LMFDB - Embedded newform 690.3.k.a.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:	$40$
Relative dimension:	$20$ 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.a.277.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(0.0159424 + 4.99997i) q^{5} -2.44949 q^{6} +(-0.165312 + 0.165312i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

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

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
$5$	0.0159424	+	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	−0.718816	−	0.695200i	$-0.755316\pi$
$7$	−0.165312	+	0.165312i	−0.0236160	+	0.0236160i	0.695200	+	0.718816i	$0.255316\pi$
$8$	−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	−0.983651	−	0.180086i	$-0.942362\pi$
$13$	−15.1286	−	15.1286i	−1.16374	−	1.16374i	−0.180086	−	0.983651i	$-0.557638\pi$
$14$			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	−0.140406	+	0.990094i	$0.544841\pi$
$17$	−19.2185	+	19.2185i	−1.13050	+	1.13050i	−0.990094	+	0.140406i	$0.955159\pi$
$18$	3.00000	+	3.00000i	0.166667	+	0.166667i
$19$			11.4869i			0.604573i	0.953217	+	0.302286i	$0.0977498\pi$
$19$			11.4869i			0.604573i	−0.953217	+	0.302286i	$0.902250\pi$
$20$	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	$0.0556950\pi$
$29$			10.0966i			0.348159i	−0.984732	+	0.174080i	$0.944305\pi$
$30$	−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	−0.997519	−	0.0704032i	$-0.977571\pi$
$37$	−34.3033	+	34.3033i	−0.927115	+	0.927115i	0.0704032	+	0.997519i	$0.477571\pi$
$38$	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	0.0757805	−	0.997125i	$-0.475855\pi$
$43$	−39.6178	−	39.6178i	−0.921344	−	0.921344i	−0.997125	+	0.0757805i	$0.975855\pi$
$44$		−	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	−0.873724	−	0.486423i	$-0.838302\pi$
$47$	−18.2031	+	18.2031i	−0.387301	+	0.387301i	0.486423	+	0.873724i	$0.338302\pi$
$48$	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	0.828113	−	0.560562i	$-0.189415\pi$
$53$	14.1802	+	14.1802i	0.267551	+	0.267551i	−0.560562	+	0.828113i	$0.689415\pi$
$54$		−	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	$0.297972\pi$
$59$			95.0201i			1.61051i	−0.592929	+	0.805255i	$0.702028\pi$
$60$	−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	−0.960117	−	0.279599i	$-0.909798\pi$
$67$	−45.5947	+	45.5947i	−0.680518	+	0.680518i	0.279599	+	0.960117i	$0.409798\pi$
$68$	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	0.999879	−	0.0155579i	$-0.00495242\pi$
$73$	71.8554	+	71.8554i	0.984321	+	0.984321i	−0.0155579	+	0.999879i	$0.504952\pi$
$74$			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	$-0.667290\pi$
$79$		−	136.677i		−	1.73009i	0.501694	−	0.865045i	$-0.332710\pi$
$80$	−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	0.658638	−	0.752460i	$-0.271133\pi$
$83$	−7.78717	−	7.78717i	−0.0938214	−	0.0938214i	−0.752460	+	0.658638i	$0.771133\pi$
$84$		−	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	$-0.666492\pi$
$89$		−	154.201i		−	1.73260i	0.499525	−	0.866300i	$-0.333508\pi$
$90$	−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	−0.498322	−	0.866992i	$-0.666050\pi$
$97$	35.7610	−	35.7610i	0.368670	−	0.368670i	0.866992	+	0.498322i	$0.166050\pi$
$98$	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	0.964961	−	0.262392i	$-0.0845113\pi$
$103$	72.3647	+	72.3647i	0.702569	+	0.702569i	−0.262392	+	0.964961i	$0.584511\pi$
$104$			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	−0.332340	+	0.943160i	$0.607838\pi$
$107$	−136.478	+	136.478i	−1.27550	+	1.27550i	−0.943160	+	0.332340i	$0.892162\pi$
$108$	−7.34847	−	7.34847i	−0.0680414	−	0.0680414i
$109$			109.558i			1.00512i	0.864541	+	0.502562i	$0.167609\pi$
$109$			109.558i			1.00512i	−0.864541	+	0.502562i	$0.832391\pi$
$110$	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	−0.999137	−	0.0415426i	$-0.986773\pi$
$113$	−117.597	−	117.597i	−1.04068	−	1.04068i	−0.0415426	−	0.999137i	$-0.513227\pi$
$114$		−	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	−0.929683	−	0.368361i	$-0.879919\pi$
$127$	−71.2879	+	71.2879i	−0.561322	+	0.561322i	0.368361	+	0.929683i	$0.379919\pi$
$128$	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	−0.0653303	−	0.997864i	$-0.520810\pi$
$137$	127.757	−	127.757i	0.932533	−	0.932533i	0.997864	+	0.0653303i	$0.0208101\pi$
$138$	−8.30662	−	8.30662i	−0.0601929	−	0.0601929i
$139$			80.2923i			0.577642i	0.957383	+	0.288821i	$0.0932633\pi$
$139$			80.2923i			0.577642i	−0.957383	+	0.288821i	$0.906737\pi$
$140$	−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	$-0.692454\pi$
$149$		−	245.171i		−	1.64545i	0.568443	−	0.822723i	$-0.307546\pi$
$150$	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	−0.411705	−	0.911317i	$-0.635067\pi$
$157$	78.4391	−	78.4391i	0.499612	−	0.499612i	0.911317	+	0.411705i	$0.135067\pi$
$158$	−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	−0.996051	−	0.0887791i	$-0.971703\pi$
$163$	−176.827	−	176.827i	−1.08483	−	1.08483i	−0.0887791	−	0.996051i	$-0.528297\pi$
$164$			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	−0.724529	−	0.689245i	$-0.757943\pi$
$167$	−5.89246	+	5.89246i	−0.0352842	+	0.0352842i	0.689245	+	0.724529i	$0.257943\pi$
$168$	−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	0.111774	−	0.993734i	$-0.464347\pi$
$173$	−152.579	−	152.579i	−0.881959	−	0.881959i	−0.993734	+	0.111774i	$0.964347\pi$
$174$		−	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	$-0.846449\pi$
$179$		−	166.077i		−	0.927806i	0.885886	−	0.463903i	$-0.153551\pi$
$180$	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	0.566653	−	0.823957i	$-0.308238\pi$
$193$	−49.6596	−	49.6596i	−0.257304	−	0.257304i	−0.823957	+	0.566653i	$0.808238\pi$
$194$		−	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	−0.604338	−	0.796728i	$-0.706562\pi$
$197$	37.9008	−	37.9008i	0.192390	−	0.192390i	0.796728	+	0.604338i	$0.206562\pi$
$198$	22.6305	+	22.6305i	0.114295	+	0.114295i
$199$			194.128i			0.975519i	0.872978	+	0.487760i	$0.162186\pi$
$199$			194.128i			0.975519i	−0.872978	+	0.487760i	$0.837814\pi$
$200$	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	0.958968	−	0.283516i	$-0.0915009\pi$
$223$	150.626	+	150.626i	0.675452	+	0.675452i	−0.283516	+	0.958968i	$0.591501\pi$
$224$		−	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	−0.731510	−	0.681830i	$-0.761184\pi$
$227$	−11.2773	+	11.2773i	−0.0496799	+	0.0496799i	0.681830	+	0.731510i	$0.261184\pi$
$228$	−28.1370	−	28.1370i	−0.123408	−	0.123408i
$229$		−	55.3008i		−	0.241488i	−0.992684	−	0.120744i	$-0.961472\pi$
$229$		−	55.3008i		−	0.241488i	0.992684	−	0.120744i	$-0.0385280\pi$
$230$	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	0.603409	−	0.797432i	$-0.293809\pi$
$233$	−45.2074	−	45.2074i	−0.194023	−	0.194023i	−0.797432	+	0.603409i	$0.793809\pi$
$234$		−	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	$0.205251\pi$
$239$			287.302i			1.20210i	−0.799211	+	0.601050i	$0.794749\pi$
$240$	−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	−0.554500	−	0.832184i	$-0.687090\pi$
$257$	71.3647	−	71.3647i	0.277684	−	0.277684i	0.832184	+	0.554500i	$0.187090\pi$
$258$	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	0.753753	−	0.657158i	$-0.228242\pi$
$263$	25.4045	+	25.4045i	0.0965951	+	0.0965951i	−0.657158	+	0.753753i	$0.728242\pi$
$264$			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	$0.308265\pi$
$269$			443.315i			1.64801i	−0.566582	+	0.824005i	$0.691735\pi$
$270$	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	−0.516712	−	0.856159i	$-0.672844\pi$
$277$	94.0269	−	94.0269i	0.339447	−	0.339447i	0.856159	+	0.516712i	$0.172844\pi$
$278$	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	0.0902473	−	0.995919i	$-0.471234\pi$
$283$	−256.305	−	256.305i	−0.905672	−	0.905672i	−0.995919	+	0.0902473i	$0.971234\pi$
$284$		−	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	0.700322	−	0.713827i	$-0.253040\pi$
$293$	−3.95685	−	3.95685i	−0.0135046	−	0.0135046i	−0.713827	+	0.700322i	$0.753040\pi$
$294$		−	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	−0.127786	−	0.991802i	$-0.540787\pi$
$307$	265.253	−	265.253i	0.864015	−	0.864015i	0.991802	+	0.127786i	$0.0407872\pi$
$308$	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	0.982841	−	0.184456i	$-0.0590523\pi$
$313$	249.894	+	249.894i	0.798385	+	0.798385i	−0.184456	+	0.982841i	$0.559052\pi$
$314$		−	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	−0.821174	−	0.570678i	$-0.806681\pi$
$317$	−79.4073	+	79.4073i	−0.250496	+	0.250496i	0.570678	+	0.821174i	$0.306681\pi$
$318$	−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	−0.626499	−	0.779422i	$-0.715513\pi$
$337$	51.5352	−	51.5352i	0.152923	−	0.152923i	0.779422	+	0.626499i	$0.215513\pi$
$338$	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	0.330569	−	0.943782i	$-0.392759\pi$
$347$	442.200	−	442.200i	1.27435	−	1.27435i	0.943782	−	0.330569i	$-0.107241\pi$
$348$	−24.7316	−	24.7316i	−0.0710677	−	0.0710677i
$349$			448.442i			1.28493i	0.766314	+	0.642467i	$0.222089\pi$
$349$			448.442i			1.28493i	−0.766314	+	0.642467i	$0.777911\pi$
$350$	−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	0.928343	−	0.371724i	$-0.121233\pi$
$353$	196.487	+	196.487i	0.556619	+	0.556619i	−0.371724	+	0.928343i	$0.621233\pi$
$354$		−	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	$0.147455\pi$
$359$			320.839i			0.893702i	−0.894608	+	0.446851i	$0.852545\pi$
$360$	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	−0.998361	−	0.0572330i	$-0.981772\pi$
$367$	−345.394	+	345.394i	−0.941128	+	0.941128i	0.0572330	+	0.998361i	$0.481772\pi$
$368$	−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	−0.947092	−	0.320963i	$-0.895994\pi$
$373$	−472.984	−	472.984i	−1.26805	−	1.26805i	−0.320963	−	0.947092i	$-0.604006\pi$
$374$			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	$0.0679827\pi$
$379$			160.661i			0.423908i	−0.977280	+	0.211954i	$0.932017\pi$
$380$	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	0.873234	−	0.487301i	$-0.162019\pi$
$383$	147.812	+	147.812i	0.385932	+	0.385932i	−0.487301	+	0.873234i	$0.662019\pi$
$384$		−	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	$-0.779904\pi$
$389$		−	496.097i		−	1.27531i	0.770320	−	0.637657i	$-0.220096\pi$
$390$	−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	−0.781073	−	0.624440i	$-0.785327\pi$
$397$	−62.1832	+	62.1832i	−0.156633	+	0.156633i	0.624440	+	0.781073i	$0.285327\pi$
$398$	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	$0.264331\pi$
$409$			603.860i			1.47643i	−0.674565	+	0.738215i	$0.735669\pi$
$410$	−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	$-0.848419\pi$
$419$		−	384.147i		−	0.916819i	0.888741	−	0.458409i	$-0.151581\pi$
$420$	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	0.936199	−	0.351470i	$-0.114318\pi$
$433$	253.188	+	253.188i	0.584730	+	0.584730i	−0.351470	+	0.936199i	$0.614318\pi$
$434$		−	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	$0.286363\pi$
$439$			687.562i			1.56620i	−0.621896	+	0.783100i	$0.713637\pi$
$440$	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	0.437479	−	0.899229i	$-0.355872\pi$
$443$	−204.555	−	204.555i	−0.461750	−	0.461750i	−0.899229	+	0.437479i	$0.855872\pi$
$444$		−	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	$-0.870101\pi$
$449$		−	356.376i		−	0.793711i	0.917881	−	0.396855i	$-0.129899\pi$
$450$	−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	−0.758123	−	0.652112i	$-0.773883\pi$
$457$	−48.4473	+	48.4473i	−0.106012	+	0.106012i	0.652112	+	0.758123i	$0.273883\pi$
$458$	−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	0.680121	−	0.733099i	$-0.261927\pi$
$463$	−24.5288	−	24.5288i	−0.0529779	−	0.0529779i	−0.733099	+	0.680121i	$0.761927\pi$
$464$		−	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	−0.830550	−	0.556944i	$-0.811974\pi$
$467$	−127.774	+	127.774i	−0.273606	+	0.273606i	0.556944	+	0.830550i	$0.311974\pi$
$468$	−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	$0.146661\pi$
$479$			425.945i			0.889239i	−0.895720	+	0.444619i	$0.853339\pi$
$480$	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	−0.994540	−	0.104355i	$-0.966722\pi$
$487$	−433.520	+	433.520i	−0.890185	+	0.890185i	0.104355	+	0.994540i	$0.466722\pi$
$488$	−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	$-0.987085\pi$
$499$		−	40.4801i		−	0.0811225i	0.999177	−	0.0405612i	$-0.0129146\pi$
$500$	−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	0.891899	−	0.452235i	$-0.149373\pi$
$503$	221.151	+	221.151i	0.439664	+	0.439664i	−0.452235	+	0.891899i	$0.649373\pi$
$504$			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	$0.211864\pi$
$509$			628.639i			1.23505i	−0.786552	+	0.617524i	$0.788136\pi$
$510$	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	0.756296	−	0.654229i	$-0.227007\pi$
$523$	53.3810	+	53.3810i	0.102067	+	0.102067i	−0.654229	+	0.756296i	$0.727007\pi$
$524$			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	−0.578470	−	0.815703i	$-0.696350\pi$
$547$	129.766	−	129.766i	0.237233	−	0.237233i	0.815703	+	0.578470i	$0.196350\pi$
$548$	−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	−0.886095	−	0.463504i	$-0.846592\pi$
$557$	−235.383	+	235.383i	−0.422591	+	0.422591i	0.463504	+	0.886095i	$0.346592\pi$
$558$	−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	0.762620	−	0.646847i	$-0.223913\pi$
$563$	65.1797	+	65.1797i	0.115772	+	0.115772i	−0.646847	+	0.762620i	$0.723913\pi$
$564$		−	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	$0.119804\pi$
$569$			418.274i			0.735104i	−0.930003	+	0.367552i	$0.880196\pi$
$570$	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	−0.411643	−	0.911345i	$-0.635045\pi$
$577$	288.328	−	288.328i	0.499703	−	0.499703i	0.911345	+	0.411643i	$0.135045\pi$
$578$	−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	−0.999202	−	0.0399411i	$-0.987283\pi$
$587$	−563.086	+	563.086i	−0.959261	+	0.959261i	0.0399411	+	0.999202i	$0.487283\pi$
$588$	−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	0.338270	−	0.941049i	$-0.390158\pi$
$593$	−357.448	−	357.448i	−0.602780	−	0.602780i	−0.941049	+	0.338270i	$0.890158\pi$
$594$		−	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	$0.204536\pi$
$599$			717.906i			1.19851i	−0.800559	+	0.599254i	$0.795464\pi$
$600$	−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	−0.418430	−	0.908249i	$-0.637420\pi$
$607$	297.320	−	297.320i	0.489818	−	0.489818i	0.908249	+	0.418430i	$0.137420\pi$
$608$	−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	0.161739	−	0.986834i	$-0.448290\pi$
$613$	−505.783	−	505.783i	−0.825095	−	0.825095i	−0.986834	+	0.161739i	$0.948290\pi$
$614$		−	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	−0.343898	−	0.939007i	$-0.611747\pi$
$617$	367.182	−	367.182i	0.595109	−	0.595109i	0.939007	+	0.343898i	$0.111747\pi$
$618$	−177.256	−	177.256i	−0.286823	−	0.286823i
$619$		−	475.667i		−	0.768444i	−0.923241	−	0.384222i	$-0.874470\pi$
$619$		−	475.667i		−	0.768444i	0.923241	−	0.384222i	$-0.125530\pi$
$620$	−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	0.967097	−	0.254409i	$-0.0818811\pi$
$643$	458.258	+	458.258i	0.712687	+	0.712687i	−0.254409	+	0.967097i	$0.581881\pi$
$644$			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	−0.975312	−	0.220832i	$-0.929123\pi$
$647$	−488.148	+	488.148i	−0.754479	+	0.754479i	0.220832	+	0.975312i	$0.429123\pi$
$648$	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	0.854941	−	0.518725i	$-0.173593\pi$
$653$	219.549	+	219.549i	0.336217	+	0.336217i	−0.518725	+	0.854941i	$0.673593\pi$
$654$		−	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	$0.0429420\pi$
$659$			177.268i			0.268995i	−0.990914	+	0.134498i	$0.957058\pi$
$660$	−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	0.961981	+	0.273117i	$0.0880547\pi$
$673$	831.221	+	831.221i	1.23510	+	1.23510i	0.273117	+	0.961981i	$0.411945\pi$
$674$		−	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	−0.999518	−	0.0310357i	$-0.990119\pi$
$677$	−655.663	+	655.663i	−0.968483	+	0.968483i	0.0310357	+	0.999518i	$0.490119\pi$
$678$	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	0.680617	−	0.732639i	$-0.261712\pi$
$683$	−35.5313	−	35.5313i	−0.0520224	−	0.0520224i	−0.732639	+	0.680617i	$0.761712\pi$
$684$			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	$0.200509\pi$
$709$			835.312i			1.17816i	−0.808076	+	0.589078i	$0.799491\pi$
$710$	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	$0.0420900\pi$
$719$			189.592i			0.263689i	−0.991270	+	0.131845i	$0.957910\pi$
$720$	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	0.00167235	−	0.999999i	$-0.499468\pi$
$727$	728.215	−	728.215i	1.00167	−	1.00167i	0.999999	−	0.00167235i	$-0.000532324\pi$
$728$	−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	0.0211431	−	0.999776i	$-0.493269\pi$
$733$	−717.338	−	717.338i	−0.978633	−	0.978633i	−0.999776	+	0.0211431i	$0.993269\pi$
$734$			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	$-0.822445\pi$
$739$		−	782.343i		−	1.05865i	0.848419	−	0.529325i	$-0.177555\pi$
$740$	−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	0.160619	−	0.987017i	$-0.448651\pi$
$743$	−614.013	−	614.013i	−0.826398	−	0.826398i	−0.987017	+	0.160619i	$0.948651\pi$
$744$		−	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	−0.242710	−	0.970099i	$-0.578036\pi$
$757$	550.633	−	550.633i	0.727388	−	0.727388i	0.970099	+	0.242710i	$0.0780365\pi$
$758$	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	$-0.594061\pi$
$769$		−	1471.34i		−	1.91331i	0.291221	−	0.956656i	$-0.405939\pi$
$770$	−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	0.709377	−	0.704829i	$-0.248976\pi$
$773$	3.51558	+	3.51558i	0.00454797	+	0.00454797i	−0.704829	+	0.709377i	$0.748976\pi$
$774$		−	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	−0.999111	−	0.0421551i	$-0.986578\pi$
$787$	−753.124	+	753.124i	−0.956956	+	0.956956i	0.0421551	+	0.999111i	$0.486578\pi$
$788$	−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	−0.824180	−	0.566328i	$-0.808364\pi$
$797$	−205.508	+	205.508i	−0.257852	+	0.257852i	0.566328	+	0.824180i	$0.308364\pi$
$798$	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	$-0.879328\pi$
$809$		−	598.802i		−	0.740176i	0.928997	−	0.370088i	$-0.120672\pi$
$810$	−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	0.996663	+	0.0816250i	$0.0260110\pi$
$823$	887.431	+	887.431i	1.07829	+	1.07829i	0.0816250	+	0.996663i	$0.473989\pi$
$824$		−	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	−0.232775	+	0.972531i	$0.574781\pi$
$827$	−996.788	+	996.788i	−1.20531	+	1.20531i	−0.972531	+	0.232775i	$0.925219\pi$
$828$	20.3470	+	20.3470i	0.0245737	+	0.0245737i
$829$			1064.14i			1.28364i	0.766856	+	0.641819i	$0.221820\pi$
$829$			1064.14i			1.28364i	−0.766856	+	0.641819i	$0.778180\pi$
$830$	−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	$0.145153\pi$
$839$			738.944i			0.880744i	−0.897815	+	0.440372i	$0.854847\pi$
$840$	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	0.631790	−	0.775139i	$-0.282320\pi$
$853$	−122.277	−	122.277i	−0.143349	−	0.143349i	−0.775139	+	0.631790i	$0.782320\pi$
$854$			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	−0.984592	−	0.174869i	$-0.944050\pi$
$857$	−693.932	+	693.932i	−0.809722	+	0.809722i	0.174869	+	0.984592i	$0.444050\pi$
$858$	279.541	+	279.541i	0.325806	+	0.325806i
$859$		−	1357.39i		−	1.58019i	−0.612981	−	0.790097i	$-0.710030\pi$
$859$		−	1357.39i		−	1.58019i	0.612981	−	0.790097i	$-0.289970\pi$
$860$	−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	0.563319	−	0.826240i	$-0.309524\pi$
$863$	−226.901	−	226.901i	−0.262921	−	0.262921i	−0.826240	+	0.563319i	$0.809524\pi$
$864$			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	−0.971878	−	0.235484i	$-0.924332\pi$
$877$	−645.817	+	645.817i	−0.736394	+	0.736394i	0.235484	+	0.971878i	$0.424332\pi$
$878$	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	0.168096	−	0.985771i	$-0.446238\pi$
$883$	−722.006	−	722.006i	−0.817674	−	0.817674i	−0.985771	+	0.168096i	$0.946238\pi$
$884$		−	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	−0.986175	−	0.165710i	$-0.947009\pi$
$887$	−727.752	+	727.752i	−0.820465	+	0.820465i	0.165710	+	0.986175i	$0.447009\pi$
$888$	−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	−0.373062	−	0.927806i	$-0.621692\pi$
$907$	503.153	−	503.153i	0.554744	−	0.554744i	0.927806	+	0.373062i	$0.121692\pi$
$908$	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	$0.0429304\pi$
$919$			247.140i			0.268923i	−0.990919	+	0.134461i	$0.957070\pi$
$920$	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	$-0.790815\pi$
$929$		−	1135.02i		−	1.22176i	0.791722	−	0.610882i	$-0.209185\pi$
$930$	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	−0.838670	−	0.544639i	$-0.816667\pi$
$937$	−275.507	+	275.507i	−0.294031	+	0.294031i	0.544639	+	0.838670i	$0.316667\pi$
$938$	−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	−0.990590	−	0.136865i	$-0.956297\pi$
$947$	−808.477	+	808.477i	−0.853724	+	0.853724i	0.136865	+	0.990590i	$0.456297\pi$
$948$	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	0.997973	−	0.0636444i	$-0.0202723\pi$
$953$	890.415	+	890.415i	0.934328	+	0.934328i	−0.0636444	+	0.997973i	$0.520272\pi$
$954$			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	−0.972345	−	0.233548i	$-0.924966\pi$
$967$	−714.417	+	714.417i	−0.738797	+	0.738797i	0.233548	+	0.972345i	$0.424966\pi$
$968$	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	−0.219891	−	0.975524i	$-0.570570\pi$
$977$	738.254	−	738.254i	0.755633	−	0.755633i	0.975524	+	0.219891i	$0.0705703\pi$
$978$	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	0.966336	+	0.257284i	$0.0828275\pi$
$983$	1202.82	+	1202.82i	1.22362	+	1.22362i	0.257284	+	0.966336i	$0.417172\pi$
$984$		−	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	−0.279973	−	0.960008i	$-0.590326\pi$
$997$	677.995	−	677.995i	0.680035	−	0.680035i	0.960008	+	0.279973i	$0.0903255\pi$
$998$	−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.553.5	yes	40
5.2	odd	4	inner	690.3.k.a.277.5	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.a.277.5	✓	40	5.2	odd	4	inner
690.3.k.a.553.5	yes	40	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)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(0.0159424 + 4.99997i) q^{5} -2.44949 q^{6} +(-0.165312 + 0.165312i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(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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