
$530$	−8.60638	+	8.77864i	−0.373837	+	0.381320i
$531$	−6.53793	−	6.53793i	−0.283722	−	0.283722i
$532$	1.04142			0.0451512
$533$			27.5318i			1.19254i
$534$			17.7953i			0.770078i
$535$	20.0737	+	19.6798i	0.867863	+	0.850833i
$536$	0.492575	−	0.492575i	0.0212760	−	0.0212760i
$537$			6.39605i			0.276010i
$538$			15.2647i			0.658108i
$539$	11.2687			0.485376
$540$	1.56540	−	1.59673i	0.0673639	−	0.0687122i
$541$	−22.2929	−	22.2929i	−0.958445	−	0.958445i	0.0407258	−	0.999170i	$-0.487033\pi$
$541$	−22.2929	−	22.2929i	−0.958445	−	0.958445i	−0.999170	+	0.0407258i	$0.987033\pi$
$542$	−14.7969			−0.635582
$543$	11.9388	+	11.9388i	0.512341	+	0.512341i
$544$		−	3.44561i		−	0.147729i
$545$	19.8008	−	20.1971i	0.848174	−	0.865150i
$546$		−	1.25654i		−	0.0537748i
$547$	33.1369			1.41683			0.708416	−	0.705795i	$-0.249410\pi$
$547$	33.1369			1.41683			0.708416	+	0.705795i	$0.249410\pi$
$548$	15.3866	+	15.3866i	0.657282	+	0.657282i
$549$	−0.144746	−	0.144746i	−0.00617760	−	0.00617760i
$550$	−0.163181	−	8.23379i	−0.00695805	−	0.351090i
$551$	−9.88776			−0.421233
$552$	2.76666	+	2.76666i	0.117757	+	0.117757i
$553$	−1.61160			−0.0685322
$554$	−3.00385			−0.127621
$555$	−10.8888	+	8.15077i	−0.462202	+	0.345981i
$556$	−2.99885			−0.127180
$557$	3.42489			0.145117			0.0725586	−	0.997364i	$-0.476884\pi$
$557$	3.42489			0.145117			0.0725586	+	0.997364i	$0.476884\pi$
$558$	6.77259	+	6.77259i	0.286706	+	0.286706i
$559$	4.02974			0.170440
$560$	−0.635494	−	0.623024i	−0.0268545	−	0.0263276i
$561$	4.01298	+	4.01298i	0.169428	+	0.169428i
$562$	8.35723	+	8.35723i	0.352529	+	0.352529i
$563$	17.6124			0.742273			0.371136	−	0.928578i	$-0.378968\pi$
$563$	17.6124			0.742273			0.371136	+	0.928578i	$0.378968\pi$
$564$			1.06465i			0.0448298i
$565$	0.00435891	+	0.439928i	0.000183381	+	0.0185079i
$566$			3.86949i			0.162647i
$567$	0.281427	+	0.281427i	0.0118188	+	0.0118188i
$568$	−11.2201			−0.470784
$569$	−13.6557	−	13.6557i	−0.572477	−	0.572477i	0.360343	−	0.932820i	$-0.382660\pi$
$569$	−13.6557	−	13.6557i	−0.572477	−	0.572477i	−0.932820	+	0.360343i	$0.882660\pi$
$570$	−5.85070	+	0.0579701i	−0.245059	+	0.00242810i
$571$	36.6093			1.53205			0.766025	−	0.642811i	$-0.222232\pi$
$571$	36.6093			1.53205			0.766025	+	0.642811i	$0.222232\pi$
$572$			5.20007i			0.217426i
$573$			26.1636i			1.09300i
$574$	−2.45418	+	2.45418i	−0.102436	+	0.102436i
$575$	19.5594	−	0.387637i	0.815684	−	0.0161656i
$576$			1.00000i			0.0416667i
$577$		−	28.6229i		−	1.19159i	−0.803137	−	0.595794i	$-0.796837\pi$
$577$		−	28.6229i		−	1.19159i	0.803137	−	0.595794i	$-0.203163\pi$
$578$	−5.12776			−0.213287
$579$	12.0950	+	12.0950i	0.502652	+	0.502652i
$580$	6.03371	+	5.91532i	0.250536	+	0.245620i
$581$	−1.94444			−0.0806690
$582$	4.89845	−	4.89845i	0.203047	−	0.203047i
$583$	6.40320	+	6.40320i	0.265193	+	0.265193i
$584$	−0.804916	−	0.804916i	−0.0333077	−	0.0333077i
$585$	0.0699446	+	7.05924i	0.00289185	+	0.291864i
$586$	−10.7523	+	10.7523i	−0.444173	+	0.444173i
$587$	−17.5944			−0.726197			−0.363099	−	0.931751i	$-0.618281\pi$
$587$	−17.5944			−0.726197			−0.363099	+	0.931751i	$0.618281\pi$
$588$	−4.83774	+	4.83774i	−0.199505	+	0.199505i
$589$		−	25.0619i		−	1.03266i
$590$	14.4737	−	14.7634i	0.595873	−	0.607799i
$591$			0.787365i			0.0323879i
$592$	0.925435	−	6.01195i	0.0380351	−	0.247090i
$593$	−5.00469	+	5.00469i	−0.205518	+	0.205518i	−0.802359	−	0.596841i	$-0.796422\pi$
$593$	−5.00469	+	5.00469i	−0.205518	+	0.205518i	0.596841	+	0.802359i	$0.296422\pi$
$594$	−1.16466	−	1.16466i	−0.0477867	−	0.0477867i
$595$	2.14670	−	2.18967i	0.0880061	−	0.0897675i
$596$		−	8.60756i		−	0.352579i
$597$			11.1887i			0.457922i
$598$	−12.3528			−0.505144
$599$			35.1064i			1.43441i	0.696863	+	0.717204i	$0.254579\pi$
$599$			35.1064i			1.43441i	−0.696863	+	0.717204i	$0.745421\pi$
$600$	3.60489	+	3.46478i	0.147169	+	0.141449i
$601$	−28.3290			−1.15556			−0.577782	−	0.816191i	$-0.696082\pi$
$601$	−28.3290			−1.15556			−0.577782	+	0.816191i	$0.696082\pi$
$602$	0.359210	+	0.359210i	0.0146403	+	0.0146403i
$603$	−0.492575	−	0.492575i	−0.0200592	−	0.0200592i
$604$		−	2.73615i		−	0.111332i
$605$	18.5297	−	0.183596i	0.753338	−	0.00746425i
$606$	−4.27436	+	4.27436i	−0.173634	+	0.173634i
$607$	−2.58147			−0.104779			−0.0523894	−	0.998627i	$-0.516684\pi$
$607$	−2.58147			−0.104779			−0.0523894	+	0.998627i	$0.516684\pi$
$608$	1.85024	−	1.85024i	0.0750373	−	0.0750373i
$609$	−1.06346	+	1.06346i	−0.0430935	+	0.0430935i
$610$	0.320439	−	0.326852i	0.0129742	−	0.0132339i
$611$	−2.37676	−	2.37676i	−0.0961535	−	0.0961535i
$612$	−3.44561			−0.139281
$613$	7.76986	+	7.76986i	0.313822	+	0.313822i	0.846388	−	0.532566i	$-0.178772\pi$
$613$	7.76986	+	7.76986i	0.313822	+	0.313822i	−0.532566	+	0.846388i	$0.678772\pi$
$614$	19.3837	−	19.3837i	0.782263	−	0.782263i
$615$	13.6510	−	13.9242i	0.550462	−	0.561479i
$616$	−0.463534	+	0.463534i	−0.0186763	+	0.0186763i
$617$	−19.3110	+	19.3110i	−0.777430	+	0.777430i	−0.979393	−	0.201963i	$-0.935268\pi$
$617$	−19.3110	+	19.3110i	−0.777430	+	0.777430i	0.201963	+	0.979393i	$0.435268\pi$
$618$	7.95943	−	7.95943i	0.320175	−	0.320175i
$619$	22.9273			0.921528			0.460764	−	0.887523i	$-0.347575\pi$
$619$	22.9273			0.921528			0.460764	+	0.887523i	$0.347575\pi$
$620$	−14.9932	+	15.2933i	−0.602140	+	0.614192i
$621$	2.76666	−	2.76666i	0.111022	−	0.111022i
$622$	9.43851	−	9.43851i	0.378450	−	0.378450i
$623$		−	7.08249i		−	0.283754i
$624$	−2.23244	−	2.23244i	−0.0893690	−	0.0893690i
$625$	24.9804	−	0.990532i	0.999215	−	0.0396213i
$626$	20.7779			0.830451
$627$			4.30982i			0.172118i
$628$	−4.40198	−	4.40198i	−0.175658	−	0.175658i
$629$	20.7149	+	3.18869i	0.825955	+	0.127141i
$630$	−0.623024	+	0.635494i	−0.0248219	+	0.0253187i
$631$	−18.8706	+	18.8706i	−0.751225	+	0.751225i	−0.974708	−	0.223483i	$-0.928257\pi$
$631$	−18.8706	+	18.8706i	−0.751225	+	0.751225i	0.223483	+	0.974708i	$0.428257\pi$
$632$	−2.86326	+	2.86326i	−0.113894	+	0.113894i
$633$	0.940014	+	0.940014i	0.0373622	+	0.0373622i
$634$	3.25873	−	3.25873i	0.129421	−	0.129421i
$635$	14.3859	+	14.1036i	0.570886	+	0.559684i
$636$	−5.49790			−0.218006
$637$		−	21.5999i		−	0.855819i
$638$	4.40103	−	4.40103i	0.174238	−	0.174238i
$639$			11.2201i			0.443860i
$640$	−2.23596	+	0.0221544i	−0.0883840	+	0.000875730i
$641$	6.78574			0.268021			0.134010	−	0.990980i	$-0.457214\pi$
$641$	6.78574			0.268021			0.134010	+	0.990980i	$0.457214\pi$
$642$			12.5718i			0.496169i
$643$		−	36.8670i		−	1.45389i	−0.686695	−	0.726945i	$-0.740939\pi$
$643$		−	36.8670i		−	1.45389i	0.686695	−	0.726945i	$-0.259061\pi$
$644$	−1.10113	−	1.10113i	−0.0433905	−	0.0433905i
$645$	−2.03804	−	1.99805i	−0.0802479	−	0.0786732i
$646$	6.37522	+	6.37522i	0.250830	+	0.250830i
$647$	−19.1501			−0.752868			−0.376434	−	0.926443i	$-0.622850\pi$
$647$	−19.1501			−0.752868			−0.376434	+	0.926443i	$0.622850\pi$
$648$	1.00000			0.0392837
$649$	−10.7685	−	10.7685i	−0.422701	−	0.422701i
$650$	−15.7826	+	0.312786i	−0.619045	+	0.0122685i
$651$	−2.69548	−	2.69548i	−0.105644	−	0.105644i
$652$		−	10.2487i		−	0.401370i
$653$			19.8305i			0.776029i	0.921653	+	0.388015i	$0.126839\pi$
$653$			19.8305i			0.776029i	−0.921653	+	0.388015i	$0.873161\pi$
$654$	12.6491			0.494618
$655$	−5.50249	+	5.61263i	−0.215000	+	0.219303i
$656$			8.72049i			0.340478i
$657$	−0.804916	+	0.804916i	−0.0314028	+	0.0314028i
$658$		−	0.423728i		−	0.0165187i
$659$	21.4129			0.834127			0.417064	−	0.908877i	$-0.363059\pi$
$659$	21.4129			0.834127			0.417064	+	0.908877i	$0.363059\pi$
$660$	2.57834	−	2.62994i	0.100362	−	0.102370i
$661$	34.3523	−	34.3523i	1.33615	−	1.33615i	0.436397	−	0.899754i	$-0.356254\pi$
$661$	34.3523	−	34.3523i	1.33615	−	1.33615i	0.899754	−	0.436397i	$-0.143746\pi$
$662$	−2.00568	−	2.00568i	−0.0779530	−	0.0779530i
$663$	7.69211	−	7.69211i	0.298737	−	0.298737i
$664$	−3.45461	+	3.45461i	−0.134065	+	0.134065i
$665$	2.32857	−	0.0230720i	0.0902979	−	0.000894693i
$666$	−6.01195	−	0.925435i	−0.232958	−	0.0358599i
$667$	10.4547	+	10.4547i	0.404806	+	0.404806i
$668$		−	2.97278i		−	0.115020i
$669$	4.34342			0.167926
$670$	1.09047	−	1.11229i	0.0421284	−	0.0429715i
$671$	−0.238408	−	0.238408i	−0.00920365	−	0.00920365i
$672$		−	0.397998i		−	0.0153531i
$673$	−19.4561	+	19.4561i	−0.749979	+	0.749979i	−0.974475	−	0.224496i	$-0.927926\pi$
$673$	−19.4561	+	19.4561i	−0.749979	+	0.749979i	0.224496	+	0.974475i	$0.427926\pi$
$674$	−8.49643	+	8.49643i	−0.327270	+	0.327270i
$675$	3.46478	−	3.60489i	0.133360	−	0.138752i
$676$	−3.03245			−0.116633
$677$	4.71937	−	4.71937i	0.181380	−	0.181380i	−0.610577	−	0.791957i	$-0.709062\pi$
$677$	4.71937	−	4.71937i	0.181380	−	0.181380i	0.791957	+	0.610577i	$0.209062\pi$
$678$	−0.139124	+	0.139124i	−0.00534303	+	0.00534303i
$679$	−1.94958	+	1.94958i	−0.0748178	+	0.0748178i
$680$	−0.0763355	−	7.70424i	−0.00292733	−	0.295444i
$681$	17.4366	−	17.4366i	0.668173	−	0.668173i
$682$	11.1550	+	11.1550i	0.427147	+	0.427147i
$683$	23.5379			0.900653			0.450327	−	0.892864i	$-0.351308\pi$
$683$	23.5379			0.900653			0.450327	+	0.892864i	$0.351308\pi$
$684$	−1.85024	−	1.85024i	−0.0707458	−	0.0707458i
$685$	34.7446	+	34.0629i	1.32752	+	1.30148i
$686$	3.89540	−	3.89540i	0.148727	−	0.148727i
$687$	10.5226	−	10.5226i	0.401462	−	0.401462i
$688$	1.27639			0.0486618
$689$	12.2737	−	12.2737i	0.467591	−	0.467591i
$690$	6.24744	+	6.12485i	0.237836	+	0.233169i
$691$		−	8.31048i		−	0.316145i	−0.987427	−	0.158073i	$-0.949472\pi$
$691$		−	8.31048i		−	0.316145i	0.987427	−	0.158073i	$-0.0505280\pi$
$692$	−5.83257	−	5.83257i	−0.221721	−	0.221721i
$693$	0.463534	+	0.463534i	0.0176082	+	0.0176082i
$694$	0.455842			0.0173035
$695$	−6.70531	+	0.0664378i	−0.254347	+	0.00252013i
$696$			3.77880i			0.143235i
$697$	−30.0474			−1.13813
$698$			18.0258i			0.682287i
$699$			20.7657i			0.785431i
$700$	−1.43474	−	1.37898i	−0.0542281	−	0.0521205i
$701$	26.9263	+	26.9263i	1.01699	+	1.01699i	0.999853	+	0.0171385i	$0.00545561\pi$
$701$	26.9263	+	26.9263i	1.01699	+	1.01699i	0.0171385	+	0.999853i	$0.494544\pi$
$702$	−2.23244	+	2.23244i	−0.0842579	+	0.0842579i
$703$	9.41129	+	12.8359i	0.354954	+	0.484113i
$704$			1.64708i			0.0620767i
$705$	0.0235867	+	2.38051i	0.000888326	+	0.0896553i
$706$			16.2235i			0.610579i
$707$	1.70119	−	1.70119i	0.0639797	−	0.0639797i
$708$	9.24603			0.347487
$709$	17.6567	−	17.6567i	0.663111	−	0.663111i	−0.293001	−	0.956112i	$-0.594654\pi$
$709$	17.6567	−	17.6567i	0.663111	−	0.663111i	0.956112	+	0.293001i	$0.0946539\pi$
$710$	−25.0876	+	0.248574i	−0.941522	+	0.00932883i
$711$	2.86326	+	2.86326i	0.107381	+	0.107381i
$712$	−12.5832	−	12.5832i	−0.471574	−	0.471574i
$713$	−26.4988	+	26.4988i	−0.992387	+	0.992387i
$714$	1.37135			0.0513214
$715$	0.115205	+	11.6271i	0.00430840	+	0.434831i
$716$	−4.52269	−	4.52269i	−0.169021	−	0.169021i
$717$	16.8289			0.628486
$718$			19.2940i			0.720046i
$719$		−	7.51201i		−	0.280151i	−0.990141	−	0.140075i	$-0.955266\pi$
$719$		−	7.51201i		−	0.280151i	0.990141	−	0.140075i	$-0.0447345\pi$
$720$	0.0221544	+	2.23596i	0.000825646	+	0.0833292i
$721$	−3.16784	+	3.16784i	−0.117976	+	0.117976i
$722$		−	12.1532i		−	0.452295i
$723$		−	22.1544i		−	0.823930i
$724$	−16.8840			−0.627487
$725$	13.6222	+	13.0927i	0.505915	+	0.486252i
$726$	5.85988	+	5.85988i	0.217481	+	0.217481i
$727$	−44.5433			−1.65202			−0.826010	−	0.563655i	$-0.809395\pi$
$727$	−44.5433			−1.65202			−0.826010	+	0.563655i	$0.809395\pi$
$728$	0.888506	+	0.888506i	0.0329302	+	0.0329302i
$729$		−	1.00000i		−	0.0370370i
$730$	−1.81759	−	1.78193i	−0.0672720	−	0.0659520i
$731$			4.39794i			0.162664i
$732$	0.204701			0.00756598
$733$	−21.8867	−	21.8867i	−0.808404	−	0.808404i	0.175988	−	0.984392i	$-0.443688\pi$
$733$	−21.8867	−	21.8867i	−0.808404	−	0.808404i	−0.984392	+	0.175988i	$0.943688\pi$
$734$	3.21053	+	3.21053i	0.118503	+	0.118503i
$735$	−10.7098	+	10.9242i	−0.395037	+	0.402944i
$736$	−3.91265			−0.144222
$737$	−0.811312	−	0.811312i	−0.0298851	−	0.0298851i
$738$	8.72049			0.321006
$739$	−4.64271			−0.170785			−0.0853925	−	0.996347i	$-0.527214\pi$
$739$	−4.64271			−0.170785			−0.0853925	+	0.996347i	$0.527214\pi$
$740$	1.93604	−	13.4630i	0.0711703	−	0.494909i
$741$	8.26110			0.303479
$742$	2.18815			0.0803296
$743$	−38.1619	−	38.1619i	−1.40003	−	1.40003i	−0.799921	−	0.600105i	$-0.795126\pi$
$743$	−38.1619	−	38.1619i	−1.40003	−	1.40003i	−0.600105	−	0.799921i	$-0.704874\pi$
$744$	−9.57788			−0.351142
$745$	−0.190695	−	19.2461i	−0.00698653	−	0.705124i
$746$	2.94440	+	2.94440i	0.107802	+	0.107802i
$747$	3.45461	+	3.45461i	0.126397	+	0.126397i
$748$	−5.67521			−0.207506
$749$		−	5.00355i		−	0.182826i
$750$	8.13715	+	7.66725i	0.297127	+	0.279968i
$751$		−	36.4153i		−	1.32881i	−0.747371	−	0.664406i	$-0.768684\pi$
$751$		−	36.4153i		−	1.32881i	0.747371	−	0.664406i	$-0.231316\pi$
$752$	−0.752821	−	0.752821i	−0.0274526	−	0.0274526i
$753$	−11.7059			−0.426588
$754$	−8.43593	−	8.43593i	−0.307219	−	0.307219i
$755$	−0.0606177	−	6.11791i	−0.00220610	−	0.222654i
$756$	−0.397998			−0.0144750
$757$			17.1425i			0.623054i	0.950237	+	0.311527i	$0.100840\pi$
$757$			17.1425i			0.623054i	−0.950237	+	0.311527i	$0.899160\pi$
$758$			25.1637i			0.913989i
$759$	4.55692	−	4.55692i	0.165406	−	0.165406i
$760$	4.09608	−	4.17806i	0.148580	−	0.151554i
$761$		−	35.6476i		−	1.29222i	−0.763243	−	0.646112i	$-0.776394\pi$
$761$		−	35.6476i		−	1.29222i	0.763243	−	0.646112i	$-0.223606\pi$
$762$			9.00960i			0.326384i
$763$	−5.03431			−0.182254
$764$	−18.5005	−	18.5005i	−0.669323	−	0.669323i
$765$	−7.70424	+	0.0763355i	−0.278548	+	0.00275991i
$766$	0.995617			0.0359731
$767$	−20.6412	+	20.6412i	−0.745310	+	0.745310i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	12.7710	+	12.7710i	0.460533	+	0.460533i	0.898830	−	0.438297i	$-0.144418\pi$
$769$	12.7710	+	12.7710i	0.460533	+	0.460533i	−0.438297	+	0.898830i	$0.644418\pi$
$770$	−1.02617	+	1.04671i	−0.0369807	+	0.0377208i
$771$	2.99965	−	2.99965i	0.108030	−	0.108030i
$772$	−17.1049			−0.615620
$773$	11.0549	−	11.0549i	0.397617	−	0.397617i	−0.479775	−	0.877392i	$-0.659282\pi$
$773$	11.0549	−	11.0549i	0.397617	−	0.397617i	0.877392	+	0.479775i	$0.159282\pi$
$774$		−	1.27639i		−	0.0458788i
$775$	−33.1853	+	34.5273i	−1.19205	+	1.24026i
$776$			6.92746i			0.248681i
$777$	2.39275	+	0.368321i	0.0858393	+	0.0132135i
$778$	19.4231	−	19.4231i	0.696350	−	0.696350i
$779$	−16.1350	−	16.1350i	−0.578097	−	0.578097i
$780$	−5.04109	−	4.94218i	−0.180500	−	0.176958i
$781$			18.4804i			0.661281i
$782$		−	13.4815i		−	0.482097i
$783$	3.77880			0.135043
$784$		−	6.84160i		−	0.244343i
$785$	−9.94017	−	9.74513i	−0.354780	−	0.347819i
$786$	−3.51508			−0.125379
$787$	13.1009	+	13.1009i	0.466997	+	0.466997i	0.900940	−	0.433944i	$-0.142878\pi$
$787$	13.1009	+	13.1009i	0.466997	+	0.466997i	−0.433944	+	0.900940i	$0.642878\pi$
$788$	−0.556751	−	0.556751i	−0.0198334	−	0.0198334i
$789$			31.6809i			1.12787i
$790$	−6.33870	+	6.46557i	−0.225521	+	0.230035i
$791$	0.0553711	−	0.0553711i	0.00196877	−	0.00196877i
$792$	1.64708			0.0585265
$793$	−0.456983	+	0.456983i	−0.0162279	+	0.0162279i
$794$	−6.49757	+	6.49757i	−0.230590	+	0.230590i
$795$	−12.2931	+	0.121803i	−0.435990	+	0.00431989i
$796$	−7.91159	−	7.91159i	−0.280419	−	0.280419i
$797$	19.8808			0.704216			0.352108	−	0.935959i	$-0.385465\pi$
$797$	19.8808			0.704216			0.352108	+	0.935959i	$0.385465\pi$
$798$	0.736393	+	0.736393i	0.0260680	+	0.0260680i
$799$	2.59393	−	2.59393i	0.0917666	−	0.0917666i
$800$	−4.99902	+	0.0990726i	−0.176742	+	0.00350275i
$801$	−12.5832	+	12.5832i	−0.444605	+	0.444605i
$802$	24.2700	−	24.2700i	0.857005	−	0.857005i
$803$	−1.32576	+	1.32576i	−0.0467851	+	0.0467851i
$804$	0.696607			0.0245674
$805$	−2.48647	−	2.43768i	−0.0876365	−	0.0859169i
$806$	21.3820	−	21.3820i	0.753149	−	0.753149i
$807$	−10.7938	+	10.7938i	−0.379959	+	0.379959i
$808$		−	6.04485i		−	0.212657i
$809$	−9.85033	−	9.85033i	−0.346319	−	0.346319i	0.512417	−	0.858737i	$-0.328750\pi$
$809$	−9.85033	−	9.85033i	−0.346319	−	0.346319i	−0.858737	+	0.512417i	$0.828750\pi$
$810$	2.23596	−	0.0221544i	0.0785636	−	0.000778426i
$811$	33.2668			1.16815			0.584077	−	0.811698i	$-0.301456\pi$
$811$	33.2668			1.16815			0.584077	+	0.811698i	$0.301456\pi$
$812$		−	1.50396i		−	0.0527785i
$813$	−10.4630	−	10.4630i	−0.366953	−	0.366953i
$814$	−9.90218	−	1.52427i	−0.347071	−	0.0534255i
$815$	−0.227054	−	22.9156i	−0.00795334	−	0.802700i
$816$	2.43642	−	2.43642i	0.0852916	−	0.0852916i
$817$	−2.36163	+	2.36163i	−0.0826229	+	0.0826229i
$818$	−24.0003	−	24.0003i	−0.839152	−	0.839152i
$819$	0.888506	−	0.888506i	0.0310469	−	0.0310469i
$820$	0.193197	+	19.4986i	0.00674674	+	0.680922i
$821$	−14.4484			−0.504251			−0.252126	−	0.967694i	$-0.581130\pi$
$821$	−14.4484			−0.504251			−0.252126	+	0.967694i	$0.581130\pi$
$822$			21.7599i			0.758964i
$823$	8.70320	−	8.70320i	0.303375	−	0.303375i	−0.538958	−	0.842333i	$-0.681182\pi$
$823$	8.70320	−	8.70320i	0.303375	−	0.303375i	0.842333	+	0.538958i	$0.181182\pi$
$824$			11.2563i			0.392133i
$825$	5.70679	−	5.93756i	0.198685	−	0.206719i
$826$	−3.67990			−0.128040
$827$		−	30.1185i		−	1.04732i	−0.851927	−	0.523661i	$-0.824566\pi$
$827$		−	30.1185i		−	1.04732i	0.851927	−	0.523661i	$-0.175434\pi$
$828$			3.91265i			0.135974i
$829$	23.9359	+	23.9359i	0.831329	+	0.831329i	0.987699	−	0.156370i	$-0.0499791\pi$
$829$	23.9359	+	23.9359i	0.831329	+	0.831329i	−0.156370	+	0.987699i	$0.549979\pi$
$830$	−7.64782	+	7.80089i	−0.265460	+	0.270773i
$831$	−2.12404	−	2.12404i	−0.0736823	−	0.0736823i
$832$	3.15714			0.109454
$833$	23.5735			0.816773
$834$	−2.12051	−	2.12051i	−0.0734272	−	0.0734272i
$835$	−0.0658601	−	6.64701i	−0.00227918	−	0.230029i
$836$	−3.04750	−	3.04750i	−0.105400	−	0.105400i
$837$			9.57788i			0.331060i
$838$			32.2473i			1.11396i
$839$	−24.1682			−0.834380			−0.417190	−	0.908819i	$-0.636985\pi$
$839$	−24.1682			−0.834380			−0.417190	+	0.908819i	$0.636985\pi$
$840$	−0.00881741	−	0.889907i	−0.000304229	−	0.0307047i
$841$		−	14.7207i		−	0.507609i
$842$	3.85720	−	3.85720i	0.132928	−	0.132928i
$843$			11.8189i			0.407065i
$844$	−1.32938			−0.0457592
$845$	−6.78043	+	0.0671821i	−0.233254	+	0.00231114i
$846$	−0.752821	+	0.752821i	−0.0258825	+	0.0258825i
$847$	−2.33222	−	2.33222i	−0.0801360	−	0.0801360i
$848$	3.88760	−	3.88760i	0.133501	−	0.133501i
$849$	−2.73615	+	2.73615i	−0.0939043	+	0.0939043i
$850$	−0.341366	−	17.2247i	−0.0117087	−	0.590801i
$851$	3.62091	−	23.5227i	0.124123	−	0.806347i
$852$	−7.93380	−	7.93380i	−0.271807	−	0.271807i
$853$			40.9694i			1.40276i	0.712785	+	0.701382i	$0.247433\pi$
$853$			40.9694i			1.40276i	−0.712785	+	0.701382i	$0.752567\pi$
$854$	−0.0814708			−0.00278787
$855$	−4.17806	−	4.09608i	−0.142887	−	0.140083i
$856$	−8.88960	−	8.88960i	−0.303840	−	0.303840i
$857$			10.8481i			0.370563i	0.982686	+	0.185281i	$0.0593197\pi$
$857$			10.8481i			0.370563i	−0.982686	+	0.185281i	$0.940680\pi$
$858$	−3.67701	+	3.67701i	−0.125531	+	0.125531i
$859$	−11.6985	+	11.6985i	−0.399147	+	0.399147i	−0.877932	−	0.478785i	$-0.841077\pi$
$859$	−11.6985	+	11.6985i	−0.399147	+	0.399147i	0.478785	+	0.877932i	$0.341077\pi$
$860$	2.85395	−	0.0282776i	0.0973189	−	0.000964258i
$861$	−3.47074			−0.118282
$862$	15.1362	−	15.1362i	0.515542	−	0.515542i
$863$	36.8955	−	36.8955i	1.25594	−	1.25594i	0.302924	−	0.953015i	$-0.402037\pi$
$863$	36.8955	−	36.8955i	1.25594	−	1.25594i	0.953015	−	0.302924i	$-0.0979629\pi$
$864$	−0.707107	+	0.707107i	−0.0240563	+	0.0240563i
$865$	−13.1706	−	12.9122i	−0.447814	−	0.439027i
$866$	27.7575	−	27.7575i	0.943239	−	0.943239i
$867$	−3.62588	−	3.62588i	−0.123141	−	0.123141i
$868$	3.81198			0.129387
$869$	4.71603	+	4.71603i	0.159980	+	0.159980i
$870$	0.0837171	+	8.44924i	0.00283827	+	0.286456i
$871$	−1.55513	+	1.55513i	−0.0526936	+	0.0526936i
$872$	−8.94425	+	8.94425i	−0.302891	+	0.302891i
$873$	6.92746			0.234459
$874$	7.23936	−	7.23936i	0.244875	−	0.244875i
$875$	−3.23857	−	3.05155i	−0.109484	−	0.103161i
$876$		−	1.13832i		−	0.0384604i
$877$	−25.8706	−	25.8706i	−0.873589	−	0.873589i	0.119273	−	0.992862i	$-0.461944\pi$
$877$	−25.8706	−	25.8706i	−0.873589	−	0.873589i	−0.992862	+	0.119273i	$0.961944\pi$
$878$	−17.1813	−	17.1813i	−0.579841	−	0.579841i
$879$	−15.2060			−0.512887
$880$	0.0364901	+	3.68281i	0.00123008	+	0.124147i
$881$			4.62987i			0.155984i	0.996954	+	0.0779921i	$0.0248509\pi$
$881$			4.62987i			0.155984i	−0.996954	+	0.0779921i	$0.975149\pi$
$882$	−6.84160			−0.230369
$883$			14.3060i			0.481435i	0.970595	+	0.240718i	$0.0773828\pi$
$883$			14.3060i			0.481435i	−0.970595	+	0.240718i	$0.922617\pi$
$884$			10.8783i			0.365876i
$885$	20.6737	−	0.204840i	0.694940	−	0.00688563i
$886$	7.22878	+	7.22878i	0.242855	+	0.242855i
$887$	−14.1138	+	14.1138i	−0.473896	+	0.473896i	−0.903173	−	0.429277i	$-0.858769\pi$
$887$	−14.1138	+	14.1138i	−0.473896	+	0.473896i	0.429277	+	0.903173i	$0.358769\pi$
$888$	4.90547	−	3.59671i	0.164617	−	0.120698i
$889$		−	3.58581i		−	0.120264i
$890$	−28.4142	−	27.8567i	−0.952447	−	0.933758i
$891$		−	1.64708i		−	0.0551793i
$892$	−3.07126	+	3.07126i	−0.102834	+	0.102834i
$893$	2.78580			0.0932234
$894$	6.08646	−	6.08646i	0.203562	−	0.203562i
$895$	−10.2127	−	10.0123i	−0.341374	−	0.334676i
$896$	0.281427	+	0.281427i	0.00940182	+	0.00940182i
$897$	−8.73475	−	8.73475i	−0.291645	−	0.291645i
$898$	−9.76421	+	9.76421i	−0.325836	+	0.325836i
$899$	−36.1929			−1.20710
$900$	0.0990726	+	4.99902i	0.00330242	+	0.166634i
$901$	13.3952	+	13.3952i	0.446257	+	0.446257i
$902$	14.3634			0.478248
$903$			0.508000i			0.0169052i
$904$		−	0.196751i		−	0.00654385i
$905$	−37.7518	+	0.374054i	−1.25491	+	0.0124340i
$906$	1.93475	−	1.93475i	0.0642777	−	0.0642777i
$907$		−	6.36519i		−	0.211353i	−0.994401	−	0.105676i	$-0.966299\pi$
$907$		−	6.36519i		−	0.211353i	0.994401	−	0.105676i	$-0.0337007\pi$
$908$			24.6591i			0.818342i
$909$	−6.04485			−0.200495
$910$	2.00635	+	1.96698i	0.0665097	+	0.0652047i
$911$	−17.2930	−	17.2930i	−0.572944	−	0.572944i	0.360006	−	0.932950i	$-0.382775\pi$
$911$	−17.2930	−	17.2930i	−0.572944	−	0.572944i	−0.932950	+	0.360006i	$0.882775\pi$
$912$	2.61664			0.0866456
$913$	5.69002	+	5.69002i	0.188312	+	0.188312i
$914$			20.5176i			0.678661i
$915$	0.457704	−	0.00453504i	0.0151312	−	0.000149924i
$916$			14.8812i			0.491689i
$917$	1.39900			0.0461989
$918$	−2.43642	−	2.43642i	−0.0804137	−	0.0804137i
$919$	22.2107	+	22.2107i	0.732663	+	0.732663i	0.971146	−	0.238484i	$-0.0766504\pi$
$919$	22.2107	+	22.2107i	0.732663	+	0.732663i	−0.238484	+	0.971146i	$0.576650\pi$
$920$	−8.74853	+	0.0866825i	−0.288430	+	0.00285784i
$921$	27.4127			0.903279
$922$	−21.6195	−	21.6195i	−0.712002	−	0.712002i
$923$	35.4234			1.16598
$924$	−0.655535			−0.0215655
$925$	4.03065	−	30.1455i	0.132527	−	0.991179i
$926$	−1.38040			−0.0453628
$927$	11.2563			0.369707
$928$	−2.67202	−	2.67202i	−0.0877132	−	0.0877132i
$929$	1.85414			0.0608325			0.0304162	−	0.999537i	$-0.490317\pi$
$929$	1.85414			0.0608325			0.0304162	+	0.999537i	$0.490317\pi$
$930$	−21.4157	+	0.212192i	−0.702250	+	0.00695806i
$931$	12.6586	+	12.6586i	0.414869	+	0.414869i
$932$	−14.6836	−	14.6836i	−0.480976	−	0.480976i
$933$	13.3481			0.436996
$934$		−	0.453871i		−	0.0148511i
$935$	−12.6895	+	0.125731i	−0.414992	+	0.00411184i
$936$		−	3.15714i		−	0.103194i
$937$	−20.7476	−	20.7476i	−0.677795	−	0.677795i	0.281706	−	0.959501i	$-0.409100\pi$
$937$	−20.7476	−	20.7476i	−0.677795	−	0.677795i	−0.959501	+	0.281706i	$0.909100\pi$
$938$	−0.277248			−0.00905247
$939$	14.6922	+	14.6922i	0.479461	+	0.479461i
$940$	−1.69995	−	1.66660i	−0.0554464	−	0.0543584i
$941$	18.4162			0.600352			0.300176	−	0.953884i	$-0.402955\pi$
$941$	18.4162			0.600352			0.300176	+	0.953884i	$0.402955\pi$
$942$		−	6.22534i		−	0.202833i
$943$			34.1202i			1.11111i
$944$	−6.53793	+	6.53793i	−0.212792	+	0.212792i
$945$	−0.889907	+	0.00881741i	−0.0289487	+	0.000286830i
$946$		−	2.10232i		−	0.0683522i
$947$			35.4933i			1.15338i	0.816964	+	0.576689i	$0.195656\pi$
$947$			35.4933i			1.15338i	−0.816964	+	0.576689i	$0.804344\pi$
$948$	−4.04926			−0.131514
$949$	2.54123	+	2.54123i	0.0824920	+	0.0824920i
$950$	9.06609	−	9.43271i	0.294143	−	0.306037i
$951$	4.60854			0.149442
$952$	−0.969688	+	0.969688i	−0.0314278	+	0.0314278i
$953$	23.7817	+	23.7817i	0.770365	+	0.770365i	0.978170	−	0.207806i	$-0.0666321\pi$
$953$	23.7817	+	23.7817i	0.770365	+	0.770365i	−0.207806	+	0.978170i	$0.566632\pi$
$954$	−3.88760	−	3.88760i	−0.125866	−	0.125866i
$955$	−41.7761	−	40.9564i	−1.35184	−	1.32532i
$956$	−11.8998	+	11.8998i	−0.384868	+	0.384868i
$957$	6.22400			0.201193
$958$	−10.7493	+	10.7493i	−0.347293	+	0.347293i
$959$		−	8.66041i		−	0.279659i
$960$	−1.59673	−	1.56540i	−0.0515341	−	0.0505229i
$961$		−	60.7358i		−	1.95922i
$962$	−2.92173	+	18.9806i	−0.0942004	+	0.611959i
$963$	−8.88960	+	8.88960i	−0.286463	+	0.286463i
$964$	15.6655	+	15.6655i	0.504552	+	0.504552i
$965$	−38.2459	+	0.378950i	−1.23118	+	0.0121988i
$966$		−	1.55723i		−	0.0501030i
$967$		−	23.3872i		−	0.752080i	−0.926603	−	0.376040i	$-0.877285\pi$
$967$		−	23.3872i		−	0.752080i	0.926603	−	0.376040i	$-0.122715\pi$
$968$	−8.28712			−0.266358
$969$			9.01592i			0.289633i
$970$	0.153474	+	15.4895i	0.00492774	+	0.497338i
$971$	−10.8563			−0.348395			−0.174198	−	0.984711i	$-0.555733\pi$
$971$	−10.8563			−0.348395			−0.174198	+	0.984711i	$0.555733\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	0.843958	+	0.843958i	0.0270561	+	0.0270561i
$974$		−	13.2268i		−	0.423815i
$975$	−11.3812	−	10.9388i	−0.364489	−	0.350323i
$976$	−0.144746	+	0.144746i	−0.00463320	+	0.00463320i
$977$	−60.9677			−1.95053			−0.975264	−	0.221043i	$-0.929054\pi$
$977$	−60.9677			−1.95053			−0.975264	+	0.221043i	$0.929054\pi$
$978$	7.24692	−	7.24692i	0.231731	−	0.231731i
$979$	−20.7255	+	20.7255i	−0.662390	+	0.662390i
$980$	−0.151571	−	15.2975i	−0.00484177	−	0.488662i
$981$	8.94425	+	8.94425i	0.285568	+	0.285568i
$982$	30.4522			0.971770
$983$	−25.7832	−	25.7832i	−0.822357	−	0.822357i	0.164088	−	0.986446i	$-0.447532\pi$
$983$	−25.7832	−	25.7832i	−0.822357	−	0.822357i	−0.986446	+	0.164088i	$0.947532\pi$
$984$	−6.16632	+	6.16632i	−0.196575	+	0.196575i
$985$	−1.25721	−	1.23254i	−0.0400579	−	0.0392719i
$986$	9.20673	−	9.20673i	0.293202	−	0.293202i
$987$	0.299621	−	0.299621i	0.00953705	−	0.00953705i
$988$	−5.84148	+	5.84148i	−0.185842	+	0.185842i
$989$	4.99406			0.158802
$990$	3.68281	−	0.0364901i	0.117047	−	0.00115973i
$991$	6.60187	−	6.60187i	0.209715	−	0.209715i	−0.594431	−	0.804147i	$-0.702623\pi$
$991$	6.60187	−	6.60187i	0.209715	−	0.209715i	0.804147	+	0.594431i	$0.202623\pi$
$992$	6.77259	−	6.77259i	0.215030	−	0.215030i
$993$		−	2.83646i		−	0.0900124i
$994$	3.15764	+	3.15764i	0.100154	+	0.100154i
$995$	−17.8653	−	17.5147i	−0.566367	−	0.555254i
$996$	−4.88555			−0.154805
$997$		−	24.6196i		−	0.779711i	−0.920876	−	0.389856i	$-0.872525\pi$
$997$		−	24.6196i		−	0.779711i	0.920876	−	0.389856i	$-0.127475\pi$
$998$	6.74452	+	6.74452i	0.213494	+	0.213494i
$999$	−3.59671	−	4.90547i	−0.113795	−	0.155202i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.o.a.487.8	yes	36
5.3	odd	4		1110.2.l.a.43.11	✓	36
37.31	odd	4		1110.2.l.a.697.11	yes	36
185.68	even	4	inner	1110.2.o.a.253.8	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.11	✓	36	5.3	odd	4
1110.2.l.a.697.11	yes	36	37.31	odd	4
1110.2.o.a.253.8	yes	36	185.68	even	4	inner
1110.2.o.a.487.8	yes	36	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(2.23596 - 0.0221544i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-0.281427 - 0.281427i) q^{7} -1.00000 q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(2.23596 - 0.0221544i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-0.281427 - 0.281427i) q^{7} -1.00000 q^{8} +1.00000i q^{9} +(-2.23596 + 0.0221544i) q^{10} +1.64708i q^{11} +(-0.707107 - 0.707107i) q^{12} +3.15714 q^{13} +(0.281427 + 0.281427i) q^{14} +(-1.59673 - 1.56540i) q^{15} +1.00000 q^{16} +3.44561i q^{17} -1.00000i q^{18} +(-1.85024 + 1.85024i) q^{19} +(2.23596 - 0.0221544i) q^{20} +0.397998i q^{21} -1.64708i q^{22} +3.91265 q^{23} +(0.707107 + 0.707107i) q^{24} +(4.99902 - 0.0990726i) q^{25} -3.15714 q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.281427 - 0.281427i) q^{28} +(2.67202 + 2.67202i) q^{29} +(1.59673 + 1.56540i) q^{30} +(-6.77259 + 6.77259i) q^{31} -1.00000 q^{32} +(1.16466 - 1.16466i) q^{33} -3.44561i q^{34} +(-0.635494 - 0.623024i) q^{35} +1.00000i q^{36} +(0.925435 - 6.01195i) q^{37} +(1.85024 - 1.85024i) q^{38} +(-2.23244 - 2.23244i) q^{39} +(-2.23596 + 0.0221544i) q^{40} +8.72049i q^{41} -0.397998i q^{42} +1.27639 q^{43} +1.64708i q^{44} +(0.0221544 + 2.23596i) q^{45} -3.91265 q^{46} +(-0.752821 - 0.752821i) q^{47} +(-0.707107 - 0.707107i) q^{48} -6.84160i q^{49} +(-4.99902 + 0.0990726i) q^{50} +(2.43642 - 2.43642i) q^{51} +3.15714 q^{52} +(3.88760 - 3.88760i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(0.0364901 + 3.68281i) q^{55} +(0.281427 + 0.281427i) q^{56} +2.61664 q^{57} +(-2.67202 - 2.67202i) q^{58} +(-6.53793 + 6.53793i) q^{59} +(-1.59673 - 1.56540i) q^{60} +(-0.144746 + 0.144746i) q^{61} +(6.77259 - 6.77259i) q^{62} +(0.281427 - 0.281427i) q^{63} +1.00000 q^{64} +(7.05924 - 0.0699446i) q^{65} +(-1.16466 + 1.16466i) q^{66} +(-0.492575 + 0.492575i) q^{67} +3.44561i q^{68} +(-2.76666 - 2.76666i) q^{69} +(0.635494 + 0.623024i) q^{70} +11.2201 q^{71} -1.00000i q^{72} +(0.804916 + 0.804916i) q^{73} +(-0.925435 + 6.01195i) q^{74} +(-3.60489 - 3.46478i) q^{75} +(-1.85024 + 1.85024i) q^{76} +(0.463534 - 0.463534i) q^{77} +(2.23244 + 2.23244i) q^{78} +(2.86326 - 2.86326i) q^{79} +(2.23596 - 0.0221544i) q^{80} -1.00000 q^{81} -8.72049i q^{82} +(3.45461 - 3.45461i) q^{83} +0.397998i q^{84} +(0.0763355 + 7.70424i) q^{85} -1.27639 q^{86} -3.77880i q^{87} -1.64708i q^{88} +(12.5832 + 12.5832i) q^{89} +(-0.0221544 - 2.23596i) q^{90} +(-0.888506 - 0.888506i) q^{91} +3.91265 q^{92} +9.57788 q^{93} +(0.752821 + 0.752821i) q^{94} +(-4.09608 + 4.17806i) q^{95} +(0.707107 + 0.707107i) q^{96} -6.92746i q^{97} +6.84160i q^{98} -1.64708 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8}+O(q^{10}) \) 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8	\( 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8} - 4 q^{10} - 8 q^{13} - 4 q^{14} + 36 q^{16} - 4 q^{19} + 4 q^{20} + 4 q^{25} + 8 q^{26} + 4 q^{28} - 36 q^{29} - 4 q^{31} - 36 q^{32} + 4 q^{33} + 28 q^{35} + 28 q^{37} + 4 q^{38} - 4 q^{39} - 4 q^{40} - 32 q^{43} + 16 q^{47} - 4 q^{50} - 8 q^{52} - 8 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 36 q^{58} + 4 q^{59} - 4 q^{61} + 4 q^{62} - 4 q^{63} + 36 q^{64} - 52 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} - 28 q^{70} - 8 q^{71} + 4 q^{73} - 28 q^{74} + 16 q^{75} - 4 q^{76} - 8 q^{77} + 4 q^{78} + 12 q^{79} + 4 q^{80} - 36 q^{81} + 8 q^{83} - 8 q^{85} + 32 q^{86} + 24 q^{89} + 56 q^{91} - 8 q^{93} - 16 q^{94} + 20 q^{95} + 8 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8 - 4 * q^10 - 8 * q^13 - 4 * q^14 + 36 * q^16 - 4 * q^19 + 4 * q^20 + 4 * q^25 + 8 * q^26 + 4 * q^28 - 36 * q^29 - 4 * q^31 - 36 * q^32 + 4 * q^33 + 28 * q^35 + 28 * q^37 + 4 * q^38 - 4 * q^39 - 4 * q^40 - 32 * q^43 + 16 * q^47 - 4 * q^50 - 8 * q^52 - 8 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 36 * q^58 + 4 * q^59 - 4 * q^61 + 4 * q^62 - 4 * q^63 + 36 * q^64 - 52 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 - 28 * q^70 - 8 * q^71 + 4 * q^73 - 28 * q^74 + 16 * q^75 - 4 * q^76 - 8 * q^77 + 4 * q^78 + 12 * q^79 + 4 * q^80 - 36 * q^81 + 8 * q^83 - 8 * q^85 + 32 * q^86 + 24 * q^89 + 56 * q^91 - 8 * q^93 - 16 * q^94 + 20 * q^95 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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