LMFDB - Embedded newform 690.3.k.a.277.5

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:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			277.5
Character	$\chi$	$=$	690.277
Dual form			690.3.k.a.553.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(0.0159424 - 4.99997i) q^{5} -2.44949 q^{6} +(-0.165312 - 0.165312i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(0.0159424 - 4.99997i) q^{5} -2.44949 q^{6} +(-0.165312 - 0.165312i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(5.01592 - 4.98403i) q^{10} +7.54349 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-15.1286 + 15.1286i) q^{13} -0.330624i q^{14} +(6.10417 + 6.14322i) q^{15} -4.00000 q^{16} +(-19.2185 - 19.2185i) q^{17} +(3.00000 - 3.00000i) q^{18} -11.4869i q^{19} +(9.99995 + 0.0318848i) q^{20} +0.404930 q^{21} +(7.54349 + 7.54349i) q^{22} +(3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(-24.9995 - 0.159423i) q^{25} -30.2572 q^{26} +(3.67423 + 3.67423i) q^{27} +(0.330624 - 0.330624i) q^{28} -10.0966i q^{29} +(-0.0390507 + 12.2474i) q^{30} -2.67257 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-9.23885 + 9.23885i) q^{33} -38.4370i q^{34} +(-0.829191 + 0.823920i) q^{35} +6.00000 q^{36} +(-34.3033 - 34.3033i) q^{37} +(11.4869 - 11.4869i) q^{38} -37.0573i q^{39} +(9.96806 + 10.0318i) q^{40} -29.0530 q^{41} +(0.404930 + 0.404930i) q^{42} +(-39.6178 + 39.6178i) q^{43} +15.0870i q^{44} +(-14.9999 - 0.0478272i) q^{45} +6.78233 q^{46} +(-18.2031 - 18.2031i) q^{47} +(4.89898 - 4.89898i) q^{48} -48.9453i q^{49} +(-24.8401 - 25.1589i) q^{50} +47.0755 q^{51} +(-30.2572 - 30.2572i) q^{52} +(14.1802 - 14.1802i) q^{53} +7.34847i q^{54} +(0.120261 - 37.7172i) q^{55} +0.661248 q^{56} +(14.0685 + 14.0685i) q^{57} +(10.0966 - 10.0966i) q^{58} -95.0201i q^{59} +(-12.2864 + 12.2083i) q^{60} +21.1653 q^{61} +(-2.67257 - 2.67257i) q^{62} +(-0.495936 + 0.495936i) q^{63} -8.00000i q^{64} +(75.4013 + 75.8837i) q^{65} -18.4777 q^{66} +(-45.5947 - 45.5947i) q^{67} +(38.4370 - 38.4370i) q^{68} +8.30662i q^{69} +(-1.65311 - 0.00527094i) q^{70} +42.7065 q^{71} +(6.00000 + 6.00000i) q^{72} +(71.8554 - 71.8554i) q^{73} -68.6065i q^{74} +(30.8133 - 30.4227i) q^{75} +22.9738 q^{76} +(-1.24703 - 1.24703i) q^{77} +(37.0573 - 37.0573i) q^{78} +136.677i q^{79} +(-0.0637696 + 19.9999i) q^{80} -9.00000 q^{81} +(-29.0530 - 29.0530i) q^{82} +(-7.78717 + 7.78717i) q^{83} +0.809860i q^{84} +(-96.3984 + 95.7857i) q^{85} -79.2356 q^{86} +(12.3658 + 12.3658i) q^{87} +(-15.0870 + 15.0870i) q^{88} +154.201i q^{89} +(-14.9521 - 15.0478i) q^{90} +5.00187 q^{91} +(6.78233 + 6.78233i) q^{92} +(3.27322 - 3.27322i) q^{93} -36.4063i q^{94} +(-57.4341 - 0.183128i) q^{95} +9.79796 q^{96} +(35.7610 + 35.7610i) q^{97} +(48.9453 - 48.9453i) q^{98} -22.6305i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) $ 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8	$ 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) $ 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8 - 16 * q^10 + 32 * q^11 + 16 * q^13 + 24 * q^15 - 160 * q^16 - 48 * q^17 + 120 * q^18 - 16 * q^20 - 96 * q^21 + 32 * q^22 + 32 * q^26 + 16 * q^28 + 24 * q^30 + 152 * q^31 - 160 * q^32 - 24 * q^33 + 48 * q^35 + 240 * q^36 + 216 * q^37 + 16 * q^38 - 168 * q^41 - 96 * q^42 - 48 * q^43 + 24 * q^45 - 232 * q^47 - 40 * q^50 + 32 * q^52 + 8 * q^53 - 272 * q^55 + 32 * q^56 - 136 * q^58 - 64 * q^61 + 152 * q^62 - 24 * q^63 + 416 * q^65 - 48 * q^66 - 32 * q^67 + 96 * q^68 + 88 * q^70 - 104 * q^71 + 240 * q^72 + 480 * q^73 - 216 * q^75 + 32 * q^76 + 280 * q^77 - 192 * q^78 + 32 * q^80 - 360 * q^81 - 168 * q^82 - 576 * q^83 - 208 * q^85 - 96 * q^86 + 24 * q^87 - 64 * q^88 + 144 * q^91 + 96 * q^93 + 168 * q^95 + 24 * q^97 + 176 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	0.0159424	−	4.99997i	0.00318848	−	0.999995i
$5$	0.0159424	−	4.99997i	0.00318848	−	0.999995i
$6$	−2.44949			−0.408248
$7$	−0.165312	−	0.165312i	−0.0236160	−	0.0236160i	0.695200	−	0.718816i	$-0.255316\pi$
$7$	−0.165312	−	0.165312i	−0.0236160	−	0.0236160i	−0.718816	+	0.695200i	$0.755316\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$	5.01592	−	4.98403i	0.501592	−	0.498403i
$11$	7.54349			0.685771			0.342886	−	0.939377i	$-0.388596\pi$
$11$	7.54349			0.685771			0.342886	+	0.939377i	$0.388596\pi$
$12$	−2.44949	−	2.44949i	−0.204124	−	0.204124i
$13$	−15.1286	+	15.1286i	−1.16374	+	1.16374i	−0.180086	+	0.983651i	$0.557638\pi$
$13$	−15.1286	+	15.1286i	−1.16374	+	1.16374i	−0.983651	+	0.180086i	$0.942362\pi$
$14$		−	0.330624i		−	0.0236160i
$15$	6.10417	+	6.14322i	0.406945	+	0.409548i
$16$	−4.00000			−0.250000
$17$	−19.2185	−	19.2185i	−1.13050	−	1.13050i	−0.990094	−	0.140406i	$-0.955159\pi$
$17$	−19.2185	−	19.2185i	−1.13050	−	1.13050i	−0.140406	−	0.990094i	$-0.544841\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$		−	11.4869i		−	0.604573i	−0.953217	−	0.302286i	$-0.902250\pi$
$19$		−	11.4869i		−	0.604573i	0.953217	−	0.302286i	$-0.0977498\pi$
$20$	9.99995	+	0.0318848i	0.499997	+	0.00159424i
$21$	0.404930			0.0192824
$22$	7.54349	+	7.54349i	0.342886	+	0.342886i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$24$		−	4.89898i		−	0.204124i
$25$	−24.9995	−	0.159423i	−0.999980	−	0.00637693i
$26$	−30.2572			−1.16374
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$	0.330624	−	0.330624i	0.0118080	−	0.0118080i
$29$		−	10.0966i		−	0.348159i	−0.984732	−	0.174080i	$-0.944305\pi$
$29$		−	10.0966i		−	0.348159i	0.984732	−	0.174080i	$-0.0556950\pi$
$30$	−0.0390507	+	12.2474i	−0.00130169	+	0.408246i
$31$	−2.67257			−0.0862120			−0.0431060	−	0.999071i	$-0.513725\pi$
$31$	−2.67257			−0.0862120			−0.0431060	+	0.999071i	$0.513725\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	−9.23885	+	9.23885i	−0.279965	+	0.279965i
$34$		−	38.4370i		−	1.13050i
$35$	−0.829191	+	0.823920i	−0.0236912	+	0.0235406i
$36$	6.00000			0.166667
$37$	−34.3033	−	34.3033i	−0.927115	−	0.927115i	0.0704032	−	0.997519i	$-0.477571\pi$
$37$	−34.3033	−	34.3033i	−0.927115	−	0.927115i	−0.997519	+	0.0704032i	$0.977571\pi$
$38$	11.4869	−	11.4869i	0.302286	−	0.302286i
$39$		−	37.0573i		−	0.950187i
$40$	9.96806	+	10.0318i	0.249202	+	0.250796i
$41$	−29.0530			−0.708609			−0.354305	−	0.935130i	$-0.615282\pi$
$41$	−29.0530			−0.708609			−0.354305	+	0.935130i	$0.615282\pi$
$42$	0.404930	+	0.404930i	0.00964119	+	0.00964119i
$43$	−39.6178	+	39.6178i	−0.921344	+	0.921344i	−0.997125	−	0.0757805i	$-0.975855\pi$
$43$	−39.6178	+	39.6178i	−0.921344	+	0.921344i	0.0757805	+	0.997125i	$0.475855\pi$
$44$			15.0870i			0.342886i
$45$	−14.9999	−	0.0478272i	−0.333332	−	0.00106283i
$46$	6.78233			0.147442
$47$	−18.2031	−	18.2031i	−0.387301	−	0.387301i	0.486423	−	0.873724i	$-0.338302\pi$
$47$	−18.2031	−	18.2031i	−0.387301	−	0.387301i	−0.873724	+	0.486423i	$0.838302\pi$
$48$	4.89898	−	4.89898i	0.102062	−	0.102062i
$49$		−	48.9453i		−	0.998885i
$50$	−24.8401	−	25.1589i	−0.496801	−	0.503178i
$51$	47.0755			0.923050
$52$	−30.2572	−	30.2572i	−0.581868	−	0.581868i
$53$	14.1802	−	14.1802i	0.267551	−	0.267551i	−0.560562	−	0.828113i	$-0.689415\pi$
$53$	14.1802	−	14.1802i	0.267551	−	0.267551i	0.828113	+	0.560562i	$0.189415\pi$
$54$			7.34847i			0.136083i
$55$	0.120261	−	37.7172i	0.00218657	−	0.685768i
$56$	0.661248			0.0118080
$57$	14.0685	+	14.0685i	0.246816	+	0.246816i
$58$	10.0966	−	10.0966i	0.174080	−	0.174080i
$59$		−	95.0201i		−	1.61051i	−0.592929	−	0.805255i	$-0.702028\pi$
$59$		−	95.0201i		−	1.61051i	0.592929	−	0.805255i	$-0.297972\pi$
$60$	−12.2864	+	12.2083i	−0.204774	+	0.203472i
$61$	21.1653			0.346971			0.173486	−	0.984836i	$-0.444497\pi$
$61$	21.1653			0.346971			0.173486	+	0.984836i	$0.444497\pi$
$62$	−2.67257	−	2.67257i	−0.0431060	−	0.0431060i
$63$	−0.495936	+	0.495936i	−0.00787200	+	0.00787200i
$64$		−	8.00000i		−	0.125000i
$65$	75.4013	+	75.8837i	1.16002	+	1.16744i
$66$	−18.4777			−0.279965
$67$	−45.5947	−	45.5947i	−0.680518	−	0.680518i	0.279599	−	0.960117i	$-0.409798\pi$
$67$	−45.5947	−	45.5947i	−0.680518	−	0.680518i	−0.960117	+	0.279599i	$0.909798\pi$
$68$	38.4370	−	38.4370i	0.565250	−	0.565250i
$69$			8.30662i			0.120386i
$70$	−1.65311	−	0.00527094i	−0.0236159	−	7.52991e-5i
$71$	42.7065			0.601501			0.300750	−	0.953703i	$-0.402763\pi$
$71$	42.7065			0.601501			0.300750	+	0.953703i	$0.402763\pi$
$72$	6.00000	+	6.00000i	0.0833333	+	0.0833333i
$73$	71.8554	−	71.8554i	0.984321	−	0.984321i	−0.0155579	−	0.999879i	$-0.504952\pi$
$73$	71.8554	−	71.8554i	0.984321	−	0.984321i	0.999879	+	0.0155579i	$0.00495242\pi$
$74$		−	68.6065i		−	0.927115i
$75$	30.8133	−	30.4227i	0.410843	−	0.405637i
$76$	22.9738			0.302286
$77$	−1.24703	−	1.24703i	−0.0161952	−	0.0161952i
$78$	37.0573	−	37.0573i	0.475094	−	0.475094i
$79$			136.677i			1.73009i	0.501694	+	0.865045i	$0.332710\pi$
$79$			136.677i			1.73009i	−0.501694	+	0.865045i	$0.667290\pi$
$80$	−0.0637696	+	19.9999i	−0.000797120	+	0.249999i
$81$	−9.00000			−0.111111
$82$	−29.0530	−	29.0530i	−0.354305	−	0.354305i
$83$	−7.78717	+	7.78717i	−0.0938214	+	0.0938214i	−0.752460	−	0.658638i	$-0.771133\pi$
$83$	−7.78717	+	7.78717i	−0.0938214	+	0.0938214i	0.658638	+	0.752460i	$0.271133\pi$
$84$			0.809860i			0.00964119i
$85$	−96.3984	+	95.7857i	−1.13410	+	1.12689i
$86$	−79.2356			−0.921344
$87$	12.3658	+	12.3658i	0.142135	+	0.142135i
$88$	−15.0870	+	15.0870i	−0.171443	+	0.171443i
$89$			154.201i			1.73260i	0.499525	+	0.866300i	$0.333508\pi$
$89$			154.201i			1.73260i	−0.499525	+	0.866300i	$0.666492\pi$
$90$	−14.9521	−	15.0478i	−0.166134	−	0.167197i
$91$	5.00187			0.0549656
$92$	6.78233	+	6.78233i	0.0737210	+	0.0737210i
$93$	3.27322	−	3.27322i	0.0351959	−	0.0351959i
$94$		−	36.4063i		−	0.387301i
$95$	−57.4341	−	0.183128i	−0.604569	−	0.00192767i
$96$	9.79796			0.102062
$97$	35.7610	+	35.7610i	0.368670	+	0.368670i	0.866992	−	0.498322i	$-0.166050\pi$
$97$	35.7610	+	35.7610i	0.368670	+	0.368670i	−0.498322	+	0.866992i	$0.666050\pi$
$98$	48.9453	−	48.9453i	0.499442	−	0.499442i
$99$		−	22.6305i		−	0.228590i
$100$	0.318846	−	49.9990i	0.00318846	−	0.499990i
$101$	106.463			1.05409			0.527044	−	0.849838i	$-0.323300\pi$
$101$	106.463			1.05409			0.527044	+	0.849838i	$0.323300\pi$
$102$	47.0755	+	47.0755i	0.461525	+	0.461525i
$103$	72.3647	−	72.3647i	0.702569	−	0.702569i	−0.262392	−	0.964961i	$-0.584511\pi$
$103$	72.3647	−	72.3647i	0.702569	−	0.702569i	0.964961	+	0.262392i	$0.0845113\pi$
$104$		−	60.5143i		−	0.581868i
$105$	0.00645555	−	2.02464i	6.14815e−5	−	0.0192823i
$106$	28.3604			0.267551
$107$	−136.478	−	136.478i	−1.27550	−	1.27550i	−0.943160	−	0.332340i	$-0.892162\pi$
$107$	−136.478	−	136.478i	−1.27550	−	1.27550i	−0.332340	−	0.943160i	$-0.607838\pi$
$108$	−7.34847	+	7.34847i	−0.0680414	+	0.0680414i
$109$		−	109.558i		−	1.00512i	−0.864541	−	0.502562i	$-0.832391\pi$
$109$		−	109.558i		−	1.00512i	0.864541	−	0.502562i	$-0.167609\pi$
$110$	37.8375	−	37.5970i	0.343977	−	0.341791i
$111$	84.0255			0.756987
$112$	0.661248	+	0.661248i	0.00590400	+	0.00590400i
$113$	−117.597	+	117.597i	−1.04068	+	1.04068i	−0.0415426	+	0.999137i	$0.513227\pi$
$113$	−117.597	+	117.597i	−1.04068	+	1.04068i	−0.999137	+	0.0415426i	$0.986773\pi$
$114$			28.1370i			0.246816i
$115$	−16.9017	−	17.0098i	−0.146971	−	0.147911i
$116$	20.1932			0.174080
$117$	45.3857	+	45.3857i	0.387912	+	0.387912i
$118$	95.0201	−	95.0201i	0.805255	−	0.805255i
$119$			6.35410i			0.0533958i
$120$	−24.4948	−	0.0781015i	−0.204123	−	0.000650846i
$121$	−64.0958			−0.529718
$122$	21.1653	+	21.1653i	0.173486	+	0.173486i
$123$	35.5825	−	35.5825i	0.289289	−	0.289289i
$124$		−	5.34514i		−	0.0431060i
$125$	−1.19566	+	124.994i	−0.00956531	+	0.999954i
$126$	−0.991872			−0.00787200
$127$	−71.2879	−	71.2879i	−0.561322	−	0.561322i	0.368361	−	0.929683i	$-0.379919\pi$
$127$	−71.2879	−	71.2879i	−0.561322	−	0.561322i	−0.929683	+	0.368361i	$0.879919\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$		−	97.0434i		−	0.752274i
$130$	−0.482372	+	151.285i	−0.00371055	+	1.16373i
$131$	−69.6458			−0.531647			−0.265824	−	0.964022i	$-0.585644\pi$
$131$	−69.6458			−0.531647			−0.265824	+	0.964022i	$0.585644\pi$
$132$	−18.4777	−	18.4777i	−0.139983	−	0.139983i
$133$	−1.89892	+	1.89892i	−0.0142776	+	0.0142776i
$134$		−	91.1894i		−	0.680518i
$135$	18.4297	−	18.3125i	0.136516	−	0.135648i
$136$	76.8740			0.565250
$137$	127.757	+	127.757i	0.932533	+	0.932533i	0.997864	−	0.0653303i	$-0.0208101\pi$
$137$	127.757	+	127.757i	0.932533	+	0.932533i	−0.0653303	+	0.997864i	$0.520810\pi$
$138$	−8.30662	+	8.30662i	−0.0601929	+	0.0601929i
$139$		−	80.2923i		−	0.577642i	−0.957383	−	0.288821i	$-0.906737\pi$
$139$		−	80.2923i		−	0.577642i	0.957383	−	0.288821i	$-0.0932633\pi$
$140$	−1.64784	−	1.65838i	−0.0117703	−	0.0118456i
$141$	44.5884			0.316230
$142$	42.7065	+	42.7065i	0.300750	+	0.300750i
$143$	−114.122	+	114.122i	−0.798057	+	0.798057i
$144$			12.0000i			0.0833333i
$145$	−50.4829	−	0.160964i	−0.348158	−	0.00111010i
$146$	143.711			0.984321
$147$	59.9456	+	59.9456i	0.407793	+	0.407793i
$148$	68.6065	−	68.6065i	0.463558	−	0.463558i
$149$			245.171i			1.64545i	0.568443	+	0.822723i	$0.307546\pi$
$149$			245.171i			1.64545i	−0.568443	+	0.822723i	$0.692454\pi$
$150$	61.2360	+	0.390505i	0.408240	+	0.00260337i
$151$	−266.303			−1.76360			−0.881800	−	0.471624i	$-0.843668\pi$
$151$	−266.303			−1.76360			−0.881800	+	0.471624i	$0.843668\pi$
$152$	22.9738	+	22.9738i	0.151143	+	0.151143i
$153$	−57.6555	+	57.6555i	−0.376833	+	0.376833i
$154$		−	2.49406i		−	0.0161952i
$155$	−0.0426072	+	13.3628i	−0.000274885	+	0.0862116i
$156$	74.1146			0.475094
$157$	78.4391	+	78.4391i	0.499612	+	0.499612i	0.911317	−	0.411705i	$-0.135067\pi$
$157$	78.4391	+	78.4391i	0.499612	+	0.499612i	−0.411705	+	0.911317i	$0.635067\pi$
$158$	−136.677	+	136.677i	−0.865045	+	0.865045i
$159$			34.7343i			0.218455i
$160$	−20.0637	+	19.9361i	−0.125398	+	0.124601i
$161$	−1.12120			−0.00696398
$162$	−9.00000	−	9.00000i	−0.0555556	−	0.0555556i
$163$	−176.827	+	176.827i	−1.08483	+	1.08483i	−0.0887791	+	0.996051i	$0.528297\pi$
$163$	−176.827	+	176.827i	−1.08483	+	1.08483i	−0.996051	+	0.0887791i	$0.971703\pi$
$164$		−	58.1060i		−	0.354305i
$165$	46.0467	+	46.3413i	0.279071	+	0.280856i
$166$	−15.5743			−0.0938214
$167$	−5.89246	−	5.89246i	−0.0352842	−	0.0352842i	0.689245	−	0.724529i	$-0.257943\pi$
$167$	−5.89246	−	5.89246i	−0.0352842	−	0.0352842i	−0.724529	+	0.689245i	$0.757943\pi$
$168$	−0.809860	+	0.809860i	−0.00482059	+	0.00482059i
$169$		−	288.748i		−	1.70857i
$170$	−192.184	−	0.612778i	−1.13049	−	0.00360458i
$171$	−34.4606			−0.201524
$172$	−79.2356	−	79.2356i	−0.460672	−	0.460672i
$173$	−152.579	+	152.579i	−0.881959	+	0.881959i	−0.993734	−	0.111774i	$-0.964347\pi$
$173$	−152.579	+	152.579i	−0.881959	+	0.881959i	0.111774	+	0.993734i	$0.464347\pi$
$174$			24.7316i			0.142135i
$175$	4.10636	+	4.15907i	0.0234649	+	0.0237661i
$176$	−30.1739			−0.171443
$177$	116.375	+	116.375i	0.657488	+	0.657488i
$178$	−154.201	+	154.201i	−0.866300	+	0.866300i
$179$			166.077i			0.927806i	0.885886	+	0.463903i	$0.153551\pi$
$179$			166.077i			0.927806i	−0.885886	+	0.463903i	$0.846449\pi$
$180$	0.0956544	−	29.9998i	0.000531413	−	0.166666i
$181$	61.0419			0.337248			0.168624	−	0.985680i	$-0.446068\pi$
$181$	61.0419			0.337248			0.168624	+	0.985680i	$0.446068\pi$
$182$	5.00187	+	5.00187i	0.0274828	+	0.0274828i
$183$	−25.9220	+	25.9220i	−0.141650	+	0.141650i
$184$			13.5647i			0.0737210i
$185$	−172.062	+	170.969i	−0.930067	+	0.924155i
$186$	6.54644			0.0351959
$187$	−144.975	−	144.975i	−0.775265	−	0.775265i
$188$	36.4063	−	36.4063i	0.193650	−	0.193650i
$189$		−	1.21479i		−	0.00642746i
$190$	−57.2510	−	57.6172i	−0.301321	−	0.303249i
$191$	255.678			1.33863			0.669315	−	0.742979i	$-0.266588\pi$
$191$	255.678			1.33863			0.669315	+	0.742979i	$0.266588\pi$
$192$	9.79796	+	9.79796i	0.0510310	+	0.0510310i
$193$	−49.6596	+	49.6596i	−0.257304	+	0.257304i	−0.823957	−	0.566653i	$-0.808238\pi$
$193$	−49.6596	+	49.6596i	−0.257304	+	0.257304i	0.566653	+	0.823957i	$0.308238\pi$
$194$			71.5220i			0.368670i
$195$	−185.286	−	0.590782i	−0.950182	−	0.00302965i
$196$	97.8907			0.499442
$197$	37.9008	+	37.9008i	0.192390	+	0.192390i	0.796728	−	0.604338i	$-0.206562\pi$
$197$	37.9008	+	37.9008i	0.192390	+	0.192390i	−0.604338	+	0.796728i	$0.706562\pi$
$198$	22.6305	−	22.6305i	0.114295	−	0.114295i
$199$		−	194.128i		−	0.975519i	−0.872978	−	0.487760i	$-0.837814\pi$
$199$		−	194.128i		−	0.975519i	0.872978	−	0.487760i	$-0.162186\pi$
$200$	50.3178	−	49.6801i	0.251589	−	0.248401i
$201$	111.684			0.555641
$202$	106.463	+	106.463i	0.527044	+	0.527044i
$203$	−1.66909	+	1.66909i	−0.00822213	+	0.00822213i
$204$			94.1511i			0.461525i
$205$	−0.463174	+	145.264i	−0.00225939	+	0.708606i
$206$	144.729			0.702569
$207$	−10.1735	−	10.1735i	−0.0491473	−	0.0491473i
$208$	60.5143	−	60.5143i	0.290934	−	0.290934i
$209$		−	86.6511i		−	0.414599i
$210$	2.03109	−	2.01818i	0.00967188	−	0.00961040i
$211$	14.4359			0.0684165			0.0342083	−	0.999415i	$-0.489109\pi$
$211$	14.4359			0.0684165			0.0342083	+	0.999415i	$0.489109\pi$
$212$	28.3604	+	28.3604i	0.133776	+	0.133776i
$213$	−52.3046	+	52.3046i	−0.245562	+	0.245562i
$214$		−	272.957i		−	1.27550i
$215$	197.456	+	198.720i	0.918402	+	0.924277i
$216$	−14.6969			−0.0680414
$217$	0.441808	+	0.441808i	0.00203598	+	0.00203598i
$218$	109.558	−	109.558i	0.502562	−	0.502562i
$219$			176.009i			0.803695i
$220$	75.4345	+	0.240523i	0.342884	+	0.00109328i
$221$	581.497			2.63121
$222$	84.0255	+	84.0255i	0.378493	+	0.378493i
$223$	150.626	−	150.626i	0.675452	−	0.675452i	−0.283516	−	0.958968i	$-0.591501\pi$
$223$	150.626	−	150.626i	0.675452	−	0.675452i	0.958968	+	0.283516i	$0.0915009\pi$
$224$			1.32250i			0.00590400i
$225$	−0.478270	+	74.9985i	−0.00212564	+	0.333327i
$226$	−235.194			−1.04068
$227$	−11.2773	−	11.2773i	−0.0496799	−	0.0496799i	0.681830	−	0.731510i	$-0.261184\pi$
$227$	−11.2773	−	11.2773i	−0.0496799	−	0.0496799i	−0.731510	+	0.681830i	$0.761184\pi$
$228$	−28.1370	+	28.1370i	−0.123408	+	0.123408i
$229$			55.3008i			0.241488i	0.992684	+	0.120744i	$0.0385280\pi$
$229$			55.3008i			0.241488i	−0.992684	+	0.120744i	$0.961472\pi$
$230$	0.108127	−	33.9115i	0.000470116	−	0.147441i
$231$	3.05458			0.0132233
$232$	20.1932	+	20.1932i	0.0870399	+	0.0870399i
$233$	−45.2074	+	45.2074i	−0.194023	+	0.194023i	−0.797432	−	0.603409i	$-0.793809\pi$
$233$	−45.2074	+	45.2074i	−0.194023	+	0.194023i	0.603409	+	0.797432i	$0.293809\pi$
$234$			90.7715i			0.387912i
$235$	−91.3055	+	90.7251i	−0.388534	+	0.386064i
$236$	190.040			0.805255
$237$	−167.395	−	167.395i	−0.706306	−	0.706306i
$238$	−6.35410	+	6.35410i	−0.0266979	+	0.0266979i
$239$		−	287.302i		−	1.20210i	−0.799211	−	0.601050i	$-0.794749\pi$
$239$		−	287.302i		−	1.20210i	0.799211	−	0.601050i	$-0.205251\pi$
$240$	−24.4167	−	24.5729i	−0.101736	−	0.102387i
$241$	−298.409			−1.23821			−0.619106	−	0.785308i	$-0.712505\pi$
$241$	−298.409			−1.23821			−0.619106	+	0.785308i	$0.712505\pi$
$242$	−64.0958	−	64.0958i	−0.264859	−	0.264859i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$			42.3305i			0.173486i
$245$	−244.725	−	0.780306i	−0.998879	−	0.00318492i
$246$	71.1650			0.289289
$247$	173.780	+	173.780i	0.703563	+	0.703563i
$248$	5.34514	−	5.34514i	0.0215530	−	0.0215530i
$249$		−	19.0746i		−	0.0766048i
$250$	−126.190	+	123.799i	−0.504760	+	0.495194i
$251$	262.970			1.04769			0.523844	−	0.851814i	$-0.324497\pi$
$251$	262.970			1.04769			0.523844	+	0.851814i	$0.324497\pi$
$252$	−0.991872	−	0.991872i	−0.00393600	−	0.00393600i
$253$	25.5812	−	25.5812i	0.101111	−	0.101111i
$254$		−	142.576i		−	0.561322i
$255$	0.750497	−	235.376i	0.00294313	−	0.923045i
$256$	16.0000			0.0625000
$257$	71.3647	+	71.3647i	0.277684	+	0.277684i	0.832184	−	0.554500i	$-0.187090\pi$
$257$	71.3647	+	71.3647i	0.277684	+	0.277684i	−0.554500	+	0.832184i	$0.687090\pi$
$258$	97.0434	−	97.0434i	0.376137	−	0.376137i
$259$			11.3415i			0.0437895i
$260$	−151.767	+	150.803i	−0.583721	+	0.580010i
$261$	−30.2899			−0.116053
$262$	−69.6458	−	69.6458i	−0.265824	−	0.265824i
$263$	25.4045	−	25.4045i	0.0965951	−	0.0965951i	−0.657158	−	0.753753i	$-0.728242\pi$
$263$	25.4045	−	25.4045i	0.0965951	−	0.0965951i	0.753753	+	0.657158i	$0.228242\pi$
$264$		−	36.9554i		−	0.139983i
$265$	−70.6747	−	71.1268i	−0.266697	−	0.268403i
$266$	−3.79784			−0.0142776
$267$	−188.857	−	188.857i	−0.707331	−	0.707331i
$268$	91.1894	−	91.1894i	0.340259	−	0.340259i
$269$		−	443.315i		−	1.64801i	−0.566582	−	0.824005i	$-0.691735\pi$
$269$		−	443.315i		−	1.64801i	0.566582	−	0.824005i	$-0.308265\pi$
$270$	36.7422	+	0.117152i	0.136082	+	0.000433897i
$271$	−30.4665			−0.112422			−0.0562112	−	0.998419i	$-0.517902\pi$
$271$	−30.4665			−0.112422			−0.0562112	+	0.998419i	$0.517902\pi$
$272$	76.8740	+	76.8740i	0.282625	+	0.282625i
$273$	−6.12601	+	6.12601i	−0.0224396	+	0.0224396i
$274$			255.514i			0.932533i
$275$	−188.583	−	1.20261i	−0.685757	−	0.00437311i
$276$	−16.6132			−0.0601929
$277$	94.0269	+	94.0269i	0.339447	+	0.339447i	0.856159	−	0.516712i	$-0.172844\pi$
$277$	94.0269	+	94.0269i	0.339447	+	0.339447i	−0.516712	+	0.856159i	$0.672844\pi$
$278$	80.2923	−	80.2923i	0.288821	−	0.288821i
$279$			8.01772i			0.0287373i
$280$	0.0105419	−	3.30622i	3.76496e−5	−	0.0118079i
$281$	448.058			1.59451			0.797256	−	0.603642i	$-0.206284\pi$
$281$	448.058			1.59451			0.797256	+	0.603642i	$0.206284\pi$
$282$	44.5884	+	44.5884i	0.158115	+	0.158115i
$283$	−256.305	+	256.305i	−0.905672	+	0.905672i	−0.995919	−	0.0902473i	$-0.971234\pi$
$283$	−256.305	+	256.305i	−0.905672	+	0.905672i	0.0902473	+	0.995919i	$0.471234\pi$
$284$			85.4131i			0.300750i
$285$	70.5664	−	70.1178i	0.247601	−	0.246027i
$286$	−228.244			−0.798057
$287$	4.80281	+	4.80281i	0.0167345	+	0.0167345i
$288$	−12.0000	+	12.0000i	−0.0416667	+	0.0416667i
$289$			449.702i			1.55606i
$290$	−50.3219	−	50.6438i	−0.173524	−	0.174634i
$291$	−87.5962			−0.301018
$292$	143.711	+	143.711i	0.492161	+	0.492161i
$293$	−3.95685	+	3.95685i	−0.0135046	+	0.0135046i	−0.713827	−	0.700322i	$-0.753040\pi$
$293$	−3.95685	+	3.95685i	−0.0135046	+	0.0135046i	0.700322	+	0.713827i	$0.253040\pi$
$294$			119.891i			0.407793i
$295$	−475.098	−	1.51485i	−1.61050	−	0.00513508i
$296$	137.213			0.463558
$297$	27.7165	+	27.7165i	0.0933217	+	0.0933217i
$298$	−245.171	+	245.171i	−0.822723	+	0.822723i
$299$			102.607i			0.343167i
$300$	60.8455	+	61.6265i	0.202818	+	0.205422i
$301$	13.0986			0.0435169
$302$	−266.303	−	266.303i	−0.881800	−	0.881800i
$303$	−130.390	+	130.390i	−0.430330	+	0.430330i
$304$			45.9475i			0.151143i
$305$	0.337425	−	105.826i	0.00110631	−	0.346970i
$306$	−115.311			−0.376833
$307$	265.253	+	265.253i	0.864015	+	0.864015i	0.991802	−	0.127786i	$-0.0407872\pi$
$307$	265.253	+	265.253i	0.864015	+	0.864015i	−0.127786	+	0.991802i	$0.540787\pi$
$308$	2.49406	−	2.49406i	0.00809759	−	0.00809759i
$309$			177.256i			0.573646i
$310$	−13.4054	+	13.3202i	−0.0432432	+	0.0429683i
$311$	81.5970			0.262370			0.131185	−	0.991358i	$-0.458122\pi$
$311$	81.5970			0.262370			0.131185	+	0.991358i	$0.458122\pi$
$312$	74.1146	+	74.1146i	0.237547	+	0.237547i
$313$	249.894	−	249.894i	0.798385	−	0.798385i	−0.184456	−	0.982841i	$-0.559052\pi$
$313$	249.894	−	249.894i	0.798385	−	0.798385i	0.982841	+	0.184456i	$0.0590523\pi$
$314$			156.878i			0.499612i
$315$	2.47176	+	2.48757i	0.00784686	+	0.00789706i
$316$	−273.354			−0.865045
$317$	−79.4073	−	79.4073i	−0.250496	−	0.250496i	0.570678	−	0.821174i	$-0.306681\pi$
$317$	−79.4073	−	79.4073i	−0.250496	−	0.250496i	−0.821174	+	0.570678i	$0.806681\pi$
$318$	−34.7343	+	34.7343i	−0.109227	+	0.109227i
$319$		−	76.1637i		−	0.238758i
$320$	−39.9998	−	0.127539i	−0.124999	−	0.000398560i
$321$	334.303			1.04144
$322$	−1.12120	−	1.12120i	−0.00348199	−	0.00348199i
$323$	−220.761	+	220.761i	−0.683469	+	0.683469i
$324$		−	18.0000i		−	0.0555556i
$325$	380.619	−	375.795i	1.17113	−	1.15629i
$326$	−353.655			−1.08483
$327$	134.181	+	134.181i	0.410340	+	0.410340i
$328$	58.1060	−	58.1060i	0.177152	−	0.177152i
$329$			6.01839i			0.0182930i
$330$	−0.294579	+	92.3880i	−0.000892663	+	0.279964i
$331$	374.515			1.13146			0.565732	−	0.824589i	$-0.308594\pi$
$331$	374.515			1.13146			0.565732	+	0.824589i	$0.308594\pi$
$332$	−15.5743	−	15.5743i	−0.0469107	−	0.0469107i
$333$	−102.910	+	102.910i	−0.309038	+	0.309038i
$334$		−	11.7849i		−	0.0352842i
$335$	−228.699	+	227.245i	−0.682684	+	0.678345i
$336$	−1.61972			−0.00482059
$337$	51.5352	+	51.5352i	0.152923	+	0.152923i	0.779422	−	0.626499i	$-0.215513\pi$
$337$	51.5352	+	51.5352i	0.152923	+	0.152923i	−0.626499	+	0.779422i	$0.715513\pi$
$338$	288.748	−	288.748i	0.854283	−	0.854283i
$339$		−	288.052i		−	0.849711i
$340$	−191.571	−	192.797i	−0.563445	−	0.567050i
$341$	−20.1605			−0.0591217
$342$	−34.4606	−	34.4606i	−0.100762	−	0.100762i
$343$	−16.1915	+	16.1915i	−0.0472056	+	0.0472056i
$344$		−	158.471i		−	0.460672i
$345$	41.5329	+	0.132428i	0.120385	+	0.000383848i
$346$	−305.158			−0.881959
$347$	442.200	+	442.200i	1.27435	+	1.27435i	0.943782	+	0.330569i	$0.107241\pi$
$347$	442.200	+	442.200i	1.27435	+	1.27435i	0.330569	+	0.943782i	$0.392759\pi$
$348$	−24.7316	+	24.7316i	−0.0710677	+	0.0710677i
$349$		−	448.442i		−	1.28493i	−0.766314	−	0.642467i	$-0.777911\pi$
$349$		−	448.442i		−	1.28493i	0.766314	−	0.642467i	$-0.222089\pi$
$350$	−0.0527091	+	8.26543i	−0.000150597	+	0.0236155i
$351$	−111.172			−0.316729
$352$	−30.1739	−	30.1739i	−0.0857214	−	0.0857214i
$353$	196.487	−	196.487i	0.556619	−	0.556619i	−0.371724	−	0.928343i	$-0.621233\pi$
$353$	196.487	−	196.487i	0.556619	−	0.556619i	0.928343	+	0.371724i	$0.121233\pi$
$354$			232.751i			0.657488i
$355$	0.680845	−	213.532i	0.00191787	−	0.601498i
$356$	−308.403			−0.866300
$357$	−7.78215	−	7.78215i	−0.0217987	−	0.0217987i
$358$	−166.077	+	166.077i	−0.463903	+	0.463903i
$359$		−	320.839i		−	0.893702i	−0.894608	−	0.446851i	$-0.852545\pi$
$359$		−	320.839i		−	0.893702i	0.894608	−	0.446851i	$-0.147455\pi$
$360$	30.0955	−	29.9042i	0.0835986	−	0.0830672i
$361$	229.052			0.634492
$362$	61.0419	+	61.0419i	0.168624	+	0.168624i
$363$	78.5010	−	78.5010i	0.216256	−	0.216256i
$364$			10.0037i			0.0274828i
$365$	−358.130	−	360.421i	−0.981178	−	0.987455i
$366$	−51.8441			−0.141650
$367$	−345.394	−	345.394i	−0.941128	−	0.941128i	0.0572330	−	0.998361i	$-0.481772\pi$
$367$	−345.394	−	345.394i	−0.941128	−	0.941128i	−0.998361	+	0.0572330i	$0.981772\pi$
$368$	−13.5647	+	13.5647i	−0.0368605	+	0.0368605i
$369$			87.1590i			0.236203i
$370$	−343.031	−	1.09375i	−0.927111	−	0.00295609i
$371$	−4.68832			−0.0126370
$372$	6.54644	+	6.54644i	0.0175980	+	0.0175980i
$373$	−472.984	+	472.984i	−1.26805	+	1.26805i	−0.320963	+	0.947092i	$0.604006\pi$
$373$	−472.984	+	472.984i	−1.26805	+	1.26805i	−0.947092	+	0.320963i	$0.895994\pi$
$374$		−	289.949i		−	0.775265i
$375$	−151.622	−	154.550i	−0.404325	−	0.412135i
$376$	72.8126			0.193650
$377$	152.748	+	152.748i	0.405166	+	0.405166i
$378$	1.21479	−	1.21479i	0.00321373	−	0.00321373i
$379$		−	160.661i		−	0.423908i	−0.977280	−	0.211954i	$-0.932017\pi$
$379$		−	160.661i		−	0.423908i	0.977280	−	0.211954i	$-0.0679827\pi$
$380$	0.366257	−	114.868i	0.000963834	−	0.302285i
$381$	174.619			0.458317
$382$	255.678	+	255.678i	0.669315	+	0.669315i
$383$	147.812	−	147.812i	0.385932	−	0.385932i	−0.487301	−	0.873234i	$-0.662019\pi$
$383$	147.812	−	147.812i	0.385932	−	0.385932i	0.873234	+	0.487301i	$0.162019\pi$
$384$			19.5959i			0.0510310i
$385$	−6.25499	+	6.21523i	−0.0162467	+	0.0161435i
$386$	−99.3192			−0.257304
$387$	118.853	+	118.853i	0.307115	+	0.307115i
$388$	−71.5220	+	71.5220i	−0.184335	+	0.184335i
$389$			496.097i			1.27531i	0.770320	+	0.637657i	$0.220096\pi$
$389$			496.097i			1.27531i	−0.770320	+	0.637657i	$0.779904\pi$
$390$	−184.695	−	185.876i	−0.473576	−	0.476606i
$391$	−130.346			−0.333366
$392$	97.8907	+	97.8907i	0.249721	+	0.249721i
$393$	85.2984	−	85.2984i	0.217044	−	0.217044i
$394$			75.8016i			0.192390i
$395$	683.382	+	2.17896i	1.73008	+	0.00551636i
$396$	45.2609			0.114295
$397$	−62.1832	−	62.1832i	−0.156633	−	0.156633i	0.624440	−	0.781073i	$-0.285327\pi$
$397$	−62.1832	−	62.1832i	−0.156633	−	0.156633i	−0.781073	+	0.624440i	$0.785327\pi$
$398$	194.128	−	194.128i	0.487760	−	0.487760i
$399$		−	4.65138i		−	0.0116576i
$400$	99.9980	+	0.637693i	0.249995	+	0.00159423i
$401$	498.128			1.24221			0.621107	−	0.783726i	$-0.286683\pi$
$401$	498.128			1.24221			0.621107	+	0.783726i	$0.286683\pi$
$402$	111.684	+	111.684i	0.277820	+	0.277820i
$403$	40.4322	−	40.4322i	0.100328	−	0.100328i
$404$			212.926i			0.527044i
$405$	−0.143482	+	44.9998i	−0.000354276	+	0.111111i
$406$	−3.33818			−0.00822213
$407$	−258.766	−	258.766i	−0.635789	−	0.635789i
$408$	−94.1511	+	94.1511i	−0.230762	+	0.230762i
$409$		−	603.860i		−	1.47643i	−0.674565	−	0.738215i	$-0.735669\pi$
$409$		−	603.860i		−	1.47643i	0.674565	−	0.738215i	$-0.264331\pi$
$410$	−145.727	+	144.801i	−0.355433	+	0.353173i
$411$	−312.940			−0.761410
$412$	144.729	+	144.729i	0.351285	+	0.351285i
$413$	−15.7080	+	15.7080i	−0.0380338	+	0.0380338i
$414$		−	20.3470i		−	0.0491473i
$415$	38.8115	+	39.0598i	0.0935217	+	0.0941200i
$416$	121.029			0.290934
$417$	98.3375	+	98.3375i	0.235821	+	0.235821i
$418$	86.6511	−	86.6511i	0.207299	−	0.207299i
$419$			384.147i			0.916819i	0.888741	+	0.458409i	$0.151581\pi$
$419$			384.147i			0.916819i	−0.888741	+	0.458409i	$0.848419\pi$
$420$	4.04928	+	0.0129111i	0.00964114	+	3.07407e-5i
$421$	−495.820			−1.17772			−0.588860	−	0.808235i	$-0.700423\pi$
$421$	−495.820			−1.17772			−0.588860	+	0.808235i	$0.700423\pi$
$422$	14.4359	+	14.4359i	0.0342083	+	0.0342083i
$423$	−54.6094	+	54.6094i	−0.129100	+	0.129100i
$424$			56.7209i			0.133776i
$425$	477.389	+	483.517i	1.12327	+	1.13769i
$426$	−104.609			−0.245562
$427$	−3.49887	−	3.49887i	−0.00819407	−	0.00819407i
$428$	272.957	−	272.957i	0.637750	−	0.637750i
$429$		−	279.541i		−	0.651611i
$430$	−1.26321	+	396.176i	−0.00293769	+	0.921339i
$431$	−226.640			−0.525846			−0.262923	−	0.964817i	$-0.584686\pi$
$431$	−226.640			−0.525846			−0.262923	+	0.964817i	$0.584686\pi$
$432$	−14.6969	−	14.6969i	−0.0340207	−	0.0340207i
$433$	253.188	−	253.188i	0.584730	−	0.584730i	−0.351470	−	0.936199i	$-0.614318\pi$
$433$	253.188	−	253.188i	0.584730	−	0.584730i	0.936199	+	0.351470i	$0.114318\pi$
$434$			0.883616i			0.00203598i
$435$	62.0258	−	61.6315i	0.142588	−	0.141682i
$436$	219.117			0.502562
$437$	−38.9539	−	38.9539i	−0.0891394	−	0.0891394i
$438$	−176.009	+	176.009i	−0.401847	+	0.401847i
$439$		−	687.562i		−	1.56620i	−0.621896	−	0.783100i	$-0.713637\pi$
$439$		−	687.562i		−	1.56620i	0.621896	−	0.783100i	$-0.286363\pi$
$440$	75.1940	+	75.6750i	0.170895	+	0.171989i
$441$	−146.836			−0.332962
$442$	581.497	+	581.497i	1.31560	+	1.31560i
$443$	−204.555	+	204.555i	−0.461750	+	0.461750i	−0.899229	−	0.437479i	$-0.855872\pi$
$443$	−204.555	+	204.555i	−0.461750	+	0.461750i	0.437479	+	0.899229i	$0.355872\pi$
$444$			168.051i			0.378493i
$445$	771.003	+	2.45834i	1.73259	+	0.00552436i
$446$	301.251			0.675452
$447$	−300.272	−	300.272i	−0.671750	−	0.671750i
$448$	−1.32250	+	1.32250i	−0.00295200	+	0.00295200i
$449$			356.376i			0.793711i	0.917881	+	0.396855i	$0.129899\pi$
$449$			356.376i			0.793711i	−0.917881	+	0.396855i	$0.870101\pi$
$450$	−75.4767	+	74.5202i	−0.167726	+	0.165600i
$451$	−219.161			−0.485944
$452$	−235.194	−	235.194i	−0.520340	−	0.520340i
$453$	326.154	−	326.154i	0.719986	−	0.719986i
$454$		−	22.5547i		−	0.0496799i
$455$	0.0797418	−	25.0092i	0.000175257	−	0.0549653i
$456$	−56.2740			−0.123408
$457$	−48.4473	−	48.4473i	−0.106012	−	0.106012i	0.652112	−	0.758123i	$-0.273883\pi$
$457$	−48.4473	−	48.4473i	−0.106012	−	0.106012i	−0.758123	+	0.652112i	$0.773883\pi$
$458$	−55.3008	+	55.3008i	−0.120744	+	0.120744i
$459$		−	141.227i		−	0.307683i
$460$	34.0196	−	33.8034i	0.0739557	−	0.0734855i
$461$	218.854			0.474737			0.237369	−	0.971420i	$-0.423715\pi$
$461$	218.854			0.474737			0.237369	+	0.971420i	$0.423715\pi$
$462$	3.05458	+	3.05458i	0.00661165	+	0.00661165i
$463$	−24.5288	+	24.5288i	−0.0529779	+	0.0529779i	−0.733099	−	0.680121i	$-0.761927\pi$
$463$	−24.5288	+	24.5288i	−0.0529779	+	0.0529779i	0.680121	+	0.733099i	$0.261927\pi$
$464$			40.3865i			0.0870399i
$465$	−16.3138	−	16.4182i	−0.0350835	−	0.0353079i
$466$	−90.4148			−0.194023
$467$	−127.774	−	127.774i	−0.273606	−	0.273606i	0.556944	−	0.830550i	$-0.311974\pi$
$467$	−127.774	−	127.774i	−0.273606	−	0.273606i	−0.830550	+	0.556944i	$0.811974\pi$
$468$	−90.7715	+	90.7715i	−0.193956	+	0.193956i
$469$			15.0747i			0.0321422i
$470$	−182.031	−	0.580404i	−0.387299	−	0.00123490i
$471$	−192.136			−0.407932
$472$	190.040	+	190.040i	0.402628	+	0.402628i
$473$	−298.856	+	298.856i	−0.631831	+	0.631831i
$474$		−	334.789i		−	0.706306i
$475$	−1.83127	+	287.166i	−0.00385531	+	0.604560i
$476$	−12.7082			−0.0266979
$477$	−42.5407	−	42.5407i	−0.0891838	−	0.0891838i
$478$	287.302	−	287.302i	0.601050	−	0.601050i
$479$		−	425.945i		−	0.889239i	−0.895720	−	0.444619i	$-0.853339\pi$
$479$		−	425.945i		−	0.889239i	0.895720	−	0.444619i	$-0.146661\pi$
$480$	0.156203	−	48.9895i	0.000325423	−	0.102062i
$481$	1037.92			2.15784
$482$	−298.409	−	298.409i	−0.619106	−	0.619106i
$483$	1.37318	−	1.37318i	0.00284303	−	0.00284303i
$484$		−	128.192i		−	0.264859i
$485$	179.374	−	178.234i	0.369844	−	0.367493i
$486$	22.0454			0.0453609
$487$	−433.520	−	433.520i	−0.890185	−	0.890185i	0.104355	−	0.994540i	$-0.466722\pi$
$487$	−433.520	−	433.520i	−0.890185	−	0.890185i	−0.994540	+	0.104355i	$0.966722\pi$
$488$	−42.3305	+	42.3305i	−0.0867428	+	0.0867428i
$489$		−	433.137i		−	0.885760i
$490$	−243.945	−	245.506i	−0.497847	−	0.501032i
$491$	−126.759			−0.258164			−0.129082	−	0.991634i	$-0.541203\pi$
$491$	−126.759			−0.258164			−0.129082	+	0.991634i	$0.541203\pi$
$492$	71.1650	+	71.1650i	0.144644	+	0.144644i
$493$	−194.042	+	194.042i	−0.393594	+	0.393594i
$494$			347.560i			0.703563i
$495$	−113.152	−	0.360784i	−0.228589	−	0.000728856i
$496$	10.6903			0.0215530
$497$	−7.05990	−	7.05990i	−0.0142050	−	0.0142050i
$498$	19.0746	−	19.0746i	0.0383024	−	0.0383024i
$499$			40.4801i			0.0811225i	0.999177	+	0.0405612i	$0.0129146\pi$
$499$			40.4801i			0.0811225i	−0.999177	+	0.0405612i	$0.987085\pi$
$500$	−249.989	−	2.39133i	−0.499977	−	0.00478266i
$501$	14.4335			0.0288094
$502$	262.970	+	262.970i	0.523844	+	0.523844i
$503$	221.151	−	221.151i	0.439664	−	0.439664i	−0.452235	−	0.891899i	$-0.649373\pi$
$503$	221.151	−	221.151i	0.439664	−	0.439664i	0.891899	+	0.452235i	$0.149373\pi$
$504$		−	1.98374i		−	0.00393600i
$505$	1.69728	−	532.312i	0.00336094	−	1.05408i
$506$	51.1624			0.101111
$507$	353.642	+	353.642i	0.697519	+	0.697519i
$508$	142.576	−	142.576i	0.280661	−	0.280661i
$509$		−	628.639i		−	1.23505i	−0.786552	−	0.617524i	$-0.788136\pi$
$509$		−	628.639i		−	1.23505i	0.786552	−	0.617524i	$-0.211864\pi$
$510$	236.127	−	234.626i	0.462994	−	0.460051i
$511$	−23.7571			−0.0464914
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	42.2055	−	42.2055i	0.0822719	−	0.0822719i
$514$			142.729i			0.277684i
$515$	−360.668	−	362.975i	−0.700326	−	0.704806i
$516$	194.087			0.376137
$517$	−137.315	−	137.315i	−0.265600	−	0.265600i
$518$	−11.3415	+	11.3415i	−0.0218947	+	0.0218947i
$519$		−	373.741i		−	0.720117i
$520$	−302.570	−	0.964743i	−0.581865	−	0.00185528i
$521$	−845.308			−1.62247			−0.811236	−	0.584719i	$-0.801205\pi$
$521$	−845.308			−1.62247			−0.811236	+	0.584719i	$0.801205\pi$
$522$	−30.2899	−	30.2899i	−0.0580266	−	0.0580266i
$523$	53.3810	−	53.3810i	0.102067	−	0.102067i	−0.654229	−	0.756296i	$-0.727007\pi$
$523$	53.3810	−	53.3810i	0.102067	−	0.102067i	0.756296	+	0.654229i	$0.227007\pi$
$524$		−	139.292i		−	0.265824i
$525$	−10.1230	−	0.0645552i	−0.0192820	−	0.000122962i
$526$	50.8090			0.0965951
$527$	51.3628	+	51.3628i	0.0974627	+	0.0974627i
$528$	36.9554	−	36.9554i	0.0699913	−	0.0699913i
$529$		−	23.0000i		−	0.0434783i
$530$	0.452133	−	141.801i	0.000853082	−	0.267550i
$531$	−285.060			−0.536837
$532$	−3.79784	−	3.79784i	−0.00713879	−	0.00713879i
$533$	439.530	−	439.530i	0.824635	−	0.824635i
$534$		−	377.715i		−	0.707331i
$535$	−684.565	+	680.213i	−1.27956	+	1.27143i
$536$	182.379			0.340259
$537$	−203.402	−	203.402i	−0.378775	−	0.378775i
$538$	443.315	−	443.315i	0.824005	−	0.824005i
$539$		−	369.219i		−	0.685007i
$540$	36.6250	+	36.8593i	0.0678241	+	0.0682580i
$541$	−517.570			−0.956691			−0.478345	−	0.878172i	$-0.658763\pi$
$541$	−517.570			−0.956691			−0.478345	+	0.878172i	$0.658763\pi$
$542$	−30.4665	−	30.4665i	−0.0562112	−	0.0562112i
$543$	−74.7607	+	74.7607i	−0.137681	+	0.137681i
$544$			153.748i			0.282625i
$545$	−547.789	−	1.74662i	−1.00512	−	0.00320482i
$546$	−12.2520			−0.0224396
$547$	129.766	+	129.766i	0.237233	+	0.237233i	0.815703	−	0.578470i	$-0.196350\pi$
$547$	129.766	+	129.766i	0.237233	+	0.237233i	−0.578470	+	0.815703i	$0.696350\pi$
$548$	−255.514	+	255.514i	−0.466267	+	0.466267i
$549$		−	63.4958i		−	0.115657i
$550$	−187.381	−	189.786i	−0.340692	−	0.345065i
$551$	−115.979			−0.210488
$552$	−16.6132	−	16.6132i	−0.0300965	−	0.0300965i
$553$	22.5944	−	22.5944i	0.0408578	−	0.0408578i
$554$			188.054i			0.339447i
$555$	1.33957	−	420.125i	0.00241364	−	0.756983i
$556$	160.585			0.288821
$557$	−235.383	−	235.383i	−0.422591	−	0.422591i	0.463504	−	0.886095i	$-0.346592\pi$
$557$	−235.383	−	235.383i	−0.422591	−	0.422591i	−0.886095	+	0.463504i	$0.846592\pi$
$558$	−8.01772	+	8.01772i	−0.0143687	+	0.0143687i
$559$		−	1198.72i		−	2.14440i
$560$	3.31676	−	3.29568i	0.00592279	−	0.00588514i
$561$	355.114			0.633001
$562$	448.058	+	448.058i	0.797256	+	0.797256i
$563$	65.1797	−	65.1797i	0.115772	−	0.115772i	−0.646847	−	0.762620i	$-0.723913\pi$
$563$	65.1797	−	65.1797i	0.115772	−	0.115772i	0.762620	+	0.646847i	$0.223913\pi$
$564$			89.1768i			0.158115i
$565$	586.106	+	589.856i	1.03736	+	1.04399i
$566$	−512.610			−0.905672
$567$	1.48781	+	1.48781i	0.00262400	+	0.00262400i
$568$	−85.4131	+	85.4131i	−0.150375	+	0.150375i
$569$		−	418.274i		−	0.735104i	−0.930003	−	0.367552i	$-0.880196\pi$
$569$		−	418.274i		−	0.735104i	0.930003	−	0.367552i	$-0.119804\pi$
$570$	140.684	+	0.448571i	0.246814	+	0.000786967i
$571$	906.028			1.58674			0.793369	−	0.608741i	$-0.208325\pi$
$571$	906.028			1.58674			0.793369	+	0.608741i	$0.208325\pi$
$572$	−228.244	−	228.244i	−0.399029	−	0.399029i
$573$	−313.141	+	313.141i	−0.546493	+	0.546493i
$574$			9.60561i			0.0167345i
$575$	−85.3180	+	84.2368i	−0.148379	+	0.146499i
$576$	−24.0000			−0.0416667
$577$	288.328	+	288.328i	0.499703	+	0.499703i	0.911345	−	0.411643i	$-0.135045\pi$
$577$	288.328	+	288.328i	0.499703	+	0.499703i	−0.411643	+	0.911345i	$0.635045\pi$
$578$	−449.702	+	449.702i	−0.778031	+	0.778031i
$579$		−	121.641i		−	0.210087i
$580$	0.321929	−	100.966i	0.000555050	−	0.174079i
$581$	2.57463			0.00443137
$582$	−87.5962	−	87.5962i	−0.150509	−	0.150509i
$583$	106.968	−	106.968i	0.183479	−	0.183479i
$584$			287.422i			0.492161i
$585$	227.651	−	226.204i	0.389147	−	0.386673i
$586$	−7.91371			−0.0135046
$587$	−563.086	−	563.086i	−0.959261	−	0.959261i	0.0399411	−	0.999202i	$-0.487283\pi$
$587$	−563.086	−	563.086i	−0.959261	−	0.959261i	−0.999202	+	0.0399411i	$0.987283\pi$
$588$	−119.891	+	119.891i	−0.203896	+	0.203896i
$589$			30.6995i			0.0521214i
$590$	−473.583	−	476.613i	−0.802683	−	0.807819i
$591$	−92.8376			−0.157086
$592$	137.213	+	137.213i	0.231779	+	0.231779i
$593$	−357.448	+	357.448i	−0.602780	+	0.602780i	−0.941049	−	0.338270i	$-0.890158\pi$
$593$	−357.448	+	357.448i	−0.602780	+	0.602780i	0.338270	+	0.941049i	$0.390158\pi$
$594$			55.4331i			0.0933217i
$595$	31.7703	+	0.101300i	0.0533955	+	0.000170251i
$596$	−490.343			−0.822723
$597$	237.758	+	237.758i	0.398254	+	0.398254i
$598$	−102.607	+	102.607i	−0.171584	+	0.171584i
$599$		−	717.906i		−	1.19851i	−0.800559	−	0.599254i	$-0.795464\pi$
$599$		−	717.906i		−	1.19851i	0.800559	−	0.599254i	$-0.204536\pi$
$600$	−0.781011	+	122.472i	−0.00130168	+	0.204120i
$601$	−634.818			−1.05627			−0.528135	−	0.849160i	$-0.677108\pi$
$601$	−634.818			−1.05627			−0.528135	+	0.849160i	$0.677108\pi$
$602$	13.0986	+	13.0986i	0.0217585	+	0.0217585i
$603$	−136.784	+	136.784i	−0.226839	+	0.226839i
$604$		−	532.607i		−	0.881800i
$605$	−1.02184	+	320.477i	−0.00168899	+	0.529715i
$606$	−260.780			−0.430330
$607$	297.320	+	297.320i	0.489818	+	0.489818i	0.908249	−	0.418430i	$-0.137420\pi$
$607$	297.320	+	297.320i	0.489818	+	0.489818i	−0.418430	+	0.908249i	$0.637420\pi$
$608$	−45.9475	+	45.9475i	−0.0755716	+	0.0755716i
$609$		−	4.08842i		−	0.00671334i
$610$	106.163	−	105.488i	0.174038	−	0.172932i
$611$	550.775			0.901433
$612$	−115.311	−	115.311i	−0.188417	−	0.188417i
$613$	−505.783	+	505.783i	−0.825095	+	0.825095i	−0.986834	−	0.161739i	$-0.948290\pi$
$613$	−505.783	+	505.783i	−0.825095	+	0.825095i	0.161739	+	0.986834i	$0.448290\pi$
$614$			530.505i			0.864015i
$615$	−177.344	−	178.479i	−0.288365	−	0.290210i
$616$	4.98811			0.00809759
$617$	367.182	+	367.182i	0.595109	+	0.595109i	0.939007	−	0.343898i	$-0.111747\pi$
$617$	367.182	+	367.182i	0.595109	+	0.595109i	−0.343898	+	0.939007i	$0.611747\pi$
$618$	−177.256	+	177.256i	−0.286823	+	0.286823i
$619$			475.667i			0.768444i	0.923241	+	0.384222i	$0.125530\pi$
$619$			475.667i			0.768444i	−0.923241	+	0.384222i	$0.874470\pi$
$620$	−26.7256	−	0.0852144i	−0.0431058	−	0.000137443i
$621$	24.9199			0.0401286
$622$	81.5970	+	81.5970i	0.131185	+	0.131185i
$623$	25.4913	−	25.4913i	0.0409170	−	0.0409170i
$624$			148.229i			0.237547i
$625$	624.949	+	7.97100i	0.999919	+	0.0127536i
$626$	499.789			0.798385
$627$	106.125	+	106.125i	0.169259	+	0.169259i
$628$	−156.878	+	156.878i	−0.249806	+	0.249806i
$629$			1318.52i			2.09621i
$630$	−0.0158128	+	4.95933i	−2.50997e−5	+	0.00787196i
$631$	−182.454			−0.289150			−0.144575	−	0.989494i	$-0.546182\pi$
$631$	−182.454			−0.289150			−0.144575	+	0.989494i	$0.546182\pi$
$632$	−273.354	−	273.354i	−0.432523	−	0.432523i
$633$	−17.6803	+	17.6803i	−0.0279309	+	0.0279309i
$634$		−	158.815i		−	0.250496i
$635$	−357.574	+	355.301i	−0.563109	+	0.559529i
$636$	−69.4686			−0.109227
$637$	740.473	+	740.473i	1.16244	+	1.16244i
$638$	76.1637	−	76.1637i	0.119379	−	0.119379i
$639$		−	128.120i		−	0.200500i
$640$	−39.8723	−	40.1273i	−0.0623004	−	0.0626990i
$641$	−834.607			−1.30204			−0.651020	−	0.759061i	$-0.725658\pi$
$641$	−834.607			−1.30204			−0.651020	+	0.759061i	$0.725658\pi$
$642$	334.303	+	334.303i	0.520721	+	0.520721i
$643$	458.258	−	458.258i	0.712687	−	0.712687i	−0.254409	−	0.967097i	$-0.581881\pi$
$643$	458.258	−	458.258i	0.712687	−	0.712687i	0.967097	+	0.254409i	$0.0818811\pi$
$644$		−	2.24240i		−	0.00348199i
$645$	−485.214	−	1.54710i	−0.752270	−	0.00239861i
$646$	−441.521			−0.683469
$647$	−488.148	−	488.148i	−0.754479	−	0.754479i	0.220832	−	0.975312i	$-0.429123\pi$
$647$	−488.148	−	488.148i	−0.754479	−	0.754479i	−0.975312	+	0.220832i	$0.929123\pi$
$648$	18.0000	−	18.0000i	0.0277778	−	0.0277778i
$649$		−	716.783i		−	1.10444i
$650$	756.414	+	4.82369i	1.16371	+	0.00742106i
$651$	−1.08220			−0.00166237
$652$	−353.655	−	353.655i	−0.542415	−	0.542415i
$653$	219.549	−	219.549i	0.336217	−	0.336217i	−0.518725	−	0.854941i	$-0.673593\pi$
$653$	219.549	−	219.549i	0.336217	−	0.336217i	0.854941	+	0.518725i	$0.173593\pi$
$654$			268.362i			0.410340i
$655$	−1.11032	+	348.227i	−0.00169515	+	0.531645i
$656$	116.212			0.177152
$657$	−215.566	−	215.566i	−0.328107	−	0.328107i
$658$	−6.01839	+	6.01839i	−0.00914650	+	0.00914650i
$659$		−	177.268i		−	0.268995i	−0.990914	−	0.134498i	$-0.957058\pi$
$659$		−	177.268i		−	0.268995i	0.990914	−	0.134498i	$-0.0429420\pi$
$660$	−92.6826	+	92.0934i	−0.140428	+	0.139535i
$661$	−670.999			−1.01513			−0.507564	−	0.861614i	$-0.669454\pi$
$661$	−670.999			−1.01513			−0.507564	+	0.861614i	$0.669454\pi$
$662$	374.515	+	374.515i	0.565732	+	0.565732i
$663$	−712.186	+	712.186i	−1.07419	+	1.07419i
$664$		−	31.1487i		−	0.0469107i
$665$	9.46427	+	9.52481i	0.0142320	+	0.0143230i
$666$	−205.820			−0.309038
$667$	−34.2393	−	34.2393i	−0.0513333	−	0.0513333i
$668$	11.7849	−	11.7849i	0.0176421	−	0.0176421i
$669$			368.956i			0.551504i
$670$	−455.945	−	1.45378i	−0.680514	−	0.00216982i
$671$	159.660			0.237943
$672$	−1.61972	−	1.61972i	−0.00241030	−	0.00241030i
$673$	831.221	−	831.221i	1.23510	−	1.23510i	0.273117	−	0.961981i	$-0.411945\pi$
$673$	831.221	−	831.221i	1.23510	−	1.23510i	0.961981	−	0.273117i	$-0.0880547\pi$
$674$			103.070i			0.152923i
$675$	−91.2682	−	92.4398i	−0.135212	−	0.136948i
$676$	577.496			0.854283
$677$	−655.663	−	655.663i	−0.968483	−	0.968483i	0.0310357	−	0.999518i	$-0.490119\pi$
$677$	−655.663	−	655.663i	−0.968483	−	0.968483i	−0.999518	+	0.0310357i	$0.990119\pi$
$678$	288.052	−	288.052i	0.424856	−	0.424856i
$679$		−	11.8234i		−	0.0174130i
$680$	1.22556	−	384.368i	0.00180229	−	0.565247i
$681$	27.6237			0.0405634
$682$	−20.1605	−	20.1605i	−0.0295609	−	0.0295609i
$683$	−35.5313	+	35.5313i	−0.0520224	+	0.0520224i	−0.732639	−	0.680617i	$-0.761712\pi$
$683$	−35.5313	+	35.5313i	−0.0520224	+	0.0520224i	0.680617	+	0.732639i	$0.261712\pi$
$684$		−	68.9213i		−	0.100762i
$685$	640.819	−	636.745i	0.935502	−	0.929555i
$686$	−32.3831			−0.0472056
$687$	−67.7293	−	67.7293i	−0.0985871	−	0.0985871i
$688$	158.471	−	158.471i	0.230336	−	0.230336i
$689$			429.053i			0.622718i
$690$	41.4005	+	41.6653i	0.0600007	+	0.0603845i
$691$	−884.743			−1.28038			−0.640191	−	0.768216i	$-0.721145\pi$
$691$	−884.743			−1.28038			−0.640191	+	0.768216i	$0.721145\pi$
$692$	−305.158	−	305.158i	−0.440980	−	0.440980i
$693$	−3.74108	+	3.74108i	−0.00539839	+	0.00539839i
$694$			884.400i			1.27435i
$695$	−401.459	−	1.28005i	−0.577639	−	0.00184180i
$696$	−49.4631			−0.0710677
$697$	558.355	+	558.355i	0.801083	+	0.801083i
$698$	448.442	−	448.442i	0.642467	−	0.642467i
$699$		−	110.735i		−	0.158419i
$700$	−8.31814	+	8.21272i	−0.0118831	+	0.0117325i
$701$	52.6049			0.0750427			0.0375214	−	0.999296i	$-0.488054\pi$
$701$	52.6049			0.0750427			0.0375214	+	0.999296i	$0.488054\pi$
$702$	−111.172	−	111.172i	−0.158365	−	0.158365i
$703$	−394.037	+	394.037i	−0.560508	+	0.560508i
$704$		−	60.3479i		−	0.0857214i
$705$	0.710846	−	222.941i	0.00100829	−	0.316228i
$706$	392.973			0.556619
$707$	−17.5996	−	17.5996i	−0.0248934	−	0.0248934i
$708$	−232.751	+	232.751i	−0.328744	+	0.328744i
$709$		−	835.312i		−	1.17816i	−0.808076	−	0.589078i	$-0.799491\pi$
$709$		−	835.312i		−	1.17816i	0.808076	−	0.589078i	$-0.200509\pi$
$710$	214.213	−	212.851i	0.301708	−	0.299790i
$711$	410.031			0.576697
$712$	−308.403	−	308.403i	−0.433150	−	0.433150i
$713$	−9.06313	+	9.06313i	−0.0127113	+	0.0127113i
$714$		−	15.5643i		−	0.0217987i
$715$	568.789	+	572.428i	0.795509	+	0.800598i
$716$	−332.155			−0.463903
$717$	351.872	+	351.872i	0.490755	+	0.490755i
$718$	320.839	−	320.839i	0.446851	−	0.446851i
$719$		−	189.592i		−	0.263689i	−0.991270	−	0.131845i	$-0.957910\pi$
$719$		−	189.592i		−	0.263689i	0.991270	−	0.131845i	$-0.0420900\pi$
$720$	59.9997	+	0.191309i	0.0833329	+	0.000265707i
$721$	−23.9255			−0.0331837
$722$	229.052	+	229.052i	0.317246	+	0.317246i
$723$	365.475	−	365.475i	0.505498	−	0.505498i
$724$			122.084i			0.168624i
$725$	−1.60964	+	252.410i	−0.00222019	+	0.348152i
$726$	157.002			0.216256
$727$	728.215	+	728.215i	1.00167	+	1.00167i	0.999999	+	0.00167235i	$0.000532324\pi$
$727$	728.215	+	728.215i	1.00167	+	1.00167i	0.00167235	+	0.999999i	$0.499468\pi$
$728$	−10.0037	+	10.0037i	−0.0137414	+	0.0137414i
$729$			27.0000i			0.0370370i
$730$	2.29110	−	718.551i	0.00313849	−	0.984316i
$731$	1522.79			2.08316
$732$	−51.8441	−	51.8441i	−0.0708252	−	0.0708252i
$733$	−717.338	+	717.338i	−0.978633	+	0.978633i	−0.999776	−	0.0211431i	$-0.993269\pi$
$733$	−717.338	+	717.338i	−0.978633	+	0.978633i	0.0211431	+	0.999776i	$0.493269\pi$
$734$		−	690.788i		−	0.941128i
$735$	300.682	−	298.771i	0.409091	−	0.406491i
$736$	−27.1293			−0.0368605
$737$	−343.943	−	343.943i	−0.466680	−	0.466680i
$738$	−87.1590	+	87.1590i	−0.118102	+	0.118102i
$739$			782.343i			1.05865i	0.848419	+	0.529325i	$0.177555\pi$
$739$			782.343i			1.05865i	−0.848419	+	0.529325i	$0.822445\pi$
$740$	−341.937	−	344.125i	−0.462077	−	0.465033i
$741$	−425.673			−0.574457
$742$	−4.68832	−	4.68832i	−0.00631849	−	0.00631849i
$743$	−614.013	+	614.013i	−0.826398	+	0.826398i	−0.987017	−	0.160619i	$-0.948651\pi$
$743$	−614.013	+	614.013i	−0.826398	+	0.826398i	0.160619	+	0.987017i	$0.448651\pi$
$744$			13.0929i			0.0175980i
$745$	1225.85	+	3.90862i	1.64544	+	0.00524647i
$746$	−945.969			−1.26805
$747$	23.3615	+	23.3615i	0.0312738	+	0.0312738i
$748$	289.949	−	289.949i	0.387632	−	0.387632i
$749$			45.1230i			0.0602444i
$750$	2.92877	−	306.172i	0.00390502	−	0.408230i
$751$	−961.079			−1.27973			−0.639866	−	0.768486i	$-0.721010\pi$
$751$	−961.079			−1.27973			−0.639866	+	0.768486i	$0.721010\pi$
$752$	72.8126	+	72.8126i	0.0968252	+	0.0968252i
$753$	−322.071	+	322.071i	−0.427717	+	0.427717i
$754$			305.495i			0.405166i
$755$	−4.24552	+	1331.51i	−0.00562320	+	1.76359i
$756$	2.42958			0.00321373
$757$	550.633	+	550.633i	0.727388	+	0.727388i	0.970099	−	0.242710i	$-0.0780365\pi$
$757$	550.633	+	550.633i	0.727388	+	0.727388i	−0.242710	+	0.970099i	$0.578036\pi$
$758$	160.661	−	160.661i	0.211954	−	0.211954i
$759$			62.6609i			0.0825572i
$760$	115.234	−	114.502i	0.151624	−	0.150660i
$761$	−503.536			−0.661677			−0.330838	−	0.943687i	$-0.607332\pi$
$761$	−503.536			−0.661677			−0.330838	+	0.943687i	$0.607332\pi$
$762$	174.619	+	174.619i	0.229159	+	0.229159i
$763$	−18.1113	+	18.1113i	−0.0237370	+	0.0237370i
$764$			511.357i			0.669315i
$765$	287.357	+	289.195i	0.375630	+	0.378033i
$766$	295.624			0.385932
$767$	1437.52	+	1437.52i	1.87421	+	1.87421i
$768$	−19.5959	+	19.5959i	−0.0255155	+	0.0255155i
$769$			1471.34i			1.91331i	0.291221	+	0.956656i	$0.405939\pi$
$769$			1471.34i			1.91331i	−0.291221	+	0.956656i	$0.594061\pi$
$770$	−12.4702	−	0.0397612i	−0.0161951	−	5.16380e-5i
$771$	−174.807			−0.226728
$772$	−99.3192	−	99.3192i	−0.128652	−	0.128652i
$773$	3.51558	−	3.51558i	0.00454797	−	0.00454797i	−0.704829	−	0.709377i	$-0.748976\pi$
$773$	3.51558	−	3.51558i	0.00454797	−	0.00454797i	0.709377	+	0.704829i	$0.248976\pi$
$774$			237.707i			0.307115i
$775$	66.8129	+	0.426070i	0.0862103	+	0.000549768i
$776$	−143.044			−0.184335
$777$	−13.8904	−	13.8904i	−0.0178770	−	0.0178770i
$778$	−496.097	+	496.097i	−0.637657	+	0.637657i
$779$			333.728i			0.428406i
$780$	1.18156	−	370.571i	0.00151483	−	0.475091i
$781$	322.156			0.412492
$782$	−130.346	−	130.346i	−0.166683	−	0.166683i
$783$	37.0974	−	37.0974i	0.0473785	−	0.0473785i
$784$			195.781i			0.249721i
$785$	393.444	−	390.943i	0.501203	−	0.498017i
$786$	170.597			0.217044
$787$	−753.124	−	753.124i	−0.956956	−	0.956956i	0.0421551	−	0.999111i	$-0.486578\pi$
$787$	−753.124	−	753.124i	−0.956956	−	0.956956i	−0.999111	+	0.0421551i	$0.986578\pi$
$788$	−75.8016	+	75.8016i	−0.0961949	+	0.0961949i
$789$			62.2281i			0.0788696i
$790$	681.203	+	685.561i	0.862283	+	0.867799i
$791$	38.8803			0.0491533
$792$	45.2609	+	45.2609i	0.0571476	+	0.0571476i
$793$	−320.200	+	320.200i	−0.403783	+	0.403783i
$794$		−	124.366i		−	0.156633i
$795$	173.671	+	0.553748i	0.218454	+	0.000696538i
$796$	388.257			0.487760
$797$	−205.508	−	205.508i	−0.257852	−	0.257852i	0.566328	−	0.824180i	$-0.308364\pi$
$797$	−205.508	−	205.508i	−0.257852	−	0.257852i	−0.824180	+	0.566328i	$0.808364\pi$
$798$	4.65138	−	4.65138i	0.00582880	−	0.00582880i
$799$			699.675i			0.875688i
$800$	99.3603	+	100.636i	0.124200	+	0.125795i
$801$	462.604			0.577533
$802$	498.128	+	498.128i	0.621107	+	0.621107i
$803$	542.041	−	542.041i	0.675019	−	0.675019i
$804$			223.368i			0.277820i
$805$	−0.0178746	+	5.60597i	−2.22045e−5	+	0.00696394i
$806$	80.8644			0.100328
$807$	542.947	+	542.947i	0.672797	+	0.672797i
$808$	−212.926	+	212.926i	−0.263522	+	0.263522i
$809$			598.802i			0.740176i	0.928997	+	0.370088i	$0.120672\pi$
$809$			598.802i			0.740176i	−0.928997	+	0.370088i	$0.879328\pi$
$810$	−45.1433	+	44.8563i	−0.0557324	+	0.0553781i
$811$	−44.4770			−0.0548421			−0.0274211	−	0.999624i	$-0.508729\pi$
$811$	−44.4770			−0.0548421			−0.0274211	+	0.999624i	$0.508729\pi$
$812$	−3.33818	−	3.33818i	−0.00411106	−	0.00411106i
$813$	37.3136	−	37.3136i	0.0458962	−	0.0458962i
$814$		−	517.532i		−	0.635789i
$815$	881.313	+	886.951i	1.08137	+	1.08828i
$816$	−188.302			−0.230762
$817$	455.085	+	455.085i	0.557019	+	0.557019i
$818$	603.860	−	603.860i	0.738215	−	0.738215i
$819$		−	15.0056i		−	0.0183219i
$820$	−290.528	−	0.926349i	−0.354303	−	0.00112969i
$821$	1533.57			1.86793			0.933964	−	0.357366i	$-0.116325\pi$
$821$	1533.57			1.86793			0.933964	+	0.357366i	$0.116325\pi$
$822$	−312.940	−	312.940i	−0.380705	−	0.380705i
$823$	887.431	−	887.431i	1.07829	−	1.07829i	0.0816250	−	0.996663i	$-0.473989\pi$
$823$	887.431	−	887.431i	1.07829	−	1.07829i	0.996663	−	0.0816250i	$-0.0260110\pi$
$824$			289.459i			0.351285i
$825$	232.439	−	229.494i	0.281745	−	0.278174i
$826$	−31.4159			−0.0380338
$827$	−996.788	−	996.788i	−1.20531	−	1.20531i	−0.972531	−	0.232775i	$-0.925219\pi$
$827$	−996.788	−	996.788i	−1.20531	−	1.20531i	−0.232775	−	0.972531i	$-0.574781\pi$
$828$	20.3470	−	20.3470i	0.0245737	−	0.0245737i
$829$		−	1064.14i		−	1.28364i	−0.766856	−	0.641819i	$-0.778180\pi$
$829$		−	1064.14i		−	1.28364i	0.766856	−	0.641819i	$-0.221820\pi$
$830$	−0.248292	+	77.8713i	−0.000299148	+	0.0938209i
$831$	−230.318			−0.277157
$832$	121.029	+	121.029i	0.145467	+	0.145467i
$833$	−940.656	+	940.656i	−1.12924	+	1.12924i
$834$			196.675i			0.235821i
$835$	−29.5561	+	29.3682i	−0.0353965	+	0.0351715i
$836$	173.302			0.207299
$837$	−9.81966	−	9.81966i	−0.0117320	−	0.0117320i
$838$	−384.147	+	384.147i	−0.458409	+	0.458409i
$839$		−	738.944i		−	0.880744i	−0.897815	−	0.440372i	$-0.854847\pi$
$839$		−	738.944i		−	0.880744i	0.897815	−	0.440372i	$-0.145153\pi$
$840$	4.03637	+	4.06219i	0.00480520	+	0.00483594i
$841$	739.058			0.878785
$842$	−495.820	−	495.820i	−0.588860	−	0.588860i
$843$	−548.756	+	548.756i	−0.650957	+	0.650957i
$844$			28.8718i			0.0342083i
$845$	−1443.73	−	4.60333i	−1.70856	−	0.00544773i
$846$	−109.219			−0.129100
$847$	10.5958	+	10.5958i	0.0125098	+	0.0125098i
$848$	−56.7209	+	56.7209i	−0.0668878	+	0.0668878i
$849$		−	627.817i		−	0.739478i
$850$	−6.12775	+	960.906i	−0.00720912	+	1.13048i
$851$	−232.656			−0.273391
$852$	−104.609	−	104.609i	−0.122781	−	0.122781i
$853$	−122.277	+	122.277i	−0.143349	+	0.143349i	−0.775139	−	0.631790i	$-0.782320\pi$
$853$	−122.277	+	122.277i	−0.143349	+	0.143349i	0.631790	+	0.775139i	$0.282320\pi$
$854$		−	6.99774i		−	0.00819407i
$855$	−0.549385	+	172.302i	−0.000642556	+	0.201523i
$856$	545.914			0.637750
$857$	−693.932	−	693.932i	−0.809722	−	0.809722i	0.174869	−	0.984592i	$-0.444050\pi$
$857$	−693.932	−	693.932i	−0.809722	−	0.809722i	−0.984592	+	0.174869i	$0.944050\pi$
$858$	279.541	−	279.541i	0.325806	−	0.325806i
$859$			1357.39i			1.58019i	0.612981	+	0.790097i	$0.289970\pi$
$859$			1357.39i			1.58019i	−0.612981	+	0.790097i	$0.710030\pi$
$860$	−397.439	+	394.913i	−0.462139	+	0.459201i
$861$	−11.7644			−0.0136637
$862$	−226.640	−	226.640i	−0.262923	−	0.262923i
$863$	−226.901	+	226.901i	−0.262921	+	0.262921i	−0.826240	−	0.563319i	$-0.809524\pi$
$863$	−226.901	+	226.901i	−0.262921	+	0.262921i	0.563319	+	0.826240i	$0.309524\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	760.458	+	765.323i	0.879143	+	0.884767i
$866$	506.376			0.584730
$867$	−550.770	−	550.770i	−0.635260	−	0.635260i
$868$	−0.883616	+	0.883616i	−0.00101799	+	0.00101799i
$869$			1031.02i			1.18645i
$870$	123.657	+	0.394281i	0.142135	+	0.000453196i
$871$	1379.57			1.58389
$872$	219.117	+	219.117i	0.251281	+	0.251281i
$873$	107.283	−	107.283i	0.122890	−	0.122890i
$874$		−	77.9078i		−	0.0891394i
$875$	20.8607	−	20.4654i	0.0238408	−	0.0233890i
$876$	−352.018			−0.401847
$877$	−645.817	−	645.817i	−0.736394	−	0.736394i	0.235484	−	0.971878i	$-0.424332\pi$
$877$	−645.817	−	645.817i	−0.736394	−	0.736394i	−0.971878	+	0.235484i	$0.924332\pi$
$878$	687.562	−	687.562i	0.783100	−	0.783100i
$879$		−	9.69227i		−	0.0110265i
$880$	−0.481045	+	150.869i	−0.000546642	+	0.171442i
$881$	362.165			0.411084			0.205542	−	0.978648i	$-0.434104\pi$
$881$	362.165			0.411084			0.205542	+	0.978648i	$0.434104\pi$
$882$	−146.836	−	146.836i	−0.166481	−	0.166481i
$883$	−722.006	+	722.006i	−0.817674	+	0.817674i	−0.985771	−	0.168096i	$-0.946238\pi$
$883$	−722.006	+	722.006i	−0.817674	+	0.817674i	0.168096	+	0.985771i	$0.446238\pi$
$884$			1162.99i			1.31560i
$885$	583.729	−	580.019i	0.659581	−	0.655388i
$886$	−409.110			−0.461750
$887$	−727.752	−	727.752i	−0.820465	−	0.820465i	0.165710	−	0.986175i	$-0.447009\pi$
$887$	−727.752	−	727.752i	−0.820465	−	0.820465i	−0.986175	+	0.165710i	$0.947009\pi$
$888$	−168.051	+	168.051i	−0.189247	+	0.189247i
$889$			23.5695i			0.0265123i
$890$	768.544	+	773.461i	0.863533	+	0.869057i
$891$	−67.8914			−0.0761968
$892$	301.251	+	301.251i	0.337726	+	0.337726i
$893$	−209.097	+	209.097i	−0.234151	+	0.234151i
$894$		−	600.545i		−	0.671750i
$895$	830.382	+	2.64767i	0.927801	+	0.00295829i
$896$	−2.64499			−0.00295200
$897$	−125.667	−	125.667i	−0.140097	−	0.140097i
$898$	−356.376	+	356.376i	−0.396855	+	0.396855i
$899$			26.9840i			0.0300155i
$900$	−149.997	−	0.956539i	−0.166663	−	0.00106282i
$901$	−545.045			−0.604934
$902$	−219.161	−	219.161i	−0.242972	−	0.242972i
$903$	−16.0424	+	16.0424i	−0.0177657	+	0.0177657i
$904$		−	470.387i		−	0.520340i
$905$	0.973154	−	305.208i	0.00107531	−	0.337246i
$906$	652.308			0.719986
$907$	503.153	+	503.153i	0.554744	+	0.554744i	0.927806	−	0.373062i	$-0.121692\pi$
$907$	503.153	+	503.153i	0.554744	+	0.554744i	−0.373062	+	0.927806i	$0.621692\pi$
$908$	22.5547	−	22.5547i	0.0248399	−	0.0248399i
$909$		−	319.389i		−	0.351363i
$910$	25.0890	−	24.9295i	0.0275703	−	0.0273950i
$911$	−32.5065			−0.0356823			−0.0178411	−	0.999841i	$-0.505679\pi$
$911$	−32.5065			−0.0356823			−0.0178411	+	0.999841i	$0.505679\pi$
$912$	−56.2740	−	56.2740i	−0.0617039	−	0.0617039i
$913$	−58.7424	+	58.7424i	−0.0643400	+	0.0643400i
$914$		−	96.8945i		−	0.106012i
$915$	129.196	+	130.023i	0.141198	+	0.142101i
$916$	−110.602			−0.120744
$917$	11.5133	+	11.5133i	0.0125554	+	0.0125554i
$918$	141.227	−	141.227i	0.153842	−	0.153842i
$919$		−	247.140i		−	0.268923i	−0.990919	−	0.134461i	$-0.957070\pi$
$919$		−	247.140i		−	0.268923i	0.990919	−	0.134461i	$-0.0429304\pi$
$920$	67.8230	+	0.216253i	0.0737206	+	0.000235058i
$921$	−649.734			−0.705466
$922$	218.854	+	218.854i	0.237369	+	0.237369i
$923$	−646.089	+	646.089i	−0.699988	+	0.699988i
$924$			6.10917i			0.00661165i
$925$	852.096	+	863.033i	0.921184	+	0.933009i
$926$	−49.0575			−0.0529779
$927$	−217.094	−	217.094i	−0.234190	−	0.234190i
$928$	−40.3865	+	40.3865i	−0.0435199	+	0.0435199i
$929$			1135.02i			1.22176i	0.791722	+	0.610882i	$0.209185\pi$
$929$			1135.02i			1.22176i	−0.791722	+	0.610882i	$0.790815\pi$
$930$	0.104366	−	32.7320i	0.000112221	−	0.0351957i
$931$	−562.229			−0.603898
$932$	−90.4148	−	90.4148i	−0.0970116	−	0.0970116i
$933$	−99.9355	+	99.9355i	−0.107112	+	0.107112i
$934$		−	255.548i		−	0.273606i
$935$	−727.180	+	722.558i	−0.777733	+	0.772789i
$936$	−181.543			−0.193956
$937$	−275.507	−	275.507i	−0.294031	−	0.294031i	0.544639	−	0.838670i	$-0.316667\pi$
$937$	−275.507	−	275.507i	−0.294031	−	0.294031i	−0.838670	+	0.544639i	$0.816667\pi$
$938$	−15.0747	+	15.0747i	−0.0160711	+	0.0160711i
$939$			612.114i			0.651878i
$940$	−181.450	−	182.611i	−0.193032	−	0.194267i
$941$	−199.738			−0.212262			−0.106131	−	0.994352i	$-0.533846\pi$
$941$	−199.738			−0.212262			−0.106131	+	0.994352i	$0.533846\pi$
$942$	−192.136	−	192.136i	−0.203966	−	0.203966i
$943$	−98.5235	+	98.5235i	−0.104479	+	0.104479i
$944$			380.080i			0.402628i
$945$	−6.07392	−	0.0193667i	−0.00642743	−	2.04938e-5i
$946$	−597.713			−0.631831
$947$	−808.477	−	808.477i	−0.853724	−	0.853724i	0.136865	−	0.990590i	$-0.456297\pi$
$947$	−808.477	−	808.477i	−0.853724	−	0.853724i	−0.990590	+	0.136865i	$0.956297\pi$
$948$	334.789	−	334.789i	0.353153	−	0.353153i
$949$			2174.14i			2.29098i
$950$	−288.997	+	285.335i	−0.304208	+	0.300352i
$951$	194.507			0.204529
$952$	−12.7082	−	12.7082i	−0.0133489	−	0.0133489i
$953$	890.415	−	890.415i	0.934328	−	0.934328i	−0.0636444	−	0.997973i	$-0.520272\pi$
$953$	890.415	−	890.415i	0.934328	−	0.934328i	0.997973	+	0.0636444i	$0.0202723\pi$
$954$		−	85.0813i		−	0.0891838i
$955$	4.07613	−	1278.39i	0.00426819	−	1.33862i
$956$	574.604			0.601050
$957$	93.2811	+	93.2811i	0.0974725	+	0.0974725i
$958$	425.945	−	425.945i	0.444619	−	0.444619i
$959$		−	42.2395i		−	0.0440454i
$960$	49.1457	−	48.8333i	0.0511935	−	0.0508681i
$961$	−953.857			−0.992567
$962$	1037.92	+	1037.92i	1.07892	+	1.07892i
$963$	−409.435	+	409.435i	−0.425167	+	0.425167i
$964$		−	596.818i		−	0.619106i
$965$	247.505	+	249.088i	0.256482	+	0.258123i
$966$	2.74637			0.00284303
$967$	−714.417	−	714.417i	−0.738797	−	0.738797i	0.233548	−	0.972345i	$-0.424966\pi$
$967$	−714.417	−	714.417i	−0.738797	−	0.738797i	−0.972345	+	0.233548i	$0.924966\pi$
$968$	128.192	−	128.192i	0.132429	−	0.132429i
$969$		−	540.751i		−	0.558050i
$970$	357.608	+	1.14023i	0.368668	+	0.00117550i
$971$	756.055			0.778636			0.389318	−	0.921103i	$-0.372711\pi$
$971$	756.055			0.778636			0.389318	+	0.921103i	$0.372711\pi$
$972$	22.0454	+	22.0454i	0.0226805	+	0.0226805i
$973$	−13.2733	+	13.2733i	−0.0136416	+	0.0136416i
$974$		−	867.040i		−	0.890185i
$975$	−5.90779	+	926.414i	−0.00605927	+	0.950168i
$976$	−84.6610			−0.0867428
$977$	738.254	+	738.254i	0.755633	+	0.755633i	0.975524	−	0.219891i	$-0.0705703\pi$
$977$	738.254	+	738.254i	0.755633	+	0.755633i	−0.219891	+	0.975524i	$0.570570\pi$
$978$	433.137	−	433.137i	0.442880	−	0.442880i
$979$			1163.22i			1.18817i
$980$	1.56061	−	489.451i	0.00159246	−	0.499440i
$981$	−328.675			−0.335041
$982$	−126.759	−	126.759i	−0.129082	−	0.129082i
$983$	1202.82	−	1202.82i	1.22362	−	1.22362i	0.257284	−	0.966336i	$-0.417172\pi$
$983$	1202.82	−	1202.82i	1.22362	−	1.22362i	0.966336	−	0.257284i	$-0.0828275\pi$
$984$			142.330i			0.144644i
$985$	190.107	−	188.899i	0.193002	−	0.191775i
$986$	−388.084			−0.393594
$987$	−7.37100	−	7.37100i	−0.00746808	−	0.00746808i
$988$	−347.560	+	347.560i	−0.351782	+	0.351782i
$989$			268.701i			0.271690i
$990$	−112.791	−	113.512i	−0.113930	−	0.114659i
$991$	990.803			0.999802			0.499901	−	0.866083i	$-0.333370\pi$
$991$	990.803			0.999802			0.499901	+	0.866083i	$0.333370\pi$
$992$	10.6903	+	10.6903i	0.0107765	+	0.0107765i
$993$	−458.685	+	458.685i	−0.461918	+	0.461918i
$994$		−	14.1198i		−	0.0142050i
$995$	−970.637	−	3.09487i	−0.975514	−	0.00311042i
$996$	38.1492			0.0383024
$997$	677.995	+	677.995i	0.680035	+	0.680035i	0.960008	−	0.279973i	$-0.0903255\pi$
$997$	677.995	+	677.995i	0.680035	+	0.680035i	−0.279973	+	0.960008i	$0.590326\pi$
$998$	−40.4801	+	40.4801i	−0.0405612	+	0.0405612i
$999$		−	252.077i		−	0.252329i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.a.277.5	✓	40
5.3	odd	4	inner	690.3.k.a.553.5	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.a.277.5	✓	40	1.1	even	1	trivial
690.3.k.a.553.5	yes	40	5.3	odd	4	inner

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)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(0.0159424 - 4.99997i) q^{5} -2.44949 q^{6} +(-0.165312 - 0.165312i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(0.0159424 - 4.99997i) q^{5} -2.44949 q^{6} +(-0.165312 - 0.165312i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(5.01592 - 4.98403i) q^{10} +7.54349 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-15.1286 + 15.1286i) q^{13} -0.330624i q^{14} +(6.10417 + 6.14322i) q^{15} -4.00000 q^{16} +(-19.2185 - 19.2185i) q^{17} +(3.00000 - 3.00000i) q^{18} -11.4869i q^{19} +(9.99995 + 0.0318848i) q^{20} +0.404930 q^{21} +(7.54349 + 7.54349i) q^{22} +(3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(-24.9995 - 0.159423i) q^{25} -30.2572 q^{26} +(3.67423 + 3.67423i) q^{27} +(0.330624 - 0.330624i) q^{28} -10.0966i q^{29} +(-0.0390507 + 12.2474i) q^{30} -2.67257 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-9.23885 + 9.23885i) q^{33} -38.4370i q^{34} +(-0.829191 + 0.823920i) q^{35} +6.00000 q^{36} +(-34.3033 - 34.3033i) q^{37} +(11.4869 - 11.4869i) q^{38} -37.0573i q^{39} +(9.96806 + 10.0318i) q^{40} -29.0530 q^{41} +(0.404930 + 0.404930i) q^{42} +(-39.6178 + 39.6178i) q^{43} +15.0870i q^{44} +(-14.9999 - 0.0478272i) q^{45} +6.78233 q^{46} +(-18.2031 - 18.2031i) q^{47} +(4.89898 - 4.89898i) q^{48} -48.9453i q^{49} +(-24.8401 - 25.1589i) q^{50} +47.0755 q^{51} +(-30.2572 - 30.2572i) q^{52} +(14.1802 - 14.1802i) q^{53} +7.34847i q^{54} +(0.120261 - 37.7172i) q^{55} +0.661248 q^{56} +(14.0685 + 14.0685i) q^{57} +(10.0966 - 10.0966i) q^{58} -95.0201i q^{59} +(-12.2864 + 12.2083i) q^{60} +21.1653 q^{61} +(-2.67257 - 2.67257i) q^{62} +(-0.495936 + 0.495936i) q^{63} -8.00000i q^{64} +(75.4013 + 75.8837i) q^{65} -18.4777 q^{66} +(-45.5947 - 45.5947i) q^{67} +(38.4370 - 38.4370i) q^{68} +8.30662i q^{69} +(-1.65311 - 0.00527094i) q^{70} +42.7065 q^{71} +(6.00000 + 6.00000i) q^{72} +(71.8554 - 71.8554i) q^{73} -68.6065i q^{74} +(30.8133 - 30.4227i) q^{75} +22.9738 q^{76} +(-1.24703 - 1.24703i) q^{77} +(37.0573 - 37.0573i) q^{78} +136.677i q^{79} +(-0.0637696 + 19.9999i) q^{80} -9.00000 q^{81} +(-29.0530 - 29.0530i) q^{82} +(-7.78717 + 7.78717i) q^{83} +0.809860i q^{84} +(-96.3984 + 95.7857i) q^{85} -79.2356 q^{86} +(12.3658 + 12.3658i) q^{87} +(-15.0870 + 15.0870i) q^{88} +154.201i q^{89} +(-14.9521 - 15.0478i) q^{90} +5.00187 q^{91} +(6.78233 + 6.78233i) q^{92} +(3.27322 - 3.27322i) q^{93} -36.4063i q^{94} +(-57.4341 - 0.183128i) q^{95} +9.79796 q^{96} +(35.7610 + 35.7610i) q^{97} +(48.9453 - 48.9453i) q^{98} -22.6305i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) \) 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8	\( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) \) 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8 - 16 * q^10 + 32 * q^11 + 16 * q^13 + 24 * q^15 - 160 * q^16 - 48 * q^17 + 120 * q^18 - 16 * q^20 - 96 * q^21 + 32 * q^22 + 32 * q^26 + 16 * q^28 + 24 * q^30 + 152 * q^31 - 160 * q^32 - 24 * q^33 + 48 * q^35 + 240 * q^36 + 216 * q^37 + 16 * q^38 - 168 * q^41 - 96 * q^42 - 48 * q^43 + 24 * q^45 - 232 * q^47 - 40 * q^50 + 32 * q^52 + 8 * q^53 - 272 * q^55 + 32 * q^56 - 136 * q^58 - 64 * q^61 + 152 * q^62 - 24 * q^63 + 416 * q^65 - 48 * q^66 - 32 * q^67 + 96 * q^68 + 88 * q^70 - 104 * q^71 + 240 * q^72 + 480 * q^73 - 216 * q^75 + 32 * q^76 + 280 * q^77 - 192 * q^78 + 32 * q^80 - 360 * q^81 - 168 * q^82 - 576 * q^83 - 208 * q^85 - 96 * q^86 + 24 * q^87 - 64 * q^88 + 144 * q^91 + 96 * q^93 + 168 * q^95 + 24 * q^97 + 176 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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