LMFDB - Embedded newform 690.3.k.b.553.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(277,690)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("690.277");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			553.4
Character	$\chi$	$=$	690.553
Dual form			690.3.k.b.277.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(3.38334 - 3.68144i) q^{5} +2.44949 q^{6} +(-2.06971 + 2.06971i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(3.38334 - 3.68144i) q^{5} +2.44949 q^{6} +(-2.06971 + 2.06971i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(0.298094 + 7.06478i) q^{10} +0.900062 q^{11} +(-2.44949 + 2.44949i) q^{12} +(6.37460 + 6.37460i) q^{13} -4.13941i q^{14} +(-8.65256 + 0.365089i) q^{15} -4.00000 q^{16} +(-18.4729 + 18.4729i) q^{17} +(-3.00000 - 3.00000i) q^{18} +9.86457i q^{19} +(-7.36288 - 6.76669i) q^{20} +5.06972 q^{21} +(-0.900062 + 0.900062i) q^{22} +(3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(-2.10597 - 24.9111i) q^{25} -12.7492 q^{26} +(3.67423 - 3.67423i) q^{27} +(4.13941 + 4.13941i) q^{28} +7.79905i q^{29} +(8.28747 - 9.01764i) q^{30} +18.5068 q^{31} +(4.00000 - 4.00000i) q^{32} +(-1.10235 - 1.10235i) q^{33} -36.9457i q^{34} +(0.616966 + 14.6220i) q^{35} +6.00000 q^{36} +(-22.8521 + 22.8521i) q^{37} +(-9.86457 - 9.86457i) q^{38} -15.6145i q^{39} +(14.1296 - 0.596187i) q^{40} +36.6804 q^{41} +(-5.06972 + 5.06972i) q^{42} +(14.6911 + 14.6911i) q^{43} -1.80012i q^{44} +(11.0443 + 10.1500i) q^{45} -6.78233 q^{46} +(27.0328 - 27.0328i) q^{47} +(4.89898 + 4.89898i) q^{48} +40.4326i q^{49} +(27.0171 + 22.8052i) q^{50} +45.2491 q^{51} +(12.7492 - 12.7492i) q^{52} +(51.0631 + 51.0631i) q^{53} +7.34847i q^{54} +(3.04522 - 3.31352i) q^{55} -8.27882 q^{56} +(12.0816 - 12.0816i) q^{57} +(-7.79905 - 7.79905i) q^{58} -91.7327i q^{59} +(0.730177 + 17.3051i) q^{60} -44.5012 q^{61} +(-18.5068 + 18.5068i) q^{62} +(-6.20912 - 6.20912i) q^{63} +8.00000i q^{64} +(45.0351 - 1.90023i) q^{65} +2.20469 q^{66} +(-21.6784 + 21.6784i) q^{67} +(36.9457 + 36.9457i) q^{68} -8.30662i q^{69} +(-15.2390 - 14.0051i) q^{70} +84.1101 q^{71} +(-6.00000 + 6.00000i) q^{72} +(77.0736 + 77.0736i) q^{73} -45.7041i q^{74} +(-27.9305 + 33.0891i) q^{75} +19.7291 q^{76} +(-1.86286 + 1.86286i) q^{77} +(15.6145 + 15.6145i) q^{78} +31.3293i q^{79} +(-13.5334 + 14.7258i) q^{80} -9.00000 q^{81} +(-36.6804 + 36.6804i) q^{82} +(8.70034 + 8.70034i) q^{83} -10.1394i q^{84} +(5.50664 + 130.507i) q^{85} -29.3822 q^{86} +(9.55185 - 9.55185i) q^{87} +(1.80012 + 1.80012i) q^{88} +32.1361i q^{89} +(-21.1943 + 0.894281i) q^{90} -26.3871 q^{91} +(6.78233 - 6.78233i) q^{92} +(-22.6662 - 22.6662i) q^{93} +54.0656i q^{94} +(36.3158 + 33.3752i) q^{95} -9.79796 q^{96} +(-104.238 + 104.238i) q^{97} +(-40.4326 - 40.4326i) q^{98} +2.70019i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$4$		−	2.00000i		−	0.500000i
$5$	3.38334	−	3.68144i	0.676669	−	0.736288i
$5$	3.38334	−	3.68144i	0.676669	−	0.736288i
$6$	2.44949			0.408248
$7$	−2.06971	+	2.06971i	−0.295672	+	0.295672i	−0.839316	−	0.543644i	$-0.817044\pi$
$7$	−2.06971	+	2.06971i	−0.295672	+	0.295672i	0.543644	+	0.839316i	$0.317044\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$			3.00000i			0.333333i
$10$	0.298094	+	7.06478i	0.0298094	+	0.706478i
$11$	0.900062			0.0818238			0.0409119	−	0.999163i	$-0.486974\pi$
$11$	0.900062			0.0818238			0.0409119	+	0.999163i	$0.486974\pi$
$12$	−2.44949	+	2.44949i	−0.204124	+	0.204124i
$13$	6.37460	+	6.37460i	0.490354	+	0.490354i	0.908418	−	0.418064i	$-0.137291\pi$
$13$	6.37460	+	6.37460i	0.490354	+	0.490354i	−0.418064	+	0.908418i	$0.637291\pi$
$14$		−	4.13941i		−	0.295672i
$15$	−8.65256	+	0.365089i	−0.576837	+	0.0243392i
$16$	−4.00000			−0.250000
$17$	−18.4729	+	18.4729i	−1.08664	+	1.08664i	−0.0907667	+	0.995872i	$0.528932\pi$
$17$	−18.4729	+	18.4729i	−1.08664	+	1.08664i	−0.995872	+	0.0907667i	$0.971068\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$			9.86457i			0.519188i	0.965718	+	0.259594i	$0.0835888\pi$
$19$			9.86457i			0.519188i	−0.965718	+	0.259594i	$0.916411\pi$
$20$	−7.36288	−	6.76669i	−0.368144	−	0.338334i
$21$	5.06972			0.241415
$22$	−0.900062	+	0.900062i	−0.0409119	+	0.0409119i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$24$		−	4.89898i		−	0.204124i
$25$	−2.10597	−	24.9111i	−0.0842387	−	0.996446i
$26$	−12.7492			−0.490354
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	4.13941	+	4.13941i	0.147836	+	0.147836i
$29$			7.79905i			0.268933i	0.990918	+	0.134466i	$0.0429320\pi$
$29$			7.79905i			0.268933i	−0.990918	+	0.134466i	$0.957068\pi$
$30$	8.28747	−	9.01764i	0.276249	−	0.300588i
$31$	18.5068			0.596995			0.298497	−	0.954410i	$-0.403515\pi$
$31$	18.5068			0.596995			0.298497	+	0.954410i	$0.403515\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	−1.10235	−	1.10235i	−0.0334044	−	0.0334044i
$34$		−	36.9457i		−	1.08664i
$35$	0.616966	+	14.6220i	0.0176276	+	0.417772i
$36$	6.00000			0.166667
$37$	−22.8521	+	22.8521i	−0.617623	+	0.617623i	−0.944921	−	0.327298i	$-0.893862\pi$
$37$	−22.8521	+	22.8521i	−0.617623	+	0.617623i	0.327298	+	0.944921i	$0.393862\pi$
$38$	−9.86457	−	9.86457i	−0.259594	−	0.259594i
$39$		−	15.6145i		−	0.400372i
$40$	14.1296	−	0.596187i	0.353239	−	0.0149047i
$41$	36.6804			0.894643			0.447322	−	0.894373i	$-0.352378\pi$
$41$	36.6804			0.894643			0.447322	+	0.894373i	$0.352378\pi$
$42$	−5.06972	+	5.06972i	−0.120708	+	0.120708i
$43$	14.6911	+	14.6911i	0.341654	+	0.341654i	0.856989	−	0.515335i	$-0.172333\pi$
$43$	14.6911	+	14.6911i	0.341654	+	0.341654i	−0.515335	+	0.856989i	$0.672333\pi$
$44$		−	1.80012i		−	0.0409119i
$45$	11.0443	+	10.1500i	0.245429	+	0.225556i
$46$	−6.78233			−0.147442
$47$	27.0328	−	27.0328i	0.575166	−	0.575166i	−0.358401	−	0.933568i	$-0.616678\pi$
$47$	27.0328	−	27.0328i	0.575166	−	0.575166i	0.933568	+	0.358401i	$0.116678\pi$
$48$	4.89898	+	4.89898i	0.102062	+	0.102062i
$49$			40.4326i			0.825156i
$50$	27.0171	+	22.8052i	0.540342	+	0.456103i
$51$	45.2491			0.887237
$52$	12.7492	−	12.7492i	0.245177	−	0.245177i
$53$	51.0631	+	51.0631i	0.963455	+	0.963455i	0.999355	−	0.0359002i	$-0.0114298\pi$
$53$	51.0631	+	51.0631i	0.963455	+	0.963455i	−0.0359002	+	0.999355i	$0.511430\pi$
$54$			7.34847i			0.136083i
$55$	3.04522	−	3.31352i	0.0553676	−	0.0602459i
$56$	−8.27882			−0.147836
$57$	12.0816	−	12.0816i	0.211958	−	0.211958i
$58$	−7.79905	−	7.79905i	−0.134466	−	0.134466i
$59$		−	91.7327i		−	1.55479i	−0.629012	−	0.777396i	$-0.716540\pi$
$59$		−	91.7327i		−	1.55479i	0.629012	−	0.777396i	$-0.283460\pi$
$60$	0.730177	+	17.3051i	0.0121696	+	0.288419i
$61$	−44.5012			−0.729528			−0.364764	−	0.931100i	$-0.618850\pi$
$61$	−44.5012			−0.729528			−0.364764	+	0.931100i	$0.618850\pi$
$62$	−18.5068	+	18.5068i	−0.298497	+	0.298497i
$63$	−6.20912	−	6.20912i	−0.0985574	−	0.0985574i
$64$			8.00000i			0.125000i
$65$	45.0351	−	1.90023i	0.692848	−	0.0292343i
$66$	2.20469			0.0334044
$67$	−21.6784	+	21.6784i	−0.323557	+	0.323557i	−0.850130	−	0.526573i	$-0.823477\pi$
$67$	−21.6784	+	21.6784i	−0.323557	+	0.323557i	0.526573	+	0.850130i	$0.323477\pi$
$68$	36.9457	+	36.9457i	0.543319	+	0.543319i
$69$		−	8.30662i		−	0.120386i
$70$	−15.2390	−	14.0051i	−0.217700	−	0.200072i
$71$	84.1101			1.18465			0.592325	−	0.805699i	$-0.298210\pi$
$71$	84.1101			1.18465			0.592325	+	0.805699i	$0.298210\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	77.0736	+	77.0736i	1.05580	+	1.05580i	0.998348	+	0.0574543i	$0.0182984\pi$
$73$	77.0736	+	77.0736i	1.05580	+	1.05580i	0.0574543	+	0.998348i	$0.481702\pi$
$74$		−	45.7041i		−	0.617623i
$75$	−27.9305	+	33.0891i	−0.372407	+	0.441188i
$76$	19.7291			0.259594
$77$	−1.86286	+	1.86286i	−0.0241930	+	0.0241930i
$78$	15.6145	+	15.6145i	0.200186	+	0.200186i
$79$			31.3293i			0.396574i	0.980144	+	0.198287i	$0.0635378\pi$
$79$			31.3293i			0.396574i	−0.980144	+	0.198287i	$0.936462\pi$
$80$	−13.5334	+	14.7258i	−0.169167	+	0.184072i
$81$	−9.00000			−0.111111
$82$	−36.6804	+	36.6804i	−0.447322	+	0.447322i
$83$	8.70034	+	8.70034i	0.104823	+	0.104823i	0.757573	−	0.652750i	$-0.226385\pi$
$83$	8.70034	+	8.70034i	0.104823	+	0.104823i	−0.652750	+	0.757573i	$0.726385\pi$
$84$		−	10.1394i		−	0.120708i
$85$	5.50664	+	130.507i	0.0647840	+	1.53537i
$86$	−29.3822			−0.341654
$87$	9.55185	−	9.55185i	0.109791	−	0.109791i
$88$	1.80012	+	1.80012i	0.0204560	+	0.0204560i
$89$			32.1361i			0.361079i	0.983568	+	0.180540i	$0.0577844\pi$
$89$			32.1361i			0.361079i	−0.983568	+	0.180540i	$0.942216\pi$
$90$	−21.1943	+	0.894281i	−0.235493	+	0.00993646i
$91$	−26.3871			−0.289968
$92$	6.78233	−	6.78233i	0.0737210	−	0.0737210i
$93$	−22.6662	−	22.6662i	−0.243722	−	0.243722i
$94$			54.0656i			0.575166i
$95$	36.3158	+	33.3752i	0.382272	+	0.351318i
$96$	−9.79796			−0.102062
$97$	−104.238	+	104.238i	−1.07461	+	1.07461i	−0.0776323	+	0.996982i	$0.524736\pi$
$97$	−104.238	+	104.238i	−1.07461	+	1.07461i	−0.996982	+	0.0776323i	$0.975264\pi$
$98$	−40.4326	−	40.4326i	−0.412578	−	0.412578i
$99$			2.70019i			0.0272746i
$100$	−49.8223	+	4.21193i	−0.498223	+	0.0421193i
$101$	62.2349			0.616187			0.308094	−	0.951356i	$-0.400309\pi$
$101$	62.2349			0.616187			0.308094	+	0.951356i	$0.400309\pi$
$102$	−45.2491	+	45.2491i	−0.443618	+	0.443618i
$103$	118.903	+	118.903i	1.15440	+	1.15440i	0.985661	+	0.168738i	$0.0539692\pi$
$103$	118.903	+	118.903i	1.15440	+	1.15440i	0.168738	+	0.985661i	$0.446031\pi$
$104$			25.4984i			0.245177i
$105$	17.1526	−	18.6639i	0.163358	−	0.177751i
$106$	−102.126			−0.963455
$107$	−18.5364	+	18.5364i	−0.173237	+	0.173237i	−0.788400	−	0.615163i	$-0.789090\pi$
$107$	−18.5364	+	18.5364i	−0.173237	+	0.173237i	0.615163	+	0.788400i	$0.289090\pi$
$108$	−7.34847	−	7.34847i	−0.0680414	−	0.0680414i
$109$			73.8874i			0.677866i	0.940811	+	0.338933i	$0.110066\pi$
$109$			73.8874i			0.677866i	−0.940811	+	0.338933i	$0.889934\pi$
$110$	0.268303	+	6.35874i	0.00243912	+	0.0578067i
$111$	55.9759			0.504287
$112$	8.27882	−	8.27882i	0.0739181	−	0.0739181i
$113$	80.0463	+	80.0463i	0.708374	+	0.708374i	0.966193	−	0.257819i	$-0.0830038\pi$
$113$	80.0463	+	80.0463i	0.708374	+	0.708374i	−0.257819	+	0.966193i	$0.583004\pi$
$114$			24.1632i			0.211958i
$115$	23.9578	−	1.01088i	0.208329	−	0.00879030i
$116$	15.5981			0.134466
$117$	−19.1238	+	19.1238i	−0.163451	+	0.163451i
$118$	91.7327	+	91.7327i	0.777396	+	0.777396i
$119$		−	76.4668i		−	0.642578i
$120$	−18.0353	−	16.5749i	−0.150294	−	0.138124i
$121$	−120.190			−0.993305
$122$	44.5012	−	44.5012i	0.364764	−	0.364764i
$123$	−44.9241	−	44.9241i	−0.365237	−	0.365237i
$124$		−	37.0137i		−	0.298497i
$125$	−98.8340	−	76.5300i	−0.790672	−	0.612240i
$126$	12.4182			0.0985574
$127$	−27.4253	+	27.4253i	−0.215947	+	0.215947i	−0.806788	−	0.590841i	$-0.798796\pi$
$127$	−27.4253	+	27.4253i	−0.215947	+	0.215947i	0.590841	+	0.806788i	$0.298796\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$		−	35.9857i		−	0.278959i
$130$	−43.1349	+	46.9354i	−0.331807	+	0.361041i
$131$	80.5645			0.614996			0.307498	−	0.951549i	$-0.400508\pi$
$131$	80.5645			0.614996			0.307498	+	0.951549i	$0.400508\pi$
$132$	−2.20469	+	2.20469i	−0.0167022	+	0.0167022i
$133$	−20.4168	−	20.4168i	−0.153510	−	0.153510i
$134$		−	43.3567i		−	0.323557i
$135$	−1.09527	−	25.9577i	−0.00811308	−	0.192279i
$136$	−73.8914			−0.543319
$137$	54.9704	−	54.9704i	0.401244	−	0.401244i	−0.477427	−	0.878671i	$-0.658431\pi$
$137$	54.9704	−	54.9704i	0.401244	−	0.401244i	0.878671	+	0.477427i	$0.158431\pi$
$138$	8.30662	+	8.30662i	0.0601929	+	0.0601929i
$139$		−	133.632i		−	0.961379i	−0.876891	−	0.480690i	$-0.840386\pi$
$139$		−	133.632i		−	0.961379i	0.876891	−	0.480690i	$-0.159614\pi$
$140$	29.2440	−	1.23393i	0.208886	−	0.00881380i
$141$	−66.2166			−0.469621
$142$	−84.1101	+	84.1101i	−0.592325	+	0.592325i
$143$	5.73753	+	5.73753i	0.0401226	+	0.0401226i
$144$		−	12.0000i		−	0.0833333i
$145$	28.7117	+	26.3869i	0.198012	+	0.181979i
$146$	−154.147			−1.05580
$147$	49.5197	−	49.5197i	0.336868	−	0.336868i
$148$	45.7041	+	45.7041i	0.308812	+	0.308812i
$149$		−	193.876i		−	1.30118i	−0.759428	−	0.650591i	$-0.774521\pi$
$149$		−	193.876i		−	1.30118i	0.759428	−	0.650591i	$-0.225479\pi$
$150$	−5.15854	−	61.0196i	−0.0343903	−	0.406797i
$151$	211.812			1.40273			0.701364	−	0.712803i	$-0.252575\pi$
$151$	211.812			1.40273			0.701364	+	0.712803i	$0.252575\pi$
$152$	−19.7291	+	19.7291i	−0.129797	+	0.129797i
$153$	−55.4186	−	55.4186i	−0.362213	−	0.362213i
$154$		−	3.72573i		−	0.0241930i
$155$	62.6150	−	68.1318i	0.403968	−	0.439560i
$156$	−31.2290			−0.200186
$157$	−134.833	+	134.833i	−0.858809	+	0.858809i	−0.991198	−	0.132389i	$-0.957735\pi$
$157$	−134.833	+	134.833i	−0.858809	+	0.858809i	0.132389	+	0.991198i	$0.457735\pi$
$158$	−31.3293	−	31.3293i	−0.198287	−	0.198287i
$159$		−	125.079i		−	0.786658i
$160$	−1.19237	−	28.2591i	−0.00745234	−	0.176620i
$161$	−14.0374			−0.0871890
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	−142.999	−	142.999i	−0.877293	−	0.877293i	0.115961	−	0.993254i	$-0.463005\pi$
$163$	−142.999	−	142.999i	−0.877293	−	0.877293i	−0.993254	+	0.115961i	$0.963005\pi$
$164$		−	73.3608i		−	0.447322i
$165$	−7.78784	+	0.328602i	−0.0471990	+	0.00199153i
$166$	−17.4007			−0.104823
$167$	−142.222	+	142.222i	−0.851630	+	0.851630i	−0.990334	−	0.138704i	$-0.955706\pi$
$167$	−142.222	+	142.222i	−0.851630	+	0.851630i	0.138704	+	0.990334i	$0.455706\pi$
$168$	10.1394	+	10.1394i	0.0603539	+	0.0603539i
$169$		−	87.7290i		−	0.519107i
$170$	−136.013	−	125.000i	−0.800079	−	0.735295i
$171$	−29.5937			−0.173063
$172$	29.3822	−	29.3822i	0.170827	−	0.170827i
$173$	147.140	+	147.140i	0.850518	+	0.850518i	0.990197	−	0.139679i	$-0.0446071\pi$
$173$	147.140	+	147.140i	0.850518	+	0.850518i	−0.139679	+	0.990197i	$0.544607\pi$
$174$			19.1037i			0.109791i
$175$	55.9175	+	47.2000i	0.319528	+	0.269714i
$176$	−3.60025			−0.0204560
$177$	−112.349	+	112.349i	−0.634741	+	0.634741i
$178$	−32.1361	−	32.1361i	−0.180540	−	0.180540i
$179$		−	119.989i		−	0.670327i	−0.942160	−	0.335164i	$-0.891208\pi$
$179$		−	119.989i		−	0.670327i	0.942160	−	0.335164i	$-0.108792\pi$
$180$	20.3001	−	22.0886i	0.112778	−	0.122715i
$181$	142.935			0.789695			0.394847	−	0.918747i	$-0.370797\pi$
$181$	142.935			0.789695			0.394847	+	0.918747i	$0.370797\pi$
$182$	26.3871	−	26.3871i	0.144984	−	0.144984i
$183$	54.5026	+	54.5026i	0.297828	+	0.297828i
$184$			13.5647i			0.0737210i
$185$	6.81206	+	161.445i	0.0368219	+	0.872675i
$186$	45.3323			0.243722
$187$	−16.6267	+	16.6267i	−0.0889129	+	0.0889129i
$188$	−54.0656	−	54.0656i	−0.287583	−	0.287583i
$189$			15.2092i			0.0804718i
$190$	−69.6911	+	2.94057i	−0.366795	+	0.0154767i
$191$	71.7202			0.375499			0.187749	−	0.982217i	$-0.439881\pi$
$191$	71.7202			0.375499			0.187749	+	0.982217i	$0.439881\pi$
$192$	9.79796	−	9.79796i	0.0510310	−	0.0510310i
$193$	15.6998	+	15.6998i	0.0813462	+	0.0813462i	0.746609	−	0.665263i	$-0.231681\pi$
$193$	15.6998	+	15.6998i	0.0813462	+	0.0813462i	−0.665263	+	0.746609i	$0.731681\pi$
$194$		−	208.475i		−	1.07461i
$195$	−57.4838	−	52.8293i	−0.294789	−	0.270919i
$196$	80.8653			0.412578
$197$	258.375	−	258.375i	1.31155	−	1.31155i	0.391274	−	0.920274i	$-0.372035\pi$
$197$	258.375	−	258.375i	1.31155	−	1.31155i	0.920274	−	0.391274i	$-0.127965\pi$
$198$	−2.70019	−	2.70019i	−0.0136373	−	0.0136373i
$199$		−	17.1356i		−	0.0861087i	−0.999073	−	0.0430544i	$-0.986291\pi$
$199$		−	17.1356i		−	0.0861087i	0.999073	−	0.0430544i	$-0.0137089\pi$
$200$	45.6103	−	54.0342i	0.228052	−	0.270171i
$201$	53.1009			0.264184
$202$	−62.2349	+	62.2349i	−0.308094	+	0.308094i
$203$	−16.1417	−	16.1417i	−0.0795160	−	0.0795160i
$204$		−	90.4982i		−	0.443618i
$205$	124.102	−	135.037i	0.605377	−	0.658715i
$206$	−237.806			−1.15440
$207$	−10.1735	+	10.1735i	−0.0491473	+	0.0491473i
$208$	−25.4984	−	25.4984i	−0.122588	−	0.122588i
$209$			8.87873i			0.0424819i
$210$	1.51125	+	35.8165i	0.00719644	+	0.170555i
$211$	−87.8965			−0.416571			−0.208286	−	0.978068i	$-0.566788\pi$
$211$	−87.8965			−0.416571			−0.208286	+	0.978068i	$0.566788\pi$
$212$	102.126	−	102.126i	0.481728	−	0.481728i
$213$	−103.013	−	103.013i	−0.483631	−	0.483631i
$214$		−	37.0728i		−	0.173237i
$215$	103.789	−	4.37933i	0.482742	−	0.0203690i
$216$	14.6969			0.0680414
$217$	−38.3037	+	38.3037i	−0.176515	+	0.176515i
$218$	−73.8874	−	73.8874i	−0.338933	−	0.338933i
$219$		−	188.791i		−	0.862059i
$220$	−6.62704	−	6.09044i	−0.0301229	−	0.0276838i
$221$	−235.514			−1.06567
$222$	−55.9759	+	55.9759i	−0.252144	+	0.252144i
$223$	−158.653	−	158.653i	−0.711447	−	0.711447i	0.255391	−	0.966838i	$-0.417796\pi$
$223$	−158.653	−	158.653i	−0.711447	−	0.711447i	−0.966838	+	0.255391i	$0.917796\pi$
$224$			16.5576i			0.0739181i
$225$	74.7334	−	6.31790i	0.332149	−	0.0280796i
$226$	−160.093			−0.708374
$227$	176.500	−	176.500i	0.777531	−	0.777531i	−0.201879	−	0.979410i	$-0.564705\pi$
$227$	176.500	−	176.500i	0.777531	−	0.777531i	0.979410	+	0.201879i	$0.0647048\pi$
$228$	−24.1632	−	24.1632i	−0.105979	−	0.105979i
$229$			140.584i			0.613902i	0.951725	+	0.306951i	$0.0993088\pi$
$229$			140.584i			0.613902i	−0.951725	+	0.306951i	$0.900691\pi$
$230$	−22.9470	+	24.9687i	−0.0997694	+	0.108560i
$231$	4.56306			0.0197535
$232$	−15.5981	+	15.5981i	−0.0672332	+	0.0672332i
$233$	23.4052	+	23.4052i	0.100451	+	0.100451i	0.755546	−	0.655095i	$-0.227371\pi$
$233$	23.4052	+	23.4052i	0.100451	+	0.100451i	−0.655095	+	0.755546i	$0.727371\pi$
$234$		−	38.2476i		−	0.163451i
$235$	−8.05831	−	190.981i	−0.0342907	−	0.812685i
$236$	−183.465			−0.777396
$237$	38.3704	−	38.3704i	0.161901	−	0.161901i
$238$	76.4668	+	76.4668i	0.321289	+	0.321289i
$239$			158.063i			0.661349i	0.943745	+	0.330675i	$0.107276\pi$
$239$			158.063i			0.661349i	−0.943745	+	0.330675i	$0.892724\pi$
$240$	34.6102	−	1.46035i	0.144209	−	0.00608481i
$241$	148.164			0.614786			0.307393	−	0.951583i	$-0.400543\pi$
$241$	148.164			0.614786			0.307393	+	0.951583i	$0.400543\pi$
$242$	120.190	−	120.190i	0.496652	−	0.496652i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$			89.0024i			0.364764i
$245$	148.850	+	136.798i	0.607552	+	0.558357i
$246$	89.8482			0.365237
$247$	−62.8827	+	62.8827i	−0.254586	+	0.254586i
$248$	37.0137	+	37.0137i	0.149249	+	0.149249i
$249$		−	21.3114i		−	0.0855879i
$250$	175.364	−	22.3040i	0.701456	−	0.0892162i
$251$	−222.580			−0.886771			−0.443386	−	0.896331i	$-0.646223\pi$
$251$	−222.580			−0.886771			−0.443386	+	0.896331i	$0.646223\pi$
$252$	−12.4182	+	12.4182i	−0.0492787	+	0.0492787i
$253$	3.05226	+	3.05226i	0.0120643	+	0.0120643i
$254$		−	54.8505i		−	0.215947i
$255$	153.093	−	166.582i	0.600366	−	0.653262i
$256$	16.0000			0.0625000
$257$	−281.297	+	281.297i	−1.09454	+	1.09454i	−0.0995018	+	0.995037i	$0.531725\pi$
$257$	−281.297	+	281.297i	−1.09454	+	1.09454i	−0.995037	+	0.0995018i	$0.968275\pi$
$258$	35.9857	+	35.9857i	0.139480	+	0.139480i
$259$		−	94.5941i		−	0.365228i
$260$	−3.80045	−	90.0703i	−0.0146171	−	0.346424i
$261$	−23.3972			−0.0896443
$262$	−80.5645	+	80.5645i	−0.307498	+	0.307498i
$263$	−177.629	−	177.629i	−0.675394	−	0.675394i	0.283560	−	0.958954i	$-0.408484\pi$
$263$	−177.629	−	177.629i	−0.675394	−	0.675394i	−0.958954	+	0.283560i	$0.908484\pi$
$264$		−	4.40938i		−	0.0167022i
$265$	360.750	−	15.2216i	1.36132	−	0.0574400i
$266$	40.8335			0.153510
$267$	39.3585	−	39.3585i	0.147410	−	0.147410i
$268$	43.3567	+	43.3567i	0.161779	+	0.161779i
$269$		−	93.2801i		−	0.346766i	−0.984854	−	0.173383i	$-0.944530\pi$
$269$		−	93.2801i		−	0.346766i	0.984854	−	0.173383i	$-0.0554699\pi$
$270$	27.0529	+	24.8624i	0.100196	+	0.0920830i
$271$	−351.552			−1.29724			−0.648620	−	0.761113i	$-0.724653\pi$
$271$	−351.552			−1.29724			−0.648620	+	0.761113i	$0.724653\pi$
$272$	73.8914	−	73.8914i	0.271660	−	0.271660i
$273$	32.3174	+	32.3174i	0.118379	+	0.118379i
$274$			109.941i			0.401244i
$275$	−1.89550	−	22.4216i	−0.00689273	−	0.0815330i
$276$	−16.6132			−0.0601929
$277$	−211.987	+	211.987i	−0.765297	+	0.765297i	−0.977275	−	0.211977i	$-0.932010\pi$
$277$	−211.987	+	211.987i	−0.765297	+	0.765297i	0.211977	+	0.977275i	$0.432010\pi$
$278$	133.632	+	133.632i	0.480690	+	0.480690i
$279$			55.5205i			0.198998i
$280$	−28.0101	+	30.4780i	−0.100036	+	0.108850i
$281$	−135.367			−0.481732			−0.240866	−	0.970558i	$-0.577431\pi$
$281$	−135.367			−0.481732			−0.240866	+	0.970558i	$0.577431\pi$
$282$	66.2166	−	66.2166i	0.234811	−	0.234811i
$283$	107.157	+	107.157i	0.378648	+	0.378648i	0.870614	−	0.491966i	$-0.163722\pi$
$283$	107.157	+	107.157i	0.378648	+	0.378648i	−0.491966	+	0.870614i	$0.663722\pi$
$284$		−	168.220i		−	0.592325i
$285$	−3.60144	−	85.3538i	−0.0126366	−	0.299487i
$286$	−11.4751			−0.0401226
$287$	−75.9176	+	75.9176i	−0.264521	+	0.264521i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$		−	393.493i		−	1.36157i
$290$	−55.0986	+	2.32485i	−0.189995	+	0.00801672i
$291$	255.329			0.877419
$292$	154.147	−	154.147i	0.527901	−	0.527901i
$293$	−130.004	−	130.004i	−0.443700	−	0.443700i	0.449553	−	0.893253i	$-0.351583\pi$
$293$	−130.004	−	130.004i	−0.443700	−	0.443700i	−0.893253	+	0.449553i	$0.851583\pi$
$294$			99.0393i			0.336868i
$295$	−337.708	−	310.363i	−1.14477	−	1.05208i
$296$	−91.4083			−0.308812
$297$	3.30704	−	3.30704i	0.0111348	−	0.0111348i
$298$	193.876	+	193.876i	0.650591	+	0.650591i
$299$			43.2346i			0.144597i
$300$	66.1781	+	55.8610i	0.220594	+	0.186203i
$301$	−60.8126			−0.202035
$302$	−211.812	+	211.812i	−0.701364	+	0.701364i
$303$	−76.2219	−	76.2219i	−0.251557	−	0.251557i
$304$		−	39.4583i		−	0.129797i
$305$	−150.563	+	163.828i	−0.493649	+	0.537142i
$306$	110.837			0.362213
$307$	6.52034	−	6.52034i	0.0212389	−	0.0212389i	−0.696408	−	0.717646i	$-0.745219\pi$
$307$	6.52034	−	6.52034i	0.0212389	−	0.0212389i	0.717646	+	0.696408i	$0.245219\pi$
$308$	3.72573	+	3.72573i	0.0120965	+	0.0120965i
$309$		−	291.252i		−	0.942563i
$310$	5.51677	+	130.747i	0.0177960	+	0.421764i
$311$	21.8579			0.0702825			0.0351412	−	0.999382i	$-0.488812\pi$
$311$	21.8579			0.0702825			0.0351412	+	0.999382i	$0.488812\pi$
$312$	31.2290	−	31.2290i	0.100093	−	0.100093i
$313$	329.807	+	329.807i	1.05369	+	1.05369i	0.998474	+	0.0552208i	$0.0175863\pi$
$313$	329.807	+	329.807i	1.05369	+	1.05369i	0.0552208	+	0.998474i	$0.482414\pi$
$314$		−	269.666i		−	0.858809i
$315$	−43.8661	+	1.85090i	−0.139257	+	0.00587587i
$316$	62.6586			0.198287
$317$	−187.213	+	187.213i	−0.590579	+	0.590579i	−0.937788	−	0.347209i	$-0.887129\pi$
$317$	−187.213	+	187.213i	−0.590579	+	0.590579i	0.347209	+	0.937788i	$0.387129\pi$
$318$	125.079	+	125.079i	0.393329	+	0.393329i
$319$			7.01963i			0.0220051i
$320$	29.4515	+	27.0668i	0.0920359	+	0.0845836i
$321$	45.4047			0.141448
$322$	14.0374	−	14.0374i	0.0435945	−	0.0435945i
$323$	−182.227	−	182.227i	−0.564170	−	0.564170i
$324$			18.0000i			0.0555556i
$325$	145.374	−	172.223i	0.447304	−	0.529917i
$326$	285.998			0.877293
$327$	90.4932	−	90.4932i	0.276738	−	0.276738i
$328$	73.3608	+	73.3608i	0.223661	+	0.223661i
$329$			111.900i			0.340122i
$330$	7.45923	−	8.11644i	0.0226037	−	0.0245953i
$331$	−514.692			−1.55496			−0.777480	−	0.628908i	$-0.783502\pi$
$331$	−514.692			−1.55496			−0.777480	+	0.628908i	$0.783502\pi$
$332$	17.4007	−	17.4007i	0.0524117	−	0.0524117i
$333$	−68.5562	−	68.5562i	−0.205874	−	0.205874i
$334$		−	284.444i		−	0.851630i
$335$	6.46218	+	153.153i	0.0192901	+	0.457173i
$336$	−20.2789			−0.0603539
$337$	−131.193	+	131.193i	−0.389296	+	0.389296i	−0.874436	−	0.485140i	$-0.838769\pi$
$337$	−131.193	+	131.193i	−0.389296	+	0.389296i	0.485140	+	0.874436i	$0.338769\pi$
$338$	87.7290	+	87.7290i	0.259553	+	0.259553i
$339$		−	196.073i		−	0.578385i
$340$	261.013	−	11.0133i	0.767687	−	0.0323920i
$341$	16.6573			0.0488484
$342$	29.5937	−	29.5937i	0.0865313	−	0.0865313i
$343$	−185.099	−	185.099i	−0.539648	−	0.539648i
$344$			58.7644i			0.170827i
$345$	−30.5803	−	28.1042i	−0.0886386	−	0.0814614i
$346$	−294.279			−0.850518
$347$	8.51905	−	8.51905i	0.0245506	−	0.0245506i	−0.694725	−	0.719276i	$-0.744474\pi$
$347$	8.51905	−	8.51905i	0.0245506	−	0.0245506i	0.719276	+	0.694725i	$0.244474\pi$
$348$	−19.1037	−	19.1037i	−0.0548957	−	0.0548957i
$349$			141.333i			0.404965i	0.979286	+	0.202482i	$0.0649009\pi$
$349$			141.333i			0.404965i	−0.979286	+	0.202482i	$0.935099\pi$
$350$	−103.117	+	8.71746i	−0.294621	+	0.0249070i
$351$	46.8435			0.133457
$352$	3.60025	−	3.60025i	0.0102280	−	0.0102280i
$353$	−358.841	−	358.841i	−1.01655	−	1.01655i	−0.999861	−	0.0166867i	$-0.994688\pi$
$353$	−358.841	−	358.841i	−1.01655	−	1.01655i	−0.0166867	−	0.999861i	$-0.505312\pi$
$354$		−	224.698i		−	0.634741i
$355$	284.574	−	309.646i	0.801616	−	0.872243i
$356$	64.2721			0.180540
$357$	−93.6523	+	93.6523i	−0.262331	+	0.262331i
$358$	119.989	+	119.989i	0.335164	+	0.335164i
$359$			233.537i			0.650520i	0.945625	+	0.325260i	$0.105452\pi$
$359$			233.537i			0.650520i	−0.945625	+	0.325260i	$0.894548\pi$
$360$	1.78856	+	42.3887i	0.00496823	+	0.117746i
$361$	263.690			0.730444
$362$	−142.935	+	142.935i	−0.394847	+	0.394847i
$363$	147.202	+	147.202i	0.405515	+	0.405515i
$364$			52.7742i			0.144984i
$365$	544.508	−	22.9751i	1.49180	−	0.0629456i
$366$	−109.005			−0.297828
$367$	−41.8520	+	41.8520i	−0.114038	+	0.114038i	−0.761823	−	0.647785i	$-0.775696\pi$
$367$	−41.8520	+	41.8520i	−0.114038	+	0.114038i	0.647785	+	0.761823i	$0.275696\pi$
$368$	−13.5647	−	13.5647i	−0.0368605	−	0.0368605i
$369$			110.041i			0.298214i
$370$	−168.257	−	154.633i	−0.454748	−	0.417926i
$371$	−211.371			−0.569734
$372$	−45.3323	+	45.3323i	−0.121861	+	0.121861i
$373$	238.065	+	238.065i	0.638243	+	0.638243i	0.950122	−	0.311879i	$-0.100958\pi$
$373$	238.065	+	238.065i	0.638243	+	0.638243i	−0.311879	+	0.950122i	$0.600958\pi$
$374$		−	33.2534i		−	0.0889129i
$375$	27.3168	+	214.776i	0.0728447	+	0.572736i
$376$	108.131			0.287583
$377$	−49.7158	+	49.7158i	−0.131872	+	0.131872i
$378$	−15.2092	−	15.2092i	−0.0402359	−	0.0402359i
$379$		−	253.908i		−	0.669941i	−0.942229	−	0.334970i	$-0.891274\pi$
$379$		−	253.908i		−	0.669941i	0.942229	−	0.334970i	$-0.108726\pi$
$380$	66.7505	−	72.6316i	0.175659	−	0.191136i
$381$	67.1779			0.176320
$382$	−71.7202	+	71.7202i	−0.187749	+	0.187749i
$383$	−68.9077	−	68.9077i	−0.179916	−	0.179916i	0.611403	−	0.791319i	$-0.290605\pi$
$383$	−68.9077	−	68.9077i	−0.179916	−	0.179916i	−0.791319	+	0.611403i	$0.790605\pi$
$384$			19.5959i			0.0510310i
$385$	0.555308	+	13.1607i	0.00144236	+	0.0341837i
$386$	−31.3996			−0.0813462
$387$	−44.0733	+	44.0733i	−0.113885	+	0.113885i
$388$	208.475	+	208.475i	0.537307	+	0.537307i
$389$		−	34.7594i		−	0.0893557i	−0.999001	−	0.0446778i	$-0.985774\pi$
$389$		−	34.7594i		−	0.0893557i	0.999001	−	0.0446778i	$-0.0142261\pi$
$390$	110.313	−	4.65459i	0.282854	−	0.0119348i
$391$	−125.289			−0.320432
$392$	−80.8653	+	80.8653i	−0.206289	+	0.206289i
$393$	−98.6709	−	98.6709i	−0.251071	−	0.251071i
$394$			516.750i			1.31155i
$395$	115.337	+	105.998i	0.291992	+	0.268349i
$396$	5.40037			0.0136373
$397$	−490.772	+	490.772i	−1.23620	+	1.23620i	−0.274659	+	0.961542i	$0.588565\pi$
$397$	−490.772	+	490.772i	−1.23620	+	1.23620i	−0.961542	+	0.274659i	$0.911435\pi$
$398$	17.1356	+	17.1356i	0.0430544	+	0.0430544i
$399$			50.0107i			0.125340i
$400$	8.42387	+	99.6446i	0.0210597	+	0.249111i
$401$	−473.229			−1.18012			−0.590061	−	0.807358i	$-0.700896\pi$
$401$	−473.229			−1.18012			−0.590061	+	0.807358i	$0.700896\pi$
$402$	−53.1009	+	53.1009i	−0.132092	+	0.132092i
$403$	117.974	+	117.974i	0.292739	+	0.292739i
$404$		−	124.470i		−	0.308094i
$405$	−30.4501	+	33.1329i	−0.0751854	+	0.0818097i
$406$	32.2835			0.0795160
$407$	−20.5683	+	20.5683i	−0.0505363	+	0.0505363i
$408$	90.4982	+	90.4982i	0.221809	+	0.221809i
$409$			285.348i			0.697671i	0.937184	+	0.348836i	$0.113423\pi$
$409$			285.348i			0.697671i	−0.937184	+	0.348836i	$0.886577\pi$
$410$	10.9342	+	259.139i	0.0266688	+	0.632046i
$411$	−134.650			−0.327614
$412$	237.806	−	237.806i	0.577200	−	0.577200i
$413$	189.860	+	189.860i	0.459709	+	0.459709i
$414$		−	20.3470i		−	0.0491473i
$415$	61.4660	−	2.59352i	0.148111	−	0.00624944i
$416$	50.9968			0.122588
$417$	−163.665	+	163.665i	−0.392481	+	0.392481i
$418$	−8.87873	−	8.87873i	−0.0212410	−	0.0212410i
$419$			290.087i			0.692331i	0.938173	+	0.346165i	$0.112516\pi$
$419$			290.087i			0.692331i	−0.938173	+	0.346165i	$0.887484\pi$
$420$	−37.3277	−	34.3052i	−0.0888756	−	0.0816791i
$421$	−442.922			−1.05207			−0.526035	−	0.850463i	$-0.676322\pi$
$421$	−442.922			−1.05207			−0.526035	+	0.850463i	$0.676322\pi$
$422$	87.8965	−	87.8965i	0.208286	−	0.208286i
$423$	81.0985	+	81.0985i	0.191722	+	0.191722i
$424$			204.252i			0.481728i
$425$	499.083	+	421.277i	1.17431	+	0.991240i
$426$	206.027			0.483631
$427$	92.1044	−	92.1044i	0.215701	−	0.215701i
$428$	37.0728	+	37.0728i	0.0866187	+	0.0866187i
$429$		−	14.0540i		−	0.0327600i
$430$	−99.4102	+	108.169i	−0.231186	+	0.251555i
$431$	377.479			0.875821			0.437910	−	0.899019i	$-0.355719\pi$
$431$	377.479			0.875821			0.437910	+	0.899019i	$0.355719\pi$
$432$	−14.6969	+	14.6969i	−0.0340207	+	0.0340207i
$433$	−567.756	−	567.756i	−1.31121	−	1.31121i	−0.920520	−	0.390695i	$-0.872235\pi$
$433$	−567.756	−	567.756i	−1.31121	−	1.31121i	−0.390695	−	0.920520i	$-0.627765\pi$
$434$		−	76.6074i		−	0.176515i
$435$	−2.84735	−	67.4818i	−0.00654562	−	0.155130i
$436$	147.775			0.338933
$437$	−33.4524	+	33.4524i	−0.0765501	+	0.0765501i
$438$	188.791	+	188.791i	0.431030	+	0.431030i
$439$		−	295.256i		−	0.672564i	−0.941761	−	0.336282i	$-0.890830\pi$
$439$		−	295.256i		−	0.672564i	0.941761	−	0.336282i	$-0.109170\pi$
$440$	12.7175	−	0.536606i	0.0289034	−	0.00121956i
$441$	−121.298			−0.275052
$442$	235.514	−	235.514i	0.532837	−	0.532837i
$443$	419.157	+	419.157i	0.946179	+	0.946179i	0.998624	−	0.0524451i	$-0.0167014\pi$
$443$	419.157	+	419.157i	0.946179	+	0.946179i	−0.0524451	+	0.998624i	$0.516701\pi$
$444$		−	111.952i		−	0.252144i
$445$	118.307	+	108.727i	0.265858	+	0.244331i
$446$	317.306			0.711447
$447$	−237.449	+	237.449i	−0.531206	+	0.531206i
$448$	−16.5576	−	16.5576i	−0.0369590	−	0.0369590i
$449$			646.254i			1.43932i	0.694328	+	0.719659i	$0.255702\pi$
$449$			646.254i			1.43932i	−0.694328	+	0.719659i	$0.744298\pi$
$450$	−68.4155	+	81.0513i	−0.152034	+	0.180114i
$451$	33.0146			0.0732031
$452$	160.093	−	160.093i	0.354187	−	0.354187i
$453$	−259.416	−	259.416i	−0.572661	−	0.572661i
$454$			352.999i			0.777531i
$455$	−89.2766	+	97.1424i	−0.196212	+	0.213500i
$456$	48.3263			0.105979
$457$	117.758	−	117.758i	0.257677	−	0.257677i	−0.566432	−	0.824109i	$-0.691677\pi$
$457$	117.758	−	117.758i	0.257677	−	0.257677i	0.824109	+	0.566432i	$0.191677\pi$
$458$	−140.584	−	140.584i	−0.306951	−	0.306951i
$459$			135.747i			0.295746i
$460$	−2.02177	−	47.9157i	−0.00439515	−	0.104165i
$461$	638.280			1.38456			0.692278	−	0.721631i	$-0.256607\pi$
$461$	638.280			1.38456			0.692278	+	0.721631i	$0.256607\pi$
$462$	−4.56306	+	4.56306i	−0.00987676	+	0.00987676i
$463$	243.006	+	243.006i	0.524851	+	0.524851i	0.919033	−	0.394182i	$-0.128972\pi$
$463$	243.006	+	243.006i	0.524851	+	0.524851i	−0.394182	+	0.919033i	$0.628972\pi$
$464$		−	31.1962i		−	0.0672332i
$465$	−160.131	+	6.75664i	−0.344369	+	0.0145304i
$466$	−46.8103			−0.100451
$467$	−180.259	+	180.259i	−0.385994	+	0.385994i	−0.873256	−	0.487262i	$-0.837996\pi$
$467$	−180.259	+	180.259i	−0.385994	+	0.385994i	0.487262	+	0.873256i	$0.337996\pi$
$468$	38.2476	+	38.2476i	0.0817256	+	0.0817256i
$469$		−	89.7356i		−	0.191334i
$470$	199.039	+	182.923i	0.423488	+	0.389197i
$471$	330.272			0.701214
$472$	183.465	−	183.465i	0.388698	−	0.388698i
$473$	13.2229	+	13.2229i	0.0279554	+	0.0279554i
$474$			76.7409i			0.161901i
$475$	245.738	−	20.7745i	0.517343	−	0.0437357i
$476$	−152.934			−0.321289
$477$	−153.189	+	153.189i	−0.321152	+	0.321152i
$478$	−158.063	−	158.063i	−0.330675	−	0.330675i
$479$		−	521.944i		−	1.08965i	−0.838549	−	0.544827i	$-0.816595\pi$
$479$		−	521.944i		−	1.08965i	0.838549	−	0.544827i	$-0.183405\pi$
$480$	−33.1499	+	36.0706i	−0.0690622	+	0.0751470i
$481$	−291.345			−0.605708
$482$	−148.164	+	148.164i	−0.307393	+	0.307393i
$483$	17.1923	+	17.1923i	0.0355948	+	0.0355948i
$484$			240.380i			0.496652i
$485$	31.0726	+	736.416i	0.0640672	+	1.51838i
$486$	−22.0454			−0.0453609
$487$	−173.549	+	173.549i	−0.356364	+	0.356364i	−0.862471	−	0.506107i	$-0.831084\pi$
$487$	−173.549	+	173.549i	−0.356364	+	0.356364i	0.506107	+	0.862471i	$0.331084\pi$
$488$	−89.0024	−	89.0024i	−0.182382	−	0.182382i
$489$			350.274i			0.716307i
$490$	−285.648	+	12.0527i	−0.582955	+	0.0245974i
$491$	−261.292			−0.532164			−0.266082	−	0.963950i	$-0.585729\pi$
$491$	−261.292			−0.532164			−0.266082	+	0.963950i	$0.585729\pi$
$492$	−89.8482	+	89.8482i	−0.182618	+	0.182618i
$493$	−144.071	−	144.071i	−0.292233	−	0.292233i
$494$		−	125.765i		−	0.254586i
$495$	9.94057	+	9.13566i	0.0200820	+	0.0184559i
$496$	−74.0274			−0.149249
$497$	−174.083	+	174.083i	−0.350268	+	0.350268i
$498$	21.3114	+	21.3114i	0.0427940	+	0.0427940i
$499$			391.452i			0.784473i	0.919864	+	0.392237i	$0.128299\pi$
$499$			391.452i			0.784473i	−0.919864	+	0.392237i	$0.871701\pi$
$500$	−153.060	+	197.668i	−0.306120	+	0.395336i
$501$	348.372			0.695353
$502$	222.580	−	222.580i	0.443386	−	0.443386i
$503$	−451.156	−	451.156i	−0.896930	−	0.896930i	0.0982331	−	0.995163i	$-0.468681\pi$
$503$	−451.156	−	451.156i	−0.896930	−	0.896930i	−0.995163	+	0.0982331i	$0.968681\pi$
$504$		−	24.8365i		−	0.0492787i
$505$	210.562	−	229.114i	0.416955	−	0.453691i
$506$	−6.10452			−0.0120643
$507$	−107.446	+	107.446i	−0.211924	+	0.211924i
$508$	54.8505	+	54.8505i	0.107973	+	0.107973i
$509$			15.5183i			0.0304878i	0.999884	+	0.0152439i	$0.00485247\pi$
$509$			15.5183i			0.0304878i	−0.999884	+	0.0152439i	$0.995148\pi$
$510$	13.4885	+	319.675i	0.0264480	+	0.626814i
$511$	−319.039			−0.624343
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	36.2448	+	36.2448i	0.0706526	+	0.0706526i
$514$		−	562.593i		−	1.09454i
$515$	840.024	−	35.4443i	1.63112	−	0.0688238i
$516$	−71.9714			−0.139480
$517$	24.3312	−	24.3312i	0.0470623	−	0.0470623i
$518$	94.5941	+	94.5941i	0.182614	+	0.182614i
$519$		−	360.417i		−	0.694445i
$520$	93.8707	+	86.2698i	0.180521	+	0.165904i
$521$	−573.680			−1.10111			−0.550556	−	0.834798i	$-0.685584\pi$
$521$	−573.680			−1.10111			−0.550556	+	0.834798i	$0.685584\pi$
$522$	23.3972	−	23.3972i	0.0448222	−	0.0448222i
$523$	159.178	+	159.178i	0.304356	+	0.304356i	0.842715	−	0.538359i	$-0.180956\pi$
$523$	159.178	+	159.178i	0.304356	+	0.304356i	−0.538359	+	0.842715i	$0.680956\pi$
$524$		−	161.129i		−	0.307498i
$525$	−10.6767	−	126.293i	−0.0203365	−	0.240557i
$526$	355.257			0.675394
$527$	−341.874	+	341.874i	−0.648718	+	0.648718i
$528$	4.40938	+	4.40938i	0.00835111	+	0.00835111i
$529$			23.0000i			0.0434783i
$530$	−345.528	+	375.971i	−0.651940	+	0.709380i
$531$	275.198			0.518264
$532$	−40.8335	+	40.8335i	−0.0767548	+	0.0767548i
$533$	233.823	+	233.823i	0.438692	+	0.438692i
$534$			78.7170i			0.147410i
$535$	5.52559	+	130.956i	0.0103282	+	0.244777i
$536$	−86.7134			−0.161779
$537$	−146.955	+	146.955i	−0.273660	+	0.273660i
$538$	93.2801	+	93.2801i	0.173383	+	0.173383i
$539$			36.3919i			0.0675174i
$540$	−51.9153	+	2.19053i	−0.0961395	+	0.00405654i
$541$	19.0291			0.0351740			0.0175870	−	0.999845i	$-0.494402\pi$
$541$	19.0291			0.0351740			0.0175870	+	0.999845i	$0.494402\pi$
$542$	351.552	−	351.552i	0.648620	−	0.648620i
$543$	−175.059	−	175.059i	−0.322392	−	0.322392i
$544$			147.783i			0.271660i
$545$	272.012	+	249.986i	0.499104	+	0.458691i
$546$	−64.6349			−0.118379
$547$	−18.2605	+	18.2605i	−0.0333830	+	0.0333830i	−0.723601	−	0.690218i	$-0.757515\pi$
$547$	−18.2605	+	18.2605i	−0.0333830	+	0.0333830i	0.690218	+	0.723601i	$0.257515\pi$
$548$	−109.941	−	109.941i	−0.200622	−	0.200622i
$549$		−	133.504i		−	0.243176i
$550$	24.3171	+	20.5261i	0.0442129	+	0.0373201i
$551$	−76.9344			−0.139627
$552$	16.6132	−	16.6132i	0.0300965	−	0.0300965i
$553$	−64.8425	−	64.8425i	−0.117256	−	0.117256i
$554$		−	423.975i		−	0.765297i
$555$	189.386	−	206.072i	0.341236	−	0.371301i
$556$	−267.263			−0.480690
$557$	602.059	−	602.059i	1.08090	−	1.08090i	0.0844703	−	0.996426i	$-0.473080\pi$
$557$	602.059	−	602.059i	1.08090	−	1.08090i	0.996426	−	0.0844703i	$-0.0269198\pi$
$558$	−55.5205	−	55.5205i	−0.0994991	−	0.0994991i
$559$			187.300i			0.335062i
$560$	−2.46787	−	58.4881i	−0.00440690	−	0.104443i
$561$	40.7270			0.0725971
$562$	135.367	−	135.367i	0.240866	−	0.240866i
$563$	−208.664	−	208.664i	−0.370628	−	0.370628i	0.497078	−	0.867706i	$-0.334406\pi$
$563$	−208.664	−	208.664i	−0.370628	−	0.370628i	−0.867706	+	0.497078i	$0.834406\pi$
$564$			132.433i			0.234811i
$565$	565.510	−	23.8613i	1.00090	−	0.0422324i
$566$	−214.315			−0.378648
$567$	18.6274	−	18.6274i	0.0328525	−	0.0328525i
$568$	168.220	+	168.220i	0.296162	+	0.296162i
$569$			375.263i			0.659513i	0.944066	+	0.329756i	$0.106967\pi$
$569$			375.263i			0.659513i	−0.944066	+	0.329756i	$0.893033\pi$
$570$	88.9552	+	81.7523i	0.156062	+	0.143425i
$571$	999.501			1.75044			0.875219	−	0.483726i	$-0.160717\pi$
$571$	999.501			1.75044			0.875219	+	0.483726i	$0.160717\pi$
$572$	11.4751	−	11.4751i	0.0200613	−	0.0200613i
$573$	−87.8390	−	87.8390i	−0.153297	−	0.153297i
$574$		−	151.835i		−	0.264521i
$575$	77.3361	−	91.6195i	0.134498	−	0.159338i
$576$	−24.0000			−0.0416667
$577$	503.643	−	503.643i	0.872866	−	0.872866i	−0.119918	−	0.992784i	$-0.538263\pi$
$577$	503.643	−	503.643i	0.872866	−	0.872866i	0.992784	+	0.119918i	$0.0382632\pi$
$578$	393.493	+	393.493i	0.680784	+	0.680784i
$579$		−	38.4566i		−	0.0664189i
$580$	52.7738	−	57.4235i	0.0909893	−	0.0990060i
$581$	−36.0143			−0.0619867
$582$	−255.329	+	255.329i	−0.438709	+	0.438709i
$583$	45.9600	+	45.9600i	0.0788336	+	0.0788336i
$584$			308.294i			0.527901i
$585$	5.70068	+	135.105i	0.00974475	+	0.230949i
$586$	260.008			0.443700
$587$	422.350	−	422.350i	0.719506	−	0.719506i	−0.248998	−	0.968504i	$-0.580101\pi$
$587$	422.350	−	422.350i	0.719506	−	0.719506i	0.968504	+	0.248998i	$0.0801013\pi$
$588$	−99.0393	−	99.0393i	−0.168434	−	0.168434i
$589$			182.562i			0.309953i
$590$	648.071	−	27.3449i	1.09843	−	0.0463473i
$591$	−632.887			−1.07087
$592$	91.4083	−	91.4083i	0.154406	−	0.154406i
$593$	−228.691	−	228.691i	−0.385651	−	0.385651i	0.487482	−	0.873133i	$-0.337916\pi$
$593$	−228.691	−	228.691i	−0.385651	−	0.385651i	−0.873133	+	0.487482i	$0.837916\pi$
$594$			6.61408i			0.0111348i
$595$	−281.508	−	258.713i	−0.473122	−	0.434812i
$596$	−387.752			−0.650591
$597$	−20.9868	+	20.9868i	−0.0351537	+	0.0351537i
$598$	−43.2346	−	43.2346i	−0.0722987	−	0.0722987i
$599$			277.402i			0.463108i	0.972822	+	0.231554i	$0.0743811\pi$
$599$			277.402i			0.463108i	−0.972822	+	0.231554i	$0.925619\pi$
$600$	−122.039	+	10.3171i	−0.203399	+	0.0171951i
$601$	−535.528			−0.891062			−0.445531	−	0.895266i	$-0.646985\pi$
$601$	−535.528			−0.891062			−0.445531	+	0.895266i	$0.646985\pi$
$602$	60.8126	−	60.8126i	0.101018	−	0.101018i
$603$	−65.0351	−	65.0351i	−0.107852	−	0.107852i
$604$		−	423.624i		−	0.701364i
$605$	−406.644	+	442.472i	−0.672138	+	0.731358i
$606$	152.444			0.251557
$607$	689.127	−	689.127i	1.13530	−	1.13530i	0.146018	−	0.989282i	$-0.453354\pi$
$607$	689.127	−	689.127i	1.13530	−	1.13530i	0.989282	−	0.146018i	$-0.0466458\pi$
$608$	39.4583	+	39.4583i	0.0648985	+	0.0648985i
$609$			39.5391i			0.0649245i
$610$	−13.2655	−	314.391i	−0.0217468	−	0.515395i
$611$	344.647			0.564070
$612$	−110.837	+	110.837i	−0.181106	+	0.181106i
$613$	212.580	+	212.580i	0.346787	+	0.346787i	0.858911	−	0.512124i	$-0.171141\pi$
$613$	212.580	+	212.580i	0.346787	+	0.346787i	−0.512124	+	0.858911i	$0.671141\pi$
$614$			13.0407i			0.0212389i
$615$	−317.379	+	13.3916i	−0.516063	+	0.0217749i
$616$	−7.45145			−0.0120965
$617$	743.093	−	743.093i	1.20437	−	1.20437i	0.231540	−	0.972825i	$-0.425624\pi$
$617$	743.093	−	743.093i	1.20437	−	1.20437i	0.972825	−	0.231540i	$-0.0743763\pi$
$618$	291.252	+	291.252i	0.471281	+	0.471281i
$619$		−	837.046i		−	1.35225i	−0.736785	−	0.676127i	$-0.763657\pi$
$619$		−	837.046i		−	1.35225i	0.736785	−	0.676127i	$-0.236343\pi$
$620$	−136.264	−	125.230i	−0.219780	−	0.201984i
$621$	24.9199			0.0401286
$622$	−21.8579	+	21.8579i	−0.0351412	+	0.0351412i
$623$	−66.5122	−	66.5122i	−0.106761	−	0.106761i
$624$			62.4580i			0.100093i
$625$	−616.130	+	104.924i	−0.985808	+	0.167879i
$626$	−659.613			−1.05369
$627$	10.8742	−	10.8742i	0.0173432	−	0.0173432i
$628$	269.666	+	269.666i	0.429404	+	0.429404i
$629$		−	844.286i		−	1.34227i
$630$	42.0152	−	45.7170i	0.0666907	−	0.0725666i
$631$	455.081			0.721206			0.360603	−	0.932719i	$-0.382571\pi$
$631$	455.081			0.721206			0.360603	+	0.932719i	$0.382571\pi$
$632$	−62.6586	+	62.6586i	−0.0991434	+	0.0991434i
$633$	107.651	+	107.651i	0.170064	+	0.170064i
$634$		−	374.427i		−	0.590579i
$635$	8.17530	+	193.754i	0.0128745	+	0.305124i
$636$	−250.157			−0.393329
$637$	−257.742	+	257.742i	−0.404618	+	0.404618i
$638$	−7.01963	−	7.01963i	−0.0110026	−	0.0110026i
$639$			252.330i			0.394883i
$640$	−56.5183	+	2.38475i	−0.0883098	+	0.00372617i
$641$	295.317			0.460713			0.230357	−	0.973106i	$-0.426011\pi$
$641$	295.317			0.460713			0.230357	+	0.973106i	$0.426011\pi$
$642$	−45.4047	+	45.4047i	−0.0707239	+	0.0707239i
$643$	5.55950	+	5.55950i	0.00864619	+	0.00864619i	0.711417	−	0.702770i	$-0.248054\pi$
$643$	5.55950	+	5.55950i	0.00864619	+	0.00864619i	−0.702770	+	0.711417i	$0.748054\pi$
$644$			28.0749i			0.0435945i
$645$	−132.479	−	121.752i	−0.205394	−	0.188763i
$646$	364.454			0.564170
$647$	220.812	−	220.812i	0.341286	−	0.341286i	−0.515565	−	0.856851i	$-0.672418\pi$
$647$	220.812	−	220.812i	0.341286	−	0.341286i	0.856851	+	0.515565i	$0.172418\pi$
$648$	−18.0000	−	18.0000i	−0.0277778	−	0.0277778i
$649$		−	82.5651i		−	0.127219i
$650$	26.8494	+	317.597i	0.0413067	+	0.488611i
$651$	93.8246			0.144124
$652$	−285.998	+	285.998i	−0.438647	+	0.438647i
$653$	−643.901	−	643.901i	−0.986065	−	0.986065i	0.0138390	−	0.999904i	$-0.495595\pi$
$653$	−643.901	−	643.901i	−0.986065	−	0.986065i	−0.999904	+	0.0138390i	$0.995595\pi$
$654$			180.986i			0.276738i
$655$	272.577	−	296.593i	0.416149	−	0.452814i
$656$	−146.722			−0.223661
$657$	−231.221	+	231.221i	−0.351934	+	0.351934i
$658$	−111.900	−	111.900i	−0.170061	−	0.170061i
$659$			576.226i			0.874395i	0.899366	+	0.437198i	$0.144029\pi$
$659$			576.226i			0.874395i	−0.899366	+	0.437198i	$0.855971\pi$
$660$	0.657205	+	15.5757i	0.000995765	+	0.0235995i
$661$	−82.0390			−0.124113			−0.0620567	−	0.998073i	$-0.519766\pi$
$661$	−82.0390			−0.124113			−0.0620567	+	0.998073i	$0.519766\pi$
$662$	514.692	−	514.692i	0.777480	−	0.777480i
$663$	288.445	+	288.445i	0.435060	+	0.435060i
$664$			34.8014i			0.0524117i
$665$	−144.240	+	6.08611i	−0.216902	+	0.00915204i
$666$	137.112			0.205874
$667$	−26.4479	+	26.4479i	−0.0396520	+	0.0396520i
$668$	284.444	+	284.444i	0.425815	+	0.425815i
$669$			388.618i			0.580894i
$670$	−159.615	−	146.691i	−0.238231	−	0.218941i
$671$	−40.0538			−0.0596927
$672$	20.2789	−	20.2789i	0.0301769	−	0.0301769i
$673$	−187.726	−	187.726i	−0.278939	−	0.278939i	0.553747	−	0.832685i	$-0.313198\pi$
$673$	−187.726	−	187.726i	−0.278939	−	0.278939i	−0.832685	+	0.553747i	$0.813198\pi$
$674$		−	262.385i		−	0.389296i
$675$	−99.2672	−	83.7916i	−0.147063	−	0.124136i
$676$	−175.458			−0.259553
$677$	−155.129	+	155.129i	−0.229142	+	0.229142i	−0.812334	−	0.583192i	$-0.801803\pi$
$677$	−155.129	+	155.129i	−0.229142	+	0.229142i	0.583192	+	0.812334i	$0.301803\pi$
$678$	196.073	+	196.073i	0.289193	+	0.289193i
$679$		−	431.482i		−	0.635467i
$680$	−250.000	+	272.027i	−0.367647	+	0.400039i
$681$	−432.334			−0.634852
$682$	−16.6573	+	16.6573i	−0.0244242	+	0.0244242i
$683$	−574.764	−	574.764i	−0.841529	−	0.841529i	0.147529	−	0.989058i	$-0.452868\pi$
$683$	−574.764	−	574.764i	−0.841529	−	0.841529i	−0.989058	+	0.147529i	$0.952868\pi$
$684$			59.1874i			0.0865313i
$685$	−16.3863	−	388.354i	−0.0239217	−	0.566940i
$686$	370.199			0.539648
$687$	172.179	−	172.179i	0.250625	−	0.250625i
$688$	−58.7644	−	58.7644i	−0.0854134	−	0.0854134i
$689$			651.014i			0.944868i
$690$	58.6845	−	2.47615i	0.0850500	−	0.00358863i
$691$	−806.478			−1.16712			−0.583559	−	0.812071i	$-0.698340\pi$
$691$	−806.478			−1.16712			−0.583559	+	0.812071i	$0.698340\pi$
$692$	294.279	−	294.279i	0.425259	−	0.425259i
$693$	−5.58859	−	5.58859i	−0.00806434	−	0.00806434i
$694$			17.0381i			0.0245506i
$695$	−491.957	−	452.122i	−0.707851	−	0.650535i
$696$	38.2074			0.0548957
$697$	−677.592	+	677.592i	−0.972154	+	0.972154i
$698$	−141.333	−	141.333i	−0.202482	−	0.202482i
$699$		−	57.3307i		−	0.0820182i
$700$	94.4000	−	111.835i	0.134857	−	0.159764i
$701$	909.201			1.29701			0.648503	−	0.761212i	$-0.275395\pi$
$701$	909.201			1.29701			0.648503	+	0.761212i	$0.275395\pi$
$702$	−46.8435	+	46.8435i	−0.0667287	+	0.0667287i
$703$	−225.426	−	225.426i	−0.320663	−	0.320663i
$704$			7.20050i			0.0102280i
$705$	−224.034	+	243.772i	−0.317778	+	0.345776i
$706$	717.683			1.01655
$707$	−128.808	+	128.808i	−0.182189	+	0.182189i
$708$	224.698	+	224.698i	0.317370	+	0.317370i
$709$		−	425.987i		−	0.600827i	−0.953809	−	0.300414i	$-0.902875\pi$
$709$		−	425.987i		−	0.600827i	0.953809	−	0.300414i	$-0.0971248\pi$
$710$	25.0727	+	594.220i	0.0353137	+	0.836929i
$711$	−93.9880			−0.132191
$712$	−64.2721	+	64.2721i	−0.0902699	+	0.0902699i
$713$	62.7598	+	62.7598i	0.0880221	+	0.0880221i
$714$		−	187.305i		−	0.262331i
$715$	40.5344	−	1.71032i	0.0566915	−	0.00239206i
$716$	−239.977			−0.335164
$717$	193.586	−	193.586i	0.269995	−	0.269995i
$718$	−233.537	−	233.537i	−0.325260	−	0.325260i
$719$			1319.34i			1.83497i	0.397776	+	0.917483i	$0.369782\pi$
$719$			1319.34i			1.83497i	−0.397776	+	0.917483i	$0.630218\pi$
$720$	−44.1773	−	40.6001i	−0.0613573	−	0.0563891i
$721$	−492.189			−0.682648
$722$	−263.690	+	263.690i	−0.365222	+	0.365222i
$723$	−181.463	−	181.463i	−0.250985	−	0.250985i
$724$		−	285.870i		−	0.394847i
$725$	194.283	−	16.4246i	0.267977	−	0.0226546i
$726$	−294.404			−0.405515
$727$	951.508	−	951.508i	1.30881	−	1.30881i	0.386544	−	0.922271i	$-0.373669\pi$
$727$	951.508	−	951.508i	1.30881	−	1.30881i	0.922271	−	0.386544i	$-0.126331\pi$
$728$	−52.7742	−	52.7742i	−0.0724920	−	0.0724920i
$729$		−	27.0000i		−	0.0370370i
$730$	−521.533	+	567.483i	−0.714429	+	0.777374i
$731$	−542.774			−0.742508
$732$	109.005	−	109.005i	0.148914	−	0.148914i
$733$	191.910	+	191.910i	0.261814	+	0.261814i	0.825791	−	0.563977i	$-0.190729\pi$
$733$	191.910	+	191.910i	0.261814	+	0.261814i	−0.563977	+	0.825791i	$0.690729\pi$
$734$		−	83.7040i		−	0.114038i
$735$	−14.7615	−	349.846i	−0.0200837	−	0.475980i
$736$	27.1293			0.0368605
$737$	−19.5119	+	19.5119i	−0.0264747	+	0.0264747i
$738$	−110.041	−	110.041i	−0.149107	−	0.149107i
$739$		−	673.498i		−	0.911363i	−0.890143	−	0.455682i	$-0.849396\pi$
$739$		−	673.498i		−	0.911363i	0.890143	−	0.455682i	$-0.150604\pi$
$740$	322.890	−	13.6241i	0.436337	−	0.0184110i
$741$	154.030			0.207868
$742$	211.371	−	211.371i	0.284867	−	0.284867i
$743$	122.642	+	122.642i	0.165063	+	0.165063i	0.784805	−	0.619743i	$-0.212763\pi$
$743$	122.642	+	122.642i	0.165063	+	0.165063i	−0.619743	+	0.784805i	$0.712763\pi$
$744$		−	90.6646i		−	0.121861i
$745$	−713.743	−	655.950i	−0.958044	−	0.880470i
$746$	−476.129			−0.638243
$747$	−26.1010	+	26.1010i	−0.0349411	+	0.0349411i
$748$	33.2534	+	33.2534i	0.0444565	+	0.0444565i
$749$		−	76.7298i		−	0.102443i
$750$	−242.093	−	187.459i	−0.322791	−	0.249946i
$751$	532.663			0.709272			0.354636	−	0.935005i	$-0.384605\pi$
$751$	532.663			0.709272			0.354636	+	0.935005i	$0.384605\pi$
$752$	−108.131	+	108.131i	−0.143792	+	0.143792i
$753$	272.603	+	272.603i	0.362023	+	0.362023i
$754$		−	99.4317i		−	0.131872i
$755$	716.633	−	779.773i	0.949182	−	1.03281i
$756$	30.4183			0.0402359
$757$	−786.166	+	786.166i	−1.03853	+	1.03853i	−0.0393009	+	0.999227i	$0.512513\pi$
$757$	−786.166	+	786.166i	−1.03853	+	1.03853i	−0.999227	+	0.0393009i	$0.987487\pi$
$758$	253.908	+	253.908i	0.334970	+	0.334970i
$759$		−	7.47648i		−	0.00985043i
$760$	5.88113	+	139.382i	0.00773833	+	0.183398i
$761$	54.7150			0.0718989			0.0359494	−	0.999354i	$-0.488554\pi$
$761$	54.7150			0.0718989			0.0359494	+	0.999354i	$0.488554\pi$
$762$	−67.1779	+	67.1779i	−0.0881600	+	0.0881600i
$763$	−152.925	−	152.925i	−0.200426	−	0.200426i
$764$		−	143.440i		−	0.187749i
$765$	−391.520	+	16.5199i	−0.511791	+	0.0215947i
$766$	137.815			0.179916
$767$	584.759	−	584.759i	0.762397	−	0.762397i
$768$	−19.5959	−	19.5959i	−0.0255155	−	0.0255155i
$769$		−	4.86567i		−	0.00632727i	−0.999995	−	0.00316363i	$-0.998993\pi$
$769$		−	4.86567i		−	0.00632727i	0.999995	−	0.00316363i	$-0.00100702\pi$
$770$	−13.7160	−	12.6054i	−0.0178130	−	0.0163707i
$771$	689.033			0.893688
$772$	31.3996	−	31.3996i	0.0406731	−	0.0406731i
$773$	−764.339	−	764.339i	−0.988795	−	0.988795i	0.0111426	−	0.999938i	$-0.496453\pi$
$773$	−764.339	−	764.339i	−0.988795	−	0.988795i	−0.999938	+	0.0111426i	$0.996453\pi$
$774$		−	88.1467i		−	0.113885i
$775$	−38.9748	−	461.027i	−0.0502901	−	0.594873i
$776$	−416.950			−0.537307
$777$	−115.854	+	115.854i	−0.149104	+	0.149104i
$778$	34.7594	+	34.7594i	0.0446778	+	0.0446778i
$779$			361.836i			0.464488i
$780$	−105.659	+	114.968i	−0.135460	+	0.147394i
$781$	75.7043			0.0969326
$782$	125.289	−	125.289i	0.160216	−	0.160216i
$783$	28.6556	+	28.6556i	0.0365971	+	0.0365971i
$784$		−	161.731i		−	0.206289i
$785$	40.1928	+	952.565i	0.0512011	+	1.21346i
$786$	197.342			0.251071
$787$	702.992	−	702.992i	0.893256	−	0.893256i	−0.101572	−	0.994828i	$-0.532387\pi$
$787$	702.992	−	702.992i	0.893256	−	0.893256i	0.994828	+	0.101572i	$0.0323873\pi$
$788$	−516.750	−	516.750i	−0.655774	−	0.655774i
$789$			435.100i			0.551457i
$790$	−221.335	+	9.33907i	−0.280171	+	0.0118216i
$791$	−331.345			−0.418893
$792$	−5.40037	+	5.40037i	−0.00681865	+	0.00681865i
$793$	−283.677	−	283.677i	−0.357727	−	0.357727i
$794$		−	981.544i		−	1.23620i
$795$	−460.469	−	423.184i	−0.579206	−	0.532307i
$796$	−34.2713			−0.0430544
$797$	−307.310	+	307.310i	−0.385583	+	0.385583i	−0.873109	−	0.487525i	$-0.837900\pi$
$797$	−307.310	+	307.310i	−0.385583	+	0.385583i	0.487525	+	0.873109i	$0.337900\pi$
$798$	−50.0107	−	50.0107i	−0.0626700	−	0.0626700i
$799$			998.747i			1.25000i
$800$	−108.068	−	91.2207i	−0.135086	−	0.114026i
$801$	−96.4082			−0.120360
$802$	473.229	−	473.229i	0.590061	−	0.590061i
$803$	69.3710	+	69.3710i	0.0863898	+	0.0863898i
$804$		−	106.202i		−	0.132092i
$805$	−47.4934	+	51.6779i	−0.0589981	+	0.0641962i
$806$	−235.947			−0.292739
$807$	−114.244	+	114.244i	−0.141567	+	0.141567i
$808$	124.470	+	124.470i	0.154047	+	0.154047i
$809$			697.617i			0.862321i	0.902275	+	0.431160i	$0.141896\pi$
$809$			697.617i			0.862321i	−0.902275	+	0.431160i	$0.858104\pi$
$810$	−2.68284	−	63.5830i	−0.00331215	−	0.0784976i
$811$	1305.11			1.60927			0.804633	−	0.593773i	$-0.202362\pi$
$811$	1305.11			1.60927			0.804633	+	0.593773i	$0.202362\pi$
$812$	−32.2835	+	32.2835i	−0.0397580	+	0.0397580i
$813$	430.561	+	430.561i	0.529596	+	0.529596i
$814$		−	41.1365i		−	0.0505363i
$815$	−1010.26	+	42.6270i	−1.23958	+	0.0523031i
$816$	−180.996			−0.221809
$817$	−144.922	+	144.922i	−0.177383	+	0.177383i
$818$	−285.348	−	285.348i	−0.348836	−	0.348836i
$819$		−	79.1613i		−	0.0966560i
$820$	−270.073	−	248.205i	−0.329357	−	0.302689i
$821$	−959.958			−1.16925			−0.584627	−	0.811302i	$-0.698759\pi$
$821$	−959.958			−1.16925			−0.584627	+	0.811302i	$0.698759\pi$
$822$	134.650	−	134.650i	0.163807	−	0.163807i
$823$	−382.034	−	382.034i	−0.464197	−	0.464197i	0.435831	−	0.900028i	$-0.356454\pi$
$823$	−382.034	−	382.034i	−0.464197	−	0.464197i	−0.900028	+	0.435831i	$0.856454\pi$
$824$			475.612i			0.577200i
$825$	−25.1392	+	29.7822i	−0.0304718	+	0.0360996i
$826$	−379.719			−0.459709
$827$	−815.819	+	815.819i	−0.986481	+	0.986481i	−0.999910	−	0.0134292i	$-0.995725\pi$
$827$	−815.819	+	815.819i	−0.986481	+	0.986481i	0.0134292	+	0.999910i	$0.495725\pi$
$828$	20.3470	+	20.3470i	0.0245737	+	0.0245737i
$829$		−	14.4275i		−	0.0174035i	−0.999962	−	0.00870173i	$-0.997230\pi$
$829$		−	14.4275i		−	0.0174035i	0.999962	−	0.00870173i	$-0.00276988\pi$
$830$	−58.8725	+	64.0595i	−0.0709307	+	0.0771802i
$831$	519.261			0.624863
$832$	−50.9968	+	50.9968i	−0.0612942	+	0.0612942i
$833$	−746.906	−	746.906i	−0.896646	−	0.896646i
$834$		−	327.329i		−	0.392481i
$835$	42.3955	+	1004.77i	0.0507731	+	1.20332i
$836$	17.7575			0.0212410
$837$	67.9985	−	67.9985i	0.0812407	−	0.0812407i
$838$	−290.087	−	290.087i	−0.346165	−	0.346165i
$839$		−	283.559i		−	0.337972i	−0.985618	−	0.168986i	$-0.945951\pi$
$839$		−	283.559i		−	0.337972i	0.985618	−	0.168986i	$-0.0540493\pi$
$840$	71.6330	−	3.02251i	0.0852774	−	0.00359822i
$841$	780.175			0.927675
$842$	442.922	−	442.922i	0.526035	−	0.526035i
$843$	165.790	+	165.790i	0.196666	+	0.196666i
$844$			175.793i			0.208286i
$845$	−322.969	−	296.817i	−0.382212	−	0.351263i
$846$	−162.197			−0.191722
$847$	248.758	−	248.758i	0.293693	−	0.293693i
$848$	−204.252	−	204.252i	−0.240864	−	0.240864i
$849$		−	262.481i		−	0.309165i
$850$	−920.360	+	77.8065i	−1.08278	+	0.0915370i
$851$	−154.990			−0.182127
$852$	−206.027	+	206.027i	−0.241816	+	0.241816i
$853$	−190.843	−	190.843i	−0.223732	−	0.223732i	0.586336	−	0.810068i	$-0.300570\pi$
$853$	−190.843	−	190.843i	−0.223732	−	0.223732i	−0.810068	+	0.586336i	$0.800570\pi$
$854$			184.209i			0.215701i
$855$	−100.126	+	108.947i	−0.117106	+	0.127424i
$856$	−74.1456			−0.0866187
$857$	966.259	−	966.259i	1.12749	−	1.12749i	0.136907	−	0.990584i	$-0.456284\pi$
$857$	966.259	−	966.259i	1.12749	−	1.12749i	0.990584	−	0.136907i	$-0.0437160\pi$
$858$	14.0540	+	14.0540i	0.0163800	+	0.0163800i
$859$		−	1296.14i		−	1.50889i	−0.656361	−	0.754447i	$-0.727905\pi$
$859$		−	1296.14i		−	1.50889i	0.656361	−	0.754447i	$-0.272095\pi$
$860$	−8.75865	−	207.579i	−0.0101845	−	0.241371i
$861$	185.959			0.215981
$862$	−377.479	+	377.479i	−0.437910	+	0.437910i
$863$	283.162	+	283.162i	0.328113	+	0.328113i	0.851869	−	0.523755i	$-0.175469\pi$
$863$	283.162	+	283.162i	0.328113	+	0.328113i	−0.523755	+	0.851869i	$0.675469\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	1039.51	−	43.8614i	1.20174	−	0.0507068i
$866$	1135.51			1.31121
$867$	−481.929	+	481.929i	−0.555858	+	0.555858i
$868$	76.6074	+	76.6074i	0.0882574	+	0.0882574i
$869$			28.1983i			0.0324492i
$870$	70.3291	+	64.6344i	0.0808380	+	0.0742924i
$871$	−276.382			−0.317315
$872$	−147.775	+	147.775i	−0.169466	+	0.169466i
$873$	−312.713	−	312.713i	−0.358205	−	0.358205i
$874$		−	66.9048i		−	0.0765501i
$875$	362.952	−	46.1628i	0.414802	−	0.0527575i
$876$	−377.582			−0.431030
$877$	704.197	−	704.197i	0.802961	−	0.802961i	−0.180596	−	0.983557i	$-0.557803\pi$
$877$	704.197	−	704.197i	0.802961	−	0.802961i	0.983557	+	0.180596i	$0.0578027\pi$
$878$	295.256	+	295.256i	0.336282	+	0.336282i
$879$			318.444i			0.362280i
$880$	−12.1809	+	13.2541i	−0.0138419	+	0.0150615i
$881$	−210.859			−0.239341			−0.119670	−	0.992814i	$-0.538184\pi$
$881$	−210.859			−0.239341			−0.119670	+	0.992814i	$0.538184\pi$
$882$	121.298	−	121.298i	0.137526	−	0.137526i
$883$	−439.742	−	439.742i	−0.498009	−	0.498009i	0.412809	−	0.910818i	$-0.364548\pi$
$883$	−439.742	−	439.742i	−0.498009	−	0.498009i	−0.910818	+	0.412809i	$0.864548\pi$
$884$			471.028i			0.532837i
$885$	33.4906	+	793.722i	0.0378424	+	0.896861i
$886$	−838.314			−0.946179
$887$	189.904	−	189.904i	0.214097	−	0.214097i	−0.591908	−	0.806005i	$-0.701625\pi$
$887$	189.904	−	189.904i	0.214097	−	0.214097i	0.806005	+	0.591908i	$0.201625\pi$
$888$	111.952	+	111.952i	0.126072	+	0.126072i
$889$		−	113.524i		−	0.127699i
$890$	−227.034	+	9.57956i	−0.255095	+	0.0107636i
$891$	−8.10056			−0.00909153
$892$	−317.306	+	317.306i	−0.355724	+	0.355724i
$893$	266.667	+	266.667i	0.298620	+	0.298620i
$894$		−	474.898i		−	0.531206i
$895$	−441.730	−	405.962i	−0.493553	−	0.453589i
$896$	33.1153			0.0369590
$897$	52.9514	−	52.9514i	0.0590316	−	0.0590316i
$898$	−646.254	−	646.254i	−0.719659	−	0.719659i
$899$			144.336i			0.160552i
$900$	−12.6358	−	149.467i	−0.0140398	−	0.166074i
$901$	−1886.56			−2.09386
$902$	−33.0146	+	33.0146i	−0.0366016	+	0.0366016i
$903$	74.4799	+	74.4799i	0.0824805	+	0.0824805i
$904$			320.185i			0.354187i
$905$	483.598	−	526.205i	0.534362	−	0.581443i
$906$	518.831			0.572661
$907$	79.6022	−	79.6022i	0.0877642	−	0.0877642i	−0.661862	−	0.749626i	$-0.730233\pi$
$907$	79.6022	−	79.6022i	0.0877642	−	0.0877642i	0.749626	+	0.661862i	$0.230233\pi$
$908$	−352.999	−	352.999i	−0.388766	−	0.388766i
$909$			186.705i			0.205396i
$910$	−7.86582	−	186.419i	−0.00864376	−	0.204856i
$911$	599.614			0.658193			0.329096	−	0.944296i	$-0.393256\pi$
$911$	599.614			0.658193			0.329096	+	0.944296i	$0.393256\pi$
$912$	−48.3263	+	48.3263i	−0.0529894	+	0.0529894i
$913$	7.83085	+	7.83085i	0.00857705	+	0.00857705i
$914$			235.516i			0.257677i
$915$	385.049	−	16.2469i	0.420819	−	0.0177562i
$916$	281.167			0.306951
$917$	−166.745	+	166.745i	−0.181837	+	0.181837i
$918$	−135.747	−	135.747i	−0.147873	−	0.147873i
$919$			694.185i			0.755370i	0.925934	+	0.377685i	$0.123280\pi$
$919$			694.185i			0.755370i	−0.925934	+	0.377685i	$0.876720\pi$
$920$	49.9375	+	45.8939i	0.0542798	+	0.0498847i
$921$	−15.9715			−0.0173415
$922$	−638.280	+	638.280i	−0.692278	+	0.692278i
$923$	536.168	+	536.168i	0.580897	+	0.580897i
$924$		−	9.12613i		−	0.00987676i
$925$	617.397	+	521.145i	0.667456	+	0.563400i
$926$	−486.012			−0.524851
$927$	−356.709	+	356.709i	−0.384800	+	0.384800i
$928$	31.1962	+	31.1962i	0.0336166	+	0.0336166i
$929$			988.592i			1.06415i	0.846699	+	0.532073i	$0.178587\pi$
$929$			988.592i			1.06415i	−0.846699	+	0.532073i	$0.821413\pi$
$930$	153.375	−	166.888i	0.164919	−	0.179450i
$931$	−398.851			−0.428411
$932$	46.8103	−	46.8103i	0.0502257	−	0.0502257i
$933$	−26.7703	−	26.7703i	−0.0286927	−	0.0286927i
$934$		−	360.518i		−	0.385994i
$935$	4.95632	+	117.464i	0.00530088	+	0.125630i
$936$	−76.4952			−0.0817256
$937$	−585.244	+	585.244i	−0.624594	+	0.624594i	−0.946703	−	0.322109i	$-0.895608\pi$
$937$	−585.244	+	585.244i	−0.624594	+	0.624594i	0.322109	+	0.946703i	$0.395608\pi$
$938$	89.7356	+	89.7356i	0.0956670	+	0.0956670i
$939$		−	807.858i		−	0.860338i
$940$	−381.962	+	16.1166i	−0.406342	+	0.0171453i
$941$	437.656			0.465097			0.232548	−	0.972585i	$-0.425294\pi$
$941$	437.656			0.465097			0.232548	+	0.972585i	$0.425294\pi$
$942$	−330.272	+	330.272i	−0.350607	+	0.350607i
$943$	124.389	+	124.389i	0.131908	+	0.131908i
$944$			366.931i			0.388698i
$945$	55.9916	+	51.4579i	0.0592504	+	0.0544528i
$946$	−26.4458			−0.0279554
$947$	386.988	−	386.988i	0.408646	−	0.408646i	−0.472620	−	0.881266i	$-0.656692\pi$
$947$	386.988	−	386.988i	0.408646	−	0.408646i	0.881266	+	0.472620i	$0.156692\pi$
$948$	−76.7409	−	76.7409i	−0.0809503	−	0.0809503i
$949$			982.626i			1.03543i
$950$	−224.963	+	266.512i	−0.236803	+	0.280539i
$951$	458.577			0.482205
$952$	152.934	−	152.934i	0.160645	−	0.160645i
$953$	354.062	+	354.062i	0.371524	+	0.371524i	0.868032	−	0.496508i	$-0.165385\pi$
$953$	354.062	+	354.062i	0.371524	+	0.371524i	−0.496508	+	0.868032i	$0.665385\pi$
$954$		−	306.379i		−	0.321152i
$955$	242.654	−	264.034i	0.254088	−	0.276475i
$956$	316.125			0.330675
$957$	8.59726	−	8.59726i	0.00898355	−	0.00898355i
$958$	521.944	+	521.944i	0.544827	+	0.544827i
$959$			227.545i			0.237273i
$960$	−2.92071	−	69.2204i	−0.00304241	−	0.0721046i
$961$	−618.497			−0.643597
$962$	291.345	−	291.345i	0.302854	−	0.302854i
$963$	−55.6092	−	55.6092i	−0.0577458	−	0.0577458i
$964$		−	296.327i		−	0.307393i
$965$	110.916	−	4.68002i	0.114939	−	0.00484976i
$966$	−34.3845			−0.0355948
$967$	−1153.10	+	1153.10i	−1.19245	+	1.19245i	−0.216075	+	0.976377i	$0.569326\pi$
$967$	−1153.10	+	1153.10i	−1.19245	+	1.19245i	−0.976377	+	0.216075i	$0.930674\pi$
$968$	−240.380	−	240.380i	−0.248326	−	0.248326i
$969$			446.363i			0.460643i
$970$	−767.488	−	705.343i	−0.791225	−	0.727158i
$971$	−96.6570			−0.0995438			−0.0497719	−	0.998761i	$-0.515849\pi$
$971$	−96.6570			−0.0995438			−0.0497719	+	0.998761i	$0.515849\pi$
$972$	22.0454	−	22.0454i	0.0226805	−	0.0226805i
$973$	276.578	+	276.578i	0.284253	+	0.284253i
$974$		−	347.098i		−	0.356364i
$975$	−388.975	+	32.8836i	−0.398949	+	0.0337268i
$976$	178.005			0.182382
$977$	1227.96	−	1227.96i	1.25687	−	1.25687i	0.304295	−	0.952578i	$-0.401579\pi$
$977$	1227.96	−	1227.96i	1.25687	−	1.25687i	0.952578	−	0.304295i	$-0.0984209\pi$
$978$	−350.274	−	350.274i	−0.358153	−	0.358153i
$979$			28.9245i			0.0295449i
$980$	273.595	−	297.700i	0.279179	−	0.303776i
$981$	−221.662			−0.225955
$982$	261.292	−	261.292i	0.266082	−	0.266082i
$983$	−1081.37	−	1081.37i	−1.10007	−	1.10007i	−0.994402	−	0.105665i	$-0.966303\pi$
$983$	−1081.37	−	1081.37i	−1.10007	−	1.10007i	−0.105665	−	0.994402i	$-0.533697\pi$
$984$		−	179.696i		−	0.182618i
$985$	−77.0199	−	1825.36i	−0.0781928	−	1.85316i
$986$	288.142			0.292233
$987$	137.049	−	137.049i	0.138854	−	0.138854i
$988$	125.765	+	125.765i	0.127293	+	0.127293i
$989$			99.6400i			0.100748i
$990$	−19.0762	+	0.804908i	−0.0192689	+	0.000813039i
$991$	582.750			0.588043			0.294021	−	0.955799i	$-0.405006\pi$
$991$	582.750			0.588043			0.294021	+	0.955799i	$0.405006\pi$
$992$	74.0274	−	74.0274i	0.0746244	−	0.0746244i
$993$	630.366	+	630.366i	0.634810	+	0.634810i
$994$		−	348.167i		−	0.350268i
$995$	−63.0838	−	57.9758i	−0.0634008	−	0.0582671i
$996$	−42.6228			−0.0427940
$997$	648.095	−	648.095i	0.650045	−	0.650045i	−0.302959	−	0.953004i	$-0.597974\pi$
$997$	648.095	−	648.095i	0.650045	−	0.650045i	0.953004	+	0.302959i	$0.0979745\pi$
$998$	−391.452	−	391.452i	−0.392237	−	0.392237i
$999$			167.928i			0.168096i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.b.553.4	yes	48
5.2	odd	4	inner	690.3.k.b.277.4	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.b.277.4	✓	48	5.2	odd	4	inner
690.3.k.b.553.4	yes	48	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(3.38334 - 3.68144i) q^{5} +2.44949 q^{6} +(-2.06971 + 2.06971i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(3.38334 - 3.68144i) q^{5} +2.44949 q^{6} +(-2.06971 + 2.06971i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(0.298094 + 7.06478i) q^{10} +0.900062 q^{11} +(-2.44949 + 2.44949i) q^{12} +(6.37460 + 6.37460i) q^{13} -4.13941i q^{14} +(-8.65256 + 0.365089i) q^{15} -4.00000 q^{16} +(-18.4729 + 18.4729i) q^{17} +(-3.00000 - 3.00000i) q^{18} +9.86457i q^{19} +(-7.36288 - 6.76669i) q^{20} +5.06972 q^{21} +(-0.900062 + 0.900062i) q^{22} +(3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(-2.10597 - 24.9111i) q^{25} -12.7492 q^{26} +(3.67423 - 3.67423i) q^{27} +(4.13941 + 4.13941i) q^{28} +7.79905i q^{29} +(8.28747 - 9.01764i) q^{30} +18.5068 q^{31} +(4.00000 - 4.00000i) q^{32} +(-1.10235 - 1.10235i) q^{33} -36.9457i q^{34} +(0.616966 + 14.6220i) q^{35} +6.00000 q^{36} +(-22.8521 + 22.8521i) q^{37} +(-9.86457 - 9.86457i) q^{38} -15.6145i q^{39} +(14.1296 - 0.596187i) q^{40} +36.6804 q^{41} +(-5.06972 + 5.06972i) q^{42} +(14.6911 + 14.6911i) q^{43} -1.80012i q^{44} +(11.0443 + 10.1500i) q^{45} -6.78233 q^{46} +(27.0328 - 27.0328i) q^{47} +(4.89898 + 4.89898i) q^{48} +40.4326i q^{49} +(27.0171 + 22.8052i) q^{50} +45.2491 q^{51} +(12.7492 - 12.7492i) q^{52} +(51.0631 + 51.0631i) q^{53} +7.34847i q^{54} +(3.04522 - 3.31352i) q^{55} -8.27882 q^{56} +(12.0816 - 12.0816i) q^{57} +(-7.79905 - 7.79905i) q^{58} -91.7327i q^{59} +(0.730177 + 17.3051i) q^{60} -44.5012 q^{61} +(-18.5068 + 18.5068i) q^{62} +(-6.20912 - 6.20912i) q^{63} +8.00000i q^{64} +(45.0351 - 1.90023i) q^{65} +2.20469 q^{66} +(-21.6784 + 21.6784i) q^{67} +(36.9457 + 36.9457i) q^{68} -8.30662i q^{69} +(-15.2390 - 14.0051i) q^{70} +84.1101 q^{71} +(-6.00000 + 6.00000i) q^{72} +(77.0736 + 77.0736i) q^{73} -45.7041i q^{74} +(-27.9305 + 33.0891i) q^{75} +19.7291 q^{76} +(-1.86286 + 1.86286i) q^{77} +(15.6145 + 15.6145i) q^{78} +31.3293i q^{79} +(-13.5334 + 14.7258i) q^{80} -9.00000 q^{81} +(-36.6804 + 36.6804i) q^{82} +(8.70034 + 8.70034i) q^{83} -10.1394i q^{84} +(5.50664 + 130.507i) q^{85} -29.3822 q^{86} +(9.55185 - 9.55185i) q^{87} +(1.80012 + 1.80012i) q^{88} +32.1361i q^{89} +(-21.1943 + 0.894281i) q^{90} -26.3871 q^{91} +(6.78233 - 6.78233i) q^{92} +(-22.6662 - 22.6662i) q^{93} +54.0656i q^{94} +(36.3158 + 33.3752i) q^{95} -9.79796 q^{96} +(-104.238 + 104.238i) q^{97} +(-40.4326 - 40.4326i) q^{98} +2.70019i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) \) 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	\( 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) \) 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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