LMFDB - Embedded newform 690.3.k.b.553.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(277,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("690.277");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.k (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:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			553.3
Character	$\chi$	$=$	690.553
Dual form			690.3.k.b.277.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-2.46815 - 4.34836i) q^{5} +2.44949 q^{6} +(-1.62328 + 1.62328i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-2.46815 - 4.34836i) q^{5} +2.44949 q^{6} +(-1.62328 + 1.62328i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(6.81651 + 1.88022i) q^{10} +0.00768588 q^{11} +(-2.44949 + 2.44949i) q^{12} +(-7.99113 - 7.99113i) q^{13} -3.24656i q^{14} +(-2.30278 + 8.34848i) q^{15} -4.00000 q^{16} +(5.07503 - 5.07503i) q^{17} +(-3.00000 - 3.00000i) q^{18} -29.4268i q^{19} +(-8.69672 + 4.93629i) q^{20} +3.97621 q^{21} +(-0.00768588 + 0.00768588i) q^{22} +(3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(-12.8165 + 21.4648i) q^{25} +15.9823 q^{26} +(3.67423 - 3.67423i) q^{27} +(3.24656 + 3.24656i) q^{28} -24.1950i q^{29} +(-6.04570 - 10.6513i) q^{30} -27.9270 q^{31} +(4.00000 - 4.00000i) q^{32} +(-0.00941325 - 0.00941325i) q^{33} +10.1501i q^{34} +(11.0651 + 3.05212i) q^{35} +6.00000 q^{36} +(-17.5169 + 17.5169i) q^{37} +(29.4268 + 29.4268i) q^{38} +19.5742i q^{39} +(3.76043 - 13.6330i) q^{40} +9.62845 q^{41} +(-3.97621 + 3.97621i) q^{42} +(33.5256 + 33.5256i) q^{43} -0.0153718i q^{44} +(13.0451 - 7.40444i) q^{45} -6.78233 q^{46} +(-48.5429 + 48.5429i) q^{47} +(4.89898 + 4.89898i) q^{48} +43.7299i q^{49} +(-8.64828 - 34.2813i) q^{50} -12.4312 q^{51} +(-15.9823 + 15.9823i) q^{52} +(41.9368 + 41.9368i) q^{53} +7.34847i q^{54} +(-0.0189699 - 0.0334210i) q^{55} -6.49313 q^{56} +(-36.0403 + 36.0403i) q^{57} +(24.1950 + 24.1950i) q^{58} +85.5954i q^{59} +(16.6970 + 4.60557i) q^{60} -10.2155 q^{61} +(27.9270 - 27.9270i) q^{62} +(-4.86985 - 4.86985i) q^{63} +8.00000i q^{64} +(-15.0251 + 54.4716i) q^{65} +0.0188265 q^{66} +(-80.3769 + 80.3769i) q^{67} +(-10.1501 - 10.1501i) q^{68} -8.30662i q^{69} +(-14.1172 + 8.01299i) q^{70} +49.4857 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-99.6326 - 99.6326i) q^{73} -35.0338i q^{74} +(41.9858 - 10.5919i) q^{75} -58.8536 q^{76} +(-0.0124764 + 0.0124764i) q^{77} +(-19.5742 - 19.5742i) q^{78} -114.819i q^{79} +(9.87259 + 17.3934i) q^{80} -9.00000 q^{81} +(-9.62845 + 9.62845i) q^{82} +(109.398 + 109.398i) q^{83} -7.95242i q^{84} +(-34.5940 - 9.54216i) q^{85} -67.0511 q^{86} +(-29.6328 + 29.6328i) q^{87} +(0.0153718 + 0.0153718i) q^{88} +16.9328i q^{89} +(-5.64065 + 20.4495i) q^{90} +25.9437 q^{91} +(6.78233 - 6.78233i) q^{92} +(34.2034 + 34.2034i) q^{93} -97.0859i q^{94} +(-127.958 + 72.6296i) q^{95} -9.79796 q^{96} +(-73.9763 + 73.9763i) q^{97} +(-43.7299 - 43.7299i) q^{98} +0.0230577i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$4$		−	2.00000i		−	0.500000i
$5$	−2.46815	−	4.34836i	−0.493629	−	0.869672i
$5$	−2.46815	−	4.34836i	−0.493629	−	0.869672i
$6$	2.44949			0.408248
$7$	−1.62328	+	1.62328i	−0.231897	+	0.231897i	−0.813484	−	0.581587i	$-0.802432\pi$
$7$	−1.62328	+	1.62328i	−0.231897	+	0.231897i	0.581587	+	0.813484i	$0.302432\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$			3.00000i			0.333333i
$10$	6.81651	+	1.88022i	0.681651	+	0.188022i
$11$	0.00768588			0.000698717			0.000349358	−	1.00000i	$-0.499889\pi$
$11$	0.00768588			0.000698717			0.000349358		1.00000i	$0.499889\pi$
$12$	−2.44949	+	2.44949i	−0.204124	+	0.204124i
$13$	−7.99113	−	7.99113i	−0.614703	−	0.614703i	0.329465	−	0.944168i	$-0.393132\pi$
$13$	−7.99113	−	7.99113i	−0.614703	−	0.614703i	−0.944168	+	0.329465i	$0.893132\pi$
$14$		−	3.24656i		−	0.231897i
$15$	−2.30278	+	8.34848i	−0.153519	+	0.556566i
$16$	−4.00000			−0.250000
$17$	5.07503	−	5.07503i	0.298531	−	0.298531i	−0.541907	−	0.840438i	$-0.682298\pi$
$17$	5.07503	−	5.07503i	0.298531	−	0.298531i	0.840438	+	0.541907i	$0.182298\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$		−	29.4268i		−	1.54878i	−0.632709	−	0.774389i	$-0.718057\pi$
$19$		−	29.4268i		−	1.54878i	0.632709	−	0.774389i	$-0.281943\pi$
$20$	−8.69672	+	4.93629i	−0.434836	+	0.246815i
$21$	3.97621			0.189343
$22$	−0.00768588	+	0.00768588i	−0.000349358	+	0.000349358i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$24$		−	4.89898i		−	0.204124i
$25$	−12.8165	+	21.4648i	−0.512660	+	0.858592i
$26$	15.9823			0.614703
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	3.24656	+	3.24656i	0.115949	+	0.115949i
$29$		−	24.1950i		−	0.834312i	−0.908835	−	0.417156i	$-0.863027\pi$
$29$		−	24.1950i		−	0.834312i	0.908835	−	0.417156i	$-0.136973\pi$
$30$	−6.04570	−	10.6513i	−0.201523	−	0.355042i
$31$	−27.9270			−0.900870			−0.450435	−	0.892809i	$-0.648731\pi$
$31$	−27.9270			−0.900870			−0.450435	+	0.892809i	$0.648731\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	−0.00941325	−	0.00941325i	−0.000285250	−	0.000285250i
$34$			10.1501i			0.298531i
$35$	11.0651	+	3.05212i	0.316146	+	0.0872034i
$36$	6.00000			0.166667
$37$	−17.5169	+	17.5169i	−0.473429	+	0.473429i	−0.903023	−	0.429593i	$-0.858657\pi$
$37$	−17.5169	+	17.5169i	−0.473429	+	0.473429i	0.429593	+	0.903023i	$0.358657\pi$
$38$	29.4268	+	29.4268i	0.774389	+	0.774389i
$39$			19.5742i			0.501903i
$40$	3.76043	−	13.6330i	0.0940108	−	0.340825i
$41$	9.62845			0.234840			0.117420	−	0.993082i	$-0.462538\pi$
$41$	9.62845			0.234840			0.117420	+	0.993082i	$0.462538\pi$
$42$	−3.97621	+	3.97621i	−0.0946717	+	0.0946717i
$43$	33.5256	+	33.5256i	0.779664	+	0.779664i	0.979774	−	0.200109i	$-0.0641297\pi$
$43$	33.5256	+	33.5256i	0.779664	+	0.779664i	−0.200109	+	0.979774i	$0.564130\pi$
$44$		−	0.0153718i		−	0.000349358i
$45$	13.0451	−	7.40444i	0.289891	−	0.164543i
$46$	−6.78233			−0.147442
$47$	−48.5429	+	48.5429i	−1.03283	+	1.03283i	−0.0333858	+	0.999443i	$0.510629\pi$
$47$	−48.5429	+	48.5429i	−1.03283	+	1.03283i	−0.999443	+	0.0333858i	$0.989371\pi$
$48$	4.89898	+	4.89898i	0.102062	+	0.102062i
$49$			43.7299i			0.892447i
$50$	−8.64828	−	34.2813i	−0.172966	−	0.685626i
$51$	−12.4312			−0.243750
$52$	−15.9823	+	15.9823i	−0.307351	+	0.307351i
$53$	41.9368	+	41.9368i	0.791260	+	0.791260i	0.981699	−	0.190439i	$-0.0609911\pi$
$53$	41.9368	+	41.9368i	0.791260	+	0.791260i	−0.190439	+	0.981699i	$0.560991\pi$
$54$			7.34847i			0.136083i
$55$	−0.0189699	−	0.0334210i	−0.000344907	−	0.000607655i
$56$	−6.49313			−0.115949
$57$	−36.0403	+	36.0403i	−0.632286	+	0.632286i
$58$	24.1950	+	24.1950i	0.417156	+	0.417156i
$59$			85.5954i			1.45077i	0.688344	+	0.725385i	$0.258338\pi$
$59$			85.5954i			1.45077i	−0.688344	+	0.725385i	$0.741662\pi$
$60$	16.6970	+	4.60557i	0.278283	+	0.0767595i
$61$	−10.2155			−0.167468			−0.0837338	−	0.996488i	$-0.526685\pi$
$61$	−10.2155			−0.167468			−0.0837338	+	0.996488i	$0.526685\pi$
$62$	27.9270	−	27.9270i	0.450435	−	0.450435i
$63$	−4.86985	−	4.86985i	−0.0772991	−	0.0772991i
$64$			8.00000i			0.125000i
$65$	−15.0251	+	54.4716i	−0.231155	+	0.838025i
$66$	0.0188265			0.000285250
$67$	−80.3769	+	80.3769i	−1.19965	+	1.19965i	−0.225385	+	0.974270i	$0.572364\pi$
$67$	−80.3769	+	80.3769i	−1.19965	+	1.19965i	−0.974270	+	0.225385i	$0.927636\pi$
$68$	−10.1501	−	10.1501i	−0.149266	−	0.149266i
$69$		−	8.30662i		−	0.120386i
$70$	−14.1172	+	8.01299i	−0.201675	+	0.114471i
$71$	49.4857			0.696981			0.348491	−	0.937312i	$-0.386694\pi$
$71$	49.4857			0.696981			0.348491	+	0.937312i	$0.386694\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	−99.6326	−	99.6326i	−1.36483	−	1.36483i	−0.867644	−	0.497185i	$-0.834367\pi$
$73$	−99.6326	−	99.6326i	−1.36483	−	1.36483i	−0.497185	−	0.867644i	$-0.665633\pi$
$74$		−	35.0338i		−	0.473429i
$75$	41.9858	−	10.5919i	0.559811	−	0.141226i
$76$	−58.8536			−0.774389
$77$	−0.0124764	+	0.0124764i	−0.000162031	+	0.000162031i
$78$	−19.5742	−	19.5742i	−0.250951	−	0.250951i
$79$		−	114.819i		−	1.45341i	−0.686950	−	0.726705i	$-0.741051\pi$
$79$		−	114.819i		−	1.45341i	0.686950	−	0.726705i	$-0.258949\pi$
$80$	9.87259	+	17.3934i	0.123407	+	0.217418i
$81$	−9.00000			−0.111111
$82$	−9.62845	+	9.62845i	−0.117420	+	0.117420i
$83$	109.398	+	109.398i	1.31805	+	1.31805i	0.915315	+	0.402738i	$0.131942\pi$
$83$	109.398	+	109.398i	1.31805	+	1.31805i	0.402738	+	0.915315i	$0.368058\pi$
$84$		−	7.95242i		−	0.0946717i
$85$	−34.5940	−	9.54216i	−0.406988	−	0.112261i
$86$	−67.0511			−0.779664
$87$	−29.6328	+	29.6328i	−0.340606	+	0.340606i
$88$	0.0153718	+	0.0153718i	0.000174679	+	0.000174679i
$89$			16.9328i			0.190257i	0.995465	+	0.0951283i	$0.0303261\pi$
$89$			16.9328i			0.190257i	−0.995465	+	0.0951283i	$0.969674\pi$
$90$	−5.64065	+	20.4495i	−0.0626739	+	0.227217i
$91$	25.9437			0.285096
$92$	6.78233	−	6.78233i	0.0737210	−	0.0737210i
$93$	34.2034	+	34.2034i	0.367779	+	0.367779i
$94$		−	97.0859i		−	1.03283i
$95$	−127.958	+	72.6296i	−1.34693	+	0.764522i
$96$	−9.79796			−0.102062
$97$	−73.9763	+	73.9763i	−0.762642	+	0.762642i	−0.976799	−	0.214157i	$-0.931299\pi$
$97$	−73.9763	+	73.9763i	−0.762642	+	0.762642i	0.214157	+	0.976799i	$0.431299\pi$
$98$	−43.7299	−	43.7299i	−0.446224	−	0.446224i
$99$			0.0230577i			0.000232906i
$100$	42.9296	+	25.6330i	0.429296	+	0.256330i
$101$	26.3637			0.261027			0.130513	−	0.991447i	$-0.458337\pi$
$101$	26.3637			0.261027			0.130513	+	0.991447i	$0.458337\pi$
$102$	12.4312	−	12.4312i	0.121875	−	0.121875i
$103$	−2.90947	−	2.90947i	−0.0282473	−	0.0282473i	0.692842	−	0.721089i	$-0.256358\pi$
$103$	−2.90947	−	2.90947i	−0.0282473	−	0.0282473i	−0.721089	+	0.692842i	$0.756358\pi$
$104$		−	31.9645i		−	0.307351i
$105$	−9.81387	−	17.2900i	−0.0934655	−	0.164667i
$106$	−83.8736			−0.791260
$107$	17.4022	−	17.4022i	0.162637	−	0.162637i	−0.621097	−	0.783734i	$-0.713313\pi$
$107$	17.4022	−	17.4022i	0.162637	−	0.162637i	0.783734	+	0.621097i	$0.213313\pi$
$108$	−7.34847	−	7.34847i	−0.0680414	−	0.0680414i
$109$		−	29.4112i		−	0.269827i	−0.990857	−	0.134914i	$-0.956924\pi$
$109$		−	29.4112i		−	0.269827i	0.990857	−	0.134914i	$-0.0430757\pi$
$110$	0.0523909	+	0.0144511i	0.000476281	+	0.000131374i
$111$	42.9074			0.386554
$112$	6.49313	−	6.49313i	0.0579744	−	0.0579744i
$113$	−19.4842	−	19.4842i	−0.172427	−	0.172427i	0.615618	−	0.788045i	$-0.288906\pi$
$113$	−19.4842	−	19.4842i	−0.172427	−	0.172427i	−0.788045	+	0.615618i	$0.788906\pi$
$114$		−	72.0806i		−	0.632286i
$115$	6.37612	−	23.1159i	0.0554445	−	0.201008i
$116$	−48.3901			−0.417156
$117$	23.9734	−	23.9734i	0.204901	−	0.204901i
$118$	−85.5954	−	85.5954i	−0.725385	−	0.725385i
$119$			16.4764i			0.138457i
$120$	−21.3025	+	12.0914i	−0.177521	+	0.100762i
$121$	−121.000			−1.00000
$122$	10.2155	−	10.2155i	0.0837338	−	0.0837338i
$123$	−11.7924	−	11.7924i	−0.0958731	−	0.0958731i
$124$			55.8539i			0.450435i
$125$	124.970	+	2.75258i	0.999758	+	0.0220206i
$126$	9.73969			0.0772991
$127$	−133.385	+	133.385i	−1.05027	+	1.05027i	−0.0516046	+	0.998668i	$0.516434\pi$
$127$	−133.385	+	133.385i	−1.05027	+	1.05027i	−0.998668	+	0.0516046i	$0.983566\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$		−	82.1205i		−	0.636593i
$130$	−39.4466	−	69.4967i	−0.303435	−	0.534590i
$131$	−51.3311			−0.391841			−0.195920	−	0.980620i	$-0.562769\pi$
$131$	−51.3311			−0.391841			−0.195920	+	0.980620i	$0.562769\pi$
$132$	−0.0188265	+	0.0188265i	−0.000142625	+	0.000142625i
$133$	47.7680	+	47.7680i	0.359158	+	0.359158i
$134$		−	160.754i		−	1.19965i
$135$	−25.0455	−	6.90835i	−0.185522	−	0.0511730i
$136$	20.3001			0.149266
$137$	−178.812	+	178.812i	−1.30520	+	1.30520i	−0.380358	+	0.924839i	$0.624199\pi$
$137$	−178.812	+	178.812i	−1.30520	+	1.30520i	−0.924839	+	0.380358i	$0.875801\pi$
$138$	8.30662	+	8.30662i	0.0601929	+	0.0601929i
$139$		−	71.0797i		−	0.511364i	−0.966761	−	0.255682i	$-0.917700\pi$
$139$		−	71.0797i		−	0.511364i	0.966761	−	0.255682i	$-0.0823001\pi$
$140$	6.10424	−	22.1302i	0.0436017	−	0.158073i
$141$	118.905			0.843301
$142$	−49.4857	+	49.4857i	−0.348491	+	0.348491i
$143$	−0.0614189	−	0.0614189i	−0.000429503	−	0.000429503i
$144$		−	12.0000i		−	0.0833333i
$145$	−105.209	+	59.7169i	−0.725578	+	0.411841i
$146$	199.265			1.36483
$147$	53.5580	−	53.5580i	0.364340	−	0.364340i
$148$	35.0338	+	35.0338i	0.236715	+	0.236715i
$149$			112.421i			0.754500i	0.926111	+	0.377250i	$0.123130\pi$
$149$			112.421i			0.754500i	−0.926111	+	0.377250i	$0.876870\pi$
$150$	−31.3939	+	52.5778i	−0.209293	+	0.350519i
$151$	85.6195			0.567016			0.283508	−	0.958970i	$-0.408502\pi$
$151$	85.6195			0.567016			0.283508	+	0.958970i	$0.408502\pi$
$152$	58.8536	−	58.8536i	0.387195	−	0.387195i
$153$	15.2251	+	15.2251i	0.0995104	+	0.0995104i
$154$		−	0.0249527i		−	0.000162031i
$155$	68.9279	+	121.437i	0.444696	+	0.783462i
$156$	39.1484			0.250951
$157$	43.2587	−	43.2587i	0.275533	−	0.275533i	−0.555790	−	0.831323i	$-0.687584\pi$
$157$	43.2587	−	43.2587i	0.275533	−	0.275533i	0.831323	+	0.555790i	$0.187584\pi$
$158$	114.819	+	114.819i	0.726705	+	0.726705i
$159$		−	102.724i		−	0.646061i
$160$	−27.2660	−	7.52086i	−0.170413	−	0.0470054i
$161$	−11.0096			−0.0683828
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	154.461	+	154.461i	0.947615	+	0.947615i	0.998695	−	0.0510794i	$-0.0162661\pi$
$163$	154.461	+	154.461i	0.947615	+	0.947615i	−0.0510794	+	0.998695i	$0.516266\pi$
$164$		−	19.2569i		−	0.117420i
$165$	−0.0176989	+	0.0641655i	−0.000107266	+	0.000388882i
$166$	−218.797			−1.31805
$167$	205.359	−	205.359i	1.22969	−	1.22969i	0.265613	−	0.964080i	$-0.414426\pi$
$167$	205.359	−	205.359i	1.22969	−	1.22969i	0.964080	−	0.265613i	$-0.0855744\pi$
$168$	7.95242	+	7.95242i	0.0473359	+	0.0473359i
$169$		−	41.2836i		−	0.244281i
$170$	44.1362	−	25.0518i	0.259624	−	0.147364i
$171$	88.2804			0.516259
$172$	67.0511	−	67.0511i	0.389832	−	0.389832i
$173$	−22.0996	−	22.0996i	−0.127744	−	0.127744i	0.640344	−	0.768088i	$-0.278792\pi$
$173$	−22.0996	−	22.0996i	−0.127744	−	0.127744i	−0.768088	+	0.640344i	$0.778792\pi$
$174$		−	59.2655i		−	0.340606i
$175$	−14.0386	−	55.6482i	−0.0802206	−	0.317990i
$176$	−0.0307435			−0.000174679
$177$	104.833	−	104.833i	0.592274	−	0.592274i
$178$	−16.9328	−	16.9328i	−0.0951283	−	0.0951283i
$179$		−	116.490i		−	0.650782i	−0.945580	−	0.325391i	$-0.894504\pi$
$179$		−	116.490i		−	0.650782i	0.945580	−	0.325391i	$-0.105496\pi$
$180$	−14.8089	−	26.0902i	−0.0822715	−	0.144945i
$181$	−179.408			−0.991205			−0.495602	−	0.868550i	$-0.665053\pi$
$181$	−179.408			−0.991205			−0.495602	+	0.868550i	$0.665053\pi$
$182$	−25.9437	+	25.9437i	−0.142548	+	0.142548i
$183$	12.5114	+	12.5114i	0.0683684	+	0.0683684i
$184$			13.5647i			0.0737210i
$185$	119.404	+	32.9355i	0.645427	+	0.178030i
$186$	−68.4068			−0.367779
$187$	0.0390061	−	0.0390061i	0.000208589	−	0.000208589i
$188$	97.0859	+	97.0859i	0.516414	+	0.516414i
$189$			11.9286i			0.0631145i
$190$	55.3287	−	200.588i	0.291204	−	1.05573i
$191$	48.4540			0.253686			0.126843	−	0.991923i	$-0.459516\pi$
$191$	48.4540			0.253686			0.126843	+	0.991923i	$0.459516\pi$
$192$	9.79796	−	9.79796i	0.0510310	−	0.0510310i
$193$	3.48571	+	3.48571i	0.0180607	+	0.0180607i	0.716079	−	0.698019i	$-0.245935\pi$
$193$	3.48571	+	3.48571i	0.0180607	+	0.0180607i	−0.698019	+	0.716079i	$0.745935\pi$
$194$		−	147.953i		−	0.762642i
$195$	85.1157	−	48.3120i	0.436491	−	0.247754i
$196$	87.4598			0.446224
$197$	−189.488	+	189.488i	−0.961868	+	0.961868i	−0.999299	−	0.0374314i	$-0.988082\pi$
$197$	−189.488	+	189.488i	−0.961868	+	0.961868i	0.0374314	+	0.999299i	$0.488082\pi$
$198$	−0.0230577	−	0.0230577i	−0.000116453	−	0.000116453i
$199$		−	320.034i		−	1.60821i	−0.594486	−	0.804106i	$-0.702645\pi$
$199$		−	320.034i		−	1.60821i	0.594486	−	0.804106i	$-0.297355\pi$
$200$	−68.5626	+	17.2966i	−0.342813	+	0.0864828i
$201$	196.882			0.979514
$202$	−26.3637	+	26.3637i	−0.130513	+	0.130513i
$203$	39.2754	+	39.2754i	0.193475	+	0.193475i
$204$			24.8625i			0.121875i
$205$	−23.7644	−	41.8680i	−0.115924	−	0.204234i
$206$	5.81895			0.0282473
$207$	−10.1735	+	10.1735i	−0.0491473	+	0.0491473i
$208$	31.9645	+	31.9645i	0.153676	+	0.153676i
$209$		−	0.226171i		−	0.00108216i
$210$	27.1039	+	7.47614i	0.129066	+	0.0356007i
$211$	−92.7388			−0.439520			−0.219760	−	0.975554i	$-0.570527\pi$
$211$	−92.7388			−0.439520			−0.219760	+	0.975554i	$0.570527\pi$
$212$	83.8736	−	83.8736i	0.395630	−	0.395630i
$213$	−60.6073	−	60.6073i	−0.284541	−	0.284541i
$214$			34.8043i			0.162637i
$215$	63.0353	−	228.527i	0.293187	−	1.06292i
$216$	14.6969			0.0680414
$217$	45.3333	−	45.3333i	0.208909	−	0.208909i
$218$	29.4112	+	29.4112i	0.134914	+	0.134914i
$219$			244.049i			1.11438i
$220$	−0.0668420	+	0.0379398i	−0.000303827	+	0.000172454i
$221$	−81.1105			−0.367016
$222$	−42.9074	+	42.9074i	−0.193277	+	0.193277i
$223$	140.439	+	140.439i	0.629769	+	0.629769i	0.948010	−	0.318241i	$-0.103092\pi$
$223$	140.439	+	140.439i	0.629769	+	0.629769i	−0.318241	+	0.948010i	$0.603092\pi$
$224$			12.9863i			0.0579744i
$225$	−64.3944	−	38.4495i	−0.286197	−	0.170887i
$226$	38.9684			0.172427
$227$	181.069	−	181.069i	0.797662	−	0.797662i	−0.185065	−	0.982726i	$-0.559249\pi$
$227$	181.069	−	181.069i	0.797662	−	0.797662i	0.982726	+	0.185065i	$0.0592495\pi$
$228$	72.0806	+	72.0806i	0.316143	+	0.316143i
$229$			215.841i			0.942537i	0.881990	+	0.471268i	$0.156204\pi$
$229$			215.841i			0.942537i	−0.881990	+	0.471268i	$0.843796\pi$
$230$	16.7398	+	29.4920i	0.0727817	+	0.128226i
$231$	0.0305607			0.000132297
$232$	48.3901	−	48.3901i	0.208578	−	0.208578i
$233$	−71.0465	−	71.0465i	−0.304921	−	0.304921i	0.538015	−	0.842935i	$-0.319174\pi$
$233$	−71.0465	−	71.0465i	−0.304921	−	0.304921i	−0.842935	+	0.538015i	$0.819174\pi$
$234$			47.9468i			0.204901i
$235$	330.893	+	91.2712i	1.40806	+	0.388388i
$236$	171.191			0.725385
$237$	−140.624	+	140.624i	−0.593352	+	0.593352i
$238$	−16.4764	−	16.4764i	−0.0692286	−	0.0692286i
$239$		−	107.797i		−	0.451035i	−0.974239	−	0.225518i	$-0.927593\pi$
$239$		−	107.797i		−	0.451035i	0.974239	−	0.225518i	$-0.0724073\pi$
$240$	9.21114	−	33.3939i	0.0383797	−	0.139141i
$241$	70.4171			0.292187			0.146094	−	0.989271i	$-0.453330\pi$
$241$	70.4171			0.292187			0.146094	+	0.989271i	$0.453330\pi$
$242$	121.000	−	121.000i	0.500000	−	0.500000i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$			20.4311i			0.0837338i
$245$	190.153	−	107.932i	0.776137	−	0.440538i
$246$	23.5848			0.0958731
$247$	−235.153	+	235.153i	−0.952038	+	0.952038i
$248$	−55.8539	−	55.8539i	−0.225218	−	0.225218i
$249$		−	267.970i		−	1.07619i
$250$	−127.722	+	122.217i	−0.510889	+	0.488868i
$251$	−145.088			−0.578041			−0.289020	−	0.957323i	$-0.593330\pi$
$251$	−145.088			−0.578041			−0.289020	+	0.957323i	$0.593330\pi$
$252$	−9.73969	+	9.73969i	−0.0386496	+	0.0386496i
$253$	0.0260641	+	0.0260641i	0.000103020	+	0.000103020i
$254$		−	266.769i		−	1.05027i
$255$	30.6821	+	54.0555i	0.120322	+	0.211982i
$256$	16.0000			0.0625000
$257$	−35.0507	+	35.0507i	−0.136384	+	0.136384i	−0.772003	−	0.635619i	$-0.780745\pi$
$257$	−35.0507	+	35.0507i	−0.136384	+	0.136384i	0.635619	+	0.772003i	$0.280745\pi$
$258$	82.1205	+	82.1205i	0.318297	+	0.318297i
$259$		−	56.8697i		−	0.219574i
$260$	108.943	+	30.0501i	0.419013	+	0.115577i
$261$	72.5851			0.278104
$262$	51.3311	−	51.3311i	0.195920	−	0.195920i
$263$	115.541	+	115.541i	0.439319	+	0.439319i	0.891783	−	0.452464i	$-0.149455\pi$
$263$	115.541	+	115.541i	0.439319	+	0.439319i	−0.452464	+	0.891783i	$0.649455\pi$
$264$		−	0.0376530i		−	0.000142625i
$265$	78.8502	−	285.862i	0.297548	−	1.07873i
$266$	−95.5360			−0.359158
$267$	20.7384	−	20.7384i	0.0776719	−	0.0776719i
$268$	160.754	+	160.754i	0.599827	+	0.599827i
$269$		−	276.254i		−	1.02697i	−0.858100	−	0.513483i	$-0.828355\pi$
$269$		−	276.254i		−	1.02697i	0.858100	−	0.513483i	$-0.171645\pi$
$270$	31.9538	−	18.1371i	0.118347	−	0.0671744i
$271$	−157.430			−0.580921			−0.290461	−	0.956887i	$-0.593809\pi$
$271$	−157.430			−0.580921			−0.290461	+	0.956887i	$0.593809\pi$
$272$	−20.3001	+	20.3001i	−0.0746328	+	0.0746328i
$273$	−31.7744	−	31.7744i	−0.116390	−	0.116390i
$274$		−	357.624i		−	1.30520i
$275$	−0.0985062	+	0.164976i	−0.000358204	+	0.000599912i
$276$	−16.6132			−0.0601929
$277$	−90.6970	+	90.6970i	−0.327426	+	0.327426i	−0.851607	−	0.524181i	$-0.824372\pi$
$277$	−90.6970	+	90.6970i	−0.327426	+	0.327426i	0.524181	+	0.851607i	$0.324372\pi$
$278$	71.0797	+	71.0797i	0.255682	+	0.255682i
$279$		−	83.7809i		−	0.300290i
$280$	16.0260	+	28.2345i	0.0572357	+	0.100837i
$281$	102.396			0.364397			0.182199	−	0.983262i	$-0.441679\pi$
$281$	102.396			0.364397			0.182199	+	0.983262i	$0.441679\pi$
$282$	−118.905	+	118.905i	−0.421650	+	0.421650i
$283$	37.0378	+	37.0378i	0.130875	+	0.130875i	0.769510	−	0.638635i	$-0.220500\pi$
$283$	37.0378	+	37.0378i	0.130875	+	0.130875i	−0.638635	+	0.769510i	$0.720500\pi$
$284$		−	98.9714i		−	0.348491i
$285$	245.669	+	67.7636i	0.861997	+	0.237767i
$286$	0.122838			0.000429503
$287$	−15.6297	+	15.6297i	−0.0544588	+	0.0544588i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$			237.488i			0.821758i
$290$	45.4919	−	164.926i	0.156869	−	0.568709i
$291$	181.204			0.622694
$292$	−199.265	+	199.265i	−0.682415	+	0.682415i
$293$	−141.513	−	141.513i	−0.482981	−	0.482981i	0.423101	−	0.906082i	$-0.360941\pi$
$293$	−141.513	−	141.513i	−0.482981	−	0.482981i	−0.906082	+	0.423101i	$0.860941\pi$
$294$			107.116i			0.364340i
$295$	372.200	−	211.262i	1.26169	−	0.716142i
$296$	−70.0676			−0.236715
$297$	0.0282397	−	0.0282397i	9.50833e−5	−	9.50833e-5i
$298$	−112.421	−	112.421i	−0.377250	−	0.377250i
$299$		−	54.1985i		−	0.181266i
$300$	−21.1839	−	83.9717i	−0.0706129	−	0.279906i
$301$	−108.843			−0.361604
$302$	−85.6195	+	85.6195i	−0.283508	+	0.283508i
$303$	−32.2888	−	32.2888i	−0.106564	−	0.106564i
$304$			117.707i			0.387195i
$305$	25.2134	+	44.4208i	0.0826669	+	0.145642i
$306$	−30.4502			−0.0995104
$307$	325.695	−	325.695i	1.06089	−	1.06089i	0.0628732	−	0.998022i	$-0.479974\pi$
$307$	325.695	−	325.695i	1.06089	−	1.06089i	0.998022	−	0.0628732i	$-0.0200264\pi$
$308$	0.0249527	+	0.0249527i	8.10153e−5	+	8.10153e-5i
$309$			7.12673i			0.0230638i
$310$	−190.364	−	52.5087i	−0.614079	−	0.169383i
$311$	−23.8835			−0.0767959			−0.0383980	−	0.999263i	$-0.512225\pi$
$311$	−23.8835			−0.0767959			−0.0383980	+	0.999263i	$0.512225\pi$
$312$	−39.1484	+	39.1484i	−0.125476	+	0.125476i
$313$	−260.353	−	260.353i	−0.831799	−	0.831799i	0.155964	−	0.987763i	$-0.450152\pi$
$313$	−260.353	−	260.353i	−0.831799	−	0.831799i	−0.987763	+	0.155964i	$0.950152\pi$
$314$			86.5174i			0.275533i
$315$	−9.15636	+	33.1953i	−0.0290678	+	0.105382i
$316$	−229.639			−0.726705
$317$	−92.2203	+	92.2203i	−0.290916	+	0.290916i	−0.837442	−	0.546526i	$-0.815950\pi$
$317$	−92.2203	+	92.2203i	−0.290916	+	0.290916i	0.546526	+	0.837442i	$0.315950\pi$
$318$	102.724	+	102.724i	0.323031	+	0.323031i
$319$		−	0.185960i		−	0.000582948i
$320$	34.7869	−	19.7452i	0.108709	−	0.0617037i
$321$	−42.6264			−0.132793
$322$	11.0096	−	11.0096i	0.0341914	−	0.0341914i
$323$	−149.342	−	149.342i	−0.462359	−	0.462359i
$324$			18.0000i			0.0555556i
$325$	273.946	−	69.1096i	0.842912	−	0.212645i
$326$	−308.923			−0.947615
$327$	−36.0212	+	36.0212i	−0.110157	+	0.110157i
$328$	19.2569	+	19.2569i	0.0587100	+	0.0587100i
$329$		−	157.598i		−	0.479020i
$330$	−0.0464665	−	0.0818644i	−0.000140808	−	0.000248074i
$331$	532.735			1.60947			0.804735	−	0.593634i	$-0.202307\pi$
$331$	532.735			1.60947			0.804735	+	0.593634i	$0.202307\pi$
$332$	218.797	−	218.797i	0.659027	−	0.659027i
$333$	−52.5507	−	52.5507i	−0.157810	−	0.157810i
$334$			410.717i			1.22969i
$335$	547.890	+	151.126i	1.63549	+	0.451122i
$336$	−15.9048			−0.0473359
$337$	−399.875	+	399.875i	−1.18657	+	1.18657i	−0.208563	+	0.978009i	$0.566878\pi$
$337$	−399.875	+	399.875i	−1.18657	+	1.18657i	−0.978009	+	0.208563i	$0.933122\pi$
$338$	41.2836	+	41.2836i	0.122141	+	0.122141i
$339$			47.7264i			0.140786i
$340$	−19.0843	+	69.1880i	−0.0561303	+	0.203494i
$341$	−0.214643			−0.000629453
$342$	−88.2804	+	88.2804i	−0.258130	+	0.258130i
$343$	−150.527	−	150.527i	−0.438854	−	0.438854i
$344$			134.102i			0.389832i
$345$	−36.1202	+	20.5020i	−0.104696	+	0.0594260i
$346$	44.1993			0.127744
$347$	−105.898	+	105.898i	−0.305182	+	0.305182i	−0.843037	−	0.537855i	$-0.819235\pi$
$347$	−105.898	+	105.898i	−0.305182	+	0.305182i	0.537855	+	0.843037i	$0.319235\pi$
$348$	59.2655	+	59.2655i	0.170303	+	0.170303i
$349$		−	171.397i		−	0.491109i	−0.969383	−	0.245555i	$-0.921030\pi$
$349$		−	171.397i		−	0.491109i	0.969383	−	0.245555i	$-0.0789701\pi$
$350$	69.6868	+	41.6096i	0.199105	+	0.118885i
$351$	−58.7226			−0.167301
$352$	0.0307435	−	0.0307435i	8.73396e−5	−	8.73396e-5i
$353$	234.785	+	234.785i	0.665113	+	0.665113i	0.956581	−	0.291468i	$-0.0941437\pi$
$353$	234.785	+	234.785i	0.665113	+	0.665113i	−0.291468	+	0.956581i	$0.594144\pi$
$354$			209.665i			0.592274i
$355$	−122.138	−	215.182i	−0.344050	−	0.606146i
$356$	33.8657			0.0951283
$357$	20.1794	−	20.1794i	0.0565249	−	0.0565249i
$358$	116.490	+	116.490i	0.325391	+	0.325391i
$359$		−	219.996i		−	0.612801i	−0.951903	−	0.306401i	$-0.900875\pi$
$359$		−	219.996i		−	0.612801i	0.951903	−	0.306401i	$-0.0991247\pi$
$360$	40.8991	+	11.2813i	0.113608	+	0.0313369i
$361$	−504.936			−1.39871
$362$	179.408	−	179.408i	0.495602	−	0.495602i
$363$	148.194	+	148.194i	0.408248	+	0.408248i
$364$		−	51.8875i		−	0.142548i
$365$	−187.331	+	679.146i	−0.513235	+	1.86067i
$366$	−25.0228			−0.0683684
$367$	−198.319	+	198.319i	−0.540380	+	0.540380i	−0.923640	−	0.383260i	$-0.874801\pi$
$367$	−198.319	+	198.319i	−0.540380	+	0.540380i	0.383260	+	0.923640i	$0.374801\pi$
$368$	−13.5647	−	13.5647i	−0.0368605	−	0.0368605i
$369$			28.8853i			0.0782800i
$370$	−152.340	+	86.4685i	−0.411729	+	0.233699i
$371$	−136.150			−0.366982
$372$	68.4068	−	68.4068i	0.183889	−	0.183889i
$373$	−357.278	−	357.278i	−0.957849	−	0.957849i	0.0412982	−	0.999147i	$-0.486851\pi$
$373$	−357.278	−	357.278i	−0.957849	−	0.957849i	−0.999147	+	0.0412982i	$0.986851\pi$
$374$			0.0780122i			0.000208589i
$375$	−149.685	−	156.427i	−0.399159	−	0.417139i
$376$	−194.172			−0.516414
$377$	−193.346	+	193.346i	−0.512854	+	0.512854i
$378$	−11.9286	−	11.9286i	−0.0315572	−	0.0315572i
$379$			632.919i			1.66997i	0.550271	+	0.834986i	$0.314524\pi$
$379$			632.919i			1.66997i	−0.550271	+	0.834986i	$0.685476\pi$
$380$	145.259	+	255.917i	0.382261	+	0.673465i
$381$	326.724			0.857544
$382$	−48.4540	+	48.4540i	−0.126843	+	0.126843i
$383$	−456.210	−	456.210i	−1.19115	−	1.19115i	−0.976745	−	0.214405i	$-0.931219\pi$
$383$	−456.210	−	456.210i	−1.19115	−	1.19115i	−0.214405	−	0.976745i	$-0.568781\pi$
$384$			19.5959i			0.0510310i
$385$	0.0850452	+	0.0234582i	0.000220897	+	6.09305e-5i
$386$	−6.97142			−0.0180607
$387$	−100.577	+	100.577i	−0.259888	+	0.259888i
$388$	147.953	+	147.953i	0.381321	+	0.381321i
$389$		−	297.456i		−	0.764667i	−0.924024	−	0.382334i	$-0.875121\pi$
$389$		−	297.456i		−	0.764667i	0.924024	−	0.382334i	$-0.124879\pi$
$390$	−36.8037	+	133.428i	−0.0943685	+	0.342122i
$391$	34.4205			0.0880321
$392$	−87.4598	+	87.4598i	−0.223112	+	0.223112i
$393$	62.8675	+	62.8675i	0.159968	+	0.159968i
$394$		−	378.976i		−	0.961868i
$395$	−499.276	+	283.391i	−1.26399	+	0.717446i
$396$	0.0461153			0.000116453
$397$	−83.7492	+	83.7492i	−0.210955	+	0.210955i	−0.804673	−	0.593718i	$-0.797659\pi$
$397$	−83.7492	+	83.7492i	−0.210955	+	0.210955i	0.593718	+	0.804673i	$0.297659\pi$
$398$	320.034	+	320.034i	0.804106	+	0.804106i
$399$		−	117.007i		−	0.293251i
$400$	51.2660	−	85.8592i	0.128165	−	0.214648i
$401$	−365.707			−0.911988			−0.455994	−	0.889983i	$-0.650716\pi$
$401$	−365.707			−0.911988			−0.455994	+	0.889983i	$0.650716\pi$
$402$	−196.882	+	196.882i	−0.489757	+	0.489757i
$403$	223.168	+	223.168i	0.553767	+	0.553767i
$404$		−	52.7274i		−	0.130513i
$405$	22.2133	+	39.1353i	0.0548477	+	0.0966303i
$406$	−78.5507			−0.193475
$407$	−0.134633	+	0.134633i	−0.000330793	+	0.000330793i
$408$	−24.8625	−	24.8625i	−0.0609374	−	0.0609374i
$409$		−	432.702i		−	1.05795i	−0.848637	−	0.528975i	$-0.822577\pi$
$409$		−	432.702i		−	1.05795i	0.848637	−	0.528975i	$-0.177423\pi$
$410$	65.6324	+	18.1036i	0.160079	+	0.0441550i
$411$	437.998			1.06569
$412$	−5.81895	+	5.81895i	−0.0141237	+	0.0141237i
$413$	−138.945	−	138.945i	−0.336430	−	0.336430i
$414$		−	20.3470i		−	0.0491473i
$415$	205.693	−	745.715i	0.495645	−	1.79690i
$416$	−63.9291			−0.153676
$417$	−87.0544	+	87.0544i	−0.208764	+	0.208764i
$418$	0.226171	+	0.226171i	0.000541079	+	0.000541079i
$419$		−	275.957i		−	0.658610i	−0.944224	−	0.329305i	$-0.893186\pi$
$419$		−	275.957i		−	0.658610i	0.944224	−	0.329305i	$-0.106814\pi$
$420$	−34.5800	+	19.6277i	−0.0823334	+	0.0467327i
$421$	−754.476			−1.79211			−0.896053	−	0.443948i	$-0.853578\pi$
$421$	−754.476			−1.79211			−0.896053	+	0.443948i	$0.853578\pi$
$422$	92.7388	−	92.7388i	0.219760	−	0.219760i
$423$	−145.629	−	145.629i	−0.344276	−	0.344276i
$424$			167.747i			0.395630i
$425$	43.8903	+	173.979i	0.103271	+	0.409362i
$426$	121.215			0.284541
$427$	16.5827	−	16.5827i	0.0388353	−	0.0388353i
$428$	−34.8043	−	34.8043i	−0.0813186	−	0.0813186i
$429$			0.150445i			0.000350688i
$430$	165.492	+	291.563i	0.384865	+	0.678053i
$431$	−479.745			−1.11310			−0.556549	−	0.830815i	$-0.687875\pi$
$431$	−479.745			−1.11310			−0.556549	+	0.830815i	$0.687875\pi$
$432$	−14.6969	+	14.6969i	−0.0340207	+	0.0340207i
$433$	381.301	+	381.301i	0.880602	+	0.880602i	0.993596	−	0.112994i	$-0.0360440\pi$
$433$	381.301	+	381.301i	0.880602	+	0.880602i	−0.112994	+	0.993596i	$0.536044\pi$
$434$			90.6667i			0.208909i
$435$	201.992	+	55.7160i	0.464349	+	0.128083i
$436$	−58.8224			−0.134914
$437$	99.7911	−	99.7911i	0.228355	−	0.228355i
$438$	−244.049	−	244.049i	−0.557189	−	0.557189i
$439$		−	171.159i		−	0.389883i	−0.980815	−	0.194942i	$-0.937548\pi$
$439$		−	171.159i		−	0.389883i	0.980815	−	0.194942i	$-0.0624518\pi$
$440$	0.0289022	−	0.104782i	6.56869e−5	−	0.000238140i
$441$	−131.190			−0.297482
$442$	81.1105	−	81.1105i	0.183508	−	0.183508i
$443$	−548.690	−	548.690i	−1.23858	−	1.23858i	−0.960583	−	0.277995i	$-0.910330\pi$
$443$	−548.690	−	548.690i	−1.23858	−	1.23858i	−0.277995	−	0.960583i	$-0.589670\pi$
$444$		−	85.8149i		−	0.193277i
$445$	73.6301	−	41.7927i	0.165461	−	0.0939162i
$446$	−280.877			−0.629769
$447$	137.687	−	137.687i	0.308024	−	0.308024i
$448$	−12.9863	−	12.9863i	−0.0289872	−	0.0289872i
$449$			422.457i			0.940883i	0.882431	+	0.470442i	$0.155905\pi$
$449$			422.457i			0.940883i	−0.882431	+	0.470442i	$0.844095\pi$
$450$	102.844	−	25.9448i	0.228542	−	0.0576552i
$451$	0.0740031			0.000164087
$452$	−38.9684	+	38.9684i	−0.0862133	+	0.0862133i
$453$	−104.862	−	104.862i	−0.231483	−	0.231483i
$454$			362.138i			0.797662i
$455$	−64.0329	−	112.813i	−0.140732	−	0.247940i
$456$	−144.161			−0.316143
$457$	−245.799	+	245.799i	−0.537854	+	0.537854i	−0.922898	−	0.385044i	$-0.874186\pi$
$457$	−245.799	+	245.799i	−0.537854	+	0.537854i	0.385044	+	0.922898i	$0.374186\pi$
$458$	−215.841	−	215.841i	−0.471268	−	0.471268i
$459$		−	37.2937i		−	0.0812499i
$460$	−46.2318	−	12.7522i	−0.100504	−	0.0277223i
$461$	−751.846			−1.63090			−0.815451	−	0.578826i	$-0.803511\pi$
$461$	−751.846			−1.63090			−0.815451	+	0.578826i	$0.803511\pi$
$462$	−0.0305607	+	0.0305607i	−6.61487e−5	+	6.61487e-5i
$463$	318.339	+	318.339i	0.687556	+	0.687556i	0.961691	−	0.274135i	$-0.0883915\pi$
$463$	318.339	+	318.339i	0.687556	+	0.687556i	−0.274135	+	0.961691i	$0.588391\pi$
$464$			96.7802i			0.208578i
$465$	64.3098	−	233.148i	0.138301	−	0.501393i
$466$	142.093			0.304921
$467$	−304.769	+	304.769i	−0.652610	+	0.652610i	−0.953621	−	0.301010i	$-0.902676\pi$
$467$	−304.769	+	304.769i	−0.652610	+	0.652610i	0.301010	+	0.953621i	$0.402676\pi$
$468$	−47.9468	−	47.9468i	−0.102450	−	0.102450i
$469$		−	260.949i		−	0.556394i
$470$	−422.165	+	239.622i	−0.898222	+	0.509834i
$471$	−105.962			−0.224972
$472$	−171.191	+	171.191i	−0.362692	+	0.362692i
$473$	0.257674	+	0.257674i	0.000544765	+	0.000544765i
$474$		−	281.249i		−	0.593352i
$475$	631.640	+	377.149i	1.32977	+	0.793997i
$476$	32.9528			0.0692286
$477$	−125.810	+	125.810i	−0.263753	+	0.263753i
$478$	107.797	+	107.797i	0.225518	+	0.225518i
$479$			511.063i			1.06694i	0.845820	+	0.533469i	$0.179112\pi$
$479$			511.063i			1.06694i	−0.845820	+	0.533469i	$0.820888\pi$
$480$	24.1828	+	42.6051i	0.0503808	+	0.0887606i
$481$	279.960			0.582037
$482$	−70.4171	+	70.4171i	−0.146094	+	0.146094i
$483$	13.4840	+	13.4840i	0.0279172	+	0.0279172i
$484$			242.000i			0.500000i
$485$	504.260	+	139.091i	1.03971	+	0.286786i
$486$	−22.0454			−0.0453609
$487$	276.565	−	276.565i	0.567895	−	0.567895i	−0.363643	−	0.931538i	$-0.618467\pi$
$487$	276.565	−	276.565i	0.567895	−	0.567895i	0.931538	+	0.363643i	$0.118467\pi$
$488$	−20.4311	−	20.4311i	−0.0418669	−	0.0418669i
$489$		−	378.351i		−	0.773725i
$490$	−82.2217	+	298.085i	−0.167799	+	0.608337i
$491$	730.914			1.48862			0.744312	−	0.667832i	$-0.232778\pi$
$491$	730.914			1.48862			0.744312	+	0.667832i	$0.232778\pi$
$492$	−23.5848	+	23.5848i	−0.0479365	+	0.0479365i
$493$	−122.791	−	122.791i	−0.249068	−	0.249068i
$494$		−	470.307i		−	0.952038i
$495$	0.100263	−	0.0569097i	0.000202552	−	0.000114969i
$496$	111.708			0.225218
$497$	−80.3292	+	80.3292i	−0.161628	+	0.161628i
$498$	267.970	+	267.970i	0.538093	+	0.538093i
$499$		−	318.628i		−	0.638533i	−0.947665	−	0.319267i	$-0.896563\pi$
$499$		−	318.628i		−	0.638533i	0.947665	−	0.319267i	$-0.103437\pi$
$500$	5.50515	−	249.939i	0.0110103	−	0.499879i
$501$	−503.024			−1.00404
$502$	145.088	−	145.088i	0.289020	−	0.289020i
$503$	123.220	+	123.220i	0.244970	+	0.244970i	0.818903	−	0.573932i	$-0.194583\pi$
$503$	123.220	+	123.220i	0.244970	+	0.244970i	−0.573932	+	0.818903i	$0.694583\pi$
$504$		−	19.4794i		−	0.0386496i
$505$	−65.0695	−	114.639i	−0.128850	−	0.227008i
$506$	−0.0521282			−0.000103020
$507$	−50.5618	+	50.5618i	−0.0997275	+	0.0997275i
$508$	266.769	+	266.769i	0.525136	+	0.525136i
$509$			785.649i			1.54352i	0.635917	+	0.771758i	$0.280622\pi$
$509$			785.649i			1.54352i	−0.635917	+	0.771758i	$0.719378\pi$
$510$	−84.7376	−	23.3734i	−0.166152	−	0.0458302i
$511$	323.463			0.633001
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−108.121	−	108.121i	−0.210762	−	0.210762i
$514$		−	70.1014i		−	0.136384i
$515$	−5.47044	+	19.8324i	−0.0106222	+	0.0385096i
$516$	−164.241			−0.318297
$517$	−0.373095	+	0.373095i	−0.000721654	+	0.000721654i
$518$	56.8697	+	56.8697i	0.109787	+	0.109787i
$519$			54.1328i			0.104302i
$520$	−138.993	+	78.8932i	−0.267295	+	0.151718i
$521$	12.4642			0.0239237			0.0119618	−	0.999928i	$-0.496192\pi$
$521$	12.4642			0.0239237			0.0119618	+	0.999928i	$0.496192\pi$
$522$	−72.5851	+	72.5851i	−0.139052	+	0.139052i
$523$	−529.257	−	529.257i	−1.01196	−	1.01196i	−0.999928	−	0.0120361i	$-0.996169\pi$
$523$	−529.257	−	529.257i	−1.01196	−	1.01196i	−0.0120361	−	0.999928i	$-0.503831\pi$
$524$			102.662i			0.195920i
$525$	−50.9612	+	85.3486i	−0.0970689	+	0.162569i
$526$	−231.082			−0.439319
$527$	−141.730	+	141.730i	−0.268938	+	0.268938i
$528$	0.0376530	+	0.0376530i	7.13125e−5	+	7.13125e-5i
$529$			23.0000i			0.0434783i
$530$	207.012	+	364.713i	0.390589	+	0.688137i
$531$	−256.786			−0.483590
$532$	95.5360	−	95.5360i	0.179579	−	0.179579i
$533$	−76.9422	−	76.9422i	−0.144357	−	0.144357i
$534$			41.4768i			0.0776719i
$535$	−118.622	−	32.7198i	−0.221723	−	0.0611586i
$536$	−321.507			−0.599827
$537$	−142.670	+	142.670i	−0.265681	+	0.265681i
$538$	276.254	+	276.254i	0.513483	+	0.513483i
$539$			0.336103i			0.000623568i
$540$	−13.8167	+	50.0909i	−0.0255865	+	0.0927609i
$541$	146.788			0.271327			0.135663	−	0.990755i	$-0.456683\pi$
$541$	146.788			0.271327			0.135663	+	0.990755i	$0.456683\pi$
$542$	157.430	−	157.430i	0.290461	−	0.290461i
$543$	219.729	+	219.729i	0.404658	+	0.404658i
$544$		−	40.6003i		−	0.0746328i
$545$	−127.890	+	72.5911i	−0.234661	+	0.133195i
$546$	63.5489			0.116390
$547$	186.682	−	186.682i	0.341283	−	0.341283i	−0.515567	−	0.856850i	$-0.672418\pi$
$547$	186.682	−	186.682i	0.341283	−	0.341283i	0.856850	+	0.515567i	$0.172418\pi$
$548$	357.624	+	357.624i	0.652599	+	0.652599i
$549$		−	30.6466i		−	0.0558226i
$550$	−0.0664697	−	0.263482i	−0.000120854	−	0.000479058i
$551$	−711.982			−1.29216
$552$	16.6132	−	16.6132i	0.0300965	−	0.0300965i
$553$	186.384	+	186.384i	0.337042	+	0.337042i
$554$		−	181.394i		−	0.327426i
$555$	−105.902	−	186.577i	−0.190814	−	0.336175i
$556$	−142.159			−0.255682
$557$	236.628	−	236.628i	0.424825	−	0.424825i	−0.462036	−	0.886861i	$-0.652881\pi$
$557$	236.628	−	236.628i	0.424825	−	0.424825i	0.886861	+	0.462036i	$0.152881\pi$
$558$	83.7809	+	83.7809i	0.150145	+	0.150145i
$559$		−	535.815i		−	0.958523i
$560$	−44.2605	−	12.2085i	−0.0790365	−	0.0218009i
$561$	−0.0955451			−0.000170312
$562$	−102.396	+	102.396i	−0.182199	+	0.182199i
$563$	181.782	+	181.782i	0.322881	+	0.322881i	0.849871	−	0.526990i	$-0.176680\pi$
$563$	181.782	+	181.782i	0.322881	+	0.322881i	−0.526990	+	0.849871i	$0.676680\pi$
$564$		−	237.811i		−	0.421650i
$565$	−36.6345	+	132.814i	−0.0648399	+	0.235070i
$566$	−74.0755			−0.130875
$567$	14.6095	−	14.6095i	0.0257664	−	0.0257664i
$568$	98.9714	+	98.9714i	0.174245	+	0.174245i
$569$			33.5112i			0.0588949i	0.999566	+	0.0294475i	$0.00937477\pi$
$569$			33.5112i			0.0588949i	−0.999566	+	0.0294475i	$0.990625\pi$
$570$	−313.433	+	177.906i	−0.549882	+	0.312115i
$571$	661.886			1.15917			0.579585	−	0.814912i	$-0.303215\pi$
$571$	661.886			1.15917			0.579585	+	0.814912i	$0.303215\pi$
$572$	−0.122838	+	0.122838i	−0.000214752	+	0.000214752i
$573$	−59.3438	−	59.3438i	−0.103567	−	0.103567i
$574$		−	31.2594i		−	0.0544588i
$575$	−116.254	+	29.3277i	−0.202180	+	0.0510048i
$576$	−24.0000			−0.0416667
$577$	162.455	−	162.455i	0.281551	−	0.281551i	−0.552176	−	0.833727i	$-0.686202\pi$
$577$	162.455	−	162.455i	0.281551	−	0.281551i	0.833727	+	0.552176i	$0.186202\pi$
$578$	−237.488	−	237.488i	−0.410879	−	0.410879i
$579$		−	8.53821i		−	0.0147465i
$580$	119.434	+	210.418i	0.205920	+	0.362789i
$581$	−355.169			−0.611306
$582$	−181.204	+	181.204i	−0.311347	+	0.311347i
$583$	0.322321	+	0.322321i	0.000552867	+	0.000552867i
$584$		−	398.530i		−	0.682415i
$585$	−163.415	−	45.0752i	−0.279342	−	0.0770516i
$586$	283.027			0.482981
$587$	−500.855	+	500.855i	−0.853245	+	0.853245i	−0.990531	−	0.137287i	$-0.956162\pi$
$587$	−500.855	+	500.855i	−0.853245	+	0.853245i	0.137287	+	0.990531i	$0.456162\pi$
$588$	−107.116	−	107.116i	−0.182170	−	0.182170i
$589$			821.801i			1.39525i
$590$	−160.938	+	583.462i	−0.272776	+	0.988918i
$591$	464.149			0.785362
$592$	70.0676	−	70.0676i	0.118357	−	0.118357i
$593$	−758.069	−	758.069i	−1.27836	−	1.27836i	−0.941584	−	0.336778i	$-0.890663\pi$
$593$	−758.069	−	758.069i	−1.27836	−	1.27836i	−0.336778	−	0.941584i	$-0.609337\pi$
$594$			0.0564795i			9.50833e-5i
$595$	71.6454	−	40.6662i	0.120412	−	0.0683466i
$596$	224.841			0.377250
$597$	−391.960	+	391.960i	−0.656550	+	0.656550i
$598$	54.1985	+	54.1985i	0.0906330	+	0.0906330i
$599$			1117.30i			1.86527i	0.360816	+	0.932637i	$0.382498\pi$
$599$			1117.30i			1.86527i	−0.360816	+	0.932637i	$0.617502\pi$
$600$	105.156	+	62.7878i	0.175259	+	0.104646i
$601$	−340.477			−0.566518			−0.283259	−	0.959043i	$-0.591416\pi$
$601$	−340.477			−0.566518			−0.283259	+	0.959043i	$0.591416\pi$
$602$	108.843	−	108.843i	0.180802	−	0.180802i
$603$	−241.131	−	241.131i	−0.399885	−	0.399885i
$604$		−	171.239i		−	0.283508i
$605$	298.646	+	526.152i	0.493629	+	0.869672i
$606$	64.5776			0.106564
$607$	−59.2413	+	59.2413i	−0.0975968	+	0.0975968i	−0.754219	−	0.656623i	$-0.771984\pi$
$607$	−59.2413	+	59.2413i	−0.0975968	+	0.0975968i	0.656623	+	0.754219i	$0.271984\pi$
$608$	−117.707	−	117.707i	−0.193597	−	0.193597i
$609$		−	96.2046i		−	0.157971i
$610$	−69.6342	−	19.2074i	−0.114154	−	0.0314875i
$611$	775.826			1.26976
$612$	30.4502	−	30.4502i	0.0497552	−	0.0497552i
$613$	106.898	+	106.898i	0.174385	+	0.174385i	0.788903	−	0.614518i	$-0.210649\pi$
$613$	106.898	+	106.898i	0.174385	+	0.174385i	−0.614518	+	0.788903i	$0.710649\pi$
$614$			651.389i			1.06089i
$615$	−22.1722	+	80.3829i	−0.0360524	+	0.130704i
$616$	−0.0499054			−8.10153e−5
$617$	579.410	−	579.410i	0.939076	−	0.939076i	−0.0591721	−	0.998248i	$-0.518846\pi$
$617$	579.410	−	579.410i	0.939076	−	0.939076i	0.998248	+	0.0591721i	$0.0188461\pi$
$618$	−7.12673	−	7.12673i	−0.0115319	−	0.0115319i
$619$			452.584i			0.731154i	0.930781	+	0.365577i	$0.119128\pi$
$619$			452.584i			0.731154i	−0.930781	+	0.365577i	$0.880872\pi$
$620$	242.873	−	137.856i	0.391731	−	0.222348i
$621$	24.9199			0.0401286
$622$	23.8835	−	23.8835i	0.0383980	−	0.0383980i
$623$	−27.4868	−	27.4868i	−0.0441200	−	0.0441200i
$624$		−	78.2968i		−	0.125476i
$625$	−296.474	−	550.207i	−0.474359	−	0.880332i
$626$	520.706			0.831799
$627$	−0.277002	+	0.277002i	−0.000441789	+	0.000441789i
$628$	−86.5174	−	86.5174i	−0.137767	−	0.137767i
$629$			177.798i			0.282667i
$630$	−24.0390	−	42.3517i	−0.0381571	−	0.0672249i
$631$	427.124			0.676900			0.338450	−	0.940984i	$-0.390097\pi$
$631$	427.124			0.676900			0.338450	+	0.940984i	$0.390097\pi$
$632$	229.639	−	229.639i	0.363353	−	0.363353i
$633$	113.581	+	113.581i	0.179433	+	0.179433i
$634$		−	184.441i		−	0.290916i
$635$	909.217	+	250.792i	1.43184	+	0.394948i
$636$	−205.447			−0.323031
$637$	349.452	−	349.452i	0.548590	−	0.548590i
$638$	0.185960	+	0.185960i	0.000291474	+	0.000291474i
$639$			148.457i			0.232327i
$640$	−15.0417	+	54.5321i	−0.0235027	+	0.0852064i
$641$	183.843			0.286806			0.143403	−	0.989664i	$-0.454195\pi$
$641$	183.843			0.286806			0.143403	+	0.989664i	$0.454195\pi$
$642$	42.6264	−	42.6264i	0.0663963	−	0.0663963i
$643$	812.847	+	812.847i	1.26415	+	1.26415i	0.949063	+	0.315085i	$0.102033\pi$
$643$	812.847	+	812.847i	1.26415	+	1.26415i	0.315085	+	0.949063i	$0.397967\pi$
$644$			22.0193i			0.0341914i
$645$	−357.090	+	202.686i	−0.553628	+	0.314241i
$646$	298.684			0.462359
$647$	452.657	−	452.657i	0.699624	−	0.699624i	−0.264706	−	0.964329i	$-0.585275\pi$
$647$	452.657	−	452.657i	0.699624	−	0.699624i	0.964329	+	0.264706i	$0.0852747\pi$
$648$	−18.0000	−	18.0000i	−0.0277778	−	0.0277778i
$649$			0.657876i			0.00101368i
$650$	−204.837	+	343.056i	−0.315134	+	0.527778i
$651$	−111.044			−0.170574
$652$	308.923	−	308.923i	0.473808	−	0.473808i
$653$	−486.664	−	486.664i	−0.745275	−	0.745275i	0.228313	−	0.973588i	$-0.426679\pi$
$653$	−486.664	−	486.664i	−0.745275	−	0.745275i	−0.973588	+	0.228313i	$0.926679\pi$
$654$		−	72.0424i		−	0.110157i
$655$	126.693	+	223.206i	0.193424	+	0.340773i
$656$	−38.5138			−0.0587100
$657$	298.898	−	298.898i	0.454943	−	0.454943i
$658$	157.598	+	157.598i	0.239510	+	0.239510i
$659$			708.304i			1.07482i	0.843322	+	0.537408i	$0.180596\pi$
$659$			708.304i			1.07482i	−0.843322	+	0.537408i	$0.819404\pi$
$660$	0.128331	+	0.0353979i	0.000194441	+	5.36331e-5i
$661$	−187.356			−0.283443			−0.141722	−	0.989907i	$-0.545264\pi$
$661$	−187.356			−0.283443			−0.141722	+	0.989907i	$0.545264\pi$
$662$	−532.735	+	532.735i	−0.804735	+	0.804735i
$663$	99.3397	+	99.3397i	0.149834	+	0.149834i
$664$			437.594i			0.659027i
$665$	89.8141	−	325.611i	0.135059	−	0.489640i
$666$	105.101			0.157810
$667$	82.0494	−	82.0494i	0.123013	−	0.123013i
$668$	−410.717	−	410.717i	−0.614846	−	0.614846i
$669$		−	344.003i		−	0.514204i
$670$	−699.015	+	396.764i	−1.04331	+	0.592185i
$671$	−0.0785154			−0.000117012
$672$	15.9048	−	15.9048i	0.0236679	−	0.0236679i
$673$	−265.316	−	265.316i	−0.394229	−	0.394229i	0.481963	−	0.876192i	$-0.339924\pi$
$673$	−265.316	−	265.316i	−0.394229	−	0.394229i	−0.876192	+	0.481963i	$0.839924\pi$
$674$		−	799.749i		−	1.18657i
$675$	31.7758	+	125.958i	0.0470753	+	0.186604i
$676$	−82.5671			−0.122141
$677$	670.523	−	670.523i	0.990433	−	0.990433i	−0.00952198	−	0.999955i	$-0.503031\pi$
$677$	670.523	−	670.523i	0.990433	−	0.990433i	0.999955	+	0.00952198i	$0.00303099\pi$
$678$	−47.7264	−	47.7264i	−0.0703929	−	0.0703929i
$679$		−	240.169i		−	0.353709i
$680$	−50.1037	−	88.2723i	−0.0736819	−	0.129812i
$681$	−443.527			−0.651288
$682$	0.214643	−	0.214643i	0.000314726	−	0.000314726i
$683$	−426.903	−	426.903i	−0.625042	−	0.625042i	0.321775	−	0.946816i	$-0.395721\pi$
$683$	−426.903	−	426.903i	−0.625042	−	0.625042i	−0.946816	+	0.321775i	$0.895721\pi$
$684$		−	176.561i		−	0.258130i
$685$	1218.87	+	336.205i	1.77938	+	0.490811i
$686$	301.054			0.438854
$687$	264.350	−	264.350i	0.384789	−	0.384789i
$688$	−134.102	−	134.102i	−0.194916	−	0.194916i
$689$		−	670.245i		−	0.972779i
$690$	15.6182	−	56.6222i	0.0226351	−	0.0820611i
$691$	−121.817			−0.176291			−0.0881456	−	0.996108i	$-0.528094\pi$
$691$	−121.817			−0.176291			−0.0881456	+	0.996108i	$0.528094\pi$
$692$	−44.1993	+	44.1993i	−0.0638718	+	0.0638718i
$693$	−0.0374291	−	0.0374291i	−5.40102e−5	−	5.40102e-5i
$694$		−	211.796i		−	0.305182i
$695$	−309.080	+	175.435i	−0.444720	+	0.252424i
$696$	−118.531			−0.170303
$697$	48.8647	−	48.8647i	0.0701071	−	0.0701071i
$698$	171.397	+	171.397i	0.245555	+	0.245555i
$699$			174.028i			0.248967i
$700$	−111.296	+	28.0772i	−0.158995	+	0.0401103i
$701$	250.675			0.357596			0.178798	−	0.983886i	$-0.442779\pi$
$701$	250.675			0.357596			0.178798	+	0.983886i	$0.442779\pi$
$702$	58.7226	−	58.7226i	0.0836504	−	0.0836504i
$703$	515.466	+	515.466i	0.733237	+	0.733237i
$704$			0.0614871i			8.73396e-5i
$705$	−293.476	−	517.044i	−0.416278	−	0.733395i
$706$	−469.570			−0.665113
$707$	−42.7957	+	42.7957i	−0.0605314	+	0.0605314i
$708$	−209.665	−	209.665i	−0.296137	−	0.296137i
$709$		−	662.354i		−	0.934209i	−0.884202	−	0.467105i	$-0.845297\pi$
$709$		−	662.354i		−	0.934209i	0.884202	−	0.467105i	$-0.154703\pi$
$710$	337.320	+	93.0438i	0.475098	+	0.131048i
$711$	344.458			0.484470
$712$	−33.8657	+	33.8657i	−0.0475642	+	0.0475642i
$713$	−94.7050	−	94.7050i	−0.132826	−	0.132826i
$714$			40.3588i			0.0565249i
$715$	−0.115481	+	0.418663i	−0.000161512	+	0.000585542i
$716$	−232.980			−0.325391
$717$	−132.024	+	132.024i	−0.184134	+	0.184134i
$718$	219.996	+	219.996i	0.306401	+	0.306401i
$719$			702.256i			0.976712i	0.872645	+	0.488356i	$0.162403\pi$
$719$			702.256i			0.976712i	−0.872645	+	0.488356i	$0.837597\pi$
$720$	−52.1803	+	29.6178i	−0.0724727	+	0.0411358i
$721$	9.44579			0.0131010
$722$	504.936	−	504.936i	0.699357	−	0.699357i
$723$	−86.2430	−	86.2430i	−0.119285	−	0.119285i
$724$			358.816i			0.495602i
$725$	519.341	+	310.096i	0.716333	+	0.427719i
$726$	−296.388			−0.408248
$727$	−745.904	+	745.904i	−1.02600	+	1.02600i	−0.0263497	+	0.999653i	$0.508388\pi$
$727$	−745.904	+	745.904i	−1.02600	+	1.02600i	−0.999653	+	0.0263497i	$0.991612\pi$
$728$	51.8875	+	51.8875i	0.0712740	+	0.0712740i
$729$		−	27.0000i		−	0.0370370i
$730$	−491.815	−	866.477i	−0.673720	−	1.18695i
$731$	340.287			0.465508
$732$	25.0228	−	25.0228i	0.0341842	−	0.0341842i
$733$	20.0570	+	20.0570i	0.0273628	+	0.0273628i	0.720656	−	0.693293i	$-0.243841\pi$
$733$	20.0570	+	20.0570i	0.0273628	+	0.0273628i	−0.693293	+	0.720656i	$0.743841\pi$
$734$		−	396.639i		−	0.540380i
$735$	−365.078	−	100.701i	−0.496705	−	0.137008i
$736$	27.1293			0.0368605
$737$	−0.617767	+	0.617767i	−0.000838219	+	0.000838219i
$738$	−28.8853	−	28.8853i	−0.0391400	−	0.0391400i
$739$			718.802i			0.972668i	0.873773	+	0.486334i	$0.161666\pi$
$739$			718.802i			0.972668i	−0.873773	+	0.486334i	$0.838334\pi$
$740$	65.8711	−	238.808i	0.0890150	−	0.322714i
$741$	576.006			0.777336
$742$	136.150	−	136.150i	0.183491	−	0.183491i
$743$	−698.586	−	698.586i	−0.940223	−	0.940223i	0.0580882	−	0.998311i	$-0.481500\pi$
$743$	−698.586	−	698.586i	−0.940223	−	0.940223i	−0.998311	+	0.0580882i	$0.981500\pi$
$744$			136.814i			0.183889i
$745$	488.845	−	277.470i	0.656168	−	0.372443i
$746$	714.555			0.957849
$747$	−328.195	+	328.195i	−0.439351	+	0.439351i
$748$	−0.0780122	−	0.0780122i	−0.000104294	−	0.000104294i
$749$			56.4973i			0.0754303i
$750$	306.112	+	6.74241i	0.408149	+	0.00898987i
$751$	−753.877			−1.00383			−0.501916	−	0.864917i	$-0.667371\pi$
$751$	−753.877			−1.00383			−0.501916	+	0.864917i	$0.667371\pi$
$752$	194.172	−	194.172i	0.258207	−	0.258207i
$753$	177.696	+	177.696i	0.235984	+	0.235984i
$754$		−	386.692i		−	0.512854i
$755$	−211.321	−	372.304i	−0.279896	−	0.493118i
$756$	23.8573			0.0315572
$757$	812.375	−	812.375i	1.07315	−	1.07315i	0.0760459	−	0.997104i	$-0.475770\pi$
$757$	812.375	−	812.375i	1.07315	−	1.07315i	0.997104	−	0.0760459i	$-0.0242296\pi$
$758$	−632.919	−	632.919i	−0.834986	−	0.834986i
$759$		−	0.0638437i		−	8.41156e-5i
$760$	−401.176	−	110.657i	−0.527863	−	0.145602i
$761$	−323.489			−0.425085			−0.212542	−	0.977152i	$-0.568174\pi$
$761$	−323.489			−0.425085			−0.212542	+	0.977152i	$0.568174\pi$
$762$	−326.724	+	326.724i	−0.428772	+	0.428772i
$763$	47.7426	+	47.7426i	0.0625723	+	0.0625723i
$764$		−	96.9081i		−	0.126843i
$765$	28.6265	−	103.782i	0.0374202	−	0.135663i
$766$	912.421			1.19115
$767$	684.004	−	684.004i	0.891792	−	0.891792i
$768$	−19.5959	−	19.5959i	−0.0255155	−	0.0255155i
$769$		−	35.2214i		−	0.0458016i	−0.999738	−	0.0229008i	$-0.992710\pi$
$769$		−	35.2214i		−	0.0458016i	0.999738	−	0.0229008i	$-0.00729019\pi$
$770$	−0.108503	+	0.0615869i	−0.000140914	+	7.99830e-5i
$771$	85.8563			0.111357
$772$	6.97142	−	6.97142i	0.00903033	−	0.00903033i
$773$	77.8234	+	77.8234i	0.100677	+	0.100677i	0.755651	−	0.654974i	$-0.227321\pi$
$773$	77.8234	+	77.8234i	0.100677	+	0.100677i	−0.654974	+	0.755651i	$0.727321\pi$
$774$		−	201.153i		−	0.259888i
$775$	357.926	−	599.447i	0.461840	−	0.773479i
$776$	−295.905			−0.381321
$777$	−69.6509	+	69.6509i	−0.0896408	+	0.0896408i
$778$	297.456	+	297.456i	0.382334	+	0.382334i
$779$		−	283.334i		−	0.363715i
$780$	−96.6240	−	170.231i	−0.123877	−	0.218245i
$781$	0.380341			0.000486993
$782$	−34.4205	+	34.4205i	−0.0440160	+	0.0440160i
$783$	−88.8983	−	88.8983i	−0.113535	−	0.113535i
$784$		−	174.920i		−	0.223112i
$785$	−294.873	−	81.3357i	−0.375635	−	0.103612i
$786$	−125.735			−0.159968
$787$	583.385	−	583.385i	0.741277	−	0.741277i	−0.231547	−	0.972824i	$-0.574379\pi$
$787$	583.385	−	583.385i	0.741277	−	0.741277i	0.972824	+	0.231547i	$0.0743788\pi$
$788$	378.976	+	378.976i	0.480934	+	0.480934i
$789$		−	283.016i		−	0.358702i
$790$	215.885	−	782.667i	0.273272	−	0.990718i
$791$	63.2567			0.0799706
$792$	−0.0461153	+	0.0461153i	−5.82264e−5	+	5.82264e-5i
$793$	81.6337	+	81.6337i	0.102943	+	0.102943i
$794$		−	167.498i		−	0.210955i
$795$	−446.680	+	253.537i	−0.561862	+	0.318915i
$796$	−640.068			−0.804106
$797$	369.662	−	369.662i	0.463817	−	0.463817i	−0.436087	−	0.899904i	$-0.643636\pi$
$797$	369.662	−	369.662i	0.463817	−	0.463817i	0.899904	+	0.436087i	$0.143636\pi$
$798$	117.007	+	117.007i	0.146626	+	0.146626i
$799$			492.714i			0.616663i
$800$	34.5931	+	137.125i	0.0432414	+	0.171406i
$801$	−50.7985			−0.0634189
$802$	365.707	−	365.707i	0.455994	−	0.455994i
$803$	−0.765764	−	0.765764i	−0.000953629	−	0.000953629i
$804$		−	393.765i		−	0.489757i
$805$	27.1734	+	47.8739i	0.0337558	+	0.0594706i
$806$	−446.336			−0.553767
$807$	−338.340	+	338.340i	−0.419257	+	0.419257i
$808$	52.7274	+	52.7274i	0.0652567	+	0.0652567i
$809$			736.871i			0.910842i	0.890276	+	0.455421i	$0.150511\pi$
$809$			736.871i			0.910842i	−0.890276	+	0.455421i	$0.849489\pi$
$810$	−61.3486	−	16.9219i	−0.0757390	−	0.0208913i
$811$	−340.553			−0.419918			−0.209959	−	0.977710i	$-0.567333\pi$
$811$	−340.553			−0.419918			−0.209959	+	0.977710i	$0.567333\pi$
$812$	78.5507	−	78.5507i	0.0967374	−	0.0967374i
$813$	192.811	+	192.811i	0.237160	+	0.237160i
$814$		−	0.269266i		−	0.000330793i
$815$	290.421	−	1052.89i	0.356344	−	1.29189i
$816$	49.7250			0.0609374
$817$	986.550	−	986.550i	1.20753	−	1.20753i
$818$	432.702	+	432.702i	0.528975	+	0.528975i
$819$			77.8312i			0.0950320i
$820$	−83.7359	+	47.5288i	−0.102117	+	0.0579620i
$821$	567.437			0.691154			0.345577	−	0.938390i	$-0.387683\pi$
$821$	567.437			0.691154			0.345577	+	0.938390i	$0.387683\pi$
$822$	−437.998	+	437.998i	−0.532845	+	0.532845i
$823$	−467.397	−	467.397i	−0.567918	−	0.567918i	0.363627	−	0.931545i	$-0.381538\pi$
$823$	−467.397	−	467.397i	−0.567918	−	0.567918i	−0.931545	+	0.363627i	$0.881538\pi$
$824$		−	11.6379i		−	0.0141237i
$825$	0.322698	−	0.0814084i	0.000391149	−	9.86769e-5i
$826$	277.891			0.336430
$827$	259.593	−	259.593i	0.313897	−	0.313897i	−0.532520	−	0.846417i	$-0.678755\pi$
$827$	259.593	−	259.593i	0.313897	−	0.313897i	0.846417	+	0.532520i	$0.178755\pi$
$828$	20.3470	+	20.3470i	0.0245737	+	0.0245737i
$829$		−	1322.04i		−	1.59474i	−0.603488	−	0.797372i	$-0.706223\pi$
$829$		−	1322.04i		−	1.59474i	0.603488	−	0.797372i	$-0.293777\pi$
$830$	540.023	+	951.408i	0.650630	+	1.14627i
$831$	222.161			0.267342
$832$	63.9291	−	63.9291i	0.0768378	−	0.0768378i
$833$	221.931	+	221.931i	0.266423	+	0.266423i
$834$		−	174.109i		−	0.208764i
$835$	−1399.83	−	386.119i	−1.67644	−	0.462418i
$836$	−0.452342			−0.000541079
$837$	−102.610	+	102.610i	−0.122593	+	0.122593i
$838$	275.957	+	275.957i	0.329305	+	0.329305i
$839$			111.060i			0.132371i	0.997807	+	0.0661857i	$0.0210830\pi$
$839$			111.060i			0.132371i	−0.997807	+	0.0661857i	$0.978917\pi$
$840$	14.9523	−	54.2078i	0.0178003	−	0.0645331i
$841$	255.600			0.303924
$842$	754.476	−	754.476i	0.896053	−	0.896053i
$843$	−125.408	−	125.408i	−0.148764	−	0.148764i
$844$			185.478i			0.219760i
$845$	−179.516	+	101.894i	−0.212445	+	0.120584i
$846$	291.258			0.344276
$847$	196.417	−	196.417i	0.231897	−	0.231897i
$848$	−167.747	−	167.747i	−0.197815	−	0.197815i
$849$		−	90.7236i		−	0.106859i
$850$	−217.869	−	130.088i	−0.256316	−	0.153045i
$851$	−118.805			−0.139607
$852$	−121.215	+	121.215i	−0.142271	+	0.142271i
$853$	−585.755	−	585.755i	−0.686700	−	0.686700i	0.274801	−	0.961501i	$-0.411388\pi$
$853$	−585.755	−	585.755i	−0.686700	−	0.686700i	−0.961501	+	0.274801i	$0.911388\pi$
$854$			33.1654i			0.0388353i
$855$	−217.889	−	383.875i	−0.254841	−	0.448977i
$856$	69.6087			0.0813186
$857$	−938.531	+	938.531i	−1.09513	+	1.09513i	−0.100164	+	0.994971i	$0.531937\pi$
$857$	−938.531	+	938.531i	−1.09513	+	1.09513i	−0.994971	+	0.100164i	$0.968063\pi$
$858$	−0.150445	−	0.150445i	−0.000175344	−	0.000175344i
$859$			246.202i			0.286614i	0.989678	+	0.143307i	$0.0457737\pi$
$859$			246.202i			0.286614i	−0.989678	+	0.143307i	$0.954226\pi$
$860$	−457.055	−	126.071i	−0.531459	−	0.146594i
$861$	38.2847			0.0444654
$862$	479.745	−	479.745i	0.556549	−	0.556549i
$863$	−95.1334	−	95.1334i	−0.110236	−	0.110236i	0.649837	−	0.760073i	$-0.274837\pi$
$863$	−95.1334	−	95.1334i	−0.110236	−	0.110236i	−0.760073	+	0.649837i	$0.774837\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	−41.5521	+	150.642i	−0.0480371	+	0.174153i
$866$	−762.601			−0.880602
$867$	290.862	−	290.862i	0.335481	−	0.335481i
$868$	−90.6667	−	90.6667i	−0.104455	−	0.104455i
$869$		−	0.882489i		−	0.00101552i
$870$	−257.708	+	146.276i	−0.296216	+	0.168133i
$871$	1284.60			1.47486
$872$	58.8224	−	58.8224i	0.0674568	−	0.0674568i
$873$	−221.929	−	221.929i	−0.254214	−	0.254214i
$874$			199.582i			0.228355i
$875$	−207.329	+	198.393i	−0.236948	+	0.226735i
$876$	488.098			0.557189
$877$	−845.619	+	845.619i	−0.964218	+	0.964218i	−0.999382	−	0.0351634i	$-0.988805\pi$
$877$	−845.619	+	845.619i	−0.964218	+	0.964218i	0.0351634	+	0.999382i	$0.488805\pi$
$878$	171.159	+	171.159i	0.194942	+	0.194942i
$879$			346.636i			0.394352i
$880$	0.0758795	+	0.133684i	8.62268e−5	+	0.000151914i
$881$	−1521.67			−1.72721			−0.863604	−	0.504171i	$-0.831798\pi$
$881$	−1521.67			−1.72721			−0.863604	+	0.504171i	$0.831798\pi$
$882$	131.190	−	131.190i	0.148741	−	0.148741i
$883$	556.408	+	556.408i	0.630133	+	0.630133i	0.948101	−	0.317968i	$-0.103000\pi$
$883$	556.408	+	556.408i	0.630133	+	0.630133i	−0.317968	+	0.948101i	$0.603000\pi$
$884$			162.221i			0.183508i
$885$	−714.592	−	197.108i	−0.807448	−	0.222721i
$886$	1097.38			1.23858
$887$	711.815	−	711.815i	0.802497	−	0.802497i	−0.180988	−	0.983485i	$-0.557930\pi$
$887$	711.815	−	711.815i	0.802497	−	0.802497i	0.983485	+	0.180988i	$0.0579296\pi$
$888$	85.8149	+	85.8149i	0.0966384	+	0.0966384i
$889$		−	433.041i		−	0.487111i
$890$	−31.8374	+	115.423i	−0.0357724	+	0.129689i
$891$	−0.0691730			−7.76352e−5
$892$	280.877	−	280.877i	0.314885	−	0.314885i
$893$	1428.46	+	1428.46i	1.59962	+	1.59962i
$894$			275.373i			0.308024i
$895$	−506.541	+	287.514i	−0.565967	+	0.321245i
$896$	25.9725			0.0289872
$897$	−66.3793	+	66.3793i	−0.0740015	+	0.0740015i
$898$	−422.457	−	422.457i	−0.470442	−	0.470442i
$899$			675.694i			0.751606i
$900$	−76.8990	+	128.789i	−0.0854434	+	0.143099i
$901$	425.661			0.472432
$902$	−0.0740031	+	0.0740031i	−8.20434e−5	+	8.20434e-5i
$903$	133.305	+	133.305i	0.147624	+	0.147624i
$904$		−	77.9368i		−	0.0862133i
$905$	442.805	+	780.131i	0.489288	+	0.862023i
$906$	209.724			0.231483
$907$	−1000.32	+	1000.32i	−1.10289	+	1.10289i	−0.108825	+	0.994061i	$0.534709\pi$
$907$	−1000.32	+	1000.32i	−1.10289	+	1.10289i	−0.994061	+	0.108825i	$0.965291\pi$
$908$	−362.138	−	362.138i	−0.398831	−	0.398831i
$909$			79.0911i			0.0870089i
$910$	176.846	+	48.7798i	0.194336	+	0.0536042i
$911$	−727.764			−0.798862			−0.399431	−	0.916763i	$-0.630792\pi$
$911$	−727.764			−0.798862			−0.399431	+	0.916763i	$0.630792\pi$
$912$	144.161	−	144.161i	0.158072	−	0.158072i
$913$	0.840824	+	0.840824i	0.000920946	+	0.000920946i
$914$		−	491.598i		−	0.537854i
$915$	23.5242	−	85.2842i	0.0257095	−	0.0932067i
$916$	431.682			0.471268
$917$	83.3249	−	83.3249i	0.0908668	−	0.0908668i
$918$	37.2937	+	37.2937i	0.0406250	+	0.0406250i
$919$		−	882.592i		−	0.960383i	−0.877164	−	0.480191i	$-0.840567\pi$
$919$		−	882.592i		−	0.960383i	0.877164	−	0.480191i	$-0.159433\pi$
$920$	58.9841	−	33.4796i	0.0641131	−	0.0363908i
$921$	−797.786			−0.866217
$922$	751.846	−	751.846i	0.815451	−	0.815451i
$923$	−395.447	−	395.447i	−0.428436	−	0.428436i
$924$		−	0.0611214i		−	6.61487e-5i
$925$	−151.491	−	600.502i	−0.163774	−	0.649191i
$926$	−636.677			−0.687556
$927$	8.72842	−	8.72842i	0.00941577	−	0.00941577i
$928$	−96.7802	−	96.7802i	−0.104289	−	0.104289i
$929$			871.159i			0.937739i	0.883267	+	0.468869i	$0.155339\pi$
$929$			871.159i			0.937739i	−0.883267	+	0.468869i	$0.844661\pi$
$930$	168.838	+	297.458i	0.181546	+	0.319847i
$931$	1286.83			1.38220
$932$	−142.093	+	142.093i	−0.152460	+	0.152460i
$933$	29.2512	+	29.2512i	0.0313518	+	0.0313518i
$934$		−	609.538i		−	0.652610i
$935$	−0.265885	−	0.0733399i	−0.000284369	−	7.84384e-5i
$936$	95.8936			0.102450
$937$	−1116.62	+	1116.62i	−1.19169	+	1.19169i	−0.215101	+	0.976592i	$0.569008\pi$
$937$	−1116.62	+	1116.62i	−1.19169	+	1.19169i	−0.976592	+	0.215101i	$0.930992\pi$
$938$	260.949	+	260.949i	0.278197	+	0.278197i
$939$			637.732i			0.679161i
$940$	182.542	−	661.787i	0.194194	−	0.704028i
$941$	149.884			0.159281			0.0796407	−	0.996824i	$-0.474623\pi$
$941$	149.884			0.159281			0.0796407	+	0.996824i	$0.474623\pi$
$942$	105.962	−	105.962i	0.112486	−	0.112486i
$943$	32.6516	+	32.6516i	0.0346253	+	0.0346253i
$944$		−	342.382i		−	0.362692i
$945$	51.8700	−	29.4416i	0.0548889	−	0.0311552i
$946$	−0.515347			−0.000544765
$947$	−154.123	+	154.123i	−0.162748	+	0.162748i	−0.783783	−	0.621035i	$-0.786713\pi$
$947$	−154.123	+	154.123i	−0.162748	+	0.162748i	0.621035	+	0.783783i	$0.286713\pi$
$948$	281.249	+	281.249i	0.296676	+	0.296676i
$949$			1592.35i			1.67793i
$950$	−1008.79	+	254.491i	−1.06188	+	0.267885i
$951$	225.893			0.237532
$952$	−32.9528	+	32.9528i	−0.0346143	+	0.0346143i
$953$	−724.299	−	724.299i	−0.760020	−	0.760020i	0.216305	−	0.976326i	$-0.430599\pi$
$953$	−724.299	−	724.299i	−0.760020	−	0.760020i	−0.976326	+	0.216305i	$0.930599\pi$
$954$		−	251.621i		−	0.263753i
$955$	−119.592	−	210.696i	−0.125227	−	0.220624i
$956$	−215.595			−0.225518
$957$	−0.227754	+	0.227754i	−0.000237987	+	0.000237987i
$958$	−511.063	−	511.063i	−0.533469	−	0.533469i
$959$		−	580.525i		−	0.605344i
$960$	−66.7879	−	18.4223i	−0.0695707	−	0.0191899i
$961$	−181.084			−0.188433
$962$	−279.960	+	279.960i	−0.291018	+	0.291018i
$963$	52.2065	+	52.2065i	0.0542124	+	0.0542124i
$964$		−	140.834i		−	0.146094i
$965$	6.55388	−	23.7604i	0.00679159	−	0.0246221i
$966$	−26.9680			−0.0279172
$967$	−462.786	+	462.786i	−0.478579	+	0.478579i	−0.904677	−	0.426098i	$-0.859888\pi$
$967$	−462.786	+	462.786i	−0.478579	+	0.478579i	0.426098	+	0.904677i	$0.359888\pi$
$968$	−242.000	−	242.000i	−0.250000	−	0.250000i
$969$			365.811i			0.377514i
$970$	−643.351	+	365.168i	−0.663249	+	0.376462i
$971$	−578.784			−0.596070			−0.298035	−	0.954555i	$-0.596331\pi$
$971$	−578.784			−0.596070			−0.298035	+	0.954555i	$0.596331\pi$
$972$	22.0454	−	22.0454i	0.0226805	−	0.0226805i
$973$	115.382	+	115.382i	0.118584	+	0.118584i
$974$			553.130i			0.567895i
$975$	−420.156	−	250.873i	−0.430929	−	0.257306i
$976$	40.8621			0.0418669
$977$	−159.692	+	159.692i	−0.163451	+	0.163451i	−0.784094	−	0.620643i	$-0.786872\pi$
$977$	−159.692	+	159.692i	−0.163451	+	0.163451i	0.620643	+	0.784094i	$0.286872\pi$
$978$	378.351	+	378.351i	0.386862	+	0.386862i
$979$			0.130144i			0.000132935i
$980$	−215.864	−	380.307i	−0.220269	−	0.388068i
$981$	88.2336			0.0899425
$982$	−730.914	+	730.914i	−0.744312	+	0.744312i
$983$	386.084	+	386.084i	0.392761	+	0.392761i	0.875670	−	0.482909i	$-0.160420\pi$
$983$	386.084	+	386.084i	0.392761	+	0.392761i	−0.482909	+	0.875670i	$0.660420\pi$
$984$		−	47.1696i		−	0.0479365i
$985$	1291.65	+	356.278i	1.31132	+	0.361704i
$986$	245.581			0.249068
$987$	−193.017	+	193.017i	−0.195559	+	0.195559i
$988$	470.307	+	470.307i	0.476019	+	0.476019i
$989$			227.381i			0.229910i
$990$	−0.0433534	+	0.157173i	−4.37913e−5	+	0.000158760i
$991$	1670.98			1.68615			0.843077	−	0.537794i	$-0.180742\pi$
$991$	1670.98			1.68615			0.843077	+	0.537794i	$0.180742\pi$
$992$	−111.708	+	111.708i	−0.112609	+	0.112609i
$993$	−652.464	−	652.464i	−0.657063	−	0.657063i
$994$		−	160.658i		−	0.161628i
$995$	−1391.62	+	789.891i	−1.39862	+	0.793860i
$996$	−535.941			−0.538093
$997$	−344.694	+	344.694i	−0.345732	+	0.345732i	−0.858517	−	0.512785i	$-0.828614\pi$
$997$	−344.694	+	344.694i	−0.345732	+	0.345732i	0.512785	+	0.858517i	$0.328614\pi$
$998$	318.628	+	318.628i	0.319267	+	0.319267i
$999$			128.722i			0.128851i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.b.553.3	yes	48
5.2	odd	4	inner	690.3.k.b.277.3	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.b.277.3	✓	48	5.2	odd	4	inner
690.3.k.b.553.3	yes	48	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-2.46815 - 4.34836i) q^{5} +2.44949 q^{6} +(-1.62328 + 1.62328i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-2.46815 - 4.34836i) q^{5} +2.44949 q^{6} +(-1.62328 + 1.62328i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(6.81651 + 1.88022i) q^{10} +0.00768588 q^{11} +(-2.44949 + 2.44949i) q^{12} +(-7.99113 - 7.99113i) q^{13} -3.24656i q^{14} +(-2.30278 + 8.34848i) q^{15} -4.00000 q^{16} +(5.07503 - 5.07503i) q^{17} +(-3.00000 - 3.00000i) q^{18} -29.4268i q^{19} +(-8.69672 + 4.93629i) q^{20} +3.97621 q^{21} +(-0.00768588 + 0.00768588i) q^{22} +(3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(-12.8165 + 21.4648i) q^{25} +15.9823 q^{26} +(3.67423 - 3.67423i) q^{27} +(3.24656 + 3.24656i) q^{28} -24.1950i q^{29} +(-6.04570 - 10.6513i) q^{30} -27.9270 q^{31} +(4.00000 - 4.00000i) q^{32} +(-0.00941325 - 0.00941325i) q^{33} +10.1501i q^{34} +(11.0651 + 3.05212i) q^{35} +6.00000 q^{36} +(-17.5169 + 17.5169i) q^{37} +(29.4268 + 29.4268i) q^{38} +19.5742i q^{39} +(3.76043 - 13.6330i) q^{40} +9.62845 q^{41} +(-3.97621 + 3.97621i) q^{42} +(33.5256 + 33.5256i) q^{43} -0.0153718i q^{44} +(13.0451 - 7.40444i) q^{45} -6.78233 q^{46} +(-48.5429 + 48.5429i) q^{47} +(4.89898 + 4.89898i) q^{48} +43.7299i q^{49} +(-8.64828 - 34.2813i) q^{50} -12.4312 q^{51} +(-15.9823 + 15.9823i) q^{52} +(41.9368 + 41.9368i) q^{53} +7.34847i q^{54} +(-0.0189699 - 0.0334210i) q^{55} -6.49313 q^{56} +(-36.0403 + 36.0403i) q^{57} +(24.1950 + 24.1950i) q^{58} +85.5954i q^{59} +(16.6970 + 4.60557i) q^{60} -10.2155 q^{61} +(27.9270 - 27.9270i) q^{62} +(-4.86985 - 4.86985i) q^{63} +8.00000i q^{64} +(-15.0251 + 54.4716i) q^{65} +0.0188265 q^{66} +(-80.3769 + 80.3769i) q^{67} +(-10.1501 - 10.1501i) q^{68} -8.30662i q^{69} +(-14.1172 + 8.01299i) q^{70} +49.4857 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-99.6326 - 99.6326i) q^{73} -35.0338i q^{74} +(41.9858 - 10.5919i) q^{75} -58.8536 q^{76} +(-0.0124764 + 0.0124764i) q^{77} +(-19.5742 - 19.5742i) q^{78} -114.819i q^{79} +(9.87259 + 17.3934i) q^{80} -9.00000 q^{81} +(-9.62845 + 9.62845i) q^{82} +(109.398 + 109.398i) q^{83} -7.95242i q^{84} +(-34.5940 - 9.54216i) q^{85} -67.0511 q^{86} +(-29.6328 + 29.6328i) q^{87} +(0.0153718 + 0.0153718i) q^{88} +16.9328i q^{89} +(-5.64065 + 20.4495i) q^{90} +25.9437 q^{91} +(6.78233 - 6.78233i) q^{92} +(34.2034 + 34.2034i) q^{93} -97.0859i q^{94} +(-127.958 + 72.6296i) q^{95} -9.79796 q^{96} +(-73.9763 + 73.9763i) q^{97} +(-43.7299 - 43.7299i) q^{98} +0.0230577i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) \) 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	\( 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) \) 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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