LMFDB - Embedded newform 690.3.k.a.553.1

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			553.1
Character	$\chi$	$=$	690.553
Dual form			690.3.k.a.277.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-4.85719 + 1.18646i) q^{5} -2.44949 q^{6} +(8.99906 - 8.99906i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-4.85719 + 1.18646i) q^{5} -2.44949 q^{6} +(8.99906 - 8.99906i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(-3.67074 + 6.04365i) q^{10} +15.1040 q^{11} +(-2.44949 + 2.44949i) q^{12} +(-3.57114 - 3.57114i) q^{13} -17.9981i q^{14} +(7.40193 + 4.49572i) q^{15} -4.00000 q^{16} +(7.84507 - 7.84507i) q^{17} +(3.00000 + 3.00000i) q^{18} -2.57794i q^{19} +(2.37291 + 9.71439i) q^{20} -22.0431 q^{21} +(15.1040 - 15.1040i) q^{22} +(-3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(22.1846 - 11.5257i) q^{25} -7.14227 q^{26} +(3.67423 - 3.67423i) q^{27} +(-17.9981 - 17.9981i) q^{28} -7.64648i q^{29} +(11.8976 - 2.90621i) q^{30} -55.4912 q^{31} +(-4.00000 + 4.00000i) q^{32} +(-18.4986 - 18.4986i) q^{33} -15.6901i q^{34} +(-33.0332 + 54.3872i) q^{35} +6.00000 q^{36} +(24.3469 - 24.3469i) q^{37} +(-2.57794 - 2.57794i) q^{38} +8.74746i q^{39} +(12.0873 + 7.34147i) q^{40} -8.82642 q^{41} +(-22.0431 + 22.0431i) q^{42} +(-6.92644 - 6.92644i) q^{43} -30.2081i q^{44} +(-3.55937 - 14.5716i) q^{45} -6.78233 q^{46} +(-45.3582 + 45.3582i) q^{47} +(4.89898 + 4.89898i) q^{48} -112.966i q^{49} +(10.6590 - 33.7103i) q^{50} -19.2164 q^{51} +(-7.14227 + 7.14227i) q^{52} +(-39.7281 - 39.7281i) q^{53} -7.34847i q^{54} +(-73.3632 + 17.9203i) q^{55} -35.9962 q^{56} +(-3.15731 + 3.15731i) q^{57} +(-7.64648 - 7.64648i) q^{58} +80.7399i q^{59} +(8.99143 - 14.8039i) q^{60} -74.8025 q^{61} +(-55.4912 + 55.4912i) q^{62} +(26.9972 + 26.9972i) q^{63} +8.00000i q^{64} +(21.5827 + 13.1087i) q^{65} -36.9972 q^{66} +(92.9564 - 92.9564i) q^{67} +(-15.6901 - 15.6901i) q^{68} +8.30662i q^{69} +(21.3540 + 87.4203i) q^{70} -0.195500 q^{71} +(6.00000 - 6.00000i) q^{72} +(-49.4310 - 49.4310i) q^{73} -48.6938i q^{74} +(-41.2866 - 13.0545i) q^{75} -5.15587 q^{76} +(135.922 - 135.922i) q^{77} +(8.74746 + 8.74746i) q^{78} -41.8460i q^{79} +(19.4288 - 4.74582i) q^{80} -9.00000 q^{81} +(-8.82642 + 8.82642i) q^{82} +(26.4027 + 26.4027i) q^{83} +44.0862i q^{84} +(-28.7972 + 47.4128i) q^{85} -13.8529 q^{86} +(-9.36499 + 9.36499i) q^{87} +(-30.2081 - 30.2081i) q^{88} -16.8125i q^{89} +(-18.1309 - 11.0122i) q^{90} -64.2738 q^{91} +(-6.78233 + 6.78233i) q^{92} +(67.9625 + 67.9625i) q^{93} +90.7164i q^{94} +(3.05861 + 12.5215i) q^{95} +9.79796 q^{96} +(-10.2900 + 10.2900i) q^{97} +(-112.966 - 112.966i) q^{98} +45.3121i 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
$5$	−4.85719	+	1.18646i	−0.971439	+	0.237291i
$5$	−4.85719	+	1.18646i	−0.971439	+	0.237291i
$6$	−2.44949			−0.408248
$7$	8.99906	−	8.99906i	1.28558	−	1.28558i	0.348136	−	0.937444i	$-0.386815\pi$
$7$	8.99906	−	8.99906i	1.28558	−	1.28558i	0.937444	−	0.348136i	$-0.113185\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$			3.00000i			0.333333i
$10$	−3.67074	+	6.04365i	−0.367074	+	0.604365i
$11$	15.1040			1.37309			0.686547	−	0.727085i	$-0.259126\pi$
$11$	15.1040			1.37309			0.686547	+	0.727085i	$0.259126\pi$
$12$	−2.44949	+	2.44949i	−0.204124	+	0.204124i
$13$	−3.57114	−	3.57114i	−0.274703	−	0.274703i	0.556287	−	0.830990i	$-0.312225\pi$
$13$	−3.57114	−	3.57114i	−0.274703	−	0.274703i	−0.830990	+	0.556287i	$0.812225\pi$
$14$		−	17.9981i		−	1.28558i
$15$	7.40193	+	4.49572i	0.493462	+	0.299714i
$16$	−4.00000			−0.250000
$17$	7.84507	−	7.84507i	0.461475	−	0.461475i	−0.437664	−	0.899139i	$-0.644194\pi$
$17$	7.84507	−	7.84507i	0.461475	−	0.461475i	0.899139	+	0.437664i	$0.144194\pi$
$18$	3.00000	+	3.00000i	0.166667	+	0.166667i
$19$		−	2.57794i		−	0.135681i	−0.997696	−	0.0678404i	$-0.978389\pi$
$19$		−	2.57794i		−	0.135681i	0.997696	−	0.0678404i	$-0.0216109\pi$
$20$	2.37291	+	9.71439i	0.118646	+	0.485719i
$21$	−22.0431			−1.04967
$22$	15.1040	−	15.1040i	0.686547	−	0.686547i
$23$	−3.39116	−	3.39116i	−0.147442	−	0.147442i
$23$	−3.39116	−	3.39116i	−0.147442	−	0.147442i
$24$			4.89898i			0.204124i
$25$	22.1846	−	11.5257i	0.887386	−	0.461028i
$26$	−7.14227			−0.274703
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	−17.9981	−	17.9981i	−0.642790	−	0.642790i
$29$		−	7.64648i		−	0.263672i	−0.991272	−	0.131836i	$-0.957913\pi$
$29$		−	7.64648i		−	0.263672i	0.991272	−	0.131836i	$-0.0420872\pi$
$30$	11.8976	−	2.90621i	0.396588	−	0.0968737i
$31$	−55.4912			−1.79004			−0.895019	−	0.446028i	$-0.852838\pi$
$31$	−55.4912			−1.79004			−0.895019	+	0.446028i	$0.852838\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	−18.4986	−	18.4986i	−0.560563	−	0.560563i
$34$		−	15.6901i		−	0.461475i
$35$	−33.0332	+	54.3872i	−0.943805	+	1.55392i
$36$	6.00000			0.166667
$37$	24.3469	−	24.3469i	0.658024	−	0.658024i	−0.296888	−	0.954912i	$-0.595949\pi$
$37$	24.3469	−	24.3469i	0.658024	−	0.658024i	0.954912	+	0.296888i	$0.0959488\pi$
$38$	−2.57794	−	2.57794i	−0.0678404	−	0.0678404i
$39$			8.74746i			0.224294i
$40$	12.0873	+	7.34147i	0.302182	+	0.183537i
$41$	−8.82642			−0.215279			−0.107639	−	0.994190i	$-0.534329\pi$
$41$	−8.82642			−0.215279			−0.107639	+	0.994190i	$0.534329\pi$
$42$	−22.0431	+	22.0431i	−0.524836	+	0.524836i
$43$	−6.92644	−	6.92644i	−0.161080	−	0.161080i	0.621965	−	0.783045i	$-0.286335\pi$
$43$	−6.92644	−	6.92644i	−0.161080	−	0.161080i	−0.783045	+	0.621965i	$0.786335\pi$
$44$		−	30.2081i		−	0.686547i
$45$	−3.55937	−	14.5716i	−0.0790971	−	0.323813i
$46$	−6.78233			−0.147442
$47$	−45.3582	+	45.3582i	−0.965068	+	0.965068i	−0.999410	−	0.0343419i	$-0.989066\pi$
$47$	−45.3582	+	45.3582i	−0.965068	+	0.965068i	0.0343419	+	0.999410i	$0.489066\pi$
$48$	4.89898	+	4.89898i	0.102062	+	0.102062i
$49$		−	112.966i		−	2.30543i
$50$	10.6590	−	33.7103i	0.213179	−	0.674207i
$51$	−19.2164			−0.376792
$52$	−7.14227	+	7.14227i	−0.137351	+	0.137351i
$53$	−39.7281	−	39.7281i	−0.749586	−	0.749586i	0.224815	−	0.974401i	$-0.427822\pi$
$53$	−39.7281	−	39.7281i	−0.749586	−	0.749586i	−0.974401	+	0.224815i	$0.927822\pi$
$54$		−	7.34847i		−	0.136083i
$55$	−73.3632	+	17.9203i	−1.33388	+	0.325823i
$56$	−35.9962			−0.642790
$57$	−3.15731	+	3.15731i	−0.0553915	+	0.0553915i
$58$	−7.64648	−	7.64648i	−0.131836	−	0.131836i
$59$			80.7399i			1.36847i	0.729260	+	0.684236i	$0.239864\pi$
$59$			80.7399i			1.36847i	−0.729260	+	0.684236i	$0.760136\pi$
$60$	8.99143	−	14.8039i	0.149857	−	0.246731i
$61$	−74.8025			−1.22627			−0.613135	−	0.789978i	$-0.710092\pi$
$61$	−74.8025			−1.22627			−0.613135	+	0.789978i	$0.710092\pi$
$62$	−55.4912	+	55.4912i	−0.895019	+	0.895019i
$63$	26.9972	+	26.9972i	0.428527	+	0.428527i
$64$			8.00000i			0.125000i
$65$	21.5827	+	13.1087i	0.332042	+	0.201672i
$66$	−36.9972			−0.560563
$67$	92.9564	−	92.9564i	1.38741	−	1.38741i	0.556684	−	0.830724i	$-0.312073\pi$
$67$	92.9564	−	92.9564i	1.38741	−	1.38741i	0.830724	−	0.556684i	$-0.187927\pi$
$68$	−15.6901	−	15.6901i	−0.230737	−	0.230737i
$69$			8.30662i			0.120386i
$70$	21.3540	+	87.4203i	0.305057	+	1.24886i
$71$	−0.195500			−0.00275352			−0.00137676	−	0.999999i	$-0.500438\pi$
$71$	−0.195500			−0.00275352			−0.00137676	+	0.999999i	$0.500438\pi$
$72$	6.00000	−	6.00000i	0.0833333	−	0.0833333i
$73$	−49.4310	−	49.4310i	−0.677137	−	0.677137i	0.282214	−	0.959351i	$-0.408931\pi$
$73$	−49.4310	−	49.4310i	−0.677137	−	0.677137i	−0.959351	+	0.282214i	$0.908931\pi$
$74$		−	48.6938i		−	0.658024i
$75$	−41.2866	−	13.0545i	−0.550487	−	0.174060i
$76$	−5.15587			−0.0678404
$77$	135.922	−	135.922i	1.76522	−	1.76522i
$78$	8.74746	+	8.74746i	0.112147	+	0.112147i
$79$		−	41.8460i		−	0.529696i	−0.964290	−	0.264848i	$-0.914678\pi$
$79$		−	41.8460i		−	0.529696i	0.964290	−	0.264848i	$-0.0853218\pi$
$80$	19.4288	−	4.74582i	0.242860	−	0.0593228i
$81$	−9.00000			−0.111111
$82$	−8.82642	+	8.82642i	−0.107639	+	0.107639i
$83$	26.4027	+	26.4027i	0.318105	+	0.318105i	0.848039	−	0.529934i	$-0.177783\pi$
$83$	26.4027	+	26.4027i	0.318105	+	0.318105i	−0.529934	+	0.848039i	$0.677783\pi$
$84$			44.0862i			0.524836i
$85$	−28.7972	+	47.4128i	−0.338790	+	0.557798i
$86$	−13.8529			−0.161080
$87$	−9.36499	+	9.36499i	−0.107644	+	0.107644i
$88$	−30.2081	−	30.2081i	−0.343274	−	0.343274i
$89$		−	16.8125i		−	0.188904i	−0.995529	−	0.0944521i	$-0.969890\pi$
$89$		−	16.8125i		−	0.188904i	0.995529	−	0.0944521i	$-0.0301099\pi$
$90$	−18.1309	−	11.0122i	−0.201455	−	0.122358i
$91$	−64.2738			−0.706305
$92$	−6.78233	+	6.78233i	−0.0737210	+	0.0737210i
$93$	67.9625	+	67.9625i	0.730780	+	0.730780i
$94$			90.7164i			0.965068i
$95$	3.05861	+	12.5215i	0.0321959	+	0.131806i
$96$	9.79796			0.102062
$97$	−10.2900	+	10.2900i	−0.106083	+	0.106083i	−0.758156	−	0.652073i	$-0.773899\pi$
$97$	−10.2900	+	10.2900i	−0.106083	+	0.106083i	0.652073	+	0.758156i	$0.273899\pi$
$98$	−112.966	−	112.966i	−1.15272	−	1.15272i
$99$			45.3121i			0.457698i
$100$	−23.0514	−	44.3693i	−0.230514	−	0.443693i
$101$	95.5471			0.946010			0.473005	−	0.881060i	$-0.343169\pi$
$101$	95.5471			0.946010			0.473005	+	0.881060i	$0.343169\pi$
$102$	−19.2164	+	19.2164i	−0.188396	+	0.188396i
$103$	26.9441	+	26.9441i	0.261593	+	0.261593i	0.825701	−	0.564108i	$-0.190780\pi$
$103$	26.9441	+	26.9441i	0.261593	+	0.261593i	−0.564108	+	0.825701i	$0.690780\pi$
$104$			14.2845i			0.137351i
$105$	107.068	−	26.1532i	1.01969	−	0.249078i
$106$	−79.4562			−0.749586
$107$	111.163	−	111.163i	1.03891	−	1.03891i	0.0396962	−	0.999212i	$-0.487361\pi$
$107$	111.163	−	111.163i	1.03891	−	1.03891i	0.999212	−	0.0396962i	$-0.0126390\pi$
$108$	−7.34847	−	7.34847i	−0.0680414	−	0.0680414i
$109$			202.618i			1.85888i	0.368969	+	0.929442i	$0.379711\pi$
$109$			202.618i			1.85888i	−0.368969	+	0.929442i	$0.620289\pi$
$110$	−55.4429	+	91.2835i	−0.504027	+	0.829850i
$111$	−59.6375			−0.537275
$112$	−35.9962	+	35.9962i	−0.321395	+	0.321395i
$113$	91.9703	+	91.9703i	0.813896	+	0.813896i	0.985216	−	0.171319i	$-0.0548029\pi$
$113$	91.9703	+	91.9703i	0.813896	+	0.813896i	−0.171319	+	0.985216i	$0.554803\pi$
$114$			6.31463i			0.0553915i
$115$	20.4950	+	12.4481i	0.178217	+	0.108244i
$116$	−15.2930			−0.131836
$117$	10.7134	−	10.7134i	0.0915676	−	0.0915676i
$118$	80.7399	+	80.7399i	0.684236	+	0.684236i
$119$		−	141.196i		−	1.18653i
$120$	−5.81242	−	23.7953i	−0.0484369	−	0.198294i
$121$	107.132			0.885388
$122$	−74.8025	+	74.8025i	−0.613135	+	0.613135i
$123$	10.8101	+	10.8101i	0.0878871	+	0.0878871i
$124$			110.982i			0.895019i
$125$	−94.0804	+	82.3036i	−0.752643	+	0.658429i
$126$	53.9944			0.428527
$127$	−160.129	+	160.129i	−1.26086	+	1.26086i	−0.310186	+	0.950676i	$0.600391\pi$
$127$	−160.129	+	160.129i	−1.26086	+	1.26086i	−0.950676	+	0.310186i	$0.899609\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$			16.9662i			0.131521i
$130$	34.6914	−	8.47399i	0.266857	−	0.0651846i
$131$	198.335			1.51400			0.757002	−	0.653413i	$-0.226663\pi$
$131$	198.335			1.51400			0.757002	+	0.653413i	$0.226663\pi$
$132$	−36.9972	+	36.9972i	−0.280282	+	0.280282i
$133$	−23.1990	−	23.1990i	−0.174429	−	0.174429i
$134$		−	185.913i		−	1.38741i
$135$	−13.4871	+	22.2058i	−0.0999048	+	0.164487i
$136$	−31.3803			−0.230737
$137$	1.71018	−	1.71018i	0.0124831	−	0.0124831i	−0.700838	−	0.713321i	$-0.747190\pi$
$137$	1.71018	−	1.71018i	0.0124831	−	0.0124831i	0.713321	+	0.700838i	$0.247190\pi$
$138$	8.30662	+	8.30662i	0.0601929	+	0.0601929i
$139$		−	123.424i		−	0.887941i	−0.896041	−	0.443971i	$-0.853569\pi$
$139$		−	123.424i		−	0.887941i	0.896041	−	0.443971i	$-0.146431\pi$
$140$	108.774	+	66.0664i	0.776959	+	0.471903i
$141$	111.104			0.787975
$142$	−0.195500	+	0.195500i	−0.00137676	+	0.00137676i
$143$	−53.9386	−	53.9386i	−0.377193	−	0.377193i
$144$		−	12.0000i		−	0.0833333i
$145$	9.07221	+	37.1404i	0.0625670	+	0.256141i
$146$	−98.8620			−0.677137
$147$	−138.355	+	138.355i	−0.941189	+	0.941189i
$148$	−48.6938	−	48.6938i	−0.329012	−	0.329012i
$149$		−	153.773i		−	1.03203i	−0.856579	−	0.516015i	$-0.827415\pi$
$149$		−	153.773i		−	1.03203i	0.856579	−	0.516015i	$-0.172585\pi$
$150$	−54.3411	+	28.2321i	−0.362274	+	0.188214i
$151$	−91.8615			−0.608354			−0.304177	−	0.952615i	$-0.598381\pi$
$151$	−91.8615			−0.608354			−0.304177	+	0.952615i	$0.598381\pi$
$152$	−5.15587	+	5.15587i	−0.0339202	+	0.0339202i
$153$	23.5352	+	23.5352i	0.153825	+	0.153825i
$154$		−	271.844i		−	1.76522i
$155$	269.531	−	65.8378i	1.73891	−	0.424760i
$156$	17.4949			0.112147
$157$	157.053	−	157.053i	1.00034	−	1.00034i	0.000337781	−	1.00000i	$-0.499892\pi$
$157$	157.053	−	157.053i	1.00034	−	1.00034i	1.00000		0.000337781i	$-0.000107519\pi$
$158$	−41.8460	−	41.8460i	−0.264848	−	0.264848i
$159$			97.3135i			0.612035i
$160$	14.6829	−	24.1746i	0.0917684	−	0.151091i
$161$	−61.0346			−0.379097
$162$	−9.00000	+	9.00000i	−0.0555556	+	0.0555556i
$163$	−138.558	−	138.558i	−0.850052	−	0.850052i	0.140087	−	0.990139i	$-0.455262\pi$
$163$	−138.558	−	138.558i	−0.850052	−	0.850052i	−0.990139	+	0.140087i	$0.955262\pi$
$164$			17.6528i			0.107639i
$165$	111.799	+	67.9035i	0.677570	+	0.411536i
$166$	52.8055			0.318105
$167$	9.08055	−	9.08055i	0.0543746	−	0.0543746i	−0.679397	−	0.733771i	$-0.737758\pi$
$167$	9.08055	−	9.08055i	0.0543746	−	0.0543746i	0.733771	+	0.679397i	$0.237758\pi$
$168$	44.0862	+	44.0862i	0.262418	+	0.262418i
$169$		−	143.494i		−	0.849077i
$170$	18.6157	+	76.2100i	0.109504	+	0.448294i
$171$	7.73381			0.0452270
$172$	−13.8529	+	13.8529i	−0.0805400	+	0.0805400i
$173$	235.387	+	235.387i	1.36062	+	1.36062i	0.873126	+	0.487495i	$0.162089\pi$
$173$	235.387	+	235.387i	1.36062	+	1.36062i	0.487495	+	0.873126i	$0.337911\pi$
$174$			18.7300i			0.107644i
$175$	95.9206	−	303.361i	0.548118	−	1.73349i
$176$	−60.4161			−0.343274
$177$	98.8857	−	98.8857i	0.558677	−	0.558677i
$178$	−16.8125	−	16.8125i	−0.0944521	−	0.0944521i
$179$		−	46.2441i		−	0.258347i	−0.991622	−	0.129174i	$-0.958768\pi$
$179$		−	46.2441i		−	0.258347i	0.991622	−	0.129174i	$-0.0412324\pi$
$180$	−29.1432	+	7.11874i	−0.161906	+	0.0395485i
$181$	99.6130			0.550348			0.275174	−	0.961394i	$-0.411265\pi$
$181$	99.6130			0.550348			0.275174	+	0.961394i	$0.411265\pi$
$182$	−64.2738	+	64.2738i	−0.353153	+	0.353153i
$183$	91.6140	+	91.6140i	0.500623	+	0.500623i
$184$			13.5647i			0.0737210i
$185$	−89.3711	+	147.144i	−0.483087	+	0.795374i
$186$	135.925			0.730780
$187$	118.492	−	118.492i	0.633648	−	0.633648i
$188$	90.7164	+	90.7164i	0.482534	+	0.482534i
$189$		−	66.1293i		−	0.349891i
$190$	15.5801	+	9.46293i	0.0820008	+	0.0498049i
$191$	9.51368			0.0498099			0.0249049	−	0.999690i	$-0.492072\pi$
$191$	9.51368			0.0498099			0.0249049	+	0.999690i	$0.492072\pi$
$192$	9.79796	−	9.79796i	0.0510310	−	0.0510310i
$193$	52.7826	+	52.7826i	0.273485	+	0.273485i	0.830501	−	0.557016i	$-0.188054\pi$
$193$	52.7826	+	52.7826i	0.273485	+	0.273485i	−0.557016	+	0.830501i	$0.688054\pi$
$194$			20.5800i			0.106083i
$195$	−10.3785	−	42.4881i	−0.0532230	−	0.217888i
$196$	−225.932			−1.15272
$197$	−117.478	+	117.478i	−0.596335	+	0.596335i	−0.939335	−	0.343000i	$-0.888557\pi$
$197$	−117.478	+	117.478i	−0.596335	+	0.596335i	0.343000	+	0.939335i	$0.388557\pi$
$198$	45.3121	+	45.3121i	0.228849	+	0.228849i
$199$		−	336.042i		−	1.68866i	−0.535827	−	0.844328i	$-0.680000\pi$
$199$		−	336.042i		−	1.68866i	0.535827	−	0.844328i	$-0.320000\pi$
$200$	−67.4207	−	21.3179i	−0.337103	−	0.106590i
$201$	−227.696			−1.13281
$202$	95.5471	−	95.5471i	0.473005	−	0.473005i
$203$	−68.8111	−	68.8111i	−0.338971	−	0.338971i
$204$			38.4328i			0.188396i
$205$	42.8716	−	10.4722i	0.209130	−	0.0510837i
$206$	53.8882			0.261593
$207$	10.1735	−	10.1735i	0.0491473	−	0.0491473i
$208$	14.2845	+	14.2845i	0.0686757	+	0.0686757i
$209$		−	38.9372i		−	0.186303i
$210$	80.9144	−	133.221i	0.385307	−	0.634385i
$211$	23.3753			0.110783			0.0553917	−	0.998465i	$-0.482359\pi$
$211$	23.3753			0.110783			0.0553917	+	0.998465i	$0.482359\pi$
$212$	−79.4562	+	79.4562i	−0.374793	+	0.374793i
$213$	0.239438	+	0.239438i	0.00112412	+	0.00112412i
$214$		−	222.326i		−	1.03891i
$215$	41.8610	+	25.4251i	0.194702	+	0.118256i
$216$	−14.6969			−0.0680414
$217$	−499.369	+	499.369i	−2.30124	+	2.30124i
$218$	202.618	+	202.618i	0.929442	+	0.929442i
$219$			121.081i			0.552880i
$220$	35.8405	+	146.726i	0.162912	+	0.666938i
$221$	−56.0316			−0.253537
$222$	−59.6375	+	59.6375i	−0.268637	+	0.268637i
$223$	247.932	+	247.932i	1.11180	+	1.11180i	0.992907	+	0.118897i	$0.0379359\pi$
$223$	247.932	+	247.932i	1.11180	+	1.11180i	0.118897	+	0.992907i	$0.462064\pi$
$224$			71.9925i			0.321395i
$225$	34.5771	+	66.5539i	0.153676	+	0.295795i
$226$	183.941			0.813896
$227$	−52.1924	+	52.1924i	−0.229922	+	0.229922i	−0.812660	−	0.582738i	$-0.801981\pi$
$227$	−52.1924	+	52.1924i	−0.229922	+	0.229922i	0.582738	+	0.812660i	$0.301981\pi$
$228$	6.31463	+	6.31463i	0.0276957	+	0.0276957i
$229$		−	46.6243i		−	0.203600i	−0.994805	−	0.101800i	$-0.967540\pi$
$229$		−	46.6243i		−	0.203600i	0.994805	−	0.101800i	$-0.0324601\pi$
$230$	32.9431	−	8.04694i	0.143231	−	0.0349867i
$231$	−332.940			−1.44130
$232$	−15.2930	+	15.2930i	−0.0659179	+	0.0659179i
$233$	76.6909	+	76.6909i	0.329146	+	0.329146i	0.852262	−	0.523116i	$-0.175231\pi$
$233$	76.6909	+	76.6909i	0.329146	+	0.329146i	−0.523116	+	0.852262i	$0.675231\pi$
$234$		−	21.4268i		−	0.0915676i
$235$	166.498	−	274.129i	0.708502	−	1.16651i
$236$	161.480			0.684236
$237$	−51.2507	+	51.2507i	−0.216248	+	0.216248i
$238$	−141.196	−	141.196i	−0.593263	−	0.593263i
$239$			23.8390i			0.0997449i	0.998756	+	0.0498725i	$0.0158815\pi$
$239$			23.8390i			0.0997449i	−0.998756	+	0.0498725i	$0.984119\pi$
$240$	−29.6077	−	17.9829i	−0.123365	−	0.0749286i
$241$	179.664			0.745495			0.372748	−	0.927933i	$-0.378416\pi$
$241$	179.664			0.745495			0.372748	+	0.927933i	$0.378416\pi$
$242$	107.132	−	107.132i	0.442694	−	0.442694i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$			149.605i			0.613135i
$245$	134.029	+	548.699i	0.547059	+	2.23959i
$246$	21.6202			0.0878871
$247$	−9.20616	+	9.20616i	−0.0372719	+	0.0372719i
$248$	110.982	+	110.982i	0.447510	+	0.447510i
$249$		−	64.6732i		−	0.259732i
$250$	−11.7768	+	176.384i	−0.0471070	+	0.705536i
$251$	−189.607			−0.755405			−0.377702	−	0.925927i	$-0.623286\pi$
$251$	−189.607			−0.755405			−0.377702	+	0.925927i	$0.623286\pi$
$252$	53.9944	−	53.9944i	0.214263	−	0.214263i
$253$	−51.2203	−	51.2203i	−0.202452	−	0.202452i
$254$			320.259i			1.26086i
$255$	93.3378	−	22.7994i	0.366031	−	0.0894095i
$256$	16.0000			0.0625000
$257$	149.850	−	149.850i	0.583072	−	0.583072i	−0.352674	−	0.935746i	$-0.614727\pi$
$257$	149.850	−	149.850i	0.583072	−	0.583072i	0.935746	+	0.352674i	$0.114727\pi$
$258$	16.9662	+	16.9662i	0.0657606	+	0.0657606i
$259$		−	438.198i		−	1.69189i
$260$	26.2174	−	43.1654i	0.100836	−	0.166021i
$261$	22.9394			0.0878906
$262$	198.335	−	198.335i	0.757002	−	0.757002i
$263$	234.599	+	234.599i	0.892010	+	0.892010i	0.994712	−	0.102702i	$-0.0327487\pi$
$263$	234.599	+	234.599i	0.892010	+	0.892010i	−0.102702	+	0.994712i	$0.532749\pi$
$264$			73.9944i			0.280282i
$265$	240.103	+	145.831i	0.906047	+	0.550307i
$266$	−46.3980			−0.174429
$267$	−20.5910	+	20.5910i	−0.0771198	+	0.0771198i
$268$	−185.913	−	185.913i	−0.693704	−	0.693704i
$269$			139.224i			0.517563i	0.965936	+	0.258782i	$0.0833210\pi$
$269$			139.224i			0.517563i	−0.965936	+	0.258782i	$0.916679\pi$
$270$	8.71864	+	35.6929i	0.0322912	+	0.132196i
$271$	−229.539			−0.847008			−0.423504	−	0.905894i	$-0.639200\pi$
$271$	−229.539			−0.847008			−0.423504	+	0.905894i	$0.639200\pi$
$272$	−31.3803	+	31.3803i	−0.115369	+	0.115369i
$273$	78.7190	+	78.7190i	0.288348	+	0.288348i
$274$		−	3.42037i		−	0.0124831i
$275$	335.078	−	174.084i	1.21846	−	0.633034i
$276$	16.6132			0.0601929
$277$	12.8688	−	12.8688i	0.0464578	−	0.0464578i	−0.683496	−	0.729954i	$-0.739541\pi$
$277$	12.8688	−	12.8688i	0.0464578	−	0.0464578i	0.729954	+	0.683496i	$0.239541\pi$
$278$	−123.424	−	123.424i	−0.443971	−	0.443971i
$279$		−	166.474i		−	0.596679i
$280$	174.841	−	42.7080i	0.624431	−	0.152528i
$281$	−363.206			−1.29255			−0.646274	−	0.763106i	$-0.723674\pi$
$281$	−363.206			−1.29255			−0.646274	+	0.763106i	$0.723674\pi$
$282$	111.104	−	111.104i	0.393987	−	0.393987i
$283$	369.525	+	369.525i	1.30574	+	1.30574i	0.924459	+	0.381282i	$0.124517\pi$
$283$	369.525	+	369.525i	1.30574	+	1.30574i	0.381282	+	0.924459i	$0.375483\pi$
$284$			0.391000i			0.00137676i
$285$	11.5897	−	19.0817i	0.0406655	−	0.0669533i
$286$	−107.877			−0.377193
$287$	−79.4295	+	79.4295i	−0.276758	+	0.276758i
$288$	−12.0000	−	12.0000i	−0.0416667	−	0.0416667i
$289$			165.910i			0.574082i
$290$	46.2126	+	28.0682i	0.159354	+	0.0967869i
$291$	25.2053			0.0866161
$292$	−98.8620	+	98.8620i	−0.338569	+	0.338569i
$293$	140.958	+	140.958i	0.481085	+	0.481085i	0.905478	−	0.424393i	$-0.139512\pi$
$293$	140.958	+	140.958i	0.481085	+	0.481085i	−0.424393	+	0.905478i	$0.639512\pi$
$294$			276.710i			0.941189i
$295$	−95.7943	−	392.169i	−0.324726	−	1.32939i
$296$	−97.3876			−0.329012
$297$	55.4958	−	55.4958i	0.186854	−	0.186854i
$298$	−153.773	−	153.773i	−0.516015	−	0.516015i
$299$			24.2206i			0.0810055i
$300$	−26.1090	+	82.5731i	−0.0870300	+	0.275244i
$301$	−124.663			−0.414162
$302$	−91.8615	+	91.8615i	−0.304177	+	0.304177i
$303$	−117.021	−	117.021i	−0.386207	−	0.386207i
$304$			10.3117i			0.0339202i
$305$	363.330	−	88.7499i	1.19125	−	0.290983i
$306$	47.0704			0.153825
$307$	173.192	−	173.192i	0.564145	−	0.564145i	−0.366337	−	0.930482i	$-0.619388\pi$
$307$	173.192	−	173.192i	0.564145	−	0.564145i	0.930482	+	0.366337i	$0.119388\pi$
$308$	−271.844	−	271.844i	−0.882611	−	0.882611i
$309$		−	65.9993i		−	0.213590i
$310$	203.694	−	335.369i	0.657076	−	1.08184i
$311$	−46.2731			−0.148788			−0.0743941	−	0.997229i	$-0.523702\pi$
$311$	−46.2731			−0.148788			−0.0743941	+	0.997229i	$0.523702\pi$
$312$	17.4949	−	17.4949i	0.0560735	−	0.0560735i
$313$	−205.897	−	205.897i	−0.657817	−	0.657817i	0.297046	−	0.954863i	$-0.403999\pi$
$313$	−205.897	−	205.897i	−0.657817	−	0.657817i	−0.954863	+	0.297046i	$0.903999\pi$
$314$		−	314.106i		−	1.00034i
$315$	−163.161	−	99.0995i	−0.517973	−	0.314602i
$316$	−83.6920			−0.264848
$317$	276.139	−	276.139i	0.871100	−	0.871100i	−0.121492	−	0.992592i	$-0.538768\pi$
$317$	276.139	−	276.139i	0.871100	−	0.871100i	0.992592	+	0.121492i	$0.0387680\pi$
$318$	97.3135	+	97.3135i	0.306017	+	0.306017i
$319$		−	115.493i		−	0.362046i
$320$	−9.49165	−	38.8575i	−0.0296614	−	0.121430i
$321$	−272.293			−0.848265
$322$	−61.0346	+	61.0346i	−0.189548	+	0.189548i
$323$	−20.2241	−	20.2241i	−0.0626133	−	0.0626133i
$324$			18.0000i			0.0555556i
$325$	−120.384	−	38.0646i	−0.370413	−	0.117122i
$326$	−277.117			−0.850052
$327$	248.156	−	248.156i	0.758886	−	0.758886i
$328$	17.6528	+	17.6528i	0.0538197	+	0.0538197i
$329$			816.363i			2.48135i
$330$	179.702	−	43.8955i	0.544553	−	0.133017i
$331$	6.88214			0.0207920			0.0103960	−	0.999946i	$-0.496691\pi$
$331$	6.88214			0.0207920			0.0103960	+	0.999946i	$0.496691\pi$
$332$	52.8055	−	52.8055i	0.159053	−	0.159053i
$333$	73.0407	+	73.0407i	0.219341	+	0.219341i
$334$		−	18.1611i		−	0.0543746i
$335$	−341.218	+	561.796i	−1.01856	+	1.67700i
$336$	88.1724			0.262418
$337$	−128.298	+	128.298i	−0.380706	+	0.380706i	−0.871356	−	0.490650i	$-0.836759\pi$
$337$	−128.298	+	128.298i	−0.380706	+	0.380706i	0.490650	+	0.871356i	$0.336759\pi$
$338$	−143.494	−	143.494i	−0.424538	−	0.424538i
$339$		−	225.280i		−	0.664544i
$340$	94.8257	+	57.5944i	0.278899	+	0.169395i
$341$	−838.141			−2.45789
$342$	7.73381	−	7.73381i	0.0226135	−	0.0226135i
$343$	−575.636	−	575.636i	−1.67824	−	1.67824i
$344$			27.7057i			0.0805400i
$345$	−9.85544	−	40.3469i	−0.0285665	−	0.116947i
$346$	470.775			1.36062
$347$	348.345	−	348.345i	1.00388	−	1.00388i	0.00388312	−	0.999992i	$-0.498764\pi$
$347$	348.345	−	348.345i	1.00388	−	1.00388i	0.999992	−	0.00388312i	$-0.00123604\pi$
$348$	18.7300	+	18.7300i	0.0538218	+	0.0538218i
$349$			143.961i			0.412497i	0.978500	+	0.206248i	$0.0661255\pi$
$349$			143.961i			0.412497i	−0.978500	+	0.206248i	$0.933875\pi$
$350$	−207.441	−	399.282i	−0.592688	−	1.14081i
$351$	−26.2424			−0.0747646
$352$	−60.4161	+	60.4161i	−0.171637	+	0.171637i
$353$	−468.876	−	468.876i	−1.32826	−	1.32826i	−0.906886	−	0.421375i	$-0.861547\pi$
$353$	−468.876	−	468.876i	−1.32826	−	1.32826i	−0.421375	−	0.906886i	$-0.638453\pi$
$354$		−	197.771i		−	0.558677i
$355$	0.949582	−	0.231952i	0.00267488	−	0.000653387i
$356$	−33.6249			−0.0944521
$357$	−172.930	+	172.930i	−0.484397	+	0.484397i
$358$	−46.2441	−	46.2441i	−0.129174	−	0.129174i
$359$		−	120.098i		−	0.334536i	−0.985911	−	0.167268i	$-0.946505\pi$
$359$		−	120.098i		−	0.334536i	0.985911	−	0.167268i	$-0.0534945\pi$
$360$	−22.0244	+	36.2619i	−0.0611789	+	0.100727i
$361$	354.354			0.981591
$362$	99.6130	−	99.6130i	0.275174	−	0.275174i
$363$	−131.209	−	131.209i	−0.361458	−	0.361458i
$364$			128.548i			0.353153i
$365$	298.744	+	181.448i	0.818476	+	0.497118i
$366$	183.228			0.500623
$367$	−167.307	+	167.307i	−0.455876	+	0.455876i	−0.897299	−	0.441423i	$-0.854474\pi$
$367$	−167.307	+	167.307i	−0.455876	+	0.455876i	0.441423	+	0.897299i	$0.354474\pi$
$368$	13.5647	+	13.5647i	0.0368605	+	0.0368605i
$369$		−	26.4793i		−	0.0717595i
$370$	57.7730	+	236.515i	0.156143	+	0.639230i
$371$	−715.031			−1.92731
$372$	135.925	−	135.925i	0.365390	−	0.365390i
$373$	426.569	+	426.569i	1.14362	+	1.14362i	0.987783	+	0.155834i	$0.0498066\pi$
$373$	426.569	+	426.569i	1.14362	+	1.14362i	0.155834	+	0.987783i	$0.450193\pi$
$374$		−	236.984i		−	0.633648i
$375$	216.025	+	14.4235i	0.576068	+	0.0384627i
$376$	181.433			0.482534
$377$	−27.3066	+	27.3066i	−0.0724314	+	0.0724314i
$378$	−66.1293	−	66.1293i	−0.174945	−	0.174945i
$379$			218.341i			0.576097i	0.957616	+	0.288049i	$0.0930065\pi$
$379$			218.341i			0.576097i	−0.957616	+	0.288049i	$0.906994\pi$
$380$	25.0431	−	6.11722i	0.0659028	−	0.0160979i
$381$	392.235			1.02949
$382$	9.51368	−	9.51368i	0.0249049	−	0.0249049i
$383$	455.658	+	455.658i	1.18971	+	1.18971i	0.977148	+	0.212559i	$0.0681797\pi$
$383$	455.658	+	455.658i	1.18971	+	1.18971i	0.212559	+	0.977148i	$0.431820\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	−498.934	+	821.466i	−1.29593	+	2.13368i
$386$	105.565			0.273485
$387$	20.7793	−	20.7793i	0.0536933	−	0.0536933i
$388$	20.5800	+	20.5800i	0.0530413	+	0.0530413i
$389$		−	300.379i		−	0.772183i	−0.922460	−	0.386092i	$-0.873825\pi$
$389$		−	300.379i		−	0.772183i	0.922460	−	0.386092i	$-0.126175\pi$
$390$	−52.8666	−	32.1096i	−0.135555	−	0.0823324i
$391$	−53.2078			−0.136081
$392$	−225.932	+	225.932i	−0.576358	+	0.576358i
$393$	−242.909	−	242.909i	−0.618090	−	0.618090i
$394$			234.956i			0.596335i
$395$	49.6484	+	203.254i	0.125692	+	0.514567i
$396$	90.6242			0.228849
$397$	−397.353	+	397.353i	−1.00089	+	1.00089i	−0.000889374		1.00000i	$0.500283\pi$
$397$	−397.353	+	397.353i	−1.00089	+	1.00089i	−1.00000		0.000889374i	$0.999717\pi$
$398$	−336.042	−	336.042i	−0.844328	−	0.844328i
$399$			56.8257i			0.142420i
$400$	−88.7386	+	46.1028i	−0.221846	+	0.115257i
$401$	328.148			0.818325			0.409163	−	0.912461i	$-0.365821\pi$
$401$	328.148			0.818325			0.409163	+	0.912461i	$0.365821\pi$
$402$	−227.696	+	227.696i	−0.566407	+	0.566407i
$403$	198.167	+	198.167i	0.491729	+	0.491729i
$404$		−	191.094i		−	0.473005i
$405$	43.7147	−	10.6781i	0.107938	−	0.0263657i
$406$	−137.622			−0.338971
$407$	367.736	−	367.736i	0.903529	−	0.903529i
$408$	38.4328	+	38.4328i	0.0941981	+	0.0941981i
$409$		−	526.651i		−	1.28766i	−0.765171	−	0.643828i	$-0.777345\pi$
$409$		−	526.651i		−	1.28766i	0.765171	−	0.643828i	$-0.222655\pi$
$410$	32.3995	−	53.3438i	0.0790231	−	0.130107i
$411$	−4.18908			−0.0101924
$412$	53.8882	−	53.8882i	0.130797	−	0.130797i
$413$	726.583	+	726.583i	1.75928	+	1.75928i
$414$		−	20.3470i		−	0.0491473i
$415$	−159.569	−	96.9175i	−0.384503	−	0.233536i
$416$	28.5691			0.0686757
$417$	−151.163	+	151.163i	−0.362501	+	0.362501i
$418$	−38.9372	−	38.9372i	−0.0931513	−	0.0931513i
$419$			17.1539i			0.0409400i	0.999790	+	0.0204700i	$0.00651626\pi$
$419$			17.1539i			0.0409400i	−0.999790	+	0.0204700i	$0.993484\pi$
$420$	−52.3064	−	214.135i	−0.124539	−	0.509846i
$421$	769.518			1.82783			0.913917	−	0.405900i	$-0.133042\pi$
$421$	769.518			1.82783			0.913917	+	0.405900i	$0.133042\pi$
$422$	23.3753	−	23.3753i	0.0553917	−	0.0553917i
$423$	−136.075	−	136.075i	−0.321689	−	0.321689i
$424$			158.912i			0.374793i
$425$	83.6202	−	264.460i	0.196753	−	0.622259i
$426$	0.478876			0.00112412
$427$	−673.152	+	673.152i	−1.57647	+	1.57647i
$428$	−222.326	−	222.326i	−0.519454	−	0.519454i
$429$			132.122i			0.307977i
$430$	67.2861	−	16.4358i	0.156479	−	0.0382228i
$431$	−292.091			−0.677706			−0.338853	−	0.940839i	$-0.610039\pi$
$431$	−292.091			−0.677706			−0.338853	+	0.940839i	$0.610039\pi$
$432$	−14.6969	+	14.6969i	−0.0340207	+	0.0340207i
$433$	−170.944	−	170.944i	−0.394790	−	0.394790i	0.481601	−	0.876391i	$-0.340056\pi$
$433$	−170.944	−	170.944i	−0.394790	−	0.394790i	−0.876391	+	0.481601i	$0.840056\pi$
$434$			998.737i			2.30124i
$435$	34.3764	−	56.5987i	0.0790262	−	0.130112i
$436$	405.237			0.929442
$437$	−8.74221	+	8.74221i	−0.0200051	+	0.0200051i
$438$	121.081	+	121.081i	0.276440	+	0.276440i
$439$		−	382.734i		−	0.871832i	−0.899987	−	0.435916i	$-0.856425\pi$
$439$		−	382.734i		−	0.871832i	0.899987	−	0.435916i	$-0.143575\pi$
$440$	182.567	+	110.886i	0.414925	+	0.252013i
$441$	338.899			0.768477
$442$	−56.0316	+	56.0316i	−0.126768	+	0.126768i
$443$	58.5707	+	58.5707i	0.132214	+	0.132214i	0.770117	−	0.637903i	$-0.220198\pi$
$443$	58.5707	+	58.5707i	0.132214	+	0.132214i	−0.637903	+	0.770117i	$0.720198\pi$
$444$			119.275i			0.268637i
$445$	19.9473	+	81.6614i	0.0448253	+	0.183509i
$446$	495.864			1.11180
$447$	−188.332	+	188.332i	−0.421325	+	0.421325i
$448$	71.9925	+	71.9925i	0.160698	+	0.160698i
$449$			268.969i			0.599040i	0.954090	+	0.299520i	$0.0968265\pi$
$449$			268.969i			0.599040i	−0.954090	+	0.299520i	$0.903174\pi$
$450$	101.131	+	31.9769i	0.224736	+	0.0710597i
$451$	−133.315			−0.295598
$452$	183.941	−	183.941i	0.406948	−	0.406948i
$453$	112.507	+	112.507i	0.248360	+	0.248360i
$454$			104.385i			0.229922i
$455$	312.190	−	76.2580i	0.686132	−	0.167600i
$456$	12.6293			0.0276957
$457$	−249.660	+	249.660i	−0.546301	+	0.546301i	−0.925369	−	0.379068i	$-0.876245\pi$
$457$	−249.660	+	249.660i	−0.546301	+	0.546301i	0.379068	+	0.925369i	$0.376245\pi$
$458$	−46.6243	−	46.6243i	−0.101800	−	0.101800i
$459$		−	57.6492i		−	0.125597i
$460$	24.8961	−	40.9900i	0.0541221	−	0.0891087i
$461$	−319.741			−0.693582			−0.346791	−	0.937942i	$-0.612729\pi$
$461$	−319.741			−0.693582			−0.346791	+	0.937942i	$0.612729\pi$
$462$	−332.940	+	332.940i	−0.720649	+	0.720649i
$463$	147.161	+	147.161i	0.317842	+	0.317842i	0.847938	−	0.530096i	$-0.177844\pi$
$463$	147.161	+	147.161i	0.317842	+	0.317842i	−0.530096	+	0.847938i	$0.677844\pi$
$464$			30.5859i			0.0659179i
$465$	−410.742	−	249.473i	−0.883316	−	0.536500i
$466$	153.382			0.329146
$467$	−604.325	+	604.325i	−1.29406	+	1.29406i	−0.361805	+	0.932254i	$0.617839\pi$
$467$	−604.325	+	604.325i	−1.29406	+	1.29406i	−0.932254	+	0.361805i	$0.882161\pi$
$468$	−21.4268	−	21.4268i	−0.0457838	−	0.0457838i
$469$		−	1673.04i		−	3.56725i
$470$	−107.631	−	440.627i	−0.229002	−	0.937505i
$471$	−384.700			−0.816772
$472$	161.480	−	161.480i	0.342118	−	0.342118i
$473$	−104.617	−	104.617i	−0.221178	−	0.221178i
$474$			102.501i			0.216248i
$475$	−29.7125	−	57.1906i	−0.0625526	−	0.120401i
$476$	−282.393			−0.593263
$477$	119.184	−	119.184i	0.249862	−	0.249862i
$478$	23.8390	+	23.8390i	0.0498725	+	0.0498725i
$479$			838.912i			1.75138i	0.482872	+	0.875691i	$0.339594\pi$
$479$			838.912i			1.75138i	−0.482872	+	0.875691i	$0.660406\pi$
$480$	−47.5906	+	11.6248i	−0.0991470	+	0.0242184i
$481$	−173.892			−0.361522
$482$	179.664	−	179.664i	0.372748	−	0.372748i
$483$	74.7518	+	74.7518i	0.154766	+	0.154766i
$484$		−	214.264i		−	0.442694i
$485$	37.7720	−	62.1893i	0.0778803	−	0.128225i
$486$	22.0454			0.0453609
$487$	416.968	−	416.968i	0.856197	−	0.856197i	−0.134690	−	0.990888i	$-0.543004\pi$
$487$	416.968	−	416.968i	0.856197	−	0.856197i	0.990888	+	0.134690i	$0.0430040\pi$
$488$	149.605	+	149.605i	0.306568	+	0.306568i
$489$			339.398i			0.694064i
$490$	682.728	+	414.669i	1.39332	+	0.846264i
$491$	−677.675			−1.38019			−0.690096	−	0.723718i	$-0.742432\pi$
$491$	−677.675			−1.38019			−0.690096	+	0.723718i	$0.742432\pi$
$492$	21.6202	−	21.6202i	0.0439436	−	0.0439436i
$493$	−59.9871	−	59.9871i	−0.121678	−	0.121678i
$494$			18.4123i			0.0372719i
$495$	−53.7608	−	220.090i	−0.108608	−	0.444626i
$496$	221.965			0.447510
$497$	−1.75932	+	1.75932i	−0.00353988	+	0.00353988i
$498$	−64.6732	−	64.6732i	−0.129866	−	0.129866i
$499$		−	649.807i		−	1.30222i	−0.758984	−	0.651110i	$-0.774304\pi$
$499$		−	649.807i		−	1.30222i	0.758984	−	0.651110i	$-0.225696\pi$
$500$	164.607	+	188.161i	0.329214	+	0.376321i
$501$	−22.2427			−0.0443966
$502$	−189.607	+	189.607i	−0.377702	+	0.377702i
$503$	−114.648	−	114.648i	−0.227928	−	0.227928i	0.583899	−	0.811827i	$-0.301527\pi$
$503$	−114.648	−	114.648i	−0.227928	−	0.227928i	−0.811827	+	0.583899i	$0.801527\pi$
$504$		−	107.989i		−	0.214263i
$505$	−464.090	+	113.362i	−0.918991	+	0.224480i
$506$	−102.441			−0.202452
$507$	−175.743	+	175.743i	−0.346634	+	0.346634i
$508$	320.259	+	320.259i	0.630431	+	0.630431i
$509$		−	291.723i		−	0.573129i	−0.958061	−	0.286564i	$-0.907487\pi$
$509$		−	291.723i		−	0.573129i	0.958061	−	0.286564i	$-0.0925133\pi$
$510$	70.5384	−	116.137i	0.138311	−	0.227720i
$511$	−889.665			−1.74103
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	−9.47194	−	9.47194i	−0.0184638	−	0.0184638i
$514$		−	299.699i		−	0.583072i
$515$	−162.841	−	98.9046i	−0.316195	−	0.192048i
$516$	33.9325			0.0657606
$517$	−685.092	+	685.092i	−1.32513	+	1.32513i
$518$	−438.198	−	438.198i	−0.845943	−	0.845943i
$519$		−	576.579i		−	1.11094i
$520$	−16.9480	−	69.3828i	−0.0325923	−	0.133428i
$521$	30.7577			0.0590358			0.0295179	−	0.999564i	$-0.490603\pi$
$521$	30.7577			0.0590358			0.0295179	+	0.999564i	$0.490603\pi$
$522$	22.9394	−	22.9394i	0.0439453	−	0.0439453i
$523$	−151.008	−	151.008i	−0.288734	−	0.288734i	0.547845	−	0.836580i	$-0.315448\pi$
$523$	−151.008	−	151.008i	−0.288734	−	0.288734i	−0.836580	+	0.547845i	$0.815448\pi$
$524$		−	396.669i		−	0.757002i
$525$	−489.018	+	254.062i	−0.931464	+	0.483928i
$526$	469.197			0.892010
$527$	−435.332	+	435.332i	−0.826057	+	0.826057i
$528$	73.9944	+	73.9944i	0.140141	+	0.140141i
$529$			23.0000i			0.0434783i
$530$	385.934	−	94.2712i	0.728177	−	0.177870i
$531$	−242.220			−0.456157
$532$	−46.3980	+	46.3980i	−0.0872143	+	0.0872143i
$533$	31.5204	+	31.5204i	0.0591376	+	0.0591376i
$534$			41.1820i			0.0771198i
$535$	−408.051	+	671.831i	−0.762712	+	1.25576i
$536$	−371.825			−0.693704
$537$	−56.6373	+	56.6373i	−0.105470	+	0.105470i
$538$	139.224	+	139.224i	0.258782	+	0.258782i
$539$		−	1706.25i		−	3.16558i
$540$	44.4116	+	26.9743i	0.0822436	+	0.0499524i
$541$	29.6112			0.0547342			0.0273671	−	0.999625i	$-0.491288\pi$
$541$	29.6112			0.0547342			0.0273671	+	0.999625i	$0.491288\pi$
$542$	−229.539	+	229.539i	−0.423504	+	0.423504i
$543$	−122.000	−	122.000i	−0.224679	−	0.224679i
$544$			62.7605i			0.115369i
$545$	−240.398	−	984.156i	−0.441097	−	1.80579i
$546$	157.438			0.288348
$547$	479.020	−	479.020i	0.875722	−	0.875722i	−0.117367	−	0.993089i	$-0.537445\pi$
$547$	479.020	−	479.020i	0.875722	−	0.875722i	0.993089	+	0.117367i	$0.0374452\pi$
$548$	−3.42037	−	3.42037i	−0.00624155	−	0.00624155i
$549$		−	224.408i		−	0.408757i
$550$	160.993	−	509.162i	0.292715	−	0.925749i
$551$	−19.7121			−0.0357752
$552$	16.6132	−	16.6132i	0.0300965	−	0.0300965i
$553$	−376.575	−	376.575i	−0.680967	−	0.680967i
$554$		−	25.7376i		−	0.0464578i
$555$	289.671	−	70.7572i	0.521929	−	0.127491i
$556$	−246.848			−0.443971
$557$	96.8915	−	96.8915i	0.173953	−	0.173953i	−0.614761	−	0.788713i	$-0.710748\pi$
$557$	96.8915	−	96.8915i	0.173953	−	0.173953i	0.788713	+	0.614761i	$0.210748\pi$
$558$	−166.474	−	166.474i	−0.298340	−	0.298340i
$559$			49.4705i			0.0884982i
$560$	132.133	−	217.549i	0.235951	−	0.388480i
$561$	−290.245			−0.517371
$562$	−363.206	+	363.206i	−0.646274	+	0.646274i
$563$	−767.945	−	767.945i	−1.36402	−	1.36402i	−0.868720	−	0.495303i	$-0.835057\pi$
$563$	−767.945	−	767.945i	−1.36402	−	1.36402i	−0.495303	−	0.868720i	$-0.664943\pi$
$564$		−	222.209i		−	0.393987i
$565$	−555.836	−	337.599i	−0.983781	−	0.597520i
$566$	739.049			1.30574
$567$	−80.9915	+	80.9915i	−0.142842	+	0.142842i
$568$	0.391000	+	0.391000i	0.000688381	+	0.000688381i
$569$		−	303.801i		−	0.533921i	−0.963707	−	0.266961i	$-0.913981\pi$
$569$		−	303.801i		−	0.533921i	0.963707	−	0.266961i	$-0.0860194\pi$
$570$	−7.49203	−	30.6714i	−0.0131439	−	0.0538094i
$571$	368.780			0.645850			0.322925	−	0.946425i	$-0.395334\pi$
$571$	368.780			0.645850			0.322925	+	0.946425i	$0.395334\pi$
$572$	−107.877	+	107.877i	−0.188596	+	0.188596i
$573$	−11.6518	−	11.6518i	−0.0203348	−	0.0203348i
$574$			158.859i			0.276758i
$575$	−114.317	−	36.1463i	−0.198813	−	0.0628631i
$576$	−24.0000			−0.0416667
$577$	−490.739	+	490.739i	−0.850501	+	0.850501i	−0.990195	−	0.139694i	$-0.955388\pi$
$577$	−490.739	+	490.739i	−0.850501	+	0.850501i	0.139694	+	0.990195i	$0.455388\pi$
$578$	165.910	+	165.910i	0.287041	+	0.287041i
$579$		−	129.290i		−	0.223300i
$580$	74.2808	−	18.1444i	0.128070	−	0.0312835i
$581$	475.200			0.817900
$582$	25.2053	−	25.2053i	0.0433081	−	0.0433081i
$583$	−600.054	−	600.054i	−1.02925	−	1.02925i
$584$			197.724i			0.338569i
$585$	−39.3261	+	64.7481i	−0.0672241	+	0.110681i
$586$	281.916			0.481085
$587$	374.363	−	374.363i	0.637757	−	0.637757i	−0.312245	−	0.950002i	$-0.601081\pi$
$587$	374.363	−	374.363i	0.637757	−	0.637757i	0.950002	+	0.312245i	$0.101081\pi$
$588$	276.710	+	276.710i	0.470594	+	0.470594i
$589$			143.053i			0.242874i
$590$	−487.963	−	296.375i	−0.827057	−	0.502330i
$591$	287.761			0.486905
$592$	−97.3876	+	97.3876i	−0.164506	+	0.164506i
$593$	593.763	+	593.763i	1.00129	+	1.00129i	0.999999	+	0.00128752i	$0.000409830\pi$
$593$	593.763	+	593.763i	1.00129	+	1.00129i	0.00128752	+	0.999999i	$0.499590\pi$
$594$		−	110.992i		−	0.186854i
$595$	167.523	+	685.819i	0.281552	+	1.15264i
$596$	−307.545			−0.516015
$597$	−411.566	+	411.566i	−0.689391	+	0.689391i
$598$	24.2206	+	24.2206i	0.0405027	+	0.0405027i
$599$			24.8982i			0.0415663i	0.999784	+	0.0207831i	$0.00661595\pi$
$599$			24.8982i			0.0415663i	−0.999784	+	0.0207831i	$0.993384\pi$
$600$	56.4641	+	108.682i	0.0941069	+	0.181137i
$601$	1067.99			1.77702			0.888511	−	0.458855i	$-0.151740\pi$
$601$	1067.99			1.77702			0.888511	+	0.458855i	$0.151740\pi$
$602$	−124.663	+	124.663i	−0.207081	+	0.207081i
$603$	278.869	+	278.869i	0.462469	+	0.462469i
$604$			183.723i			0.304177i
$605$	−520.360	+	127.107i	−0.860100	+	0.210095i
$606$	−234.042			−0.386207
$607$	690.397	−	690.397i	1.13739	−	1.13739i	0.148477	−	0.988916i	$-0.452563\pi$
$607$	690.397	−	690.397i	1.13739	−	1.13739i	0.988916	−	0.148477i	$-0.0474371\pi$
$608$	10.3117	+	10.3117i	0.0169601	+	0.0169601i
$609$			168.552i			0.276769i
$610$	274.580	−	452.080i	0.450132	−	0.741115i
$611$	323.961			0.530214
$612$	47.0704	−	47.0704i	0.0769124	−	0.0769124i
$613$	726.595	+	726.595i	1.18531	+	1.18531i	0.978349	+	0.206962i	$0.0663575\pi$
$613$	726.595	+	726.595i	1.18531	+	1.18531i	0.206962	+	0.978349i	$0.433642\pi$
$614$		−	346.385i		−	0.564145i
$615$	−65.3325	−	39.6811i	−0.106232	−	0.0645221i
$616$	−543.689			−0.882611
$617$	−175.696	+	175.696i	−0.284759	+	0.284759i	−0.835004	−	0.550244i	$-0.814535\pi$
$617$	−175.696	+	175.696i	−0.284759	+	0.284759i	0.550244	+	0.835004i	$0.314535\pi$
$618$	−65.9993	−	65.9993i	−0.106795	−	0.106795i
$619$			296.780i			0.479451i	0.970841	+	0.239725i	$0.0770574\pi$
$619$			296.780i			0.479451i	−0.970841	+	0.239725i	$0.922943\pi$
$620$	−131.676	−	539.063i	−0.212380	−	0.869456i
$621$	−24.9199			−0.0401286
$622$	−46.2731	+	46.2731i	−0.0743941	+	0.0743941i
$623$	−151.296	−	151.296i	−0.242851	−	0.242851i
$624$		−	34.9899i		−	0.0560735i
$625$	359.317	−	511.387i	0.574907	−	0.818219i
$626$	−411.794			−0.657817
$627$	−47.6882	+	47.6882i	−0.0760577	+	0.0760577i
$628$	−314.106	−	314.106i	−0.500169	−	0.500169i
$629$		−	382.006i		−	0.607323i
$630$	−262.261	+	64.0619i	−0.416287	+	0.101686i
$631$	−348.114			−0.551686			−0.275843	−	0.961203i	$-0.588957\pi$
$631$	−348.114			−0.551686			−0.275843	+	0.961203i	$0.588957\pi$
$632$	−83.6920	+	83.6920i	−0.132424	+	0.132424i
$633$	−28.6288	−	28.6288i	−0.0452271	−	0.0452271i
$634$		−	552.277i		−	0.871100i
$635$	587.793	−	967.766i	0.925658	−	1.52404i
$636$	194.627			0.306017
$637$	−403.418	+	403.418i	−0.633309	+	0.633309i
$638$	−115.493	−	115.493i	−0.181023	−	0.181023i
$639$		−	0.586501i		−	0.000917841i
$640$	−48.3492	−	29.3659i	−0.0755456	−	0.0458842i
$641$	−104.423			−0.162907			−0.0814534	−	0.996677i	$-0.525956\pi$
$641$	−104.423			−0.162907			−0.0814534	+	0.996677i	$0.525956\pi$
$642$	−272.293	+	272.293i	−0.424132	+	0.424132i
$643$	786.591	+	786.591i	1.22331	+	1.22331i	0.966447	+	0.256868i	$0.0826905\pi$
$643$	786.591	+	786.591i	1.22331	+	1.22331i	0.256868	+	0.966447i	$0.417310\pi$
$644$			122.069i			0.189548i
$645$	−20.1297	−	82.4083i	−0.0312088	−	0.127765i
$646$	−40.4482			−0.0626133
$647$	−601.105	+	601.105i	−0.929065	+	0.929065i	−0.997646	−	0.0685808i	$-0.978153\pi$
$647$	−601.105	+	601.105i	−0.929065	+	0.929065i	0.0685808	+	0.997646i	$0.478153\pi$
$648$	18.0000	+	18.0000i	0.0277778	+	0.0277778i
$649$			1219.50i			1.87904i
$650$	−158.449	+	82.3196i	−0.243767	+	0.126646i
$651$	1223.20			1.87895
$652$	−277.117	+	277.117i	−0.425026	+	0.425026i
$653$	−191.262	−	191.262i	−0.292897	−	0.292897i	0.545327	−	0.838224i	$-0.316406\pi$
$653$	−191.262	−	191.262i	−0.292897	−	0.292897i	−0.838224	+	0.545327i	$0.816406\pi$
$654$		−	496.311i		−	0.758886i
$655$	−963.349	+	235.315i	−1.47076	+	0.359260i
$656$	35.3057			0.0538197
$657$	148.293	−	148.293i	0.225712	−	0.225712i
$658$	816.363	+	816.363i	1.24067	+	1.24067i
$659$			1018.97i			1.54624i	0.634260	+	0.773120i	$0.281305\pi$
$659$			1018.97i			1.54624i	−0.634260	+	0.773120i	$0.718695\pi$
$660$	135.807	−	223.598i	0.205768	−	0.338785i
$661$	210.000			0.317700			0.158850	−	0.987303i	$-0.449221\pi$
$661$	210.000			0.317700			0.158850	+	0.987303i	$0.449221\pi$
$662$	6.88214	−	6.88214i	0.0103960	−	0.0103960i
$663$	68.6244	+	68.6244i	0.103506	+	0.103506i
$664$		−	105.611i		−	0.159053i
$665$	140.207	+	85.1574i	0.210837	+	0.128056i
$666$	146.081			0.219341
$667$	−25.9305	+	25.9305i	−0.0388763	+	0.0388763i
$668$	−18.1611	−	18.1611i	−0.0271873	−	0.0271873i
$669$		−	607.307i		−	0.907784i
$670$	220.577	+	903.014i	0.329220	+	1.34778i
$671$	−1129.82			−1.68379
$672$	88.1724	−	88.1724i	0.131209	−	0.131209i
$673$	11.3881	+	11.3881i	0.0169214	+	0.0169214i	0.715517	−	0.698595i	$-0.246191\pi$
$673$	11.3881	+	11.3881i	0.0169214	+	0.0169214i	−0.698595	+	0.715517i	$0.746191\pi$
$674$			256.596i			0.380706i
$675$	39.1635	−	123.860i	0.0580200	−	0.183496i
$676$	−286.988			−0.424538
$677$	929.286	−	929.286i	1.37265	−	1.37265i	0.516163	−	0.856491i	$-0.327360\pi$
$677$	929.286	−	929.286i	1.37265	−	1.37265i	0.856491	−	0.516163i	$-0.172640\pi$
$678$	−225.280	−	225.280i	−0.332272	−	0.332272i
$679$			185.201i			0.272756i
$680$	152.420	−	37.2313i	0.224147	−	0.0547519i
$681$	127.845			0.187731
$682$	−838.141	+	838.141i	−1.22895	+	1.22895i
$683$	584.472	+	584.472i	0.855742	+	0.855742i	0.990833	−	0.135091i	$-0.0431327\pi$
$683$	584.472	+	584.472i	0.855742	+	0.855742i	−0.135091	+	0.990833i	$0.543133\pi$
$684$		−	15.4676i		−	0.0226135i
$685$	−6.27764	+	10.3358i	−0.00916444	+	0.0150887i
$686$	−1151.27			−1.67824
$687$	−57.1029	+	57.1029i	−0.0831192	+	0.0831192i
$688$	27.7057	+	27.7057i	0.0402700	+	0.0402700i
$689$			283.749i			0.411827i
$690$	−50.2023	−	30.4914i	−0.0727570	−	0.0441905i
$691$	842.687			1.21952			0.609759	−	0.792587i	$-0.291266\pi$
$691$	842.687			1.21952			0.609759	+	0.792587i	$0.291266\pi$
$692$	470.775	−	470.775i	0.680310	−	0.680310i
$693$	407.766	+	407.766i	0.588408	+	0.588408i
$694$		−	696.690i		−	1.00388i
$695$	146.437	+	599.493i	0.210701	+	0.862580i
$696$	37.4599			0.0538218
$697$	−69.2439	+	69.2439i	−0.0993456	+	0.0993456i
$698$	143.961	+	143.961i	0.206248	+	0.206248i
$699$		−	187.854i		−	0.268746i
$700$	−606.723	−	191.841i	−0.866747	−	0.274059i
$701$	841.413			1.20030			0.600152	−	0.799886i	$-0.295107\pi$
$701$	841.413			1.20030			0.600152	+	0.799886i	$0.295107\pi$
$702$	−26.2424	+	26.2424i	−0.0373823	+	0.0373823i
$703$	−62.7648	−	62.7648i	−0.0892813	−	0.0892813i
$704$			120.832i			0.171637i
$705$	−539.656	+	131.821i	−0.765469	+	0.186980i
$706$	−937.753			−1.32826
$707$	859.834	−	859.834i	1.21617	−	1.21617i
$708$	−197.771	−	197.771i	−0.279338	−	0.279338i
$709$			249.971i			0.352569i	0.984339	+	0.176284i	$0.0564078\pi$
$709$			249.971i			0.352569i	−0.984339	+	0.176284i	$0.943592\pi$
$710$	0.717630	−	1.18153i	0.00101075	−	0.00166413i
$711$	125.538			0.176565
$712$	−33.6249	+	33.6249i	−0.0472260	+	0.0472260i
$713$	188.180	+	188.180i	0.263927	+	0.263927i
$714$			345.859i			0.484397i
$715$	325.986	+	197.994i	0.455924	+	0.276915i
$716$	−92.4883			−0.129174
$717$	29.1967	−	29.1967i	0.0407207	−	0.0407207i
$718$	−120.098	−	120.098i	−0.167268	−	0.167268i
$719$		−	50.7687i		−	0.0706102i	−0.999377	−	0.0353051i	$-0.988760\pi$
$719$		−	50.7687i		−	0.0706102i	0.999377	−	0.0353051i	$-0.0112403\pi$
$720$	14.2375	+	58.2863i	0.0197743	+	0.0809532i
$721$	484.943			0.672598
$722$	354.354	−	354.354i	0.490795	−	0.490795i
$723$	−220.043	−	220.043i	−0.304347	−	0.304347i
$724$		−	199.226i		−	0.275174i
$725$	−88.1310	−	169.634i	−0.121560	−	0.233979i
$726$	−262.419			−0.361458
$727$	97.6824	−	97.6824i	0.134364	−	0.134364i	−0.636726	−	0.771090i	$-0.719712\pi$
$727$	97.6824	−	97.6824i	0.134364	−	0.134364i	0.771090	+	0.636726i	$0.219712\pi$
$728$	128.548	+	128.548i	0.176576	+	0.176576i
$729$		−	27.0000i		−	0.0370370i
$730$	480.192	−	117.295i	0.657797	−	0.160679i
$731$	−108.677			−0.148669
$732$	183.228	−	183.228i	0.250311	−	0.250311i
$733$	−391.414	−	391.414i	−0.533990	−	0.533990i	0.387768	−	0.921757i	$-0.373246\pi$
$733$	−391.414	−	391.414i	−0.533990	−	0.533990i	−0.921757	+	0.387768i	$0.873246\pi$
$734$			334.613i			0.455876i
$735$	507.864	−	836.168i	0.690971	−	1.13764i
$736$	27.1293			0.0368605
$737$	1404.02	−	1404.02i	1.90504	−	1.90504i
$738$	−26.4793	−	26.4793i	−0.0358798	−	0.0358798i
$739$			1224.73i			1.65728i	0.559785	+	0.828638i	$0.310884\pi$
$739$			1224.73i			1.65728i	−0.559785	+	0.828638i	$0.689116\pi$
$740$	294.288	+	178.742i	0.397687	+	0.241543i
$741$	22.5504			0.0304324
$742$	−715.031	+	715.031i	−0.963653	+	0.963653i
$743$	−876.956	−	876.956i	−1.18029	−	1.18029i	−0.979669	−	0.200623i	$-0.935703\pi$
$743$	−876.956	−	876.956i	−1.18029	−	1.18029i	−0.200623	−	0.979669i	$-0.564297\pi$
$744$		−	271.850i		−	0.365390i
$745$	182.444	+	746.903i	0.244892	+	1.00255i
$746$	853.139			1.14362
$747$	−79.2082	+	79.2082i	−0.106035	+	0.106035i
$748$	−236.984	−	236.984i	−0.316824	−	0.316824i
$749$		−	2000.73i		−	2.67120i
$750$	230.449	−	201.602i	0.307265	−	0.268802i
$751$	−456.098			−0.607321			−0.303660	−	0.952780i	$-0.598209\pi$
$751$	−456.098			−0.607321			−0.303660	+	0.952780i	$0.598209\pi$
$752$	181.433	−	181.433i	0.241267	−	0.241267i
$753$	232.220	+	232.220i	0.308393	+	0.308393i
$754$			54.6132i			0.0724314i
$755$	446.189	−	108.990i	0.590979	−	0.144357i
$756$	−132.259			−0.174945
$757$	520.228	−	520.228i	0.687223	−	0.687223i	−0.274394	−	0.961617i	$-0.588477\pi$
$757$	520.228	−	520.228i	0.687223	−	0.687223i	0.961617	+	0.274394i	$0.0884773\pi$
$758$	218.341	+	218.341i	0.288049	+	0.288049i
$759$			125.464i			0.165301i
$760$	18.9259	−	31.1603i	0.0249024	−	0.0410004i
$761$	369.811			0.485954			0.242977	−	0.970032i	$-0.421876\pi$
$761$	369.811			0.485954			0.242977	+	0.970032i	$0.421876\pi$
$762$	392.235	−	392.235i	0.514745	−	0.514745i
$763$	1823.37	+	1823.37i	2.38974	+	2.38974i
$764$		−	19.0274i		−	0.0249049i
$765$	−142.239	−	86.3915i	−0.185933	−	0.112930i
$766$	911.316			1.18971
$767$	288.333	−	288.333i	0.375923	−	0.375923i
$768$	−19.5959	−	19.5959i	−0.0255155	−	0.0255155i
$769$			601.554i			0.782255i	0.920336	+	0.391128i	$0.127915\pi$
$769$			601.554i			0.782255i	−0.920336	+	0.391128i	$0.872085\pi$
$770$	322.531	+	1320.40i	0.418872	+	1.71481i
$771$	−367.055			−0.476077
$772$	105.565	−	105.565i	0.136742	−	0.136742i
$773$	426.317	+	426.317i	0.551510	+	0.551510i	0.926876	−	0.375367i	$-0.122483\pi$
$773$	426.317	+	426.317i	0.551510	+	0.551510i	−0.375367	+	0.926876i	$0.622483\pi$
$774$		−	41.5586i		−	0.0536933i
$775$	−1231.05	+	639.574i	−1.58845	+	0.825257i
$776$	41.1601			0.0530413
$777$	−536.681	+	536.681i	−0.690710	+	0.690710i
$778$	−300.379	−	300.379i	−0.386092	−	0.386092i
$779$			22.7540i			0.0292092i
$780$	−84.9762	+	20.7570i	−0.108944	+	0.0266115i
$781$	−2.95284			−0.00378085
$782$	−53.2078	+	53.2078i	−0.0680407	+	0.0680407i
$783$	−28.0950	−	28.0950i	−0.0358812	−	0.0358812i
$784$			451.865i			0.576358i
$785$	−576.500	+	949.173i	−0.734395	+	1.20914i
$786$	−485.818			−0.618090
$787$	259.149	−	259.149i	0.329288	−	0.329288i	−0.523028	−	0.852316i	$-0.675198\pi$
$787$	259.149	−	259.149i	0.329288	−	0.329288i	0.852316	+	0.523028i	$0.175198\pi$
$788$	234.956	+	234.956i	0.298167	+	0.298167i
$789$		−	574.647i		−	0.728323i
$790$	252.903	+	153.606i	0.320130	+	0.194438i
$791$	1655.29			2.09266
$792$	90.6242	−	90.6242i	0.114425	−	0.114425i
$793$	267.130	+	267.130i	0.336860	+	0.336860i
$794$			794.706i			1.00089i
$795$	−115.458	−	472.670i	−0.145230	−	0.594554i
$796$	−672.085			−0.844328
$797$	−855.241	+	855.241i	−1.07308	+	1.07308i	−0.0759646	+	0.997111i	$0.524204\pi$
$797$	−855.241	+	855.241i	−1.07308	+	1.07308i	−0.997111	+	0.0759646i	$0.975796\pi$
$798$	56.8257	+	56.8257i	0.0712102	+	0.0712102i
$799$			711.676i			0.890709i
$800$	−42.6358	+	134.841i	−0.0532948	+	0.168552i
$801$	50.4374			0.0629680
$802$	328.148	−	328.148i	0.409163	−	0.409163i
$803$	−746.608	−	746.608i	−0.929773	−	0.929773i
$804$			455.391i			0.566407i
$805$	296.457	−	72.4149i	0.368269	−	0.0899564i
$806$	396.333			0.491729
$807$	170.514	−	170.514i	0.211294	−	0.211294i
$808$	−191.094	−	191.094i	−0.236503	−	0.236503i
$809$			1011.37i			1.25015i	0.780563	+	0.625077i	$0.214932\pi$
$809$			1011.37i			1.25015i	−0.780563	+	0.625077i	$0.785068\pi$
$810$	33.0366	−	54.3928i	0.0407860	−	0.0671517i
$811$	833.267			1.02746			0.513728	−	0.857953i	$-0.328264\pi$
$811$	833.267			1.02746			0.513728	+	0.857953i	$0.328264\pi$
$812$	−137.622	+	137.622i	−0.169486	+	0.169486i
$813$	281.127	+	281.127i	0.345789	+	0.345789i
$814$		−	735.473i		−	0.903529i
$815$	837.399	+	508.612i	1.02748	+	0.624063i
$816$	76.8657			0.0941981
$817$	−17.8559	+	17.8559i	−0.0218555	+	0.0218555i
$818$	−526.651	−	526.651i	−0.643828	−	0.643828i
$819$		−	192.821i		−	0.235435i
$820$	−20.9443	−	85.7433i	−0.0255419	−	0.104565i
$821$	−241.671			−0.294362			−0.147181	−	0.989110i	$-0.547020\pi$
$821$	−241.671			−0.294362			−0.147181	+	0.989110i	$0.547020\pi$
$822$	−4.18908	+	4.18908i	−0.00509621	+	0.00509621i
$823$	549.346	+	549.346i	0.667493	+	0.667493i	0.957135	−	0.289642i	$-0.0935364\pi$
$823$	549.346	+	549.346i	0.667493	+	0.667493i	−0.289642	+	0.957135i	$0.593536\pi$
$824$		−	107.776i		−	0.130797i
$825$	−623.594	−	197.176i	−0.755871	−	0.239001i
$826$	1453.17			1.75928
$827$	237.152	−	237.152i	0.286762	−	0.286762i	−0.549037	−	0.835798i	$-0.685005\pi$
$827$	237.152	−	237.152i	0.286762	−	0.286762i	0.835798	+	0.549037i	$0.185005\pi$
$828$	−20.3470	−	20.3470i	−0.0245737	−	0.0245737i
$829$			1532.35i			1.84843i	0.381873	+	0.924215i	$0.375279\pi$
$829$			1532.35i			1.84843i	−0.381873	+	0.924215i	$0.624721\pi$
$830$	−256.486	+	62.6514i	−0.309020	+	0.0754836i
$831$	−31.5220			−0.0379326
$832$	28.5691	−	28.5691i	0.0343379	−	0.0343379i
$833$	−886.227	−	886.227i	−1.06390	−	1.06390i
$834$			302.325i			0.362501i
$835$	−33.3323	+	54.8797i	−0.0399189	+	0.0657242i
$836$	−77.8745			−0.0931513
$837$	−203.888	+	203.888i	−0.243593	+	0.243593i
$838$	17.1539	+	17.1539i	0.0204700	+	0.0204700i
$839$			446.569i			0.532263i	0.963937	+	0.266132i	$0.0857456\pi$
$839$			446.569i			0.532263i	−0.963937	+	0.266132i	$0.914254\pi$
$840$	−266.442	−	161.829i	−0.317192	−	0.192653i
$841$	782.531			0.930477
$842$	769.518	−	769.518i	0.913917	−	0.913917i
$843$	444.835	+	444.835i	0.527680	+	0.527680i
$844$		−	46.7506i		−	0.0553917i
$845$	170.249	+	696.978i	0.201478	+	0.824826i
$846$	−272.149			−0.321689
$847$	964.087	−	964.087i	1.13824	−	1.13824i
$848$	158.912	+	158.912i	0.187397	+	0.187397i
$849$		−	905.147i		−	1.06613i
$850$	−180.840	−	348.080i	−0.212753	−	0.409506i
$851$	−165.129			−0.194041
$852$	0.478876	−	0.478876i	0.000562061	−	0.000562061i
$853$	−791.294	−	791.294i	−0.927660	−	0.927660i	0.0698947	−	0.997554i	$-0.477734\pi$
$853$	−791.294	−	791.294i	−0.927660	−	0.927660i	−0.997554	+	0.0698947i	$0.977734\pi$
$854$			1346.30i			1.57647i
$855$	−37.5646	+	9.17582i	−0.0439352	+	0.0107320i
$856$	−444.653			−0.519454
$857$	−707.801	+	707.801i	−0.825905	+	0.825905i	−0.986948	−	0.161042i	$-0.948514\pi$
$857$	−707.801	+	707.801i	−0.825905	+	0.825905i	0.161042	+	0.986948i	$0.448514\pi$
$858$	132.122	+	132.122i	0.153988	+	0.153988i
$859$		−	934.513i		−	1.08791i	−0.839115	−	0.543954i	$-0.816927\pi$
$859$		−	934.513i		−	1.08791i	0.839115	−	0.543954i	$-0.183073\pi$
$860$	50.8503	−	83.7219i	0.0591282	−	0.0973510i
$861$	194.562			0.225972
$862$	−292.091	+	292.091i	−0.338853	+	0.338853i
$863$	308.184	+	308.184i	0.357107	+	0.357107i	0.862746	−	0.505638i	$-0.168743\pi$
$863$	308.184	+	308.184i	0.357107	+	0.357107i	−0.505638	+	0.862746i	$0.668743\pi$
$864$			29.3939i			0.0340207i
$865$	−1422.60	−	864.045i	−1.64462	−	0.998896i
$866$	−341.888			−0.394790
$867$	203.197	−	203.197i	0.234368	−	0.234368i
$868$	998.737	+	998.737i	1.15062	+	1.15062i
$869$		−	632.044i		−	0.727323i
$870$	−22.2223	−	90.9751i	−0.0255429	−	0.104569i
$871$	−663.920			−0.762250
$872$	405.237	−	405.237i	0.464721	−	0.464721i
$873$	−30.8701	−	30.8701i	−0.0353609	−	0.0353609i
$874$			17.4844i			0.0200051i
$875$	−105.980	+	1587.29i	−0.121120	+	1.81405i
$876$	242.161			0.276440
$877$	619.759	−	619.759i	0.706680	−	0.706680i	−0.259155	−	0.965836i	$-0.583444\pi$
$877$	619.759	−	619.759i	0.706680	−	0.706680i	0.965836	+	0.259155i	$0.0834442\pi$
$878$	−382.734	−	382.734i	−0.435916	−	0.435916i
$879$		−	345.275i		−	0.392805i
$880$	293.453	−	71.6811i	0.333469	−	0.0814558i
$881$	1268.12			1.43941			0.719707	−	0.694278i	$-0.244276\pi$
$881$	1268.12			1.43941			0.719707	+	0.694278i	$0.244276\pi$
$882$	338.899	−	338.899i	0.384239	−	0.384239i
$883$	−881.882	−	881.882i	−0.998734	−	0.998734i	0.00126479	−	0.999999i	$-0.499597\pi$
$883$	−881.882	−	881.882i	−0.998734	−	0.998734i	−0.999999	+	0.00126479i	$0.999597\pi$
$884$			112.063i			0.126768i
$885$	−362.984	+	597.631i	−0.410151	+	0.675289i
$886$	117.141			0.132214
$887$	−283.798	+	283.798i	−0.319953	+	0.319953i	−0.848749	−	0.528796i	$-0.822644\pi$
$887$	−283.798	+	283.798i	−0.319953	+	0.319953i	0.528796	+	0.848749i	$0.322644\pi$
$888$	119.275	+	119.275i	0.134319	+	0.134319i
$889$			2882.03i			3.24188i
$890$	101.609	+	61.7141i	0.114167	+	0.0693417i
$891$	−135.936			−0.152566
$892$	495.864	−	495.864i	0.555902	−	0.555902i
$893$	116.931	+	116.931i	0.130941	+	0.130941i
$894$			376.664i			0.421325i
$895$	54.8666	+	224.617i	0.0613035	+	0.250968i
$896$	143.985			0.160698
$897$	29.6641	−	29.6641i	0.0330703	−	0.0330703i
$898$	268.969	+	268.969i	0.299520	+	0.299520i
$899$			424.312i			0.471982i
$900$	133.108	−	69.1541i	0.147898	−	0.0768379i
$901$	−623.339			−0.691830
$902$	−133.315	+	133.315i	−0.147799	+	0.147799i
$903$	152.680	+	152.680i	0.169081	+	0.169081i
$904$		−	367.881i		−	0.406948i
$905$	−483.839	+	118.186i	−0.534629	+	0.130593i
$906$	225.014			0.248360
$907$	845.703	−	845.703i	0.932418	−	0.932418i	−0.0654387	−	0.997857i	$-0.520845\pi$
$907$	845.703	−	845.703i	0.932418	−	0.932418i	0.997857	+	0.0654387i	$0.0208447\pi$
$908$	104.385	+	104.385i	0.114961	+	0.114961i
$909$			286.641i			0.315337i
$910$	235.932	−	388.448i	0.259266	−	0.426866i
$911$	−421.560			−0.462744			−0.231372	−	0.972865i	$-0.574321\pi$
$911$	−421.560			−0.462744			−0.231372	+	0.972865i	$0.574321\pi$
$912$	12.6293	−	12.6293i	0.0138479	−	0.0138479i
$913$	398.788	+	398.788i	0.436789	+	0.436789i
$914$			499.319i			0.546301i
$915$	−553.683	−	336.291i	−0.605118	−	0.367531i
$916$	−93.2487			−0.101800
$917$	1784.82	−	1784.82i	1.94637	−	1.94637i
$918$	−57.6492	−	57.6492i	−0.0627987	−	0.0627987i
$919$		−	837.616i		−	0.911443i	−0.890122	−	0.455722i	$-0.849381\pi$
$919$		−	837.616i		−	0.911443i	0.890122	−	0.455722i	$-0.150619\pi$
$920$	−16.0939	−	65.8862i	−0.0174933	−	0.0716154i
$921$	−424.233			−0.460622
$922$	−319.741	+	319.741i	−0.346791	+	0.346791i
$923$	0.698158	+	0.698158i	0.000756401	+	0.000756401i
$924$			665.880i			0.720649i
$925$	259.512	−	820.742i	0.280554	−	0.887289i
$926$	294.321			0.317842
$927$	−80.8323	+	80.8323i	−0.0871977	+	0.0871977i
$928$	30.5859	+	30.5859i	0.0329590	+	0.0329590i
$929$		−	430.234i		−	0.463115i	−0.972821	−	0.231557i	$-0.925618\pi$
$929$		−	430.234i		−	0.463115i	0.972821	−	0.231557i	$-0.0743821\pi$
$930$	−660.214	+	161.269i	−0.709908	+	0.173408i
$931$	−291.220			−0.312803
$932$	153.382	−	153.382i	0.164573	−	0.164573i
$933$	56.6727	+	56.6727i	0.0607425	+	0.0607425i
$934$			1208.65i			1.29406i
$935$	−434.954	+	716.125i	−0.465191	+	0.765909i
$936$	−42.8536			−0.0457838
$937$	−167.127	+	167.127i	−0.178364	+	0.178364i	−0.790642	−	0.612278i	$-0.790253\pi$
$937$	−167.127	+	167.127i	−0.178364	+	0.178364i	0.612278	+	0.790642i	$0.290253\pi$
$938$	−1673.04	−	1673.04i	−1.78362	−	1.78362i
$939$			504.342i			0.537106i
$940$	−548.258	−	332.996i	−0.583253	−	0.354251i
$941$	−887.412			−0.943052			−0.471526	−	0.881852i	$-0.656297\pi$
$941$	−887.412			−0.943052			−0.471526	+	0.881852i	$0.656297\pi$
$942$	−384.700	+	384.700i	−0.408386	+	0.408386i
$943$	29.9319	+	29.9319i	0.0317411	+	0.0317411i
$944$		−	322.960i		−	0.342118i
$945$	78.4595	+	321.203i	0.0830260	+	0.339897i
$946$	−209.234			−0.221178
$947$	−500.988	+	500.988i	−0.529026	+	0.529026i	−0.920282	−	0.391256i	$-0.872041\pi$
$947$	−500.988	+	500.988i	−0.529026	+	0.529026i	0.391256	+	0.920282i	$0.372041\pi$
$948$	102.501	+	102.501i	0.108124	+	0.108124i
$949$			353.050i			0.372023i
$950$	−86.9031	−	27.4781i	−0.0914770	−	0.0289243i
$951$	−676.399			−0.711250
$952$	−282.393	+	282.393i	−0.296631	+	0.296631i
$953$	368.475	+	368.475i	0.386647	+	0.386647i	0.873490	−	0.486842i	$-0.161851\pi$
$953$	368.475	+	368.475i	0.386647	+	0.386647i	−0.486842	+	0.873490i	$0.661851\pi$
$954$		−	238.368i		−	0.249862i
$955$	−46.2098	+	11.2876i	−0.0483872	+	0.0118194i
$956$	47.6781			0.0498725
$957$	−141.449	+	141.449i	−0.147805	+	0.147805i
$958$	838.912	+	838.912i	0.875691	+	0.875691i
$959$		−	30.7801i		−	0.0320961i
$960$	−35.9657	+	59.2154i	−0.0374643	+	0.0616827i
$961$	2118.27			2.20424
$962$	−173.892	+	173.892i	−0.180761	+	0.180761i
$963$	333.489	+	333.489i	0.346303	+	0.346303i
$964$		−	359.329i		−	0.372748i
$965$	−319.000	−	193.751i	−0.330569	−	0.200778i
$966$	149.504			0.154766
$967$	1009.40	−	1009.40i	1.04385	−	1.04385i	0.0448527	−	0.998994i	$-0.485718\pi$
$967$	1009.40	−	1009.40i	1.04385	−	1.04385i	0.998994	−	0.0448527i	$-0.0142818\pi$
$968$	−214.264	−	214.264i	−0.221347	−	0.221347i
$969$			49.5387i			0.0511235i
$970$	−24.4173	−	99.9612i	−0.0251725	−	0.103053i
$971$	136.929			0.141018			0.0705092	−	0.997511i	$-0.477538\pi$
$971$	136.929			0.141018			0.0705092	+	0.997511i	$0.477538\pi$
$972$	22.0454	−	22.0454i	0.0226805	−	0.0226805i
$973$	−1110.70	−	1110.70i	−1.14152	−	1.14152i
$974$		−	833.936i		−	0.856197i
$975$	100.821	+	194.059i	0.103406	+	0.199035i
$976$	299.210			0.306568
$977$	1015.93	−	1015.93i	1.03985	−	1.03985i	0.0406756	−	0.999172i	$-0.487049\pi$
$977$	1015.93	−	1015.93i	1.03985	−	1.03985i	0.999172	−	0.0406756i	$-0.0129510\pi$
$978$	339.398	+	339.398i	0.347032	+	0.347032i
$979$		−	253.936i		−	0.259383i
$980$	1097.40	−	268.059i	1.11979	−	0.273529i
$981$	−607.855			−0.619628
$982$	−677.675	+	677.675i	−0.690096	+	0.690096i
$983$	12.5868	+	12.5868i	0.0128045	+	0.0128045i	0.713480	−	0.700676i	$-0.247118\pi$
$983$	12.5868	+	12.5868i	0.0128045	+	0.0128045i	−0.700676	+	0.713480i	$0.747118\pi$
$984$		−	43.2405i		−	0.0439436i
$985$	431.231	−	709.995i	0.437798	−	0.720808i
$986$	−119.974			−0.121678
$987$	999.836	−	999.836i	1.01300	−	1.01300i
$988$	18.4123	+	18.4123i	0.0186360	+	0.0186360i
$989$			46.9774i			0.0474999i
$990$	−273.850	−	166.329i	−0.276617	−	0.168009i
$991$	271.127			0.273589			0.136795	−	0.990599i	$-0.456320\pi$
$991$	271.127			0.273589			0.136795	+	0.990599i	$0.456320\pi$
$992$	221.965	−	221.965i	0.223755	−	0.223755i
$993$	−8.42887	−	8.42887i	−0.00848829	−	0.00848829i
$994$			3.51864i			0.00353988i
$995$	398.699	+	1632.22i	0.400703	+	1.64042i
$996$	−129.346			−0.129866
$997$	464.797	−	464.797i	0.466196	−	0.466196i	−0.434484	−	0.900680i	$-0.643069\pi$
$997$	464.797	−	464.797i	0.466196	−	0.466196i	0.900680	+	0.434484i	$0.143069\pi$
$998$	−649.807	−	649.807i	−0.651110	−	0.651110i
$999$		−	178.912i		−	0.179092i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.a.553.1	yes	40
5.2	odd	4	inner	690.3.k.a.277.1	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.a.277.1	✓	40	5.2	odd	4	inner
690.3.k.a.553.1	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)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-4.85719 + 1.18646i) q^{5} -2.44949 q^{6} +(8.99906 - 8.99906i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-4.85719 + 1.18646i) q^{5} -2.44949 q^{6} +(8.99906 - 8.99906i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(-3.67074 + 6.04365i) q^{10} +15.1040 q^{11} +(-2.44949 + 2.44949i) q^{12} +(-3.57114 - 3.57114i) q^{13} -17.9981i q^{14} +(7.40193 + 4.49572i) q^{15} -4.00000 q^{16} +(7.84507 - 7.84507i) q^{17} +(3.00000 + 3.00000i) q^{18} -2.57794i q^{19} +(2.37291 + 9.71439i) q^{20} -22.0431 q^{21} +(15.1040 - 15.1040i) q^{22} +(-3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(22.1846 - 11.5257i) q^{25} -7.14227 q^{26} +(3.67423 - 3.67423i) q^{27} +(-17.9981 - 17.9981i) q^{28} -7.64648i q^{29} +(11.8976 - 2.90621i) q^{30} -55.4912 q^{31} +(-4.00000 + 4.00000i) q^{32} +(-18.4986 - 18.4986i) q^{33} -15.6901i q^{34} +(-33.0332 + 54.3872i) q^{35} +6.00000 q^{36} +(24.3469 - 24.3469i) q^{37} +(-2.57794 - 2.57794i) q^{38} +8.74746i q^{39} +(12.0873 + 7.34147i) q^{40} -8.82642 q^{41} +(-22.0431 + 22.0431i) q^{42} +(-6.92644 - 6.92644i) q^{43} -30.2081i q^{44} +(-3.55937 - 14.5716i) q^{45} -6.78233 q^{46} +(-45.3582 + 45.3582i) q^{47} +(4.89898 + 4.89898i) q^{48} -112.966i q^{49} +(10.6590 - 33.7103i) q^{50} -19.2164 q^{51} +(-7.14227 + 7.14227i) q^{52} +(-39.7281 - 39.7281i) q^{53} -7.34847i q^{54} +(-73.3632 + 17.9203i) q^{55} -35.9962 q^{56} +(-3.15731 + 3.15731i) q^{57} +(-7.64648 - 7.64648i) q^{58} +80.7399i q^{59} +(8.99143 - 14.8039i) q^{60} -74.8025 q^{61} +(-55.4912 + 55.4912i) q^{62} +(26.9972 + 26.9972i) q^{63} +8.00000i q^{64} +(21.5827 + 13.1087i) q^{65} -36.9972 q^{66} +(92.9564 - 92.9564i) q^{67} +(-15.6901 - 15.6901i) q^{68} +8.30662i q^{69} +(21.3540 + 87.4203i) q^{70} -0.195500 q^{71} +(6.00000 - 6.00000i) q^{72} +(-49.4310 - 49.4310i) q^{73} -48.6938i q^{74} +(-41.2866 - 13.0545i) q^{75} -5.15587 q^{76} +(135.922 - 135.922i) q^{77} +(8.74746 + 8.74746i) q^{78} -41.8460i q^{79} +(19.4288 - 4.74582i) q^{80} -9.00000 q^{81} +(-8.82642 + 8.82642i) q^{82} +(26.4027 + 26.4027i) q^{83} +44.0862i q^{84} +(-28.7972 + 47.4128i) q^{85} -13.8529 q^{86} +(-9.36499 + 9.36499i) q^{87} +(-30.2081 - 30.2081i) q^{88} -16.8125i q^{89} +(-18.1309 - 11.0122i) q^{90} -64.2738 q^{91} +(-6.78233 + 6.78233i) q^{92} +(67.9625 + 67.9625i) q^{93} +90.7164i q^{94} +(3.05861 + 12.5215i) q^{95} +9.79796 q^{96} +(-10.2900 + 10.2900i) q^{97} +(-112.966 - 112.966i) q^{98} +45.3121i 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

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Database

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