LMFDB - Embedded newform 690.3.k.a.277.1

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			277.1
Character	$\chi$	$=$	690.277
Dual form			690.3.k.a.553.1

$q$-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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$			2.00000i			0.500000i
$5$	−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	0.937444	+	0.348136i	$0.113185\pi$
$7$	8.99906	+	8.99906i	1.28558	+	1.28558i	0.348136	+	0.937444i	$0.386815\pi$
$8$	−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	−0.830990	−	0.556287i	$-0.812225\pi$
$13$	−3.57114	+	3.57114i	−0.274703	+	0.274703i	0.556287	+	0.830990i	$0.312225\pi$
$14$			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	0.899139	−	0.437664i	$-0.144194\pi$
$17$	7.84507	+	7.84507i	0.461475	+	0.461475i	−0.437664	+	0.899139i	$0.644194\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$			2.57794i			0.135681i	0.997696	+	0.0678404i	$0.0216109\pi$
$19$			2.57794i			0.135681i	−0.997696	+	0.0678404i	$0.978389\pi$
$20$	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	$0.0420872\pi$
$29$			7.64648i			0.263672i	−0.991272	+	0.131836i	$0.957913\pi$
$30$	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	0.954912	−	0.296888i	$-0.0959488\pi$
$37$	24.3469	+	24.3469i	0.658024	+	0.658024i	−0.296888	+	0.954912i	$0.595949\pi$
$38$	−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	−0.783045	−	0.621965i	$-0.786335\pi$
$43$	−6.92644	+	6.92644i	−0.161080	+	0.161080i	0.621965	+	0.783045i	$0.286335\pi$
$44$			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	0.0343419	−	0.999410i	$-0.489066\pi$
$47$	−45.3582	−	45.3582i	−0.965068	−	0.965068i	−0.999410	+	0.0343419i	$0.989066\pi$
$48$	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	−0.974401	−	0.224815i	$-0.927822\pi$
$53$	−39.7281	+	39.7281i	−0.749586	+	0.749586i	0.224815	+	0.974401i	$0.427822\pi$
$54$			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	$-0.760136\pi$
$59$		−	80.7399i		−	1.36847i	0.729260	−	0.684236i	$-0.239864\pi$
$60$	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	0.830724	+	0.556684i	$0.187927\pi$
$67$	92.9564	+	92.9564i	1.38741	+	1.38741i	0.556684	+	0.830724i	$0.312073\pi$
$68$	−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	−0.959351	−	0.282214i	$-0.908931\pi$
$73$	−49.4310	+	49.4310i	−0.677137	+	0.677137i	0.282214	+	0.959351i	$0.408931\pi$
$74$			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	$0.0853218\pi$
$79$			41.8460i			0.529696i	−0.964290	+	0.264848i	$0.914678\pi$
$80$	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	−0.529934	−	0.848039i	$-0.677783\pi$
$83$	26.4027	−	26.4027i	0.318105	−	0.318105i	0.848039	+	0.529934i	$0.177783\pi$
$84$		−	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	$0.0301099\pi$
$89$			16.8125i			0.188904i	−0.995529	+	0.0944521i	$0.969890\pi$
$90$	−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	0.652073	−	0.758156i	$-0.273899\pi$
$97$	−10.2900	−	10.2900i	−0.106083	−	0.106083i	−0.758156	+	0.652073i	$0.773899\pi$
$98$	−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	−0.564108	−	0.825701i	$-0.690780\pi$
$103$	26.9441	−	26.9441i	0.261593	−	0.261593i	0.825701	+	0.564108i	$0.190780\pi$
$104$		−	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	0.999212	+	0.0396962i	$0.0126390\pi$
$107$	111.163	+	111.163i	1.03891	+	1.03891i	0.0396962	+	0.999212i	$0.487361\pi$
$108$	−7.34847	+	7.34847i	−0.0680414	+	0.0680414i
$109$		−	202.618i		−	1.85888i	−0.368969	−	0.929442i	$-0.620289\pi$
$109$		−	202.618i		−	1.85888i	0.368969	−	0.929442i	$-0.379711\pi$
$110$	−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	−0.171319	−	0.985216i	$-0.554803\pi$
$113$	91.9703	−	91.9703i	0.813896	−	0.813896i	0.985216	+	0.171319i	$0.0548029\pi$
$114$		−	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	−0.950676	−	0.310186i	$-0.899609\pi$
$127$	−160.129	−	160.129i	−1.26086	−	1.26086i	−0.310186	−	0.950676i	$-0.600391\pi$
$128$	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	0.713321	−	0.700838i	$-0.247190\pi$
$137$	1.71018	+	1.71018i	0.0124831	+	0.0124831i	−0.700838	+	0.713321i	$0.747190\pi$
$138$	8.30662	−	8.30662i	0.0601929	−	0.0601929i
$139$			123.424i			0.887941i	0.896041	+	0.443971i	$0.146431\pi$
$139$			123.424i			0.887941i	−0.896041	+	0.443971i	$0.853569\pi$
$140$	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	$0.172585\pi$
$149$			153.773i			1.03203i	−0.856579	+	0.516015i	$0.827415\pi$
$150$	−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	1.00000		0.000337781i	$0.000107519\pi$
$157$	157.053	+	157.053i	1.00034	+	1.00034i	0.000337781		1.00000i	$0.499892\pi$
$158$	−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	−0.990139	−	0.140087i	$-0.955262\pi$
$163$	−138.558	+	138.558i	−0.850052	+	0.850052i	0.140087	+	0.990139i	$0.455262\pi$
$164$		−	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	0.733771	−	0.679397i	$-0.237758\pi$
$167$	9.08055	+	9.08055i	0.0543746	+	0.0543746i	−0.679397	+	0.733771i	$0.737758\pi$
$168$	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	0.487495	−	0.873126i	$-0.337911\pi$
$173$	235.387	−	235.387i	1.36062	−	1.36062i	0.873126	−	0.487495i	$-0.162089\pi$
$174$		−	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	$0.0412324\pi$
$179$			46.2441i			0.258347i	−0.991622	+	0.129174i	$0.958768\pi$
$180$	−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	−0.557016	−	0.830501i	$-0.688054\pi$
$193$	52.7826	−	52.7826i	0.273485	−	0.273485i	0.830501	+	0.557016i	$0.188054\pi$
$194$		−	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	0.343000	−	0.939335i	$-0.388557\pi$
$197$	−117.478	−	117.478i	−0.596335	−	0.596335i	−0.939335	+	0.343000i	$0.888557\pi$
$198$	45.3121	−	45.3121i	0.228849	−	0.228849i
$199$			336.042i			1.68866i	0.535827	+	0.844328i	$0.320000\pi$
$199$			336.042i			1.68866i	−0.535827	+	0.844328i	$0.680000\pi$
$200$	−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	0.118897	−	0.992907i	$-0.462064\pi$
$223$	247.932	−	247.932i	1.11180	−	1.11180i	0.992907	−	0.118897i	$-0.0379359\pi$
$224$		−	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	0.582738	−	0.812660i	$-0.301981\pi$
$227$	−52.1924	−	52.1924i	−0.229922	−	0.229922i	−0.812660	+	0.582738i	$0.801981\pi$
$228$	6.31463	−	6.31463i	0.0276957	−	0.0276957i
$229$			46.6243i			0.203600i	0.994805	+	0.101800i	$0.0324601\pi$
$229$			46.6243i			0.203600i	−0.994805	+	0.101800i	$0.967540\pi$
$230$	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	−0.523116	−	0.852262i	$-0.675231\pi$
$233$	76.6909	−	76.6909i	0.329146	−	0.329146i	0.852262	+	0.523116i	$0.175231\pi$
$234$			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	$-0.984119\pi$
$239$		−	23.8390i		−	0.0997449i	0.998756	−	0.0498725i	$-0.0158815\pi$
$240$	−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	0.935746	−	0.352674i	$-0.114727\pi$
$257$	149.850	+	149.850i	0.583072	+	0.583072i	−0.352674	+	0.935746i	$0.614727\pi$
$258$	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	−0.102702	−	0.994712i	$-0.532749\pi$
$263$	234.599	−	234.599i	0.892010	−	0.892010i	0.994712	+	0.102702i	$0.0327487\pi$
$264$		−	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	$-0.916679\pi$
$269$		−	139.224i		−	0.517563i	0.965936	−	0.258782i	$-0.0833210\pi$
$270$	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	0.729954	−	0.683496i	$-0.239541\pi$
$277$	12.8688	+	12.8688i	0.0464578	+	0.0464578i	−0.683496	+	0.729954i	$0.739541\pi$
$278$	−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	0.381282	−	0.924459i	$-0.375483\pi$
$283$	369.525	−	369.525i	1.30574	−	1.30574i	0.924459	−	0.381282i	$-0.124517\pi$
$284$		−	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	−0.424393	−	0.905478i	$-0.639512\pi$
$293$	140.958	−	140.958i	0.481085	−	0.481085i	0.905478	+	0.424393i	$0.139512\pi$
$294$		−	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	0.930482	−	0.366337i	$-0.119388\pi$
$307$	173.192	+	173.192i	0.564145	+	0.564145i	−0.366337	+	0.930482i	$0.619388\pi$
$308$	−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	−0.954863	−	0.297046i	$-0.903999\pi$
$313$	−205.897	+	205.897i	−0.657817	+	0.657817i	0.297046	+	0.954863i	$0.403999\pi$
$314$			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	0.992592	−	0.121492i	$-0.0387680\pi$
$317$	276.139	+	276.139i	0.871100	+	0.871100i	−0.121492	+	0.992592i	$0.538768\pi$
$318$	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	0.490650	−	0.871356i	$-0.336759\pi$
$337$	−128.298	−	128.298i	−0.380706	−	0.380706i	−0.871356	+	0.490650i	$0.836759\pi$
$338$	−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	0.999992	+	0.00388312i	$0.00123604\pi$
$347$	348.345	+	348.345i	1.00388	+	1.00388i	0.00388312	+	0.999992i	$0.498764\pi$
$348$	18.7300	−	18.7300i	0.0538218	−	0.0538218i
$349$		−	143.961i		−	0.412497i	−0.978500	−	0.206248i	$-0.933875\pi$
$349$		−	143.961i		−	0.412497i	0.978500	−	0.206248i	$-0.0661255\pi$
$350$	−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	−0.421375	+	0.906886i	$0.638453\pi$
$353$	−468.876	+	468.876i	−1.32826	+	1.32826i	−0.906886	+	0.421375i	$0.861547\pi$
$354$			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	$0.0534945\pi$
$359$			120.098i			0.334536i	−0.985911	+	0.167268i	$0.946505\pi$
$360$	−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	0.441423	−	0.897299i	$-0.354474\pi$
$367$	−167.307	−	167.307i	−0.455876	−	0.455876i	−0.897299	+	0.441423i	$0.854474\pi$
$368$	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	0.155834	−	0.987783i	$-0.450193\pi$
$373$	426.569	−	426.569i	1.14362	−	1.14362i	0.987783	−	0.155834i	$-0.0498066\pi$
$374$			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	$-0.906994\pi$
$379$		−	218.341i		−	0.576097i	0.957616	−	0.288049i	$-0.0930065\pi$
$380$	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	0.212559	−	0.977148i	$-0.431820\pi$
$383$	455.658	−	455.658i	1.18971	−	1.18971i	0.977148	−	0.212559i	$-0.0681797\pi$
$384$			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	$0.126175\pi$
$389$			300.379i			0.772183i	−0.922460	+	0.386092i	$0.873825\pi$
$390$	−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	−1.00000		0.000889374i	$-0.999717\pi$
$397$	−397.353	−	397.353i	−1.00089	−	1.00089i	−0.000889374	−	1.00000i	$-0.500283\pi$
$398$	−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	$0.222655\pi$
$409$			526.651i			1.28766i	−0.765171	+	0.643828i	$0.777345\pi$
$410$	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	$-0.993484\pi$
$419$		−	17.1539i		−	0.0409400i	0.999790	−	0.0204700i	$-0.00651626\pi$
$420$	−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	−0.876391	−	0.481601i	$-0.840056\pi$
$433$	−170.944	+	170.944i	−0.394790	+	0.394790i	0.481601	+	0.876391i	$0.340056\pi$
$434$		−	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	$0.143575\pi$
$439$			382.734i			0.871832i	−0.899987	+	0.435916i	$0.856425\pi$
$440$	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	−0.637903	−	0.770117i	$-0.720198\pi$
$443$	58.5707	−	58.5707i	0.132214	−	0.132214i	0.770117	+	0.637903i	$0.220198\pi$
$444$		−	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	$-0.903174\pi$
$449$		−	268.969i		−	0.599040i	0.954090	−	0.299520i	$-0.0968265\pi$
$450$	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	0.379068	−	0.925369i	$-0.376245\pi$
$457$	−249.660	−	249.660i	−0.546301	−	0.546301i	−0.925369	+	0.379068i	$0.876245\pi$
$458$	−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	−0.530096	−	0.847938i	$-0.677844\pi$
$463$	147.161	−	147.161i	0.317842	−	0.317842i	0.847938	+	0.530096i	$0.177844\pi$
$464$		−	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	−0.932254	−	0.361805i	$-0.882161\pi$
$467$	−604.325	−	604.325i	−1.29406	−	1.29406i	−0.361805	−	0.932254i	$-0.617839\pi$
$468$	−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	$-0.660406\pi$
$479$		−	838.912i		−	1.75138i	0.482872	−	0.875691i	$-0.339594\pi$
$480$	−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	0.990888	−	0.134690i	$-0.0430040\pi$
$487$	416.968	+	416.968i	0.856197	+	0.856197i	−0.134690	+	0.990888i	$0.543004\pi$
$488$	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	$0.225696\pi$
$499$			649.807i			1.30222i	−0.758984	+	0.651110i	$0.774304\pi$
$500$	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	−0.811827	−	0.583899i	$-0.801527\pi$
$503$	−114.648	+	114.648i	−0.227928	+	0.227928i	0.583899	+	0.811827i	$0.301527\pi$
$504$			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	$0.0925133\pi$
$509$			291.723i			0.573129i	−0.958061	+	0.286564i	$0.907487\pi$
$510$	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	−0.836580	−	0.547845i	$-0.815448\pi$
$523$	−151.008	+	151.008i	−0.288734	+	0.288734i	0.547845	+	0.836580i	$0.315448\pi$
$524$			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	0.993089	−	0.117367i	$-0.0374452\pi$
$547$	479.020	+	479.020i	0.875722	+	0.875722i	−0.117367	+	0.993089i	$0.537445\pi$
$548$	−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	0.788713	−	0.614761i	$-0.210748\pi$
$557$	96.8915	+	96.8915i	0.173953	+	0.173953i	−0.614761	+	0.788713i	$0.710748\pi$
$558$	−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	−0.495303	+	0.868720i	$0.664943\pi$
$563$	−767.945	+	767.945i	−1.36402	+	1.36402i	−0.868720	+	0.495303i	$0.835057\pi$
$564$			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	$0.0860194\pi$
$569$			303.801i			0.533921i	−0.963707	+	0.266961i	$0.913981\pi$
$570$	−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	0.139694	−	0.990195i	$-0.455388\pi$
$577$	−490.739	−	490.739i	−0.850501	−	0.850501i	−0.990195	+	0.139694i	$0.955388\pi$
$578$	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	0.950002	−	0.312245i	$-0.101081\pi$
$587$	374.363	+	374.363i	0.637757	+	0.637757i	−0.312245	+	0.950002i	$0.601081\pi$
$588$	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	0.00128752	−	0.999999i	$-0.499590\pi$
$593$	593.763	−	593.763i	1.00129	−	1.00129i	0.999999	−	0.00128752i	$-0.000409830\pi$
$594$			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	$-0.993384\pi$
$599$		−	24.8982i		−	0.0415663i	0.999784	−	0.0207831i	$-0.00661595\pi$
$600$	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	0.988916	+	0.148477i	$0.0474371\pi$
$607$	690.397	+	690.397i	1.13739	+	1.13739i	0.148477	+	0.988916i	$0.452563\pi$
$608$	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	0.206962	−	0.978349i	$-0.433642\pi$
$613$	726.595	−	726.595i	1.18531	−	1.18531i	0.978349	−	0.206962i	$-0.0663575\pi$
$614$			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	0.550244	−	0.835004i	$-0.314535\pi$
$617$	−175.696	−	175.696i	−0.284759	−	0.284759i	−0.835004	+	0.550244i	$0.814535\pi$
$618$	−65.9993	+	65.9993i	−0.106795	+	0.106795i
$619$		−	296.780i		−	0.479451i	−0.970841	−	0.239725i	$-0.922943\pi$
$619$		−	296.780i		−	0.479451i	0.970841	−	0.239725i	$-0.0770574\pi$
$620$	−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	0.256868	−	0.966447i	$-0.417310\pi$
$643$	786.591	−	786.591i	1.22331	−	1.22331i	0.966447	−	0.256868i	$-0.0826905\pi$
$644$		−	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	0.0685808	−	0.997646i	$-0.478153\pi$
$647$	−601.105	−	601.105i	−0.929065	−	0.929065i	−0.997646	+	0.0685808i	$0.978153\pi$
$648$	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	−0.838224	−	0.545327i	$-0.816406\pi$
$653$	−191.262	+	191.262i	−0.292897	+	0.292897i	0.545327	+	0.838224i	$0.316406\pi$
$654$			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	$-0.718695\pi$
$659$		−	1018.97i		−	1.54624i	0.634260	−	0.773120i	$-0.281305\pi$
$660$	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	−0.698595	−	0.715517i	$-0.746191\pi$
$673$	11.3881	−	11.3881i	0.0169214	−	0.0169214i	0.715517	+	0.698595i	$0.246191\pi$
$674$		−	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	0.856491	+	0.516163i	$0.172640\pi$
$677$	929.286	+	929.286i	1.37265	+	1.37265i	0.516163	+	0.856491i	$0.327360\pi$
$678$	−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	−0.135091	−	0.990833i	$-0.543133\pi$
$683$	584.472	−	584.472i	0.855742	−	0.855742i	0.990833	+	0.135091i	$0.0431327\pi$
$684$			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	$-0.943592\pi$
$709$		−	249.971i		−	0.352569i	0.984339	−	0.176284i	$-0.0564078\pi$
$710$	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	$0.0112403\pi$
$719$			50.7687i			0.0706102i	−0.999377	+	0.0353051i	$0.988760\pi$
$720$	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	0.771090	−	0.636726i	$-0.219712\pi$
$727$	97.6824	+	97.6824i	0.134364	+	0.134364i	−0.636726	+	0.771090i	$0.719712\pi$
$728$	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	−0.921757	−	0.387768i	$-0.873246\pi$
$733$	−391.414	+	391.414i	−0.533990	+	0.533990i	0.387768	+	0.921757i	$0.373246\pi$
$734$		−	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	$-0.689116\pi$
$739$		−	1224.73i		−	1.65728i	0.559785	−	0.828638i	$-0.310884\pi$
$740$	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	−0.200623	+	0.979669i	$0.564297\pi$
$743$	−876.956	+	876.956i	−1.18029	+	1.18029i	−0.979669	+	0.200623i	$0.935703\pi$
$744$			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	0.961617	−	0.274394i	$-0.0884773\pi$
$757$	520.228	+	520.228i	0.687223	+	0.687223i	−0.274394	+	0.961617i	$0.588477\pi$
$758$	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	$-0.872085\pi$
$769$		−	601.554i		−	0.782255i	0.920336	−	0.391128i	$-0.127915\pi$
$770$	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	−0.375367	−	0.926876i	$-0.622483\pi$
$773$	426.317	−	426.317i	0.551510	−	0.551510i	0.926876	+	0.375367i	$0.122483\pi$
$774$			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	0.852316	−	0.523028i	$-0.175198\pi$
$787$	259.149	+	259.149i	0.329288	+	0.329288i	−0.523028	+	0.852316i	$0.675198\pi$
$788$	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	−0.997111	−	0.0759646i	$-0.975796\pi$
$797$	−855.241	−	855.241i	−1.07308	−	1.07308i	−0.0759646	−	0.997111i	$-0.524204\pi$
$798$	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	$-0.785068\pi$
$809$		−	1011.37i		−	1.25015i	0.780563	−	0.625077i	$-0.214932\pi$
$810$	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	−0.289642	−	0.957135i	$-0.593536\pi$
$823$	549.346	−	549.346i	0.667493	−	0.667493i	0.957135	+	0.289642i	$0.0935364\pi$
$824$			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	0.835798	−	0.549037i	$-0.185005\pi$
$827$	237.152	+	237.152i	0.286762	+	0.286762i	−0.549037	+	0.835798i	$0.685005\pi$
$828$	−20.3470	+	20.3470i	−0.0245737	+	0.0245737i
$829$		−	1532.35i		−	1.84843i	−0.381873	−	0.924215i	$-0.624721\pi$
$829$		−	1532.35i		−	1.84843i	0.381873	−	0.924215i	$-0.375279\pi$
$830$	−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	$-0.914254\pi$
$839$		−	446.569i		−	0.532263i	0.963937	−	0.266132i	$-0.0857456\pi$
$840$	−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	−0.997554	−	0.0698947i	$-0.977734\pi$
$853$	−791.294	+	791.294i	−0.927660	+	0.927660i	0.0698947	+	0.997554i	$0.477734\pi$
$854$		−	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	0.161042	−	0.986948i	$-0.448514\pi$
$857$	−707.801	−	707.801i	−0.825905	−	0.825905i	−0.986948	+	0.161042i	$0.948514\pi$
$858$	132.122	−	132.122i	0.153988	−	0.153988i
$859$			934.513i			1.08791i	0.839115	+	0.543954i	$0.183073\pi$
$859$			934.513i			1.08791i	−0.839115	+	0.543954i	$0.816927\pi$
$860$	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	−0.505638	−	0.862746i	$-0.668743\pi$
$863$	308.184	−	308.184i	0.357107	−	0.357107i	0.862746	+	0.505638i	$0.168743\pi$
$864$		−	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	0.965836	−	0.259155i	$-0.0834442\pi$
$877$	619.759	+	619.759i	0.706680	+	0.706680i	−0.259155	+	0.965836i	$0.583444\pi$
$878$	−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	−0.999999	−	0.00126479i	$-0.999597\pi$
$883$	−881.882	+	881.882i	−0.998734	+	0.998734i	0.00126479	+	0.999999i	$0.499597\pi$
$884$		−	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	0.528796	−	0.848749i	$-0.322644\pi$
$887$	−283.798	−	283.798i	−0.319953	−	0.319953i	−0.848749	+	0.528796i	$0.822644\pi$
$888$	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	0.997857	−	0.0654387i	$-0.0208447\pi$
$907$	845.703	+	845.703i	0.932418	+	0.932418i	−0.0654387	+	0.997857i	$0.520845\pi$
$908$	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	$0.150619\pi$
$919$			837.616i			0.911443i	−0.890122	+	0.455722i	$0.849381\pi$
$920$	−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	$0.0743821\pi$
$929$			430.234i			0.463115i	−0.972821	+	0.231557i	$0.925618\pi$
$930$	−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	0.612278	−	0.790642i	$-0.290253\pi$
$937$	−167.127	−	167.127i	−0.178364	−	0.178364i	−0.790642	+	0.612278i	$0.790253\pi$
$938$	−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	0.391256	−	0.920282i	$-0.372041\pi$
$947$	−500.988	−	500.988i	−0.529026	−	0.529026i	−0.920282	+	0.391256i	$0.872041\pi$
$948$	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	−0.486842	−	0.873490i	$-0.661851\pi$
$953$	368.475	−	368.475i	0.386647	−	0.386647i	0.873490	+	0.486842i	$0.161851\pi$
$954$			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	0.998994	+	0.0448527i	$0.0142818\pi$
$967$	1009.40	+	1009.40i	1.04385	+	1.04385i	0.0448527	+	0.998994i	$0.485718\pi$
$968$	−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	0.999172	+	0.0406756i	$0.0129510\pi$
$977$	1015.93	+	1015.93i	1.03985	+	1.03985i	0.0406756	+	0.999172i	$0.487049\pi$
$978$	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	−0.700676	−	0.713480i	$-0.747118\pi$
$983$	12.5868	−	12.5868i	0.0128045	−	0.0128045i	0.713480	+	0.700676i	$0.247118\pi$
$984$			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	0.900680	−	0.434484i	$-0.143069\pi$
$997$	464.797	+	464.797i	0.466196	+	0.466196i	−0.434484	+	0.900680i	$0.643069\pi$
$998$	−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.277.1	✓	40
5.3	odd	4	inner	690.3.k.a.553.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.a.277.1	✓	40	1.1	even	1	trivial
690.3.k.a.553.1	yes	40	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.85719 - 1.18646i) q^{5} -2.44949 q^{6} +(8.99906 + 8.99906i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(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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