LMFDB - Embedded newform 690.3.k.b.553.5

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			553.5
Character	$\chi$	$=$	690.553
Dual form			690.3.k.b.277.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(0.0428394 + 4.99982i) q^{5} +2.44949 q^{6} +(0.599576 - 0.599576i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(0.0428394 + 4.99982i) q^{5} +2.44949 q^{6} +(0.599576 - 0.599576i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(-5.04266 - 4.95698i) q^{10} +2.79269 q^{11} +(-2.44949 + 2.44949i) q^{12} +(10.4226 + 10.4226i) q^{13} +1.19915i q^{14} +(6.07103 - 6.17597i) q^{15} -4.00000 q^{16} +(8.12418 - 8.12418i) q^{17} +(-3.00000 - 3.00000i) q^{18} -19.7629i q^{19} +(9.99963 - 0.0856788i) q^{20} -1.46866 q^{21} +(-2.79269 + 2.79269i) q^{22} +(-3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(-24.9963 + 0.428378i) q^{25} -20.8451 q^{26} +(3.67423 - 3.67423i) q^{27} +(-1.19915 - 1.19915i) q^{28} +53.8793i q^{29} +(0.104935 + 12.2470i) q^{30} -24.2777 q^{31} +(4.00000 - 4.00000i) q^{32} +(-3.42033 - 3.42033i) q^{33} +16.2484i q^{34} +(3.02346 + 2.97209i) q^{35} +6.00000 q^{36} +(21.3933 - 21.3933i) q^{37} +(19.7629 + 19.7629i) q^{38} -25.5299i q^{39} +(-9.91395 + 10.0853i) q^{40} +68.1650 q^{41} +(1.46866 - 1.46866i) q^{42} +(-16.0395 - 16.0395i) q^{43} -5.58538i q^{44} +(-14.9994 + 0.128518i) q^{45} +6.78233 q^{46} +(-10.0218 + 10.0218i) q^{47} +(4.89898 + 4.89898i) q^{48} +48.2810i q^{49} +(24.5680 - 25.4247i) q^{50} -19.9001 q^{51} +(20.8451 - 20.8451i) q^{52} +(20.3778 + 20.3778i) q^{53} +7.34847i q^{54} +(0.119637 + 13.9629i) q^{55} +2.39831 q^{56} +(-24.2045 + 24.2045i) q^{57} +(-53.8793 - 53.8793i) q^{58} +113.656i q^{59} +(-12.3519 - 12.1421i) q^{60} -70.3213 q^{61} +(24.2777 - 24.2777i) q^{62} +(1.79873 + 1.79873i) q^{63} +8.00000i q^{64} +(-51.6643 + 52.5573i) q^{65} +6.84066 q^{66} +(-40.1198 + 40.1198i) q^{67} +(-16.2484 - 16.2484i) q^{68} +8.30662i q^{69} +(-5.99554 + 0.0513710i) q^{70} +117.779 q^{71} +(-6.00000 + 6.00000i) q^{72} +(75.3919 + 75.3919i) q^{73} +42.7867i q^{74} +(31.1388 + 30.0895i) q^{75} -39.5257 q^{76} +(1.67443 - 1.67443i) q^{77} +(25.5299 + 25.5299i) q^{78} +84.1235i q^{79} +(-0.171358 - 19.9993i) q^{80} -9.00000 q^{81} +(-68.1650 + 68.1650i) q^{82} +(-78.5983 - 78.5983i) q^{83} +2.93731i q^{84} +(40.9674 + 40.2714i) q^{85} +32.0790 q^{86} +(65.9883 - 65.9883i) q^{87} +(5.58538 + 5.58538i) q^{88} +67.9727i q^{89} +(14.8709 - 15.1280i) q^{90} +12.4982 q^{91} +(-6.78233 + 6.78233i) q^{92} +(29.7340 + 29.7340i) q^{93} -20.0436i q^{94} +(98.8106 - 0.846629i) q^{95} -9.79796 q^{96} +(-74.6956 + 74.6956i) q^{97} +(-48.2810 - 48.2810i) q^{98} +8.37807i 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
$5$	0.0428394	+	4.99982i	0.00856788	+	0.999963i
$5$	0.0428394	+	4.99982i	0.00856788	+	0.999963i
$6$	2.44949			0.408248
$7$	0.599576	−	0.599576i	0.0856538	−	0.0856538i	−0.662982	−	0.748636i	$-0.730709\pi$
$7$	0.599576	−	0.599576i	0.0856538	−	0.0856538i	0.748636	+	0.662982i	$0.230709\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$			3.00000i			0.333333i
$10$	−5.04266	−	4.95698i	−0.504266	−	0.495698i
$11$	2.79269			0.253881			0.126940	−	0.991910i	$-0.459484\pi$
$11$	2.79269			0.253881			0.126940	+	0.991910i	$0.459484\pi$
$12$	−2.44949	+	2.44949i	−0.204124	+	0.204124i
$13$	10.4226	+	10.4226i	0.801735	+	0.801735i	0.983367	−	0.181632i	$-0.0581379\pi$
$13$	10.4226	+	10.4226i	0.801735	+	0.801735i	−0.181632	+	0.983367i	$0.558138\pi$
$14$			1.19915i			0.0856538i
$15$	6.07103	−	6.17597i	0.404735	−	0.411731i
$16$	−4.00000			−0.250000
$17$	8.12418	−	8.12418i	0.477893	−	0.477893i	−0.426564	−	0.904457i	$-0.640276\pi$
$17$	8.12418	−	8.12418i	0.477893	−	0.477893i	0.904457	+	0.426564i	$0.140276\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$		−	19.7629i		−	1.04015i	−0.854121	−	0.520075i	$-0.825904\pi$
$19$		−	19.7629i		−	1.04015i	0.854121	−	0.520075i	$-0.174096\pi$
$20$	9.99963	−	0.0856788i	0.499982	−	0.00428394i
$21$	−1.46866			−0.0699360
$22$	−2.79269	+	2.79269i	−0.126940	+	0.126940i
$23$	−3.39116	−	3.39116i	−0.147442	−	0.147442i
$23$	−3.39116	−	3.39116i	−0.147442	−	0.147442i
$24$		−	4.89898i		−	0.204124i
$25$	−24.9963	+	0.428378i	−0.999853	+	0.0171351i
$26$	−20.8451			−0.801735
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	−1.19915	−	1.19915i	−0.0428269	−	0.0428269i
$29$			53.8793i			1.85791i	0.370198	+	0.928953i	$0.379290\pi$
$29$			53.8793i			1.85791i	−0.370198	+	0.928953i	$0.620710\pi$
$30$	0.104935	+	12.2470i	0.00349782	+	0.408233i
$31$	−24.2777			−0.783153			−0.391576	−	0.920146i	$-0.628070\pi$
$31$	−24.2777			−0.783153			−0.391576	+	0.920146i	$0.628070\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	−3.42033	−	3.42033i	−0.103646	−	0.103646i
$34$			16.2484i			0.477893i
$35$	3.02346	+	2.97209i	0.0863845	+	0.0849167i
$36$	6.00000			0.166667
$37$	21.3933	−	21.3933i	0.578198	−	0.578198i	−0.356208	−	0.934407i	$-0.615931\pi$
$37$	21.3933	−	21.3933i	0.578198	−	0.578198i	0.934407	+	0.356208i	$0.115931\pi$
$38$	19.7629	+	19.7629i	0.520075	+	0.520075i
$39$		−	25.5299i		−	0.654614i
$40$	−9.91395	+	10.0853i	−0.247849	+	0.252133i
$41$	68.1650			1.66256			0.831281	−	0.555853i	$-0.187608\pi$
$41$	68.1650			1.66256			0.831281	+	0.555853i	$0.187608\pi$
$42$	1.46866	−	1.46866i	0.0349680	−	0.0349680i
$43$	−16.0395	−	16.0395i	−0.373012	−	0.373012i	0.495561	−	0.868573i	$-0.334962\pi$
$43$	−16.0395	−	16.0395i	−0.373012	−	0.373012i	−0.868573	+	0.495561i	$0.834962\pi$
$44$		−	5.58538i		−	0.126940i
$45$	−14.9994	+	0.128518i	−0.333321	+	0.00285596i
$46$	6.78233			0.147442
$47$	−10.0218	+	10.0218i	−0.213229	+	0.213229i	−0.805638	−	0.592408i	$-0.798177\pi$
$47$	−10.0218	+	10.0218i	−0.213229	+	0.213229i	0.592408	+	0.805638i	$0.298177\pi$
$48$	4.89898	+	4.89898i	0.102062	+	0.102062i
$49$			48.2810i			0.985327i
$50$	24.5680	−	25.4247i	0.491359	−	0.508494i
$51$	−19.9001			−0.390198
$52$	20.8451	−	20.8451i	0.400867	−	0.400867i
$53$	20.3778	+	20.3778i	0.384487	+	0.384487i	0.872716	−	0.488228i	$-0.162357\pi$
$53$	20.3778	+	20.3778i	0.384487	+	0.384487i	−0.488228	+	0.872716i	$0.662357\pi$
$54$			7.34847i			0.136083i
$55$	0.119637	+	13.9629i	0.00217522	+	0.253872i
$56$	2.39831			0.0428269
$57$	−24.2045	+	24.2045i	−0.424640	+	0.424640i
$58$	−53.8793	−	53.8793i	−0.928953	−	0.928953i
$59$			113.656i			1.92637i	0.268846	+	0.963183i	$0.413358\pi$
$59$			113.656i			1.92637i	−0.268846	+	0.963183i	$0.586642\pi$
$60$	−12.3519	−	12.1421i	−0.205866	−	0.202368i
$61$	−70.3213			−1.15281			−0.576404	−	0.817165i	$-0.695545\pi$
$61$	−70.3213			−1.15281			−0.576404	+	0.817165i	$0.695545\pi$
$62$	24.2777	−	24.2777i	0.391576	−	0.391576i
$63$	1.79873	+	1.79873i	0.0285513	+	0.0285513i
$64$			8.00000i			0.125000i
$65$	−51.6643	+	52.5573i	−0.794836	+	0.808574i
$66$	6.84066			0.103646
$67$	−40.1198	+	40.1198i	−0.598803	+	0.598803i	−0.939994	−	0.341191i	$-0.889170\pi$
$67$	−40.1198	+	40.1198i	−0.598803	+	0.598803i	0.341191	+	0.939994i	$0.389170\pi$
$68$	−16.2484	−	16.2484i	−0.238946	−	0.238946i
$69$			8.30662i			0.120386i
$70$	−5.99554	+	0.0513710i	−0.0856506	+	0.000733871i
$71$	117.779			1.65886			0.829428	−	0.558614i	$-0.188667\pi$
$71$	117.779			1.65886			0.829428	+	0.558614i	$0.188667\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	75.3919	+	75.3919i	1.03277	+	1.03277i	0.999445	+	0.0333207i	$0.0106083\pi$
$73$	75.3919	+	75.3919i	1.03277	+	1.03277i	0.0333207	+	0.999445i	$0.489392\pi$
$74$			42.7867i			0.578198i
$75$	31.1388	+	30.0895i	0.415184	+	0.401193i
$76$	−39.5257			−0.520075
$77$	1.67443	−	1.67443i	0.0217458	−	0.0217458i
$78$	25.5299	+	25.5299i	0.327307	+	0.327307i
$79$			84.1235i			1.06485i	0.846476	+	0.532427i	$0.178720\pi$
$79$			84.1235i			1.06485i	−0.846476	+	0.532427i	$0.821280\pi$
$80$	−0.171358	−	19.9993i	−0.00214197	−	0.249991i
$81$	−9.00000			−0.111111
$82$	−68.1650	+	68.1650i	−0.831281	+	0.831281i
$83$	−78.5983	−	78.5983i	−0.946967	−	0.946967i	0.0516956	−	0.998663i	$-0.483537\pi$
$83$	−78.5983	−	78.5983i	−0.946967	−	0.946967i	−0.998663	+	0.0516956i	$0.983537\pi$
$84$			2.93731i			0.0349680i
$85$	40.9674	+	40.2714i	0.481970	+	0.473781i
$86$	32.0790			0.373012
$87$	65.9883	−	65.9883i	0.758487	−	0.758487i
$88$	5.58538	+	5.58538i	0.0634702	+	0.0634702i
$89$			67.9727i			0.763739i	0.924216	+	0.381869i	$0.124720\pi$
$89$			67.9727i			0.763739i	−0.924216	+	0.381869i	$0.875280\pi$
$90$	14.8709	−	15.1280i	0.165233	−	0.168089i
$91$	12.4982			0.137343
$92$	−6.78233	+	6.78233i	−0.0737210	+	0.0737210i
$93$	29.7340	+	29.7340i	0.319721	+	0.319721i
$94$		−	20.0436i		−	0.213229i
$95$	98.8106	−	0.846629i	1.04011	−	0.00891188i
$96$	−9.79796			−0.102062
$97$	−74.6956	+	74.6956i	−0.770057	+	0.770057i	−0.978116	−	0.208059i	$-0.933285\pi$
$97$	−74.6956	+	74.6956i	−0.770057	+	0.770057i	0.208059	+	0.978116i	$0.433285\pi$
$98$	−48.2810	−	48.2810i	−0.492663	−	0.492663i
$99$			8.37807i			0.0846269i
$100$	0.856757	+	49.9927i	0.00856757	+	0.499927i
$101$	−50.8982			−0.503942			−0.251971	−	0.967735i	$-0.581079\pi$
$101$	−50.8982			−0.503942			−0.251971	+	0.967735i	$0.581079\pi$
$102$	19.9001	−	19.9001i	0.195099	−	0.195099i
$103$	−15.8762	−	15.8762i	−0.154138	−	0.154138i	0.625825	−	0.779963i	$-0.284762\pi$
$103$	−15.8762	−	15.8762i	−0.154138	−	0.154138i	−0.779963	+	0.625825i	$0.784762\pi$
$104$			41.6902i			0.400867i
$105$	−0.0629163	−	7.34301i	−0.000599203	−	0.0699334i
$106$	−40.7557			−0.384487
$107$	−33.7185	+	33.7185i	−0.315126	+	0.315126i	−0.846892	−	0.531766i	$-0.821529\pi$
$107$	−33.7185	+	33.7185i	−0.315126	+	0.315126i	0.531766	+	0.846892i	$0.321529\pi$
$108$	−7.34847	−	7.34847i	−0.0680414	−	0.0680414i
$109$			136.307i			1.25053i	0.780414	+	0.625263i	$0.215008\pi$
$109$			136.307i			1.25053i	−0.780414	+	0.625263i	$0.784992\pi$
$110$	−14.0826	−	13.8433i	−0.128023	−	0.125848i
$111$	−52.4028			−0.472097
$112$	−2.39831	+	2.39831i	−0.0214134	+	0.0214134i
$113$	66.5396	+	66.5396i	0.588846	+	0.588846i	0.937319	−	0.348473i	$-0.113300\pi$
$113$	66.5396	+	66.5396i	0.588846	+	0.588846i	−0.348473	+	0.937319i	$0.613300\pi$
$114$		−	48.4089i		−	0.424640i
$115$	16.8099	−	17.1005i	0.146173	−	0.148700i
$116$	107.759			0.928953
$117$	−31.2677	+	31.2677i	−0.267245	+	0.267245i
$118$	−113.656	−	113.656i	−0.963183	−	0.963183i
$119$		−	9.74213i		−	0.0818666i
$120$	24.4940	−	0.209869i	0.204117	−	0.00174891i
$121$	−113.201			−0.935545
$122$	70.3213	−	70.3213i	0.576404	−	0.576404i
$123$	−83.4847	−	83.4847i	−0.678738	−	0.678738i
$124$			48.5555i			0.391576i
$125$	−3.21264	−	124.959i	−0.0257011	−	0.999670i
$126$	−3.59746			−0.0285513
$127$	52.1973	−	52.1973i	0.411002	−	0.411002i	−0.471085	−	0.882088i	$-0.656138\pi$
$127$	52.1973	−	52.1973i	0.411002	−	0.411002i	0.882088	+	0.471085i	$0.156138\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$			39.2886i			0.304563i
$130$	−0.892992	−	104.222i	−0.00686917	−	0.801705i
$131$	−184.660			−1.40962			−0.704809	−	0.709397i	$-0.748967\pi$
$131$	−184.660			−1.40962			−0.704809	+	0.709397i	$0.748967\pi$
$132$	−6.84066	+	6.84066i	−0.0518232	+	0.0518232i
$133$	−11.8493	−	11.8493i	−0.0890928	−	0.0890928i
$134$		−	80.2396i		−	0.598803i
$135$	18.5279	+	18.2131i	0.137244	+	0.134912i
$136$	32.4967			0.238946
$137$	126.402	−	126.402i	0.922642	−	0.922642i	−0.0745733	−	0.997216i	$-0.523759\pi$
$137$	126.402	−	126.402i	0.922642	−	0.922642i	0.997216	+	0.0745733i	$0.0237595\pi$
$138$	−8.30662	−	8.30662i	−0.0601929	−	0.0601929i
$139$			217.770i			1.56669i	0.621589	+	0.783344i	$0.286487\pi$
$139$			217.770i			1.56669i	−0.621589	+	0.783344i	$0.713513\pi$
$140$	5.94417	−	6.04691i	0.0424584	−	0.0431922i
$141$	24.5482			0.174101
$142$	−117.779	+	117.779i	−0.829428	+	0.829428i
$143$	29.1069	+	29.1069i	0.203545	+	0.203545i
$144$		−	12.0000i		−	0.0833333i
$145$	−269.386	+	2.30816i	−1.85784	+	0.0159183i
$146$	−150.784			−1.03277
$147$	59.1319	−	59.1319i	0.402258	−	0.402258i
$148$	−42.7867	−	42.7867i	−0.289099	−	0.289099i
$149$			75.9518i			0.509744i	0.966975	+	0.254872i	$0.0820333\pi$
$149$			75.9518i			0.509744i	−0.966975	+	0.254872i	$0.917967\pi$
$150$	−61.2283	+	1.04931i	−0.408188	+	0.00699539i
$151$	36.4482			0.241379			0.120689	−	0.992690i	$-0.461489\pi$
$151$	36.4482			0.241379			0.120689	+	0.992690i	$0.461489\pi$
$152$	39.5257	−	39.5257i	0.260038	−	0.260038i
$153$	24.3725	+	24.3725i	0.159298	+	0.159298i
$154$			3.34886i			0.0217458i
$155$	−1.04004	−	121.384i	−0.00670996	−	0.783124i
$156$	−51.0599			−0.327307
$157$	172.089	−	172.089i	1.09611	−	1.09611i	0.101244	−	0.994862i	$-0.467718\pi$
$157$	172.089	−	172.089i	1.09611	−	1.09611i	0.994862	−	0.101244i	$-0.0322822\pi$
$158$	−84.1235	−	84.1235i	−0.532427	−	0.532427i
$159$		−	49.9153i		−	0.313933i
$160$	20.1706	+	19.8279i	0.126066	+	0.123924i
$161$	−4.06652			−0.0252579
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	−81.8088	−	81.8088i	−0.501895	−	0.501895i	0.410132	−	0.912026i	$-0.365483\pi$
$163$	−81.8088	−	81.8088i	−0.501895	−	0.501895i	−0.912026	+	0.410132i	$0.865483\pi$
$164$		−	136.330i		−	0.831281i
$165$	16.9545	−	17.2476i	0.102755	−	0.104531i
$166$	157.197			0.946967
$167$	47.7793	−	47.7793i	0.286103	−	0.286103i	−0.549434	−	0.835537i	$-0.685157\pi$
$167$	47.7793	−	47.7793i	0.286103	−	0.286103i	0.835537	+	0.549434i	$0.185157\pi$
$168$	−2.93731	−	2.93731i	−0.0174840	−	0.0174840i
$169$			48.2591i			0.285557i
$170$	−81.2388	+	0.696070i	−0.477875	+	0.00409453i
$171$	59.2886			0.346717
$172$	−32.0790	+	32.0790i	−0.186506	+	0.186506i
$173$	115.524	+	115.524i	0.667770	+	0.667770i	0.957199	−	0.289429i	$-0.0934655\pi$
$173$	115.524	+	115.524i	0.667770	+	0.667770i	−0.289429	+	0.957199i	$0.593466\pi$
$174$			131.977i			0.758487i
$175$	−14.7304	+	15.2441i	−0.0841735	+	0.0871089i
$176$	−11.1708			−0.0634702
$177$	139.199	−	139.199i	0.786436	−	0.786436i
$178$	−67.9727	−	67.9727i	−0.381869	−	0.381869i
$179$			55.5826i			0.310518i	0.987874	+	0.155259i	$0.0496211\pi$
$179$			55.5826i			0.310518i	−0.987874	+	0.155259i	$0.950379\pi$
$180$	0.257036	+	29.9989i	0.00142798	+	0.166661i
$181$	25.4089			0.140381			0.0701903	−	0.997534i	$-0.477639\pi$
$181$	25.4089			0.140381			0.0701903	+	0.997534i	$0.477639\pi$
$182$	−12.4982	+	12.4982i	−0.0686716	+	0.0686716i
$183$	86.1256	+	86.1256i	0.470632	+	0.470632i
$184$		−	13.5647i		−	0.0737210i
$185$	107.879	+	106.046i	0.583131	+	0.573223i
$186$	−59.4681			−0.319721
$187$	22.6883	−	22.6883i	0.121328	−	0.121328i
$188$	20.0436	+	20.0436i	0.106615	+	0.106615i
$189$		−	4.40597i		−	0.0233120i
$190$	−97.9640	+	99.6573i	−0.515600	+	0.524512i
$191$	80.7623			0.422839			0.211420	−	0.977395i	$-0.432191\pi$
$191$	80.7623			0.422839			0.211420	+	0.977395i	$0.432191\pi$
$192$	9.79796	−	9.79796i	0.0510310	−	0.0510310i
$193$	−171.972	−	171.972i	−0.891047	−	0.891047i	0.103575	−	0.994622i	$-0.466972\pi$
$193$	−171.972	−	171.972i	−0.891047	−	0.891047i	−0.994622	+	0.103575i	$0.966972\pi$
$194$		−	149.391i		−	0.770057i
$195$	127.645	−	1.09369i	0.654590	−	0.00560865i
$196$	96.5620			0.492663
$197$	−85.6447	+	85.6447i	−0.434745	+	0.434745i	−0.890239	−	0.455494i	$-0.849463\pi$
$197$	−85.6447	+	85.6447i	−0.434745	+	0.434745i	0.455494	+	0.890239i	$0.349463\pi$
$198$	−8.37807	−	8.37807i	−0.0423135	−	0.0423135i
$199$		−	309.137i		−	1.55345i	−0.629838	−	0.776726i	$-0.716879\pi$
$199$		−	309.137i		−	1.55345i	0.629838	−	0.776726i	$-0.283121\pi$
$200$	−50.8494	−	49.1359i	−0.254247	−	0.245680i
$201$	98.2730			0.488920
$202$	50.8982	−	50.8982i	0.251971	−	0.251971i
$203$	32.3047	+	32.3047i	0.159137	+	0.159137i
$204$			39.8002i			0.195099i
$205$	2.92015	+	340.813i	0.0142446	+	1.66250i
$206$	31.7524			0.154138
$207$	10.1735	−	10.1735i	0.0491473	−	0.0491473i
$208$	−41.6902	−	41.6902i	−0.200434	−	0.200434i
$209$		−	55.1915i		−	0.264074i
$210$	7.40593	+	7.28009i	0.0352663	+	0.0346671i
$211$	166.044			0.786937			0.393469	−	0.919338i	$-0.371275\pi$
$211$	166.044			0.786937			0.393469	+	0.919338i	$0.371275\pi$
$212$	40.7557	−	40.7557i	0.192244	−	0.192244i
$213$	−144.249	−	144.249i	−0.677225	−	0.677225i
$214$		−	67.4370i		−	0.315126i
$215$	79.5074	−	80.8817i	0.369802	−	0.376194i
$216$	14.6969			0.0680414
$217$	−14.5564	+	14.5564i	−0.0670800	+	0.0670800i
$218$	−136.307	−	136.307i	−0.625263	−	0.625263i
$219$		−	184.672i		−	0.843249i
$220$	27.9259	−	0.239274i	0.126936	−	0.00108761i
$221$	169.349			0.766287
$222$	52.4028	−	52.4028i	0.236048	−	0.236048i
$223$	33.5693	+	33.5693i	0.150535	+	0.150535i	0.778357	−	0.627822i	$-0.216053\pi$
$223$	33.5693	+	33.5693i	0.150535	+	0.150535i	−0.627822	+	0.778357i	$0.716053\pi$
$224$		−	4.79661i		−	0.0214134i
$225$	−1.28514	−	74.9890i	−0.00571171	−	0.333284i
$226$	−133.079			−0.588846
$227$	201.604	−	201.604i	0.888125	−	0.888125i	−0.106218	−	0.994343i	$-0.533874\pi$
$227$	201.604	−	201.604i	0.888125	−	0.888125i	0.994343	+	0.106218i	$0.0338742\pi$
$228$	48.4089	+	48.4089i	0.212320	+	0.212320i
$229$		−	91.1570i		−	0.398066i	−0.979993	−	0.199033i	$-0.936220\pi$
$229$		−	91.1570i		−	0.398066i	0.979993	−	0.199033i	$-0.0637800\pi$
$230$	0.290551	+	33.9104i	0.00126327	+	0.147437i
$231$	−4.10150			−0.0177554
$232$	−107.759	+	107.759i	−0.464476	+	0.464476i
$233$	−186.981	−	186.981i	−0.802495	−	0.802495i	0.180990	−	0.983485i	$-0.442070\pi$
$233$	−186.981	−	186.981i	−0.802495	−	0.802495i	−0.983485	+	0.180990i	$0.942070\pi$
$234$		−	62.5353i		−	0.267245i
$235$	−50.5364	−	49.6777i	−0.215048	−	0.211395i
$236$	227.311			0.963183
$237$	103.030	−	103.030i	0.434725	−	0.434725i
$238$	9.74213	+	9.74213i	0.0409333	+	0.0409333i
$239$		−	171.742i		−	0.718586i	−0.933225	−	0.359293i	$-0.883018\pi$
$239$		−	171.742i		−	0.718586i	0.933225	−	0.359293i	$-0.116982\pi$
$240$	−24.2841	+	24.7039i	−0.101184	+	0.102933i
$241$	−119.663			−0.496527			−0.248263	−	0.968693i	$-0.579860\pi$
$241$	−119.663			−0.496527			−0.248263	+	0.968693i	$0.579860\pi$
$242$	113.201	−	113.201i	0.467772	−	0.467772i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$			140.643i			0.576404i
$245$	−241.396	+	2.06833i	−0.985291	+	0.00844216i
$246$	166.969			0.678738
$247$	205.979	−	205.979i	0.833925	−	0.833925i
$248$	−48.5555	−	48.5555i	−0.195788	−	0.195788i
$249$			192.526i			0.773196i
$250$	128.171	+	121.746i	0.512685	+	0.486984i
$251$	353.988			1.41031			0.705156	−	0.709052i	$-0.250877\pi$
$251$	353.988			1.41031			0.705156	+	0.709052i	$0.250877\pi$
$252$	3.59746	−	3.59746i	0.0142756	−	0.0142756i
$253$	−9.47047	−	9.47047i	−0.0374327	−	0.0374327i
$254$			104.395i			0.411002i
$255$	−0.852508	−	99.4968i	−0.00334317	−	0.390184i
$256$	16.0000			0.0625000
$257$	121.719	−	121.719i	0.473614	−	0.473614i	−0.429468	−	0.903082i	$-0.641299\pi$
$257$	121.719	−	121.719i	0.473614	−	0.473614i	0.903082	+	0.429468i	$0.141299\pi$
$258$	−39.2886	−	39.2886i	−0.152281	−	0.152281i
$259$		−	25.6539i		−	0.0990497i
$260$	105.115	+	103.329i	0.404287	+	0.397418i
$261$	−161.638			−0.619302
$262$	184.660	−	184.660i	0.704809	−	0.704809i
$263$	325.892	+	325.892i	1.23913	+	1.23913i	0.960356	+	0.278775i	$0.0899284\pi$
$263$	325.892	+	325.892i	1.23913	+	1.23913i	0.278775	+	0.960356i	$0.410072\pi$
$264$		−	13.6813i		−	0.0518232i
$265$	−101.012	+	102.758i	−0.381179	+	0.387768i
$266$	23.6987			0.0890928
$267$	83.2493	−	83.2493i	0.311795	−	0.311795i
$268$	80.2396	+	80.2396i	0.299401	+	0.299401i
$269$			510.361i			1.89725i	0.316400	+	0.948626i	$0.397526\pi$
$269$			510.361i			1.89725i	−0.316400	+	0.948626i	$0.602474\pi$
$270$	−36.7410	+	0.314804i	−0.136078	+	0.00116594i
$271$	57.8719			0.213550			0.106775	−	0.994283i	$-0.465948\pi$
$271$	57.8719			0.213550			0.106775	+	0.994283i	$0.465948\pi$
$272$	−32.4967	+	32.4967i	−0.119473	+	0.119473i
$273$	−15.3071	−	15.3071i	−0.0560701	−	0.0560701i
$274$			252.804i			0.922642i
$275$	−69.8070	+	1.19633i	−0.253844	+	0.00435028i
$276$	16.6132			0.0601929
$277$	210.527	−	210.527i	0.760027	−	0.760027i	−0.216300	−	0.976327i	$-0.569399\pi$
$277$	210.527	−	210.527i	0.760027	−	0.760027i	0.976327	+	0.216300i	$0.0693989\pi$
$278$	−217.770	−	217.770i	−0.783344	−	0.783344i
$279$		−	72.8332i		−	0.261051i
$280$	0.102742	+	11.9911i	0.000366936	+	0.0428253i
$281$	34.0038			0.121010			0.0605049	−	0.998168i	$-0.480729\pi$
$281$	34.0038			0.121010			0.0605049	+	0.998168i	$0.480729\pi$
$282$	−24.5482	+	24.5482i	−0.0870505	+	0.0870505i
$283$	172.081	+	172.081i	0.608060	+	0.608060i	0.942439	−	0.334379i	$-0.108526\pi$
$283$	172.081	+	172.081i	0.608060	+	0.608060i	−0.334379	+	0.942439i	$0.608526\pi$
$284$		−	235.557i		−	0.829428i
$285$	−122.055	−	119.981i	−0.428262	−	0.420986i
$286$	−58.2139			−0.203545
$287$	40.8701	−	40.8701i	0.142405	−	0.142405i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$			156.995i			0.543237i
$290$	267.078	−	271.695i	0.920959	−	0.936878i
$291$	182.966			0.628749
$292$	150.784	−	150.784i	0.516383	−	0.516383i
$293$	66.0033	+	66.0033i	0.225267	+	0.225267i	0.810712	−	0.585445i	$-0.199080\pi$
$293$	66.0033	+	66.0033i	0.225267	+	0.225267i	−0.585445	+	0.810712i	$0.699080\pi$
$294$			118.264i			0.402258i
$295$	−568.257	+	4.86894i	−1.92630	+	0.0165049i
$296$	85.5733			0.289099
$297$	10.2610	−	10.2610i	0.0345488	−	0.0345488i
$298$	−75.9518	−	75.9518i	−0.254872	−	0.254872i
$299$		−	70.6892i		−	0.236419i
$300$	60.1789	−	62.2776i	0.200596	−	0.207592i
$301$	−19.2338			−0.0638997
$302$	−36.4482	+	36.4482i	−0.120689	+	0.120689i
$303$	62.3373	+	62.3373i	0.205734	+	0.205734i
$304$			79.0514i			0.260038i
$305$	−3.01252	−	351.594i	−0.00987712	−	1.15277i
$306$	−48.7451			−0.159298
$307$	−182.604	+	182.604i	−0.594801	+	0.594801i	−0.938924	−	0.344123i	$-0.888176\pi$
$307$	−182.604	+	182.604i	−0.594801	+	0.594801i	0.344123	+	0.938924i	$0.388176\pi$
$308$	−3.34886	−	3.34886i	−0.0108729	−	0.0108729i
$309$			38.8886i			0.125853i
$310$	122.424	+	120.344i	0.394917	+	0.388207i
$311$	−412.663			−1.32689			−0.663446	−	0.748224i	$-0.730907\pi$
$311$	−412.663			−1.32689			−0.663446	+	0.748224i	$0.730907\pi$
$312$	51.0599	−	51.0599i	0.163653	−	0.163653i
$313$	−417.460	−	417.460i	−1.33374	−	1.33374i	−0.901997	−	0.431743i	$-0.857899\pi$
$313$	−417.460	−	417.460i	−1.33374	−	1.33374i	−0.431743	−	0.901997i	$-0.642101\pi$
$314$			344.177i			1.09611i
$315$	−8.91626	+	9.07037i	−0.0283056	+	0.0287948i
$316$	168.247			0.532427
$317$	−290.923	+	290.923i	−0.917738	+	0.917738i	−0.996865	−	0.0791268i	$-0.974787\pi$
$317$	−290.923	+	290.923i	−0.917738	+	0.917738i	0.0791268	+	0.996865i	$0.474787\pi$
$318$	49.9153	+	49.9153i	0.156966	+	0.156966i
$319$			150.468i			0.471687i
$320$	−39.9985	+	0.342715i	−0.124995	+	0.00107099i
$321$	82.5931			0.257299
$322$	4.06652	−	4.06652i	0.0126290	−	0.0126290i
$323$	−160.557	−	160.557i	−0.497080	−	0.497080i
$324$			18.0000i			0.0555556i
$325$	−264.990	−	256.061i	−0.815355	−	0.787879i
$326$	163.618			0.501895
$327$	166.942	−	166.942i	0.510525	−	0.510525i
$328$	136.330	+	136.330i	0.415640	+	0.415640i
$329$			12.0176i			0.0365278i
$330$	0.293050	+	34.2021i	0.000888030	+	0.103643i
$331$	52.5667			0.158812			0.0794058	−	0.996842i	$-0.474698\pi$
$331$	52.5667			0.158812			0.0794058	+	0.996842i	$0.474698\pi$
$332$	−157.197	+	157.197i	−0.473484	+	0.473484i
$333$	64.1800	+	64.1800i	0.192733	+	0.192733i
$334$			95.5585i			0.286103i
$335$	−202.310	−	198.873i	−0.603911	−	0.593650i
$336$	5.87462			0.0174840
$337$	−52.9222	+	52.9222i	−0.157039	+	0.157039i	−0.781253	−	0.624214i	$-0.785419\pi$
$337$	−52.9222	+	52.9222i	−0.157039	+	0.157039i	0.624214	+	0.781253i	$0.285419\pi$
$338$	−48.2591	−	48.2591i	−0.142778	−	0.142778i
$339$		−	162.988i		−	0.480790i
$340$	80.5427	−	81.9349i	0.236890	−	0.240985i
$341$	−67.8002			−0.198827
$342$	−59.2886	+	59.2886i	−0.173358	+	0.173358i
$343$	58.3274	+	58.3274i	0.170051	+	0.170051i
$344$		−	64.1580i		−	0.186506i
$345$	−41.5316	+	0.355851i	−0.120381	+	0.00103145i
$346$	−231.048			−0.667770
$347$	−118.619	+	118.619i	−0.341843	+	0.341843i	−0.857060	−	0.515217i	$-0.827711\pi$
$347$	−118.619	+	118.619i	−0.341843	+	0.341843i	0.515217	+	0.857060i	$0.327711\pi$
$348$	−131.977	−	131.977i	−0.379243	−	0.379243i
$349$		−	398.115i		−	1.14073i	−0.821391	−	0.570366i	$-0.806801\pi$
$349$		−	398.115i		−	1.14073i	0.821391	−	0.570366i	$-0.193199\pi$
$350$	−0.513691	−	29.9744i	−0.00146769	−	0.0856412i
$351$	76.5898			0.218205
$352$	11.1708	−	11.1708i	0.0317351	−	0.0317351i
$353$	171.724	+	171.724i	0.486470	+	0.486470i	0.907190	−	0.420721i	$-0.138223\pi$
$353$	171.724	+	171.724i	0.486470	+	0.486470i	−0.420721	+	0.907190i	$0.638223\pi$
$354$			278.398i			0.786436i
$355$	5.04557	+	588.872i	0.0142129	+	1.65879i
$356$	135.945			0.381869
$357$	−11.9316	+	11.9316i	−0.0334219	+	0.0334219i
$358$	−55.5826	−	55.5826i	−0.155259	−	0.155259i
$359$		−	544.606i		−	1.51701i	−0.651669	−	0.758504i	$-0.725931\pi$
$359$		−	544.606i		−	1.51701i	0.651669	−	0.758504i	$-0.274069\pi$
$360$	−30.2559	−	29.7419i	−0.0840443	−	0.0826163i
$361$	−29.5704			−0.0819126
$362$	−25.4089	+	25.4089i	−0.0701903	+	0.0701903i
$363$	138.642	+	138.642i	0.381934	+	0.381934i
$364$		−	24.9965i		−	0.0686716i
$365$	−373.716	+	380.175i	−1.02388	+	1.04158i
$366$	−172.251			−0.470632
$367$	98.8242	−	98.8242i	0.269276	−	0.269276i	−0.559533	−	0.828808i	$-0.689019\pi$
$367$	98.8242	−	98.8242i	0.269276	−	0.269276i	0.828808	+	0.559533i	$0.189019\pi$
$368$	13.5647	+	13.5647i	0.0368605	+	0.0368605i
$369$			204.495i			0.554187i
$370$	−213.925	+	1.83296i	−0.578177	+	0.00495393i
$371$	24.4361			0.0658656
$372$	59.4681	−	59.4681i	0.159860	−	0.159860i
$373$	−407.257	−	407.257i	−1.09184	−	1.09184i	−0.995332	−	0.0965103i	$-0.969232\pi$
$373$	−407.257	−	407.257i	−1.09184	−	1.09184i	−0.0965103	−	0.995332i	$-0.530768\pi$
$374$			45.3766i			0.121328i
$375$	−149.108	+	156.977i	−0.397621	+	0.418606i
$376$	−40.0871			−0.106615
$377$	−561.559	+	561.559i	−1.48955	+	1.48955i
$378$	4.40597	+	4.40597i	0.0116560	+	0.0116560i
$379$		−	237.240i		−	0.625962i	−0.949759	−	0.312981i	$-0.898672\pi$
$379$		−	237.240i		−	0.625962i	0.949759	−	0.312981i	$-0.101328\pi$
$380$	−1.69326	−	197.621i	−0.00445594	−	0.520056i
$381$	−127.857			−0.335582
$382$	−80.7623	+	80.7623i	−0.211420	+	0.211420i
$383$	−204.845	−	204.845i	−0.534842	−	0.534842i	0.387167	−	0.922010i	$-0.373454\pi$
$383$	−204.845	−	204.845i	−0.534842	−	0.534842i	−0.922010	+	0.387167i	$0.873454\pi$
$384$			19.5959i			0.0510310i
$385$	8.44357	+	8.30011i	0.0219314	+	0.0215587i
$386$	343.944			0.891047
$387$	48.1185	−	48.1185i	0.124337	−	0.124337i
$388$	149.391	+	149.391i	0.385029	+	0.385029i
$389$			398.431i			1.02425i	0.858912	+	0.512123i	$0.171141\pi$
$389$			398.431i			1.02425i	−0.858912	+	0.512123i	$0.828859\pi$
$390$	−126.551	+	128.739i	−0.324490	+	0.330099i
$391$	−55.1009			−0.140923
$392$	−96.5620	+	96.5620i	−0.246332	+	0.246332i
$393$	226.161	+	226.161i	0.575474	+	0.575474i
$394$		−	171.289i		−	0.434745i
$395$	−420.602	+	3.60380i	−1.06482	+	0.00912355i
$396$	16.7561			0.0423135
$397$	257.697	−	257.697i	0.649112	−	0.649112i	−0.303666	−	0.952778i	$-0.598211\pi$
$397$	257.697	−	257.697i	0.649112	−	0.649112i	0.952778	+	0.303666i	$0.0982108\pi$
$398$	309.137	+	309.137i	0.776726	+	0.776726i
$399$			29.0248i			0.0727439i
$400$	99.9853	−	1.71351i	0.249963	−	0.00428378i
$401$	−415.912			−1.03719			−0.518594	−	0.855021i	$-0.673544\pi$
$401$	−415.912			−1.03719			−0.518594	+	0.855021i	$0.673544\pi$
$402$	−98.2730	+	98.2730i	−0.244460	+	0.244460i
$403$	−253.036	−	253.036i	−0.627881	−	0.627881i
$404$			101.796i			0.251971i
$405$	−0.385555	−	44.9983i	−0.000951987	−	0.111107i
$406$	−64.6094			−0.159137
$407$	59.7449	−	59.7449i	0.146793	−	0.146793i
$408$	−39.8002	−	39.8002i	−0.0975495	−	0.0975495i
$409$		−	287.346i		−	0.702557i	−0.936271	−	0.351278i	$-0.885747\pi$
$409$		−	287.346i		−	0.702557i	0.936271	−	0.351278i	$-0.114253\pi$
$410$	−343.733	−	337.892i	−0.838372	−	0.824128i
$411$	−309.620			−0.753334
$412$	−31.7524	+	31.7524i	−0.0770690	+	0.0770690i
$413$	68.1452	+	68.1452i	0.165001	+	0.165001i
$414$			20.3470i			0.0491473i
$415$	389.610	−	396.344i	0.938819	−	0.955046i
$416$	83.3804			0.200434
$417$	266.712	−	266.712i	0.639597	−	0.639597i
$418$	55.1915	+	55.1915i	0.132037	+	0.132037i
$419$			832.842i			1.98769i	0.110778	+	0.993845i	$0.464666\pi$
$419$			832.842i			1.98769i	−0.110778	+	0.993845i	$0.535334\pi$
$420$	−14.6860	+	0.125833i	−0.0349667	+	0.000299602i
$421$	503.773			1.19661			0.598305	−	0.801269i	$-0.295841\pi$
$421$	503.773			1.19661			0.598305	+	0.801269i	$0.295841\pi$
$422$	−166.044	+	166.044i	−0.393469	+	0.393469i
$423$	−30.0653	−	30.0653i	−0.0710764	−	0.0710764i
$424$			81.5113i			0.192244i
$425$	−199.594	+	206.555i	−0.469634	+	0.486011i
$426$	288.498			0.677225
$427$	−42.1630	+	42.1630i	−0.0987423	+	0.0987423i
$428$	67.4370	+	67.4370i	0.157563	+	0.157563i
$429$		−	71.2972i		−	0.166194i
$430$	1.37425	+	160.389i	0.00319592	+	0.372998i
$431$	213.988			0.496492			0.248246	−	0.968697i	$-0.420146\pi$
$431$	213.988			0.496492			0.248246	+	0.968697i	$0.420146\pi$
$432$	−14.6969	+	14.6969i	−0.0340207	+	0.0340207i
$433$	4.82654	+	4.82654i	0.0111467	+	0.0111467i	0.712658	−	0.701511i	$-0.247491\pi$
$433$	4.82654	+	4.82654i	0.0111467	+	0.0111467i	−0.701511	+	0.712658i	$0.747491\pi$
$434$		−	29.1127i		−	0.0670800i
$435$	332.757	+	327.103i	0.764958	+	0.751960i
$436$	272.615			0.625263
$437$	−67.0191	+	67.0191i	−0.153362	+	0.153362i
$438$	184.672	+	184.672i	0.421625	+	0.421625i
$439$			770.632i			1.75543i	0.479187	+	0.877713i	$0.340932\pi$
$439$			770.632i			1.75543i	−0.479187	+	0.877713i	$0.659068\pi$
$440$	−27.6866	+	28.1651i	−0.0629241	+	0.0640117i
$441$	−144.843			−0.328442
$442$	−169.349	+	169.349i	−0.383143	+	0.383143i
$443$	83.6593	+	83.6593i	0.188847	+	0.188847i	0.795198	−	0.606350i	$-0.207367\pi$
$443$	83.6593	+	83.6593i	0.188847	+	0.188847i	−0.606350	+	0.795198i	$0.707367\pi$
$444$			104.806i			0.236048i
$445$	−339.851	+	2.91191i	−0.763711	+	0.00654362i
$446$	−67.1385			−0.150535
$447$	93.0216	−	93.0216i	0.208102	−	0.208102i
$448$	4.79661	+	4.79661i	0.0107067	+	0.0107067i
$449$		−	544.988i		−	1.21378i	−0.794785	−	0.606891i	$-0.792416\pi$
$449$		−	544.988i		−	1.21378i	0.794785	−	0.606891i	$-0.207584\pi$
$450$	76.2741	+	73.7039i	0.169498	+	0.163786i
$451$	190.364			0.422092
$452$	133.079	−	133.079i	0.294423	−	0.294423i
$453$	−44.6398	−	44.6398i	−0.0985425	−	0.0985425i
$454$			403.209i			0.888125i
$455$	0.535417	+	62.4888i	0.00117674	+	0.137338i
$456$	−96.8178			−0.212320
$457$	−429.596	+	429.596i	−0.940035	+	0.940035i	−0.998301	−	0.0582661i	$-0.981443\pi$
$457$	−429.596	+	429.596i	−0.940035	+	0.940035i	0.0582661	+	0.998301i	$0.481443\pi$
$458$	91.1570	+	91.1570i	0.199033	+	0.199033i
$459$		−	59.7003i		−	0.130066i
$460$	−34.2010	−	33.6199i	−0.0743499	−	0.0730866i
$461$	327.982			0.711458			0.355729	−	0.934589i	$-0.384233\pi$
$461$	327.982			0.711458			0.355729	+	0.934589i	$0.384233\pi$
$462$	4.10150	−	4.10150i	0.00887770	−	0.00887770i
$463$	412.976	+	412.976i	0.891957	+	0.891957i	0.994707	−	0.102750i	$-0.0327641\pi$
$463$	412.976	+	412.976i	0.891957	+	0.891957i	−0.102750	+	0.994707i	$0.532764\pi$
$464$		−	215.517i		−	0.464476i
$465$	−147.391	+	149.939i	−0.316970	+	0.322448i
$466$	373.963			0.802495
$467$	553.078	−	553.078i	1.18432	−	1.18432i	0.205708	−	0.978613i	$-0.434050\pi$
$467$	553.078	−	553.078i	1.18432	−	1.18432i	0.978613	−	0.205708i	$-0.0659496\pi$
$468$	62.5353	+	62.5353i	0.133622	+	0.133622i
$469$			48.1097i			0.102579i
$470$	100.214	−	0.858654i	0.213221	−	0.00182692i
$471$	−421.529			−0.894966
$472$	−227.311	+	227.311i	−0.481592	+	0.481592i
$473$	−44.7933	−	44.7933i	−0.0947005	−	0.0947005i
$474$			206.060i			0.434725i
$475$	8.46598	+	493.999i	0.0178231	+	1.04000i
$476$	−19.4843			−0.0409333
$477$	−61.1335	+	61.1335i	−0.128162	+	0.128162i
$478$	171.742	+	171.742i	0.359293	+	0.359293i
$479$			560.923i			1.17103i	0.810662	+	0.585514i	$0.199107\pi$
$479$			560.923i			1.17103i	−0.810662	+	0.585514i	$0.800893\pi$
$480$	−0.419739	−	48.9880i	−0.000874456	−	0.102058i
$481$	445.946			0.927123
$482$	119.663	−	119.663i	0.248263	−	0.248263i
$483$	4.98045	+	4.98045i	0.0103115	+	0.0103115i
$484$			226.402i			0.467772i
$485$	−376.664	−	370.264i	−0.776627	−	0.763431i
$486$	−22.0454			−0.0453609
$487$	455.931	−	455.931i	0.936203	−	0.936203i	−0.0618802	−	0.998084i	$-0.519710\pi$
$487$	455.931	−	455.931i	0.936203	−	0.936203i	0.998084	+	0.0618802i	$0.0197097\pi$
$488$	−140.643	−	140.643i	−0.288202	−	0.288202i
$489$			200.390i			0.409795i
$490$	239.328	−	243.465i	0.488424	−	0.496866i
$491$	−419.688			−0.854762			−0.427381	−	0.904072i	$-0.640564\pi$
$491$	−419.688			−0.854762			−0.427381	+	0.904072i	$0.640564\pi$
$492$	−166.969	+	166.969i	−0.339369	+	0.339369i
$493$	437.725	+	437.725i	0.887880	+	0.887880i
$494$			411.959i			0.833925i
$495$	−41.8888	+	0.358911i	−0.0846238	+	0.000725074i
$496$	97.1110			0.195788
$497$	70.6173	−	70.6173i	0.142087	−	0.142087i
$498$	−192.526	−	192.526i	−0.386598	−	0.386598i
$499$		−	338.152i		−	0.677659i	−0.940848	−	0.338830i	$-0.889969\pi$
$499$		−	338.152i		−	0.677659i	0.940848	−	0.338830i	$-0.110031\pi$
$500$	−249.917	+	6.42528i	−0.499835	+	0.0128506i
$501$	−117.035			−0.233602
$502$	−353.988	+	353.988i	−0.705156	+	0.705156i
$503$	−153.284	−	153.284i	−0.304740	−	0.304740i	0.538125	−	0.842865i	$-0.319133\pi$
$503$	−153.284	−	153.284i	−0.304740	−	0.304740i	−0.842865	+	0.538125i	$0.819133\pi$
$504$			7.19492i			0.0142756i
$505$	−2.18045	−	254.481i	−0.00431772	−	0.503924i
$506$	18.9409			0.0374327
$507$	59.1051	−	59.1051i	0.116578	−	0.116578i
$508$	−104.395	−	104.395i	−0.205501	−	0.205501i
$509$		−	706.177i		−	1.38738i	−0.720273	−	0.693691i	$-0.755983\pi$
$509$		−	706.177i		−	1.38738i	0.720273	−	0.693691i	$-0.244017\pi$
$510$	100.349	+	98.6443i	0.196763	+	0.193420i
$511$	90.4064			0.176920
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−72.6134	−	72.6134i	−0.141547	−	0.141547i
$514$			243.438i			0.473614i
$515$	78.6980	−	80.0583i	0.152812	−	0.155453i
$516$	78.5772			0.152281
$517$	−27.9877	+	27.9877i	−0.0541348	+	0.0541348i
$518$	25.6539	+	25.6539i	0.0495248	+	0.0495248i
$519$		−	282.975i		−	0.545232i
$520$	−208.443	+	1.78598i	−0.400853	+	0.00343458i
$521$	−701.348			−1.34616			−0.673079	−	0.739571i	$-0.735028\pi$
$521$	−701.348			−1.34616			−0.673079	+	0.739571i	$0.735028\pi$
$522$	161.638	−	161.638i	0.309651	−	0.309651i
$523$	467.174	+	467.174i	0.893258	+	0.893258i	0.994828	−	0.101571i	$-0.0323868\pi$
$523$	467.174	+	467.174i	0.893258	+	0.893258i	−0.101571	+	0.994828i	$0.532387\pi$
$524$			369.320i			0.704809i
$525$	36.7110	−	0.629140i	0.0699257	−	0.00119836i
$526$	−651.783			−1.23913
$527$	−197.237	+	197.237i	−0.374263	+	0.374263i
$528$	13.6813	+	13.6813i	0.0259116	+	0.0259116i
$529$			23.0000i			0.0434783i
$530$	−1.74595	−	203.771i	−0.00329424	−	0.384473i
$531$	−340.967			−0.642122
$532$	−23.6987	+	23.6987i	−0.0445464	+	0.0445464i
$533$	710.453	+	710.453i	1.33293	+	1.33293i
$534$			166.499i			0.311795i
$535$	−170.031	−	167.142i	−0.317815	−	0.312415i
$536$	−160.479			−0.299401
$537$	68.0746	−	68.0746i	0.126768	−	0.126768i
$538$	−510.361	−	510.361i	−0.948626	−	0.948626i
$539$			134.834i			0.250156i
$540$	36.4262	−	37.0558i	0.0674559	−	0.0686219i
$541$	−397.941			−0.735565			−0.367783	−	0.929912i	$-0.619883\pi$
$541$	−397.941			−0.735565			−0.367783	+	0.929912i	$0.619883\pi$
$542$	−57.8719	+	57.8719i	−0.106775	+	0.106775i
$543$	−31.1194	−	31.1194i	−0.0573101	−	0.0573101i
$544$		−	64.9934i		−	0.119473i
$545$	−681.512	+	5.83932i	−1.25048	+	0.0107144i
$546$	30.6143			0.0560701
$547$	266.491	−	266.491i	0.487187	−	0.487187i	−0.420230	−	0.907417i	$-0.638051\pi$
$547$	266.491	−	266.491i	0.487187	−	0.487187i	0.907417	+	0.420230i	$0.138051\pi$
$548$	−252.804	−	252.804i	−0.461321	−	0.461321i
$549$		−	210.964i		−	0.384269i
$550$	68.6106	−	71.0033i	0.124747	−	0.129097i
$551$	1064.81			1.93250
$552$	−16.6132	+	16.6132i	−0.0300965	+	0.0300965i
$553$	50.4384	+	50.4384i	0.0912088	+	0.0912088i
$554$			421.055i			0.760027i
$555$	−2.24490	−	262.004i	−0.00404487	−	0.472080i
$556$	435.539			0.783344
$557$	218.918	−	218.918i	0.393031	−	0.393031i	−0.482736	−	0.875766i	$-0.660357\pi$
$557$	218.918	−	218.918i	0.393031	−	0.393031i	0.875766	+	0.482736i	$0.160357\pi$
$558$	72.8332	+	72.8332i	0.130525	+	0.130525i
$559$		−	334.345i		−	0.598113i
$560$	−12.0938	−	11.8883i	−0.0215961	−	0.0212292i
$561$	−55.5748			−0.0990638
$562$	−34.0038	+	34.0038i	−0.0605049	+	0.0605049i
$563$	144.453	+	144.453i	0.256577	+	0.256577i	0.823660	−	0.567083i	$-0.191928\pi$
$563$	144.453	+	144.453i	0.256577	+	0.256577i	−0.567083	+	0.823660i	$0.691928\pi$
$564$		−	49.0965i		−	0.0870505i
$565$	−329.835	+	335.536i	−0.583779	+	0.593869i
$566$	−344.162			−0.608060
$567$	−5.39619	+	5.39619i	−0.00951708	+	0.00951708i
$568$	235.557	+	235.557i	0.414714	+	0.414714i
$569$			282.359i			0.496238i	0.968730	+	0.248119i	$0.0798124\pi$
$569$			282.359i			0.496238i	−0.968730	+	0.248119i	$0.920188\pi$
$570$	242.036	−	2.07381i	0.424624	−	0.00363826i
$571$	234.186			0.410133			0.205067	−	0.978748i	$-0.434259\pi$
$571$	234.186			0.410133			0.205067	+	0.978748i	$0.434259\pi$
$572$	58.2139	−	58.2139i	0.101773	−	0.101773i
$573$	−98.9132	−	98.9132i	−0.172623	−	0.172623i
$574$			81.7402i			0.142405i
$575$	86.2194	+	83.3140i	0.149947	+	0.144894i
$576$	−24.0000			−0.0416667
$577$	501.679	−	501.679i	0.869461	−	0.869461i	−0.122952	−	0.992413i	$-0.539236\pi$
$577$	501.679	−	501.679i	0.869461	−	0.869461i	0.992413	+	0.122952i	$0.0392361\pi$
$578$	−156.995	−	156.995i	−0.271618	−	0.271618i
$579$			421.244i			0.727537i
$580$	4.61631	+	538.773i	0.00795916	+	0.928919i
$581$	−94.2513			−0.162223
$582$	−182.966	+	182.966i	−0.314375	+	0.314375i
$583$	56.9090	+	56.9090i	0.0976140	+	0.0976140i
$584$			301.568i			0.516383i
$585$	−157.672	−	154.993i	−0.269525	−	0.264945i
$586$	−132.007			−0.225267
$587$	−729.488	+	729.488i	−1.24274	+	1.24274i	−0.283880	+	0.958860i	$0.591622\pi$
$587$	−729.488	+	729.488i	−1.24274	+	1.24274i	−0.958860	+	0.283880i	$0.908378\pi$
$588$	−118.264	−	118.264i	−0.201129	−	0.201129i
$589$			479.797i			0.814597i
$590$	563.388	−	573.126i	0.954895	−	0.971400i
$591$	209.786			0.354968
$592$	−85.5733	+	85.5733i	−0.144550	+	0.144550i
$593$	223.415	+	223.415i	0.376754	+	0.376754i	0.869930	−	0.493176i	$-0.164164\pi$
$593$	223.415	+	223.415i	0.376754	+	0.376754i	−0.493176	+	0.869930i	$0.664164\pi$
$594$			20.5220i			0.0345488i
$595$	48.7089	−	0.417347i	0.0818636	−	0.000701424i
$596$	151.904			0.254872
$597$	−378.614	+	378.614i	−0.634194	+	0.634194i
$598$	70.6892	+	70.6892i	0.118209	+	0.118209i
$599$		−	267.169i		−	0.446024i	−0.974816	−	0.223012i	$-0.928411\pi$
$599$		−	267.169i		−	0.446024i	0.974816	−	0.223012i	$-0.0715890\pi$
$600$	2.09862	+	122.457i	0.00349769	+	0.204094i
$601$	−123.350			−0.205240			−0.102620	−	0.994721i	$-0.532723\pi$
$601$	−123.350			−0.205240			−0.102620	+	0.994721i	$0.532723\pi$
$602$	19.2338	−	19.2338i	0.0319498	−	0.0319498i
$603$	−120.359	−	120.359i	−0.199601	−	0.199601i
$604$		−	72.8964i		−	0.120689i
$605$	−4.84946	−	565.984i	−0.00801563	−	0.935510i
$606$	−124.675			−0.205734
$607$	328.996	−	328.996i	0.542003	−	0.542003i	−0.382113	−	0.924116i	$-0.624803\pi$
$607$	328.996	−	328.996i	0.542003	−	0.542003i	0.924116	+	0.382113i	$0.124803\pi$
$608$	−79.0514	−	79.0514i	−0.130019	−	0.130019i
$609$		−	79.1301i		−	0.129934i
$610$	354.606	+	348.581i	0.581321	+	0.571444i
$611$	−208.905			−0.341907
$612$	48.7451	−	48.7451i	0.0796488	−	0.0796488i
$613$	−218.431	−	218.431i	−0.356331	−	0.356331i	0.506128	−	0.862459i	$-0.331076\pi$
$613$	−218.431	−	218.431i	−0.356331	−	0.356331i	−0.862459	+	0.506128i	$0.831076\pi$
$614$		−	365.208i		−	0.594801i
$615$	413.832	−	420.985i	0.672897	−	0.684528i
$616$	6.69772			0.0108729
$617$	−746.090	+	746.090i	−1.20922	+	1.20922i	−0.237943	+	0.971279i	$0.576473\pi$
$617$	−746.090	+	746.090i	−1.20922	+	1.20922i	−0.971279	+	0.237943i	$0.923527\pi$
$618$	−38.8886	−	38.8886i	−0.0629266	−	0.0629266i
$619$		−	545.374i		−	0.881056i	−0.897739	−	0.440528i	$-0.854791\pi$
$619$		−	545.374i		−	0.881056i	0.897739	−	0.440528i	$-0.145209\pi$
$620$	−242.768	+	2.08009i	−0.391562	+	0.00335498i
$621$	−24.9199			−0.0401286
$622$	412.663	−	412.663i	0.663446	−	0.663446i
$623$	40.7548	+	40.7548i	0.0654171	+	0.0654171i
$624$			102.120i			0.163653i
$625$	624.633	−	21.4158i	0.999413	−	0.0342652i
$626$	834.921			1.33374
$627$	−67.5955	+	67.5955i	−0.107808	+	0.107808i
$628$	−344.177	−	344.177i	−0.548053	−	0.548053i
$629$		−	347.607i		−	0.552634i
$630$	−0.154113	−	17.9866i	−0.000244624	−	0.0285502i
$631$	−794.740			−1.25949			−0.629746	−	0.776801i	$-0.716841\pi$
$631$	−794.740			−1.25949			−0.629746	+	0.776801i	$0.716841\pi$
$632$	−168.247	+	168.247i	−0.266214	+	0.266214i
$633$	−203.361	−	203.361i	−0.321266	−	0.321266i
$634$		−	581.846i		−	0.917738i
$635$	263.213	+	258.741i	0.414509	+	0.407466i
$636$	−99.8306			−0.156966
$637$	−503.211	+	503.211i	−0.789971	+	0.789971i
$638$	−150.468	−	150.468i	−0.235843	−	0.235843i
$639$			353.336i			0.552952i
$640$	39.6558	−	40.3412i	0.0619622	−	0.0630332i
$641$	1123.20			1.75226			0.876128	−	0.482079i	$-0.160118\pi$
$641$	1123.20			1.75226			0.876128	+	0.482079i	$0.160118\pi$
$642$	−82.5931	+	82.5931i	−0.128650	+	0.128650i
$643$	−274.942	−	274.942i	−0.427593	−	0.427593i	0.460215	−	0.887808i	$-0.347772\pi$
$643$	−274.942	−	274.942i	−0.427593	−	0.427593i	−0.887808	+	0.460215i	$0.847772\pi$
$644$			8.13305i			0.0126290i
$645$	−196.436	+	1.68310i	−0.304552	+	0.00260946i
$646$	321.114			0.497080
$647$	73.7474	−	73.7474i	0.113984	−	0.113984i	−0.647815	−	0.761798i	$-0.724317\pi$
$647$	73.7474	−	73.7474i	0.113984	−	0.113984i	0.761798	+	0.647815i	$0.224317\pi$
$648$	−18.0000	−	18.0000i	−0.0277778	−	0.0277778i
$649$			317.405i			0.489067i
$650$	521.051	−	8.92959i	0.801617	−	0.0137378i
$651$	35.6556			0.0547706
$652$	−163.618	+	163.618i	−0.250947	+	0.250947i
$653$	606.822	+	606.822i	0.929284	+	0.929284i	0.997660	−	0.0683758i	$-0.0217817\pi$
$653$	606.822	+	606.822i	0.929284	+	0.929284i	−0.0683758	+	0.997660i	$0.521782\pi$
$654$			333.883i			0.510525i
$655$	−7.91073	−	923.266i	−0.0120774	−	1.40957i
$656$	−272.660			−0.415640
$657$	−226.176	+	226.176i	−0.344255	+	0.344255i
$658$	−12.0176	−	12.0176i	−0.0182639	−	0.0182639i
$659$		−	377.512i		−	0.572856i	−0.958102	−	0.286428i	$-0.907532\pi$
$659$		−	377.512i		−	0.572856i	0.958102	−	0.286428i	$-0.0924678\pi$
$660$	−34.4951	−	33.9090i	−0.0522653	−	0.0513773i
$661$	1170.11			1.77020			0.885102	−	0.465396i	$-0.154088\pi$
$661$	1170.11			1.77020			0.885102	+	0.465396i	$0.154088\pi$
$662$	−52.5667	+	52.5667i	−0.0794058	+	0.0794058i
$663$	−207.410	−	207.410i	−0.312835	−	0.312835i
$664$		−	314.393i		−	0.473484i
$665$	58.7369	−	59.7521i	0.0883262	−	0.0898528i
$666$	−128.360			−0.192733
$667$	182.713	−	182.713i	0.273933	−	0.273933i
$668$	−95.5585	−	95.5585i	−0.143052	−	0.143052i
$669$		−	82.2275i		−	0.122911i
$670$	401.183	−	3.43742i	0.598781	−	0.00513047i
$671$	−196.385			−0.292676
$672$	−5.87462	+	5.87462i	−0.00874200	+	0.00874200i
$673$	−245.453	−	245.453i	−0.364715	−	0.364715i	0.500831	−	0.865545i	$-0.333028\pi$
$673$	−245.453	−	245.453i	−0.364715	−	0.364715i	−0.865545	+	0.500831i	$0.833028\pi$
$674$		−	105.844i		−	0.157039i
$675$	−90.2684	+	93.4163i	−0.133731	+	0.138395i
$676$	96.5182			0.142778
$677$	−121.820	+	121.820i	−0.179940	+	0.179940i	−0.791330	−	0.611389i	$-0.790611\pi$
$677$	−121.820	+	121.820i	−0.179940	+	0.179940i	0.611389	+	0.791330i	$0.290611\pi$
$678$	162.988	+	162.988i	0.240395	+	0.240395i
$679$			89.5714i			0.131917i
$680$	1.39214	+	162.478i	0.00204726	+	0.238938i
$681$	−493.828			−0.725151
$682$	67.8002	−	67.8002i	0.0994137	−	0.0994137i
$683$	293.160	+	293.160i	0.429224	+	0.429224i	0.888364	−	0.459140i	$-0.151842\pi$
$683$	293.160	+	293.160i	0.429224	+	0.429224i	−0.459140	+	0.888364i	$0.651842\pi$
$684$		−	118.577i		−	0.173358i
$685$	637.402	+	626.572i	0.930513	+	0.914703i
$686$	−116.655			−0.170051
$687$	−111.644	+	111.644i	−0.162510	+	0.162510i
$688$	64.1580	+	64.1580i	0.0932529	+	0.0932529i
$689$			424.778i			0.616514i
$690$	41.1757	−	41.8874i	0.0596750	−	0.0607064i
$691$	711.388			1.02950			0.514752	−	0.857339i	$-0.327884\pi$
$691$	711.388			1.02950			0.514752	+	0.857339i	$0.327884\pi$
$692$	231.048	−	231.048i	0.333885	−	0.333885i
$693$	5.02329	+	5.02329i	0.00724862	+	0.00724862i
$694$		−	237.239i		−	0.341843i
$695$	−1088.81	+	9.32912i	−1.56663	+	0.0134232i
$696$	263.953			0.379243
$697$	553.785	−	553.785i	0.794526	−	0.794526i
$698$	398.115	+	398.115i	0.570366	+	0.570366i
$699$			458.009i			0.655235i
$700$	30.4881	+	29.4607i	0.0435544	+	0.0420867i
$701$	−78.4101			−0.111855			−0.0559273	−	0.998435i	$-0.517812\pi$
$701$	−78.4101			−0.111855			−0.0559273	+	0.998435i	$0.517812\pi$
$702$	−76.5898	+	76.5898i	−0.109102	+	0.109102i
$703$	−422.793	−	422.793i	−0.601413	−	0.601413i
$704$			22.3415i			0.0317351i
$705$	1.05163	+	122.737i	0.00149168	+	0.174095i
$706$	−343.448			−0.486470
$707$	−30.5173	+	30.5173i	−0.0431645	+	0.0431645i
$708$	−278.398	−	278.398i	−0.393218	−	0.393218i
$709$		−	398.925i		−	0.562659i	−0.959611	−	0.281330i	$-0.909225\pi$
$709$		−	398.925i		−	0.562659i	0.959611	−	0.281330i	$-0.0907754\pi$
$710$	−593.917	−	583.826i	−0.836504	−	0.822291i
$711$	−252.370			−0.354951
$712$	−135.945	+	135.945i	−0.190935	+	0.190935i
$713$	82.3298	+	82.3298i	0.115470	+	0.115470i
$714$		−	23.8632i		−	0.0334219i
$715$	−144.282	+	146.776i	−0.201794	+	0.205282i
$716$	111.165			0.155259
$717$	−210.340	+	210.340i	−0.293361	+	0.293361i
$718$	544.606	+	544.606i	0.758504	+	0.758504i
$719$		−	774.146i		−	1.07670i	−0.842722	−	0.538349i	$-0.819048\pi$
$719$		−	774.146i		−	1.07670i	0.842722	−	0.538349i	$-0.180952\pi$
$720$	59.9978	−	0.514073i	0.0833303	−	0.000713990i
$721$	−19.0380			−0.0264050
$722$	29.5704	−	29.5704i	0.0409563	−	0.0409563i
$723$	146.557	+	146.557i	0.202706	+	0.202706i
$724$		−	50.8178i		−	0.0701903i
$725$	−23.0807	−	1346.78i	−0.0318355	−	1.85763i
$726$	−277.284			−0.381934
$727$	832.259	−	832.259i	1.14479	−	1.14479i	0.157223	−	0.987563i	$-0.449746\pi$
$727$	832.259	−	832.259i	1.14479	−	1.14479i	0.987563	−	0.157223i	$-0.0502541\pi$
$728$	24.9965	+	24.9965i	0.0343358	+	0.0343358i
$729$		−	27.0000i		−	0.0370370i
$730$	−6.45949	−	753.891i	−0.00884861	−	1.03273i
$731$	−260.616			−0.356519
$732$	172.251	−	172.251i	0.235316	−	0.235316i
$733$	−56.0242	−	56.0242i	−0.0764313	−	0.0764313i	0.667858	−	0.744289i	$-0.267211\pi$
$733$	−56.0242	−	56.0242i	−0.0764313	−	0.0764313i	−0.744289	+	0.667858i	$0.767211\pi$
$734$			197.648i			0.269276i
$735$	298.182	+	293.116i	0.405690	+	0.398797i
$736$	−27.1293			−0.0368605
$737$	−112.042	+	112.042i	−0.152025	+	0.152025i
$738$	−204.495	−	204.495i	−0.277094	−	0.277094i
$739$		−	717.045i		−	0.970291i	−0.874433	−	0.485145i	$-0.838767\pi$
$739$		−	717.045i		−	0.970291i	0.874433	−	0.485145i	$-0.161233\pi$
$740$	212.093	−	215.758i	0.286612	−	0.291565i
$741$	−504.544			−0.680897
$742$	−24.4361	+	24.4361i	−0.0329328	+	0.0329328i
$743$	305.067	+	305.067i	0.410588	+	0.410588i	0.881943	−	0.471355i	$-0.156235\pi$
$743$	305.067	+	305.067i	0.410588	+	0.410588i	−0.471355	+	0.881943i	$0.656235\pi$
$744$			118.936i			0.159860i
$745$	−379.745	+	3.25373i	−0.509725	+	0.00436742i
$746$	814.514			1.09184
$747$	235.795	−	235.795i	0.315656	−	0.315656i
$748$	−45.3766	−	45.3766i	−0.0606639	−	0.0606639i
$749$			40.4336i			0.0539835i
$750$	−7.86933	−	306.085i	−0.0104924	−	0.408113i
$751$	1169.74			1.55757			0.778786	−	0.627290i	$-0.215836\pi$
$751$	1169.74			1.55757			0.778786	+	0.627290i	$0.215836\pi$
$752$	40.0871	−	40.0871i	0.0533073	−	0.0533073i
$753$	−433.545	−	433.545i	−0.575757	−	0.575757i
$754$		−	1123.12i		−	1.48955i
$755$	1.56142	+	182.234i	0.00206811	+	0.241370i
$756$	−8.81194			−0.0116560
$757$	−405.514	+	405.514i	−0.535685	+	0.535685i	−0.922259	−	0.386573i	$-0.873659\pi$
$757$	−405.514	+	405.514i	−0.535685	+	0.535685i	0.386573	+	0.922259i	$0.373659\pi$
$758$	237.240	+	237.240i	0.312981	+	0.312981i
$759$			23.1978i			0.0305637i
$760$	199.315	+	195.928i	0.262256	+	0.257800i
$761$	−327.256			−0.430034			−0.215017	−	0.976610i	$-0.568981\pi$
$761$	−327.256			−0.430034			−0.215017	+	0.976610i	$0.568981\pi$
$762$	127.857	−	127.857i	0.167791	−	0.167791i
$763$	81.7266	+	81.7266i	0.107112	+	0.107112i
$764$		−	161.525i		−	0.211420i
$765$	−120.814	+	122.902i	−0.157927	+	0.160657i
$766$	409.689			0.534842
$767$	−1184.58	+	1184.58i	−1.54443	+	1.54443i
$768$	−19.5959	−	19.5959i	−0.0255155	−	0.0255155i
$769$			75.4942i			0.0981719i	0.998795	+	0.0490860i	$0.0156308\pi$
$769$			75.4942i			0.0981719i	−0.998795	+	0.0490860i	$0.984369\pi$
$770$	−16.7437	+	0.143463i	−0.0217450	+	0.000186316i
$771$	−298.149			−0.386704
$772$	−343.944	+	343.944i	−0.445523	+	0.445523i
$773$	734.361	+	734.361i	0.950015	+	0.950015i	0.998809	−	0.0487940i	$-0.0155378\pi$
$773$	734.361	+	734.361i	0.950015	+	0.950015i	−0.0487940	+	0.998809i	$0.515538\pi$
$774$			96.2370i			0.124337i
$775$	606.854	−	10.4001i	0.783038	−	0.0134194i
$776$	−298.782			−0.385029
$777$	−31.4194	+	31.4194i	−0.0404369	+	0.0404369i
$778$	−398.431	−	398.431i	−0.512123	−	0.512123i
$779$		−	1347.14i		−	1.72931i
$780$	−2.18737	−	255.290i	−0.00280433	−	0.327295i
$781$	328.919			0.421151
$782$	55.1009	−	55.1009i	0.0704615	−	0.0704615i
$783$	197.965	+	197.965i	0.252829	+	0.252829i
$784$		−	193.124i		−	0.246332i
$785$	867.783	+	853.039i	1.10546	+	1.08667i
$786$	−452.323			−0.575474
$787$	−24.2702	+	24.2702i	−0.0308389	+	0.0308389i	−0.722358	−	0.691519i	$-0.756942\pi$
$787$	−24.2702	+	24.2702i	−0.0308389	+	0.0308389i	0.691519	+	0.722358i	$0.256942\pi$
$788$	171.289	+	171.289i	0.217372	+	0.217372i
$789$		−	798.268i		−	1.01175i
$790$	416.998	−	424.206i	0.527846	−	0.536969i
$791$	79.7911			0.100874
$792$	−16.7561	+	16.7561i	−0.0211567	+	0.0211567i
$793$	−732.927	−	732.927i	−0.924246	−	0.924246i
$794$			515.395i			0.649112i
$795$	249.567	−	2.13834i	0.313921	−	0.00268974i
$796$	−618.274			−0.776726
$797$	474.328	−	474.328i	0.595141	−	0.595141i	−0.343874	−	0.939016i	$-0.611739\pi$
$797$	474.328	−	474.328i	0.595141	−	0.595141i	0.939016	+	0.343874i	$0.111739\pi$
$798$	−29.0248	−	29.0248i	−0.0363720	−	0.0363720i
$799$			162.837i			0.203802i
$800$	−98.2718	+	101.699i	−0.122840	+	0.127124i
$801$	−203.918			−0.254580
$802$	415.912	−	415.912i	0.518594	−	0.518594i
$803$	210.546	+	210.546i	0.262199	+	0.262199i
$804$		−	196.546i		−	0.244460i
$805$	−0.174207	−	20.3319i	−0.000216407	−	0.0252570i
$806$	506.072			0.627881
$807$	625.062	−	625.062i	0.774550	−	0.774550i
$808$	−101.796	−	101.796i	−0.125986	−	0.125986i
$809$		−	785.591i		−	0.971065i	−0.874219	−	0.485532i	$-0.838626\pi$
$809$		−	785.591i		−	0.971065i	0.874219	−	0.485532i	$-0.161374\pi$
$810$	45.3839	+	44.6128i	0.0560295	+	0.0550775i
$811$	549.645			0.677737			0.338868	−	0.940834i	$-0.389956\pi$
$811$	549.645			0.677737			0.338868	+	0.940834i	$0.389956\pi$
$812$	64.6094	−	64.6094i	0.0795683	−	0.0795683i
$813$	−70.8783	−	70.8783i	−0.0871812	−	0.0871812i
$814$			119.490i			0.146793i
$815$	405.524	−	412.534i	0.497576	−	0.506176i
$816$	79.6004			0.0975495
$817$	−316.986	+	316.986i	−0.387988	+	0.387988i
$818$	287.346	+	287.346i	0.351278	+	0.351278i
$819$			37.4947i			0.0457811i
$820$	681.625	−	5.84030i	0.831250	−	0.00712231i
$821$	758.950			0.924421			0.462211	−	0.886770i	$-0.347056\pi$
$821$	758.950			0.924421			0.462211	+	0.886770i	$0.347056\pi$
$822$	309.620	−	309.620i	0.376667	−	0.376667i
$823$	−319.243	−	319.243i	−0.387901	−	0.387901i	0.486037	−	0.873938i	$-0.338442\pi$
$823$	−319.243	−	319.243i	−0.387901	−	0.387901i	−0.873938	+	0.486037i	$0.838442\pi$
$824$		−	63.5048i		−	0.0770690i
$825$	86.9609	+	84.0305i	0.105407	+	0.101855i
$826$	−136.290			−0.165001
$827$	−417.087	+	417.087i	−0.504337	+	0.504337i	−0.912783	−	0.408446i	$-0.866071\pi$
$827$	−417.087	+	417.087i	−0.504337	+	0.504337i	0.408446	+	0.912783i	$0.366071\pi$
$828$	−20.3470	−	20.3470i	−0.0245737	−	0.0245737i
$829$		−	876.552i		−	1.05736i	−0.848821	−	0.528680i	$-0.822687\pi$
$829$		−	876.552i		−	1.05736i	0.848821	−	0.528680i	$-0.177313\pi$
$830$	6.73421	+	785.954i	0.00811350	+	0.946933i
$831$	−515.685			−0.620559
$832$	−83.3804	+	83.3804i	−0.100217	+	0.100217i
$833$	392.244	+	392.244i	0.470881	+	0.470881i
$834$			533.424i			0.639597i
$835$	240.934	+	236.841i	0.288544	+	0.283642i
$836$	−110.383			−0.132037
$837$	−89.2021	+	89.2021i	−0.106574	+	0.106574i
$838$	−832.842	−	832.842i	−0.993845	−	0.993845i
$839$		−	240.841i		−	0.287058i	−0.989646	−	0.143529i	$-0.954155\pi$
$839$		−	240.841i		−	0.287058i	0.989646	−	0.143529i	$-0.0458450\pi$
$840$	14.5602	−	14.8119i	0.0173336	−	0.0176332i
$841$	−2061.97			−2.45181
$842$	−503.773	+	503.773i	−0.598305	+	0.598305i
$843$	−41.6459	−	41.6459i	−0.0494020	−	0.0494020i
$844$		−	332.087i		−	0.393469i
$845$	−241.287	+	2.06739i	−0.285546	+	0.00244662i
$846$	60.1307			0.0710764
$847$	−67.8726	+	67.8726i	−0.0801329	+	0.0801329i
$848$	−81.5113	−	81.5113i	−0.0961219	−	0.0961219i
$849$		−	421.511i		−	0.496479i
$850$	−6.96044	−	406.149i	−0.00818876	−	0.477823i
$851$	−145.097			−0.170501
$852$	−288.498	+	288.498i	−0.338612	+	0.338612i
$853$	62.0445	+	62.0445i	0.0727368	+	0.0727368i	0.742539	−	0.669802i	$-0.233621\pi$
$853$	62.0445	+	62.0445i	0.0727368	+	0.0727368i	−0.669802	+	0.742539i	$0.733621\pi$
$854$		−	84.3259i		−	0.0987423i
$855$	2.53989	+	296.432i	0.00297063	+	0.346704i
$856$	−134.874			−0.157563
$857$	642.883	−	642.883i	0.750155	−	0.750155i	−0.224353	−	0.974508i	$-0.572027\pi$
$857$	642.883	−	642.883i	0.750155	−	0.750155i	0.974508	+	0.224353i	$0.0720269\pi$
$858$	71.2972	+	71.2972i	0.0830969	+	0.0830969i
$859$			1201.48i			1.39870i	0.714780	+	0.699350i	$0.246527\pi$
$859$			1201.48i			1.39870i	−0.714780	+	0.699350i	$0.753473\pi$
$860$	−161.763	−	159.015i	−0.188097	−	0.184901i
$861$	−100.111			−0.116273
$862$	−213.988	+	213.988i	−0.248246	+	0.248246i
$863$	−1077.87	−	1077.87i	−1.24898	−	1.24898i	−0.956170	−	0.292812i	$-0.905409\pi$
$863$	−1077.87	−	1077.87i	−1.24898	−	1.24898i	−0.292812	−	0.956170i	$-0.594591\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	−572.651	+	582.549i	−0.662024	+	0.673467i
$866$	−9.65308			−0.0111467
$867$	192.279	−	192.279i	0.221775	−	0.221775i
$868$	29.1127	+	29.1127i	0.0335400	+	0.0335400i
$869$			234.931i			0.270346i
$870$	−659.859	+	5.65380i	−0.758459	+	0.00649862i
$871$	−836.301			−0.960162
$872$	−272.615	+	272.615i	−0.312631	+	0.312631i
$873$	−224.087	−	224.087i	−0.256686	−	0.256686i
$874$		−	134.038i		−	0.153362i
$875$	−76.8485	−	72.9961i	−0.0878269	−	0.0834241i
$876$	−369.343			−0.421625
$877$	108.190	−	108.190i	0.123363	−	0.123363i	−0.642730	−	0.766093i	$-0.722198\pi$
$877$	108.190	−	108.190i	0.123363	−	0.123363i	0.766093	+	0.642730i	$0.222198\pi$
$878$	−770.632	−	770.632i	−0.877713	−	0.877713i
$879$		−	161.674i		−	0.183930i
$880$	−0.478549	−	55.8517i	−0.000543805	−	0.0634679i
$881$	885.563			1.00518			0.502590	−	0.864525i	$-0.332381\pi$
$881$	885.563			1.00518			0.502590	+	0.864525i	$0.332381\pi$
$882$	144.843	−	144.843i	0.164221	−	0.164221i
$883$	−82.2691	−	82.2691i	−0.0931700	−	0.0931700i	0.658986	−	0.752156i	$-0.270986\pi$
$883$	−82.2691	−	82.2691i	−0.0931700	−	0.0931700i	−0.752156	+	0.658986i	$0.770986\pi$
$884$		−	338.699i		−	0.383143i
$885$	701.933	+	690.007i	0.793145	+	0.779669i
$886$	−167.319			−0.188847
$887$	−104.248	+	104.248i	−0.117528	+	0.117528i	−0.763425	−	0.645897i	$-0.776484\pi$
$887$	−104.248	+	104.248i	−0.117528	+	0.117528i	0.645897	+	0.763425i	$0.276484\pi$
$888$	−104.806	−	104.806i	−0.118024	−	0.118024i
$889$		−	62.5925i		−	0.0704078i
$890$	336.939	−	342.763i	0.378583	−	0.385127i
$891$	−25.1342			−0.0282090
$892$	67.1385	−	67.1385i	0.0752674	−	0.0752674i
$893$	198.059	+	198.059i	0.221790	+	0.221790i
$894$			186.043i			0.208102i
$895$	−277.903	+	2.38113i	−0.310506	+	0.00266048i
$896$	−9.59322			−0.0107067
$897$	−86.5762	+	86.5762i	−0.0965175	+	0.0965175i
$898$	544.988	+	544.988i	0.606891	+	0.606891i
$899$		−	1308.07i		−	1.45502i
$900$	−149.978	+	2.57027i	−0.166642	+	0.00285586i
$901$	331.106			0.367488
$902$	−190.364	+	190.364i	−0.211046	+	0.211046i
$903$	23.5565	+	23.5565i	0.0260869	+	0.0260869i
$904$			266.158i			0.294423i
$905$	1.08850	+	127.040i	0.00120276	+	0.140375i
$906$	89.2795			0.0985425
$907$	481.826	−	481.826i	0.531230	−	0.531230i	−0.389708	−	0.920938i	$-0.627424\pi$
$907$	481.826	−	481.826i	0.531230	−	0.531230i	0.920938	+	0.389708i	$0.127424\pi$
$908$	−403.209	−	403.209i	−0.444062	−	0.444062i
$909$		−	152.695i		−	0.167981i
$910$	−63.0243	−	61.9534i	−0.0692574	−	0.0680807i
$911$	−976.616			−1.07203			−0.536013	−	0.844210i	$-0.680070\pi$
$911$	−976.616			−1.07203			−0.536013	+	0.844210i	$0.680070\pi$
$912$	96.8178	−	96.8178i	0.106160	−	0.106160i
$913$	−219.501	−	219.501i	−0.240417	−	0.240417i
$914$		−	859.192i		−	0.940035i
$915$	−426.923	+	434.302i	−0.466582	+	0.474647i
$916$	−182.314			−0.199033
$917$	−110.718	+	110.718i	−0.120739	+	0.120739i
$918$	59.7003	+	59.7003i	0.0650330	+	0.0650330i
$919$		−	1265.62i		−	1.37717i	−0.725155	−	0.688585i	$-0.758232\pi$
$919$		−	1265.62i		−	1.37717i	0.725155	−	0.688585i	$-0.241768\pi$
$920$	67.8208	−	0.581102i	0.0737183	−	0.000631633i
$921$	447.286			0.485653
$922$	−327.982	+	327.982i	−0.355729	+	0.355729i
$923$	1227.55	+	1227.55i	1.32996	+	1.32996i
$924$			8.20300i			0.00887770i
$925$	−525.590	+	543.919i	−0.568206	+	0.588021i
$926$	−825.953			−0.891957
$927$	47.6286	−	47.6286i	0.0513793	−	0.0513793i
$928$	215.517	+	215.517i	0.232238	+	0.232238i
$929$			853.614i			0.918852i	0.888216	+	0.459426i	$0.151945\pi$
$929$			853.614i			0.918852i	−0.888216	+	0.459426i	$0.848055\pi$
$930$	−2.54758	−	297.329i	−0.00273933	−	0.319709i
$931$	954.171			1.02489
$932$	−373.963	+	373.963i	−0.401248	+	0.401248i
$933$	505.407	+	505.407i	0.541701	+	0.541701i
$934$			1106.16i			1.18432i
$935$	114.409	+	112.465i	0.122363	+	0.120284i
$936$	−125.071			−0.133622
$937$	487.479	−	487.479i	0.520255	−	0.520255i	−0.397394	−	0.917648i	$-0.630085\pi$
$937$	487.479	−	487.479i	0.520255	−	0.520255i	0.917648	+	0.397394i	$0.130085\pi$
$938$	−48.1097	−	48.1097i	−0.0512897	−	0.0512897i
$939$			1022.57i			1.08899i
$940$	−99.3554	+	101.073i	−0.105697	+	0.107524i
$941$	52.7415			0.0560484			0.0280242	−	0.999607i	$-0.491078\pi$
$941$	52.7415			0.0560484			0.0280242	+	0.999607i	$0.491078\pi$
$942$	421.529	−	421.529i	0.447483	−	0.447483i
$943$	−231.159	−	231.159i	−0.245131	−	0.245131i
$944$		−	454.622i		−	0.481592i
$945$	22.0290	−	0.188749i	0.0233111	−	0.000199734i
$946$	89.5867			0.0947005
$947$	23.5284	−	23.5284i	0.0248452	−	0.0248452i	−0.694575	−	0.719420i	$-0.744408\pi$
$947$	23.5284	−	23.5284i	0.0248452	−	0.0248452i	0.719420	+	0.694575i	$0.244408\pi$
$948$	−206.060	−	206.060i	−0.217362	−	0.217362i
$949$			1571.55i			1.65601i
$950$	−502.465	−	485.533i	−0.528910	−	0.511087i
$951$	712.613			0.749330
$952$	19.4843	−	19.4843i	0.0204667	−	0.0204667i
$953$	−417.312	−	417.312i	−0.437893	−	0.437893i	0.453409	−	0.891303i	$-0.350208\pi$
$953$	−417.312	−	417.312i	−0.437893	−	0.437893i	−0.891303	+	0.453409i	$0.850208\pi$
$954$		−	122.267i		−	0.128162i
$955$	3.45981	+	403.797i	0.00362284	+	0.422824i
$956$	−343.484			−0.359293
$957$	184.285	−	184.285i	0.192565	−	0.192565i
$958$	−560.923	−	560.923i	−0.585514	−	0.585514i
$959$		−	151.575i		−	0.158056i
$960$	49.4077	+	48.5683i	0.0514664	+	0.0505919i
$961$	−371.591			−0.386672
$962$	−445.946	+	445.946i	−0.463562	+	0.463562i
$963$	−101.155	−	101.155i	−0.105042	−	0.105042i
$964$			239.326i			0.248263i
$965$	852.461	−	867.196i	0.883380	−	0.898649i
$966$	−9.96091			−0.0103115
$967$	709.298	−	709.298i	0.733504	−	0.733504i	−0.237808	−	0.971312i	$-0.576429\pi$
$967$	709.298	−	709.298i	0.733504	−	0.733504i	0.971312	+	0.237808i	$0.0764289\pi$
$968$	−226.402	−	226.402i	−0.233886	−	0.233886i
$969$			393.283i			0.405864i
$970$	746.928	−	6.39983i	0.770029	−	0.00659776i
$971$	−976.934			−1.00611			−0.503056	−	0.864254i	$-0.667791\pi$
$971$	−976.934			−1.00611			−0.503056	+	0.864254i	$0.667791\pi$
$972$	22.0454	−	22.0454i	0.0226805	−	0.0226805i
$973$	130.569	+	130.569i	0.134193	+	0.134193i
$974$			911.862i			0.936203i
$975$	10.9365	+	638.155i	0.0112169	+	0.654517i
$976$	281.285			0.288202
$977$	−1182.67	+	1182.67i	−1.21052	+	1.21052i	−0.239658	+	0.970857i	$0.577035\pi$
$977$	−1182.67	+	1182.67i	−1.21052	+	1.21052i	−0.970857	+	0.239658i	$0.922965\pi$
$978$	−200.390	−	200.390i	−0.204898	−	0.204898i
$979$			189.827i			0.193899i
$980$	4.13666	+	482.792i	0.00422108	+	0.492645i
$981$	−408.922			−0.416842
$982$	419.688	−	419.688i	0.427381	−	0.427381i
$983$	−460.951	−	460.951i	−0.468922	−	0.468922i	0.432643	−	0.901565i	$-0.357581\pi$
$983$	−460.951	−	460.951i	−0.468922	−	0.468922i	−0.901565	+	0.432643i	$0.857581\pi$
$984$		−	333.939i		−	0.339369i
$985$	−431.877	−	424.539i	−0.438454	−	0.431004i
$986$	−875.449			−0.887880
$987$	14.7185	−	14.7185i	0.0149124	−	0.0149124i
$988$	−411.959	−	411.959i	−0.416962	−	0.416962i
$989$			108.785i			0.109995i
$990$	41.5299	−	42.2477i	0.0419494	−	0.0426745i
$991$	−309.567			−0.312379			−0.156189	−	0.987727i	$-0.549921\pi$
$991$	−309.567			−0.312379			−0.156189	+	0.987727i	$0.549921\pi$
$992$	−97.1110	+	97.1110i	−0.0978941	+	0.0978941i
$993$	−64.3808	−	64.3808i	−0.0648346	−	0.0648346i
$994$			141.235i			0.142087i
$995$	1545.63	−	13.2432i	1.55340	−	0.0133098i
$996$	385.051			0.386598
$997$	−587.640	+	587.640i	−0.589408	+	0.589408i	−0.937471	−	0.348063i	$-0.886840\pi$
$997$	−587.640	+	587.640i	−0.589408	+	0.589408i	0.348063	+	0.937471i	$0.386840\pi$
$998$	338.152	+	338.152i	0.338830	+	0.338830i
$999$		−	157.208i		−	0.157366i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.b.553.5	yes	48
5.2	odd	4	inner	690.3.k.b.277.5	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.b.277.5	✓	48	5.2	odd	4	inner
690.3.k.b.553.5	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)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(0.0428394 + 4.99982i) q^{5} +2.44949 q^{6} +(0.599576 - 0.599576i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(0.0428394 + 4.99982i) q^{5} +2.44949 q^{6} +(0.599576 - 0.599576i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(-5.04266 - 4.95698i) q^{10} +2.79269 q^{11} +(-2.44949 + 2.44949i) q^{12} +(10.4226 + 10.4226i) q^{13} +1.19915i q^{14} +(6.07103 - 6.17597i) q^{15} -4.00000 q^{16} +(8.12418 - 8.12418i) q^{17} +(-3.00000 - 3.00000i) q^{18} -19.7629i q^{19} +(9.99963 - 0.0856788i) q^{20} -1.46866 q^{21} +(-2.79269 + 2.79269i) q^{22} +(-3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(-24.9963 + 0.428378i) q^{25} -20.8451 q^{26} +(3.67423 - 3.67423i) q^{27} +(-1.19915 - 1.19915i) q^{28} +53.8793i q^{29} +(0.104935 + 12.2470i) q^{30} -24.2777 q^{31} +(4.00000 - 4.00000i) q^{32} +(-3.42033 - 3.42033i) q^{33} +16.2484i q^{34} +(3.02346 + 2.97209i) q^{35} +6.00000 q^{36} +(21.3933 - 21.3933i) q^{37} +(19.7629 + 19.7629i) q^{38} -25.5299i q^{39} +(-9.91395 + 10.0853i) q^{40} +68.1650 q^{41} +(1.46866 - 1.46866i) q^{42} +(-16.0395 - 16.0395i) q^{43} -5.58538i q^{44} +(-14.9994 + 0.128518i) q^{45} +6.78233 q^{46} +(-10.0218 + 10.0218i) q^{47} +(4.89898 + 4.89898i) q^{48} +48.2810i q^{49} +(24.5680 - 25.4247i) q^{50} -19.9001 q^{51} +(20.8451 - 20.8451i) q^{52} +(20.3778 + 20.3778i) q^{53} +7.34847i q^{54} +(0.119637 + 13.9629i) q^{55} +2.39831 q^{56} +(-24.2045 + 24.2045i) q^{57} +(-53.8793 - 53.8793i) q^{58} +113.656i q^{59} +(-12.3519 - 12.1421i) q^{60} -70.3213 q^{61} +(24.2777 - 24.2777i) q^{62} +(1.79873 + 1.79873i) q^{63} +8.00000i q^{64} +(-51.6643 + 52.5573i) q^{65} +6.84066 q^{66} +(-40.1198 + 40.1198i) q^{67} +(-16.2484 - 16.2484i) q^{68} +8.30662i q^{69} +(-5.99554 + 0.0513710i) q^{70} +117.779 q^{71} +(-6.00000 + 6.00000i) q^{72} +(75.3919 + 75.3919i) q^{73} +42.7867i q^{74} +(31.1388 + 30.0895i) q^{75} -39.5257 q^{76} +(1.67443 - 1.67443i) q^{77} +(25.5299 + 25.5299i) q^{78} +84.1235i q^{79} +(-0.171358 - 19.9993i) q^{80} -9.00000 q^{81} +(-68.1650 + 68.1650i) q^{82} +(-78.5983 - 78.5983i) q^{83} +2.93731i q^{84} +(40.9674 + 40.2714i) q^{85} +32.0790 q^{86} +(65.9883 - 65.9883i) q^{87} +(5.58538 + 5.58538i) q^{88} +67.9727i q^{89} +(14.8709 - 15.1280i) q^{90} +12.4982 q^{91} +(-6.78233 + 6.78233i) q^{92} +(29.7340 + 29.7340i) q^{93} -20.0436i q^{94} +(98.8106 - 0.846629i) q^{95} -9.79796 q^{96} +(-74.6956 + 74.6956i) q^{97} +(-48.2810 - 48.2810i) q^{98} +8.37807i 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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