LMFDB - Embedded newform 690.3.k.b.277.14

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			277.14
Character	$\chi$	$=$	690.277
Dual form			690.3.k.b.553.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-1.86672 + 4.63846i) q^{5} -2.44949 q^{6} +(2.71586 + 2.71586i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-1.86672 + 4.63846i) q^{5} -2.44949 q^{6} +(2.71586 + 2.71586i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(6.50519 - 2.77174i) q^{10} -20.1942 q^{11} +(2.44949 + 2.44949i) q^{12} +(0.746801 - 0.746801i) q^{13} -5.43173i q^{14} +(3.39468 + 7.96719i) q^{15} -4.00000 q^{16} +(0.556028 + 0.556028i) q^{17} +(-3.00000 + 3.00000i) q^{18} -19.9846i q^{19} +(-9.27693 - 3.73345i) q^{20} +6.65248 q^{21} +(20.1942 + 20.1942i) q^{22} +(-3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(-18.0307 - 17.3175i) q^{25} -1.49360 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-5.43173 + 5.43173i) q^{28} -48.8362i q^{29} +(4.57252 - 11.3619i) q^{30} +50.2284 q^{31} +(4.00000 + 4.00000i) q^{32} +(-24.7327 + 24.7327i) q^{33} -1.11206i q^{34} +(-17.6672 + 7.52767i) q^{35} +6.00000 q^{36} +(-16.5528 - 16.5528i) q^{37} +(-19.9846 + 19.9846i) q^{38} -1.82928i q^{39} +(5.54348 + 13.0104i) q^{40} +57.2091 q^{41} +(-6.65248 - 6.65248i) q^{42} +(58.6184 - 58.6184i) q^{43} -40.3884i q^{44} +(13.9154 + 5.60017i) q^{45} +6.78233 q^{46} +(-41.3244 - 41.3244i) q^{47} +(-4.89898 + 4.89898i) q^{48} -34.2482i q^{49} +(0.713239 + 35.3481i) q^{50} +1.36199 q^{51} +(1.49360 + 1.49360i) q^{52} +(28.0837 - 28.0837i) q^{53} +7.34847i q^{54} +(37.6970 - 93.6701i) q^{55} +10.8635 q^{56} +(-24.4761 - 24.4761i) q^{57} +(-48.8362 + 48.8362i) q^{58} +46.2872i q^{59} +(-15.9344 + 6.78935i) q^{60} -80.6788 q^{61} +(-50.2284 - 50.2284i) q^{62} +(8.14759 - 8.14759i) q^{63} -8.00000i q^{64} +(2.06994 + 4.85808i) q^{65} +49.4655 q^{66} +(3.70461 + 3.70461i) q^{67} +(-1.11206 + 1.11206i) q^{68} +8.30662i q^{69} +(25.1949 + 10.1395i) q^{70} -45.0042 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-19.9215 + 19.9215i) q^{73} +33.1057i q^{74} +(-43.2925 + 0.873535i) q^{75} +39.9693 q^{76} +(-54.8447 - 54.8447i) q^{77} +(-1.82928 + 1.82928i) q^{78} -11.9143i q^{79} +(7.46689 - 18.5539i) q^{80} -9.00000 q^{81} +(-57.2091 - 57.2091i) q^{82} +(51.9727 - 51.9727i) q^{83} +13.3050i q^{84} +(-3.61707 + 1.54117i) q^{85} -117.237 q^{86} +(-59.8118 - 59.8118i) q^{87} +(-40.3884 + 40.3884i) q^{88} +153.052i q^{89} +(-8.31522 - 19.5156i) q^{90} +4.05642 q^{91} +(-6.78233 - 6.78233i) q^{92} +(61.5170 - 61.5170i) q^{93} +82.6487i q^{94} +(92.6980 + 37.3058i) q^{95} +9.79796 q^{96} +(109.557 + 109.557i) q^{97} +(-34.2482 + 34.2482i) q^{98} +60.5826i 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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

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

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
$5$	−1.86672	+	4.63846i	−0.373345	+	0.927693i
$5$	−1.86672	+	4.63846i	−0.373345	+	0.927693i
$6$	−2.44949			−0.408248
$7$	2.71586	+	2.71586i	0.387980	+	0.387980i	0.873967	−	0.485986i	$-0.161539\pi$
$7$	2.71586	+	2.71586i	0.387980	+	0.387980i	−0.485986	+	0.873967i	$0.661539\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$	6.50519	−	2.77174i	0.650519	−	0.277174i
$11$	−20.1942			−1.83584			−0.917918	−	0.396770i	$-0.870131\pi$
$11$	−20.1942			−1.83584			−0.917918	+	0.396770i	$0.870131\pi$
$12$	2.44949	+	2.44949i	0.204124	+	0.204124i
$13$	0.746801	−	0.746801i	0.0574462	−	0.0574462i	−0.677800	−	0.735246i	$-0.737066\pi$
$13$	0.746801	−	0.746801i	0.0574462	−	0.0574462i	0.735246	+	0.677800i	$0.237066\pi$
$14$		−	5.43173i		−	0.387980i
$15$	3.39468	+	7.96719i	0.226312	+	0.531146i
$16$	−4.00000			−0.250000
$17$	0.556028	+	0.556028i	0.0327075	+	0.0327075i	0.723271	−	0.690564i	$-0.242638\pi$
$17$	0.556028	+	0.556028i	0.0327075	+	0.0327075i	−0.690564	+	0.723271i	$0.742638\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$		−	19.9846i		−	1.05182i	−0.850539	−	0.525911i	$-0.823724\pi$
$19$		−	19.9846i		−	1.05182i	0.850539	−	0.525911i	$-0.176276\pi$
$20$	−9.27693	−	3.73345i	−0.463846	−	0.186672i
$21$	6.65248			0.316785
$22$	20.1942	+	20.1942i	0.917918	+	0.917918i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$24$		−	4.89898i		−	0.204124i
$25$	−18.0307	−	17.3175i	−0.721228	−	0.692698i
$26$	−1.49360			−0.0574462
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$	−5.43173	+	5.43173i	−0.193990	+	0.193990i
$29$		−	48.8362i		−	1.68401i	−0.539473	−	0.842003i	$-0.681377\pi$
$29$		−	48.8362i		−	1.68401i	0.539473	−	0.842003i	$-0.318623\pi$
$30$	4.57252	−	11.3619i	0.152417	−	0.378729i
$31$	50.2284			1.62027			0.810136	−	0.586242i	$-0.199393\pi$
$31$	50.2284			1.62027			0.810136	+	0.586242i	$0.199393\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	−24.7327	+	24.7327i	−0.749477	+	0.749477i
$34$		−	1.11206i		−	0.0327075i
$35$	−17.6672	+	7.52767i	−0.504777	+	0.215076i
$36$	6.00000			0.166667
$37$	−16.5528	−	16.5528i	−0.447374	−	0.447374i	0.447106	−	0.894481i	$-0.352455\pi$
$37$	−16.5528	−	16.5528i	−0.447374	−	0.447374i	−0.894481	+	0.447106i	$0.852455\pi$
$38$	−19.9846	+	19.9846i	−0.525911	+	0.525911i
$39$		−	1.82928i		−	0.0469047i
$40$	5.54348	+	13.0104i	0.138587	+	0.325259i
$41$	57.2091			1.39534			0.697672	−	0.716418i	$-0.254219\pi$
$41$	57.2091			1.39534			0.697672	+	0.716418i	$0.254219\pi$
$42$	−6.65248	−	6.65248i	−0.158392	−	0.158392i
$43$	58.6184	−	58.6184i	1.36322	−	1.36322i	0.493437	−	0.869781i	$-0.335740\pi$
$43$	58.6184	−	58.6184i	1.36322	−	1.36322i	0.869781	−	0.493437i	$-0.164260\pi$
$44$		−	40.3884i		−	0.917918i
$45$	13.9154	+	5.60017i	0.309231	+	0.124448i
$46$	6.78233			0.147442
$47$	−41.3244	−	41.3244i	−0.879242	−	0.879242i	0.114214	−	0.993456i	$-0.463565\pi$
$47$	−41.3244	−	41.3244i	−0.879242	−	0.879242i	−0.993456	+	0.114214i	$0.963565\pi$
$48$	−4.89898	+	4.89898i	−0.102062	+	0.102062i
$49$		−	34.2482i		−	0.698942i
$50$	0.713239	+	35.3481i	0.0142648	+	0.706963i
$51$	1.36199			0.0267056
$52$	1.49360	+	1.49360i	0.0287231	+	0.0287231i
$53$	28.0837	−	28.0837i	0.529882	−	0.529882i	−0.390655	−	0.920537i	$-0.627752\pi$
$53$	28.0837	−	28.0837i	0.529882	−	0.529882i	0.920537	+	0.390655i	$0.127752\pi$
$54$			7.34847i			0.136083i
$55$	37.6970	−	93.6701i	0.685400	−	1.70309i
$56$	10.8635			0.193990
$57$	−24.4761	−	24.4761i	−0.429405	−	0.429405i
$58$	−48.8362	+	48.8362i	−0.842003	+	0.842003i
$59$			46.2872i			0.784529i	0.919852	+	0.392265i	$0.128308\pi$
$59$			46.2872i			0.784529i	−0.919852	+	0.392265i	$0.871692\pi$
$60$	−15.9344	+	6.78935i	−0.265573	+	0.113156i
$61$	−80.6788			−1.32260			−0.661302	−	0.750120i	$-0.729996\pi$
$61$	−80.6788			−1.32260			−0.661302	+	0.750120i	$0.729996\pi$
$62$	−50.2284	−	50.2284i	−0.810136	−	0.810136i
$63$	8.14759	−	8.14759i	0.129327	−	0.129327i
$64$		−	8.00000i		−	0.125000i
$65$	2.06994	+	4.85808i	0.0318452	+	0.0747397i
$66$	49.4655			0.749477
$67$	3.70461	+	3.70461i	0.0552926	+	0.0552926i	0.734212	−	0.678920i	$-0.237552\pi$
$67$	3.70461	+	3.70461i	0.0552926	+	0.0552926i	−0.678920	+	0.734212i	$0.737552\pi$
$68$	−1.11206	+	1.11206i	−0.0163538	+	0.0163538i
$69$			8.30662i			0.120386i
$70$	25.1949	+	10.1395i	0.359927	+	0.144850i
$71$	−45.0042			−0.633862			−0.316931	−	0.948449i	$-0.602652\pi$
$71$	−45.0042			−0.633862			−0.316931	+	0.948449i	$0.602652\pi$
$72$	−6.00000	−	6.00000i	−0.0833333	−	0.0833333i
$73$	−19.9215	+	19.9215i	−0.272897	+	0.272897i	−0.830265	−	0.557369i	$-0.811811\pi$
$73$	−19.9215	+	19.9215i	−0.272897	+	0.272897i	0.557369	+	0.830265i	$0.311811\pi$
$74$			33.1057i			0.447374i
$75$	−43.2925	+	0.873535i	−0.577233	+	0.0116471i
$76$	39.9693			0.525911
$77$	−54.8447	−	54.8447i	−0.712269	−	0.712269i
$78$	−1.82928	+	1.82928i	−0.0234523	+	0.0234523i
$79$		−	11.9143i		−	0.150814i	−0.997153	−	0.0754069i	$-0.975974\pi$
$79$		−	11.9143i		−	0.150814i	0.997153	−	0.0754069i	$-0.0240256\pi$
$80$	7.46689	−	18.5539i	0.0933361	−	0.231923i
$81$	−9.00000			−0.111111
$82$	−57.2091	−	57.2091i	−0.697672	−	0.697672i
$83$	51.9727	−	51.9727i	0.626177	−	0.626177i	−0.320927	−	0.947104i	$-0.603994\pi$
$83$	51.9727	−	51.9727i	0.626177	−	0.626177i	0.947104	+	0.320927i	$0.103994\pi$
$84$			13.3050i			0.158392i
$85$	−3.61707	+	1.54117i	−0.0425537	+	0.0181314i
$86$	−117.237			−1.36322
$87$	−59.8118	−	59.8118i	−0.687492	−	0.687492i
$88$	−40.3884	+	40.3884i	−0.458959	+	0.458959i
$89$			153.052i			1.71968i	0.510562	+	0.859841i	$0.329437\pi$
$89$			153.052i			1.71968i	−0.510562	+	0.859841i	$0.670563\pi$
$90$	−8.31522	−	19.5156i	−0.0923914	−	0.216840i
$91$	4.05642			0.0445760
$92$	−6.78233	−	6.78233i	−0.0737210	−	0.0737210i
$93$	61.5170	−	61.5170i	0.661473	−	0.661473i
$94$			82.6487i			0.879242i
$95$	92.6980	+	37.3058i	0.975768	+	0.392692i
$96$	9.79796			0.102062
$97$	109.557	+	109.557i	1.12946	+	1.12946i	0.990265	+	0.139192i	$0.0444504\pi$
$97$	109.557	+	109.557i	1.12946	+	1.12946i	0.139192	+	0.990265i	$0.455550\pi$
$98$	−34.2482	+	34.2482i	−0.349471	+	0.349471i
$99$			60.5826i			0.611945i
$100$	34.6349	−	36.0614i	0.346349	−	0.360614i
$101$	−186.217			−1.84373			−0.921866	−	0.387508i	$-0.873336\pi$
$101$	−186.217			−1.84373			−0.921866	+	0.387508i	$0.873336\pi$
$102$	−1.36199	−	1.36199i	−0.0133528	−	0.0133528i
$103$	−69.1652	+	69.1652i	−0.671507	+	0.671507i	−0.958063	−	0.286556i	$-0.907489\pi$
$103$	−69.1652	+	69.1652i	−0.671507	+	0.671507i	0.286556	+	0.958063i	$0.407489\pi$
$104$		−	2.98720i		−	0.0287231i
$105$	−12.4183	+	30.8573i	−0.118270	+	0.293879i
$106$	−56.1675			−0.529882
$107$	−95.3930	−	95.3930i	−0.891524	−	0.891524i	0.103143	−	0.994667i	$-0.467110\pi$
$107$	−95.3930	−	95.3930i	−0.891524	−	0.891524i	−0.994667	+	0.103143i	$0.967110\pi$
$108$	7.34847	−	7.34847i	0.0680414	−	0.0680414i
$109$		−	86.6994i		−	0.795407i	−0.917514	−	0.397704i	$-0.869807\pi$
$109$		−	86.6994i		−	0.795407i	0.917514	−	0.397704i	$-0.130193\pi$
$110$	−131.367	+	55.9731i	−1.19425	+	0.508846i
$111$	−40.5460			−0.365280
$112$	−10.8635	−	10.8635i	−0.0969951	−	0.0969951i
$113$	−106.499	+	106.499i	−0.942470	+	0.942470i	−0.998433	−	0.0559628i	$-0.982177\pi$
$113$	−106.499	+	106.499i	−0.942470	+	0.942470i	0.0559628	+	0.998433i	$0.482177\pi$
$114$			48.9522i			0.429405i
$115$	−9.39943	−	22.0602i	−0.0817342	−	0.191827i
$116$	97.6723			0.842003
$117$	−2.24040	−	2.24040i	−0.0191487	−	0.0191487i
$118$	46.2872	−	46.2872i	0.392265	−	0.392265i
$119$			3.02019i			0.0253798i
$120$	22.7237	+	9.14504i	0.189364	+	0.0762086i
$121$	286.806			2.37030
$122$	80.6788	+	80.6788i	0.661302	+	0.661302i
$123$	70.0665	−	70.0665i	0.569647	−	0.569647i
$124$			100.457i			0.810136i
$125$	113.985	−	51.3078i	0.911877	−	0.410463i
$126$	−16.2952			−0.129327
$127$	−165.125	−	165.125i	−1.30020	−	1.30020i	−0.928254	−	0.371947i	$-0.878690\pi$
$127$	−165.125	−	165.125i	−1.30020	−	1.30020i	−0.371947	−	0.928254i	$-0.621310\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$		−	143.585i		−	1.11306i
$130$	2.78814	−	6.92802i	0.0214472	−	0.0532925i
$131$	−98.3677			−0.750898			−0.375449	−	0.926843i	$-0.622512\pi$
$131$	−98.3677			−0.750898			−0.375449	+	0.926843i	$0.622512\pi$
$132$	−49.4655	−	49.4655i	−0.374739	−	0.374739i
$133$	54.2755	−	54.2755i	0.408087	−	0.408087i
$134$		−	7.40921i		−	0.0552926i
$135$	23.9016	−	10.1840i	0.177049	−	0.0754372i
$136$	2.22411			0.0163538
$137$	−151.564	−	151.564i	−1.10631	−	1.10631i	−0.993632	−	0.112676i	$-0.964058\pi$
$137$	−151.564	−	151.564i	−1.10631	−	1.10631i	−0.112676	−	0.993632i	$-0.535942\pi$
$138$	8.30662	−	8.30662i	0.0601929	−	0.0601929i
$139$		−	24.6988i		−	0.177689i	−0.996045	−	0.0888446i	$-0.971683\pi$
$139$		−	24.6988i		−	0.177689i	0.996045	−	0.0888446i	$-0.0283175\pi$
$140$	−15.0553	−	35.3344i	−0.107538	−	0.252389i
$141$	−101.224			−0.717898
$142$	45.0042	+	45.0042i	0.316931	+	0.316931i
$143$	−15.0811	+	15.0811i	−0.105462	+	0.105462i
$144$			12.0000i			0.0833333i
$145$	226.525	+	91.1636i	1.56224	+	0.628714i
$146$	39.8429			0.272897
$147$	−41.9453	−	41.9453i	−0.285342	−	0.285342i
$148$	33.1057	−	33.1057i	0.223687	−	0.223687i
$149$			26.1452i			0.175471i	0.996144	+	0.0877355i	$0.0279630\pi$
$149$			26.1452i			0.175471i	−0.996144	+	0.0877355i	$0.972037\pi$
$150$	44.1660	+	42.4189i	0.294440	+	0.282793i
$151$	149.368			0.989191			0.494596	−	0.869123i	$-0.335316\pi$
$151$	149.368			0.989191			0.494596	+	0.869123i	$0.335316\pi$
$152$	−39.9693	−	39.9693i	−0.262956	−	0.262956i
$153$	1.66808	−	1.66808i	0.0109025	−	0.0109025i
$154$			109.689i			0.712269i
$155$	−93.7626	+	232.983i	−0.604920	+	1.50312i
$156$	3.65856			0.0234523
$157$	−93.1332	−	93.1332i	−0.593205	−	0.593205i	0.345291	−	0.938496i	$-0.387780\pi$
$157$	−93.1332	−	93.1332i	−0.593205	−	0.593205i	−0.938496	+	0.345291i	$0.887780\pi$
$158$	−11.9143	+	11.9143i	−0.0754069	+	0.0754069i
$159$		−	68.7908i		−	0.432647i
$160$	−26.0207	+	11.0870i	−0.162630	+	0.0692935i
$161$	−18.4199			−0.114409
$162$	9.00000	+	9.00000i	0.0555556	+	0.0555556i
$163$	160.565	−	160.565i	0.985062	−	0.985062i	−0.0148284	−	0.999890i	$-0.504720\pi$
$163$	160.565	−	160.565i	0.985062	−	0.985062i	0.999890	+	0.0148284i	$0.00472019\pi$
$164$			114.418i			0.697672i
$165$	−68.5528	−	160.891i	−0.415471	−	0.975098i
$166$	−103.945			−0.626177
$167$	−197.089	−	197.089i	−1.18017	−	1.18017i	−0.979699	−	0.200473i	$-0.935752\pi$
$167$	−197.089	−	197.089i	−1.18017	−	1.18017i	−0.200473	−	0.979699i	$-0.564248\pi$
$168$	13.3050	−	13.3050i	0.0791962	−	0.0791962i
$169$			167.885i			0.993400i
$170$	5.15823	+	2.07590i	0.0303425	+	0.0122112i
$171$	−59.9539			−0.350608
$172$	117.237	+	117.237i	0.681609	+	0.681609i
$173$	17.1387	−	17.1387i	0.0990678	−	0.0990678i	−0.655836	−	0.754904i	$-0.727684\pi$
$173$	17.1387	−	17.1387i	0.0990678	−	0.0990678i	0.754904	+	0.655836i	$0.227684\pi$
$174$			119.624i			0.687492i
$175$	−1.93706	−	96.0007i	−0.0110689	−	0.548576i
$176$	80.7768			0.458959
$177$	56.6900	+	56.6900i	0.320283	+	0.320283i
$178$	153.052	−	153.052i	0.859841	−	0.859841i
$179$		−	118.734i		−	0.663318i	−0.943399	−	0.331659i	$-0.892392\pi$
$179$		−	118.734i		−	0.663318i	0.943399	−	0.331659i	$-0.107608\pi$
$180$	−11.2003	+	27.8308i	−0.0622241	+	0.154615i
$181$	−20.8622			−0.115261			−0.0576303	−	0.998338i	$-0.518354\pi$
$181$	−20.8622			−0.115261			−0.0576303	+	0.998338i	$0.518354\pi$
$182$	−4.05642	−	4.05642i	−0.0222880	−	0.0222880i
$183$	−98.8109	+	98.8109i	−0.539951	+	0.539951i
$184$			13.5647i			0.0737210i
$185$	107.679	−	45.8802i	0.582051	−	0.248001i
$186$	−123.034			−0.661473
$187$	−11.2285	−	11.2285i	−0.0600457	−	0.0600457i
$188$	82.6487	−	82.6487i	0.439621	−	0.439621i
$189$		−	19.9574i		−	0.105595i
$190$	−55.3922	−	130.004i	−0.291538	−	0.684230i
$191$	252.640			1.32272			0.661361	−	0.750068i	$-0.269979\pi$
$191$	252.640			1.32272			0.661361	+	0.750068i	$0.269979\pi$
$192$	−9.79796	−	9.79796i	−0.0510310	−	0.0510310i
$193$	−31.5274	+	31.5274i	−0.163354	+	0.163354i	−0.784051	−	0.620697i	$-0.786850\pi$
$193$	−31.5274	+	31.5274i	−0.163354	+	0.163354i	0.620697	+	0.784051i	$0.286850\pi$
$194$		−	219.115i		−	1.12946i
$195$	8.48506	+	3.41476i	0.0435131	+	0.0175116i
$196$	68.4963			0.349471
$197$	125.808	+	125.808i	0.638618	+	0.638618i	0.950214	−	0.311597i	$-0.100864\pi$
$197$	125.808	+	125.808i	0.638618	+	0.638618i	−0.311597	+	0.950214i	$0.600864\pi$
$198$	60.5826	−	60.5826i	0.305973	−	0.305973i
$199$			213.068i			1.07069i	0.844633	+	0.535346i	$0.179819\pi$
$199$			213.068i			1.07069i	−0.844633	+	0.535346i	$0.820181\pi$
$200$	−70.6963	+	1.42648i	−0.353481	+	0.00713239i
$201$	9.07439			0.0451462
$202$	186.217	+	186.217i	0.921866	+	0.921866i
$203$	132.632	−	132.632i	0.653361	−	0.653361i
$204$			2.72397i			0.0133528i
$205$	−106.793	+	265.362i	−0.520944	+	1.29445i
$206$	138.330			0.671507
$207$	10.1735	+	10.1735i	0.0491473	+	0.0491473i
$208$	−2.98720	+	2.98720i	−0.0143616	+	0.0143616i
$209$			403.574i			1.93097i
$210$	43.2756	−	18.4389i	0.206074	−	0.0878045i
$211$	381.486			1.80799			0.903996	−	0.427540i	$-0.140620\pi$
$211$	381.486			1.80799			0.903996	+	0.427540i	$0.140620\pi$
$212$	56.1675	+	56.1675i	0.264941	+	0.264941i
$213$	−55.1186	+	55.1186i	−0.258773	+	0.258773i
$214$			190.786i			0.891524i
$215$	162.475	+	381.324i	0.755698	+	1.77360i
$216$	−14.6969			−0.0680414
$217$	136.414	+	136.414i	0.628634	+	0.628634i
$218$	−86.6994	+	86.6994i	−0.397704	+	0.397704i
$219$			48.7974i			0.222819i
$220$	187.340	+	75.3940i	0.851546	+	0.342700i
$221$	0.830485			0.00375785
$222$	40.5460	+	40.5460i	0.182640	+	0.182640i
$223$	−43.6482	+	43.6482i	−0.195732	+	0.195732i	−0.798167	−	0.602436i	$-0.794197\pi$
$223$	−43.6482	+	43.6482i	−0.195732	+	0.195732i	0.602436	+	0.798167i	$0.294197\pi$
$224$			21.7269i			0.0969951i
$225$	−51.9524	+	54.0921i	−0.230899	+	0.240409i
$226$	212.998			0.942470
$227$	148.529	+	148.529i	0.654314	+	0.654314i	0.954029	−	0.299714i	$-0.0968914\pi$
$227$	148.529	+	148.529i	0.654314	+	0.654314i	−0.299714	+	0.954029i	$0.596891\pi$
$228$	48.9522	−	48.9522i	0.214702	−	0.214702i
$229$			176.625i			0.771289i	0.922647	+	0.385645i	$0.126021\pi$
$229$			176.625i			0.771289i	−0.922647	+	0.385645i	$0.873979\pi$
$230$	−12.6607	+	31.4596i	−0.0550467	+	0.136781i
$231$	−134.341			−0.581565
$232$	−97.6723	−	97.6723i	−0.421001	−	0.421001i
$233$	−86.0763	+	86.0763i	−0.369426	+	0.369426i	−0.867268	−	0.497842i	$-0.834126\pi$
$233$	−86.0763	+	86.0763i	−0.369426	+	0.369426i	0.497842	+	0.867268i	$0.334126\pi$
$234$			4.48081i			0.0191487i
$235$	268.823	−	114.540i	1.14393	−	0.487406i
$236$	−92.5745			−0.392265
$237$	−14.5920	−	14.5920i	−0.0615694	−	0.0615694i
$238$	3.02019	−	3.02019i	0.0126899	−	0.0126899i
$239$		−	83.0954i		−	0.347680i	−0.984774	−	0.173840i	$-0.944383\pi$
$239$		−	83.0954i		−	0.347680i	0.984774	−	0.173840i	$-0.0556175\pi$
$240$	−13.5787	−	31.8688i	−0.0565779	−	0.132787i
$241$	−458.620			−1.90299			−0.951494	−	0.307667i	$-0.900452\pi$
$241$	−458.620			−1.90299			−0.951494	+	0.307667i	$0.900452\pi$
$242$	−286.806	−	286.806i	−1.18515	−	1.18515i
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$		−	161.358i		−	0.661302i
$245$	158.859	+	63.9318i	0.648404	+	0.260946i
$246$	−140.133			−0.569647
$247$	−14.9245	−	14.9245i	−0.0604233	−	0.0604233i
$248$	100.457	−	100.457i	0.405068	−	0.405068i
$249$		−	127.307i		−	0.511271i
$250$	−165.293	−	62.6769i	−0.661170	−	0.250707i
$251$	297.824			1.18655			0.593275	−	0.805000i	$-0.297835\pi$
$251$	297.824			1.18655			0.593275	+	0.805000i	$0.297835\pi$
$252$	16.2952	+	16.2952i	0.0646634	+	0.0646634i
$253$	68.4819	−	68.4819i	0.270679	−	0.270679i
$254$			330.251i			1.30020i
$255$	−2.54245	+	6.31752i	−0.00997039	+	0.0247746i
$256$	16.0000			0.0625000
$257$	−133.100	−	133.100i	−0.517899	−	0.517899i	0.399036	−	0.916935i	$-0.369345\pi$
$257$	−133.100	−	133.100i	−0.517899	−	0.517899i	−0.916935	+	0.399036i	$0.869345\pi$
$258$	−143.585	+	143.585i	−0.556532	+	0.556532i
$259$		−	89.9105i		−	0.347145i
$260$	−9.71616	+	4.13988i	−0.0373699	+	0.0159226i
$261$	−146.508			−0.561335
$262$	98.3677	+	98.3677i	0.375449	+	0.375449i
$263$	107.267	−	107.267i	0.407860	−	0.407860i	−0.473132	−	0.880992i	$-0.656877\pi$
$263$	107.267	−	107.267i	0.407860	−	0.407860i	0.880992	+	0.473132i	$0.156877\pi$
$264$			98.9310i			0.374739i
$265$	77.8408	+	182.690i	0.293739	+	0.689396i
$266$	−108.551			−0.408087
$267$	187.449	+	187.449i	0.702057	+	0.702057i
$268$	−7.40921	+	7.40921i	−0.0276463	+	0.0276463i
$269$		−	68.2440i		−	0.253695i	−0.991922	−	0.126848i	$-0.959514\pi$
$269$		−	68.2440i		−	0.253695i	0.991922	−	0.126848i	$-0.0404859\pi$
$270$	−34.0856	−	13.7176i	−0.126243	−	0.0508058i
$271$	−166.004			−0.612560			−0.306280	−	0.951941i	$-0.599084\pi$
$271$	−166.004			−0.612560			−0.306280	+	0.951941i	$0.599084\pi$
$272$	−2.22411	−	2.22411i	−0.00817688	−	0.00817688i
$273$	4.96808	−	4.96808i	0.0181981	−	0.0181981i
$274$			303.128i			1.10631i
$275$	364.115	+	349.712i	1.32406	+	1.27168i
$276$	−16.6132			−0.0601929
$277$	166.997	+	166.997i	0.602878	+	0.602878i	0.941075	−	0.338197i	$-0.109817\pi$
$277$	166.997	+	166.997i	0.602878	+	0.602878i	−0.338197	+	0.941075i	$0.609817\pi$
$278$	−24.6988	+	24.6988i	−0.0888446	+	0.0888446i
$279$		−	150.685i		−	0.540091i
$280$	−20.2791	+	50.3897i	−0.0724252	+	0.179963i
$281$	−138.196			−0.491802			−0.245901	−	0.969295i	$-0.579084\pi$
$281$	−138.196			−0.491802			−0.245901	+	0.969295i	$0.579084\pi$
$282$	101.224	+	101.224i	0.358949	+	0.358949i
$283$	−55.6688	+	55.6688i	−0.196710	+	0.196710i	−0.798588	−	0.601878i	$-0.794419\pi$
$283$	−55.6688	+	55.6688i	−0.196710	+	0.196710i	0.601878	+	0.798588i	$0.294419\pi$
$284$		−	90.0083i		−	0.316931i
$285$	159.221	−	67.8413i	0.558672	−	0.238040i
$286$	30.1621			0.105462
$287$	155.372	+	155.372i	0.541366	+	0.541366i
$288$	12.0000	−	12.0000i	0.0416667	−	0.0416667i
$289$		−	288.382i		−	0.997860i
$290$	−135.361	−	317.688i	−0.466763	−	1.09548i
$291$	268.360			0.922198
$292$	−39.8429	−	39.8429i	−0.136448	−	0.136448i
$293$	147.374	−	147.374i	0.502984	−	0.502984i	−0.409380	−	0.912364i	$-0.634255\pi$
$293$	147.374	−	147.374i	0.502984	−	0.502984i	0.912364	+	0.409380i	$0.134255\pi$
$294$			83.8905i			0.285342i
$295$	−214.702	−	86.4054i	−0.727802	−	0.292900i
$296$	−66.2114			−0.223687
$297$	74.1982	+	74.1982i	0.249826	+	0.249826i
$298$	26.1452	−	26.1452i	0.0877355	−	0.0877355i
$299$			5.06505i			0.0169400i
$300$	−1.74707	−	86.5849i	−0.00582357	−	0.288616i
$301$	318.399			1.05780
$302$	−149.368	−	149.368i	−0.494596	−	0.494596i
$303$	−228.068	+	228.068i	−0.752701	+	0.752701i
$304$			79.9385i			0.262956i
$305$	150.605	−	374.226i	0.493787	−	1.22697i
$306$	−3.33617			−0.0109025
$307$	−299.704	−	299.704i	−0.976234	−	0.976234i	0.0234903	−	0.999724i	$-0.492522\pi$
$307$	−299.704	−	299.704i	−0.976234	−	0.976234i	−0.999724	+	0.0234903i	$0.992522\pi$
$308$	109.689	−	109.689i	0.356134	−	0.356134i
$309$			169.419i			0.548283i
$310$	326.745	−	139.220i	1.05402	−	0.449098i
$311$	−259.066			−0.833009			−0.416504	−	0.909134i	$-0.636745\pi$
$311$	−259.066			−0.833009			−0.416504	+	0.909134i	$0.636745\pi$
$312$	−3.65856	−	3.65856i	−0.0117262	−	0.0117262i
$313$	−163.064	+	163.064i	−0.520972	+	0.520972i	−0.917865	−	0.396893i	$-0.870088\pi$
$313$	−163.064	+	163.064i	−0.520972	+	0.520972i	0.396893	+	0.917865i	$0.370088\pi$
$314$			186.266i			0.593205i
$315$	22.5830	+	53.0016i	0.0716921	+	0.168259i
$316$	23.8286			0.0754069
$317$	−147.096	−	147.096i	−0.464025	−	0.464025i	0.435947	−	0.899972i	$-0.356413\pi$
$317$	−147.096	−	147.096i	−0.464025	−	0.464025i	−0.899972	+	0.435947i	$0.856413\pi$
$318$	−68.7908	+	68.7908i	−0.216323	+	0.216323i
$319$			986.207i			3.09156i
$320$	37.1077	+	14.9338i	0.115962	+	0.0466681i
$321$	−233.664			−0.727926
$322$	18.4199	+	18.4199i	0.0572046	+	0.0572046i
$323$	11.1120	−	11.1120i	0.0344025	−	0.0344025i
$324$		−	18.0000i		−	0.0555556i
$325$	−26.3980	+	0.532647i	−0.0812247	+	0.00163892i
$326$	−321.130			−0.985062
$327$	−106.185	−	106.185i	−0.324724	−	0.324724i
$328$	114.418	−	114.418i	0.348836	−	0.348836i
$329$		−	224.463i		−	0.682257i
$330$	−92.3384	+	229.444i	−0.279813	+	0.695284i
$331$	354.624			1.07137			0.535686	−	0.844417i	$-0.320053\pi$
$331$	354.624			1.07137			0.535686	+	0.844417i	$0.320053\pi$
$332$	103.945	+	103.945i	0.313088	+	0.313088i
$333$	−49.6585	+	49.6585i	−0.149125	+	0.149125i
$334$			394.177i			1.18017i
$335$	−24.0991	+	10.2682i	−0.0719378	+	0.0306514i
$336$	−26.6099			−0.0791962
$337$	−70.1245	−	70.1245i	−0.208084	−	0.208084i	0.595368	−	0.803453i	$-0.297006\pi$
$337$	−70.1245	−	70.1245i	−0.208084	−	0.208084i	−0.803453	+	0.595368i	$0.797006\pi$
$338$	167.885	−	167.885i	0.496700	−	0.496700i
$339$			260.868i			0.769524i
$340$	−3.08233	−	7.23413i	−0.00906568	−	0.0212769i
$341$	−1014.32			−2.97456
$342$	59.9539	+	59.9539i	0.175304	+	0.175304i
$343$	226.091	−	226.091i	0.659156	−	0.659156i
$344$		−	234.474i		−	0.681609i
$345$	−38.5300	−	15.5062i	−0.111681	−	0.0449454i
$346$	−34.2775			−0.0990678
$347$	−70.2036	−	70.2036i	−0.202316	−	0.202316i	0.598676	−	0.800992i	$-0.295694\pi$
$347$	−70.2036	−	70.2036i	−0.202316	−	0.202316i	−0.800992	+	0.598676i	$0.795694\pi$
$348$	119.624	−	119.624i	0.343746	−	0.343746i
$349$		−	361.402i		−	1.03554i	−0.855521	−	0.517769i	$-0.826763\pi$
$349$		−	361.402i		−	1.03554i	0.855521	−	0.517769i	$-0.173237\pi$
$350$	−94.0637	+	97.9378i	−0.268753	+	0.279822i
$351$	−5.48785			−0.0156349
$352$	−80.7768	−	80.7768i	−0.229480	−	0.229480i
$353$	176.815	−	176.815i	0.500892	−	0.500892i	−0.410823	−	0.911715i	$-0.634759\pi$
$353$	176.815	−	176.815i	0.500892	−	0.500892i	0.911715	+	0.410823i	$0.134759\pi$
$354$		−	113.380i		−	0.320283i
$355$	84.0103	−	208.750i	0.236649	−	0.588029i
$356$	−306.103			−0.859841
$357$	3.69897	+	3.69897i	0.0103612	+	0.0103612i
$358$	−118.734	+	118.734i	−0.331659	+	0.331659i
$359$			247.653i			0.689841i	0.938632	+	0.344921i	$0.112094\pi$
$359$			247.653i			0.689841i	−0.938632	+	0.344921i	$0.887906\pi$
$360$	39.0311	−	16.6304i	0.108420	−	0.0461957i
$361$	−38.3856			−0.106331
$362$	20.8622	+	20.8622i	0.0576303	+	0.0576303i
$363$	351.264	−	351.264i	0.967669	−	0.967669i
$364$			8.11284i			0.0222880i
$365$	−55.2171	−	129.593i	−0.151280	−	0.355049i
$366$	197.622			0.539951
$367$	227.941	+	227.941i	0.621094	+	0.621094i	0.945811	−	0.324717i	$-0.105269\pi$
$367$	227.941	+	227.941i	0.621094	+	0.621094i	−0.324717	+	0.945811i	$0.605269\pi$
$368$	13.5647	−	13.5647i	0.0368605	−	0.0368605i
$369$		−	171.627i		−	0.465114i
$370$	−153.560	−	61.7992i	−0.415026	−	0.167025i
$371$	152.543			0.411168
$372$	123.034	+	123.034i	0.330737	+	0.330737i
$373$	96.9161	−	96.9161i	0.259829	−	0.259829i	−0.565156	−	0.824984i	$-0.691184\pi$
$373$	96.9161	−	96.9161i	0.259829	−	0.259829i	0.824984	+	0.565156i	$0.191184\pi$
$374$			22.4571i			0.0600457i
$375$	76.7632	−	202.441i	0.204702	−	0.539843i
$376$	−165.297			−0.439621
$377$	−36.4709	−	36.4709i	−0.0967398	−	0.0967398i
$378$	−19.9574	+	19.9574i	−0.0527975	+	0.0527975i
$379$			233.612i			0.616390i	0.951323	+	0.308195i	$0.0997249\pi$
$379$			233.612i			0.616390i	−0.951323	+	0.308195i	$0.900275\pi$
$380$	−74.6115	+	185.396i	−0.196346	+	0.487884i
$381$	−404.473			−1.06161
$382$	−252.640	−	252.640i	−0.661361	−	0.661361i
$383$	159.974	−	159.974i	0.417687	−	0.417687i	−0.466719	−	0.884406i	$-0.654564\pi$
$383$	159.974	−	159.974i	0.417687	−	0.417687i	0.884406	+	0.466719i	$0.154564\pi$
$384$			19.5959i			0.0510310i
$385$	356.775	−	152.015i	0.926688	−	0.394845i
$386$	63.0548			0.163354
$387$	−175.855	−	175.855i	−0.454406	−	0.454406i
$388$	−219.115	+	219.115i	−0.564729	+	0.564729i
$389$			218.431i			0.561520i	0.959778	+	0.280760i	$0.0905865\pi$
$389$			218.431i			0.561520i	−0.959778	+	0.280760i	$0.909413\pi$
$390$	−5.07030	−	11.8998i	−0.0130008	−	0.0305124i
$391$	−3.77117			−0.00964493
$392$	−68.4963	−	68.4963i	−0.174736	−	0.174736i
$393$	−120.475	+	120.475i	−0.306553	+	0.306553i
$394$		−	251.615i		−	0.638618i
$395$	55.2640	+	22.2407i	0.139909	+	0.0563055i
$396$	−121.165			−0.305973
$397$	−349.255	−	349.255i	−0.879735	−	0.879735i	0.113772	−	0.993507i	$-0.463707\pi$
$397$	−349.255	−	349.255i	−0.879735	−	0.879735i	−0.993507	+	0.113772i	$0.963707\pi$
$398$	213.068	−	213.068i	0.535346	−	0.535346i
$399$		−	132.947i		−	0.333201i
$400$	72.1228	+	69.2698i	0.180307	+	0.173175i
$401$	18.8951			0.0471199			0.0235599	−	0.999722i	$-0.492500\pi$
$401$	18.8951			0.0471199			0.0235599	+	0.999722i	$0.492500\pi$
$402$	−9.07439	−	9.07439i	−0.0225731	−	0.0225731i
$403$	37.5107	−	37.5107i	0.0930786	−	0.0930786i
$404$		−	372.434i		−	0.921866i
$405$	16.8005	−	41.7462i	0.0414827	−	0.103077i
$406$	−265.265			−0.653361
$407$	334.272	+	334.272i	0.821306	+	0.821306i
$408$	2.72397	−	2.72397i	0.00667640	−	0.00667640i
$409$		−	455.514i		−	1.11373i	−0.830605	−	0.556863i	$-0.812005\pi$
$409$		−	455.514i		−	1.11373i	0.830605	−	0.556863i	$-0.187995\pi$
$410$	372.156	−	158.569i	0.907697	−	0.386753i
$411$	−371.255			−0.903296
$412$	−138.330	−	138.330i	−0.335753	−	0.335753i
$413$	−125.710	+	125.710i	−0.304382	+	0.304382i
$414$		−	20.3470i		−	0.0491473i
$415$	144.055	+	338.092i	0.347120	+	0.814679i
$416$	5.97441			0.0143616
$417$	−30.2497	−	30.2497i	−0.0725413	−	0.0725413i
$418$	403.574	−	403.574i	0.965487	−	0.965487i
$419$			348.362i			0.831414i	0.909499	+	0.415707i	$0.136466\pi$
$419$			348.362i			0.831414i	−0.909499	+	0.415707i	$0.863534\pi$
$420$	−61.7146	−	24.8367i	−0.146939	−	0.0591349i
$421$	−394.574			−0.937231			−0.468615	−	0.883402i	$-0.655247\pi$
$421$	−394.574			−0.937231			−0.468615	+	0.883402i	$0.655247\pi$
$422$	−381.486	−	381.486i	−0.903996	−	0.903996i
$423$	−123.973	+	123.973i	−0.293081	+	0.293081i
$424$		−	112.335i		−	0.264941i
$425$	−0.396581	−	19.6546i	−0.000933131	−	0.0462460i
$426$	110.237			0.258773
$427$	−219.113	−	219.113i	−0.513144	−	0.513144i
$428$	190.786	−	190.786i	0.445762	−	0.445762i
$429$			36.9409i			0.0861093i
$430$	218.849	−	543.799i	0.508950	−	1.26465i
$431$	719.875			1.67024			0.835122	−	0.550065i	$-0.185397\pi$
$431$	719.875			1.67024			0.835122	+	0.550065i	$0.185397\pi$
$432$	14.6969	+	14.6969i	0.0340207	+	0.0340207i
$433$	−543.789	+	543.789i	−1.25586	+	1.25586i	−0.302815	+	0.953049i	$0.597926\pi$
$433$	−543.789	+	543.789i	−1.25586	+	1.25586i	−0.953049	+	0.302815i	$0.902074\pi$
$434$		−	272.827i		−	0.628634i
$435$	389.087	−	165.783i	0.894453	−	0.381110i
$436$	173.399			0.397704
$437$	67.7712	+	67.7712i	0.155083	+	0.155083i
$438$	48.7974	−	48.7974i	0.111410	−	0.111410i
$439$			478.471i			1.08991i	0.838465	+	0.544956i	$0.183453\pi$
$439$			478.471i			1.08991i	−0.838465	+	0.544956i	$0.816547\pi$
$440$	−111.946	−	262.734i	−0.254423	−	0.597123i
$441$	−102.745			−0.232981
$442$	−0.830485	−	0.830485i	−0.00187893	−	0.00187893i
$443$	324.161	−	324.161i	0.731741	−	0.731741i	−0.239223	−	0.970965i	$-0.576893\pi$
$443$	324.161	−	324.161i	0.731741	−	0.731741i	0.970965	+	0.239223i	$0.0768928\pi$
$444$		−	81.0921i		−	0.182640i
$445$	−709.924	−	285.705i	−1.59534	−	0.642034i
$446$	87.2963			0.195732
$447$	32.0212	+	32.0212i	0.0716357	+	0.0716357i
$448$	21.7269	−	21.7269i	0.0484976	−	0.0484976i
$449$		−	316.099i		−	0.704007i	−0.935999	−	0.352003i	$-0.885501\pi$
$449$		−	316.099i		−	0.704007i	0.935999	−	0.352003i	$-0.114499\pi$
$450$	106.044	−	2.13972i	0.235654	−	0.00475492i
$451$	−1155.29			−2.56162
$452$	−212.998	−	212.998i	−0.471235	−	0.471235i
$453$	182.938	−	182.938i	0.403836	−	0.403836i
$454$		−	297.059i		−	0.654314i
$455$	−7.57221	+	18.8156i	−0.0166422	+	0.0413529i
$456$	−97.9043			−0.214702
$457$	−572.671	−	572.671i	−1.25311	−	1.25311i	−0.954318	−	0.298791i	$-0.903417\pi$
$457$	−572.671	−	572.671i	−1.25311	−	1.25311i	−0.298791	−	0.954318i	$-0.596583\pi$
$458$	176.625	−	176.625i	0.385645	−	0.385645i
$459$		−	4.08596i		−	0.00890186i
$460$	44.1203	−	18.7989i	0.0959137	−	0.0408671i
$461$	664.538			1.44151			0.720757	−	0.693187i	$-0.243794\pi$
$461$	664.538			1.44151			0.720757	+	0.693187i	$0.243794\pi$
$462$	134.341	+	134.341i	0.290782	+	0.290782i
$463$	−32.2968	+	32.2968i	−0.0697555	+	0.0697555i	−0.741124	−	0.671368i	$-0.765707\pi$
$463$	−32.2968	+	32.2968i	−0.0697555	+	0.0697555i	0.671368	+	0.741124i	$0.265707\pi$
$464$			195.345i			0.421001i
$465$	170.509	+	400.180i	0.366687	+	0.860602i
$466$	172.153			0.369426
$467$	107.272	+	107.272i	0.229705	+	0.229705i	0.812569	−	0.582864i	$-0.198068\pi$
$467$	107.272	+	107.272i	0.229705	+	0.229705i	−0.582864	+	0.812569i	$0.698068\pi$
$468$	4.48081	−	4.48081i	0.00957437	−	0.00957437i
$469$			20.1224i			0.0429049i
$470$	−383.363	−	154.282i	−0.815666	−	0.328260i
$471$	−228.129			−0.484350
$472$	92.5745	+	92.5745i	0.196132	+	0.196132i
$473$	−1183.75	+	1183.75i	−2.50265	+	2.50265i
$474$			29.1839i			0.0615694i
$475$	−346.083	+	360.337i	−0.728596	+	0.758604i
$476$	−6.04039			−0.0126899
$477$	−84.2512	−	84.2512i	−0.176627	−	0.176627i
$478$	−83.0954	+	83.0954i	−0.173840	+	0.173840i
$479$			199.437i			0.416360i	0.978091	+	0.208180i	$0.0667540\pi$
$479$			199.437i			0.416360i	−0.978091	+	0.208180i	$0.933246\pi$
$480$	−18.2901	+	45.4475i	−0.0381043	+	0.0946822i
$481$	−24.7234			−0.0513999
$482$	458.620	+	458.620i	0.951494	+	0.951494i
$483$	−22.5597	+	22.5597i	−0.0467074	+	0.0467074i
$484$			573.611i			1.18515i
$485$	−712.691	+	303.665i	−1.46947	+	0.626113i
$486$	22.0454			0.0453609
$487$	−202.028	−	202.028i	−0.414842	−	0.414842i	0.468580	−	0.883421i	$-0.344766\pi$
$487$	−202.028	−	202.028i	−0.414842	−	0.414842i	−0.883421	+	0.468580i	$0.844766\pi$
$488$	−161.358	+	161.358i	−0.330651	+	0.330651i
$489$		−	393.302i		−	0.804299i
$490$	−94.9271	−	222.791i	−0.193729	−	0.454675i
$491$	642.465			1.30848			0.654241	−	0.756286i	$-0.272988\pi$
$491$	642.465			1.30848			0.654241	+	0.756286i	$0.272988\pi$
$492$	140.133	+	140.133i	0.284823	+	0.284823i
$493$	27.1543	−	27.1543i	0.0550797	−	0.0550797i
$494$			29.8491i			0.0604233i
$495$	−281.010	−	113.091i	−0.567697	−	0.228467i
$496$	−200.914			−0.405068
$497$	−122.225	−	122.225i	−0.245926	−	0.245926i
$498$	−127.307	+	127.307i	−0.255636	+	0.255636i
$499$		−	745.571i		−	1.49413i	−0.664751	−	0.747065i	$-0.731462\pi$
$499$		−	745.571i		−	1.49413i	0.664751	−	0.747065i	$-0.268538\pi$
$500$	102.616	+	227.969i	0.205231	+	0.455939i
$501$	−482.767			−0.963606
$502$	−297.824	−	297.824i	−0.593275	−	0.593275i
$503$	133.917	−	133.917i	0.266237	−	0.266237i	−0.561345	−	0.827582i	$-0.689716\pi$
$503$	133.917	−	133.917i	0.266237	−	0.266237i	0.827582	+	0.561345i	$0.189716\pi$
$504$		−	32.5904i		−	0.0646634i
$505$	347.615	−	863.761i	0.688347	−	1.71042i
$506$	−136.964			−0.270679
$507$	205.616	+	205.616i	0.405554	+	0.405554i
$508$	330.251	−	330.251i	0.650100	−	0.650100i
$509$			553.510i			1.08745i	0.839265	+	0.543723i	$0.182986\pi$
$509$			553.510i			1.08745i	−0.839265	+	0.543723i	$0.817014\pi$
$510$	8.85997	−	3.77507i	0.0173725	−	0.00740210i
$511$	−108.208			−0.211757
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	−73.4282	+	73.4282i	−0.143135	+	0.143135i
$514$			266.200i			0.517899i
$515$	−191.708	−	449.933i	−0.372249	−	0.873656i
$516$	287.170			0.556532
$517$	834.512	+	834.512i	1.61414	+	1.61414i
$518$	−89.9105	+	89.9105i	−0.173572	+	0.173572i
$519$		−	41.9812i		−	0.0808885i
$520$	13.8560	+	5.57628i	0.0266462	+	0.0107236i
$521$	516.860			0.992053			0.496027	−	0.868307i	$-0.334792\pi$
$521$	516.860			0.992053			0.496027	+	0.868307i	$0.334792\pi$
$522$	146.508	+	146.508i	0.280668	+	0.280668i
$523$	−346.867	+	346.867i	−0.663225	+	0.663225i	−0.956139	−	0.292914i	$-0.905375\pi$
$523$	−346.867	+	346.867i	−0.663225	+	0.663225i	0.292914	+	0.956139i	$0.405375\pi$
$524$		−	196.735i		−	0.375449i
$525$	−119.949	−	115.204i	−0.228474	−	0.219436i
$526$	−214.534			−0.407860
$527$	27.9284	+	27.9284i	0.0529951	+	0.0529951i
$528$	98.9310	−	98.9310i	0.187369	−	0.187369i
$529$		−	23.0000i		−	0.0434783i
$530$	104.849	−	260.531i	0.197828	−	0.491568i
$531$	138.862			0.261510
$532$	108.551	+	108.551i	0.204043	+	0.204043i
$533$	42.7238	−	42.7238i	0.0801572	−	0.0801572i
$534$		−	374.898i		−	0.702057i
$535$	620.549	−	264.405i	1.15991	−	0.494215i
$536$	14.8184			0.0276463
$537$	−145.419	−	145.419i	−0.270798	−	0.270798i
$538$	−68.2440	+	68.2440i	−0.126848	+	0.126848i
$539$			691.614i			1.28314i
$540$	20.3681	+	47.8032i	0.0377186	+	0.0885244i
$541$	−99.7425			−0.184367			−0.0921835	−	0.995742i	$-0.529385\pi$
$541$	−99.7425			−0.184367			−0.0921835	+	0.995742i	$0.529385\pi$
$542$	166.004	+	166.004i	0.306280	+	0.306280i
$543$	−25.5508	+	25.5508i	−0.0470550	+	0.0470550i
$544$			4.44823i			0.00817688i
$545$	402.152	+	161.844i	0.737893	+	0.296961i
$546$	−9.93616			−0.0181981
$547$	−187.087	−	187.087i	−0.342023	−	0.342023i	0.515104	−	0.857127i	$-0.327753\pi$
$547$	−187.087	−	187.087i	−0.342023	−	0.342023i	−0.857127	+	0.515104i	$0.827753\pi$
$548$	303.128	−	303.128i	0.553154	−	0.553154i
$549$			242.036i			0.440868i
$550$	−14.4033	−	713.827i	−0.0261878	−	1.29787i
$551$	−975.973			−1.77128
$552$	16.6132	+	16.6132i	0.0300965	+	0.0300965i
$553$	32.3576	−	32.3576i	0.0585128	−	0.0585128i
$554$		−	333.995i		−	0.602878i
$555$	75.6882	−	188.071i	0.136375	−	0.338867i
$556$	49.3976			0.0888446
$557$	−471.806	−	471.806i	−0.847049	−	0.847049i	0.142715	−	0.989764i	$-0.454417\pi$
$557$	−471.806	−	471.806i	−0.847049	−	0.847049i	−0.989764	+	0.142715i	$0.954417\pi$
$558$	−150.685	+	150.685i	−0.270045	+	0.270045i
$559$		−	87.5526i		−	0.156624i
$560$	70.6688	−	30.1107i	0.126194	−	0.0537691i
$561$	−27.5042			−0.0490271
$562$	138.196	+	138.196i	0.245901	+	0.245901i
$563$	−49.5630	+	49.5630i	−0.0880338	+	0.0880338i	−0.749752	−	0.661719i	$-0.769827\pi$
$563$	−49.5630	+	49.5630i	−0.0880338	+	0.0880338i	0.661719	+	0.749752i	$0.269827\pi$
$564$		−	202.447i		−	0.358949i
$565$	−295.188	−	692.797i	−0.522457	−	1.22619i
$566$	111.338			0.196710
$567$	−24.4428	−	24.4428i	−0.0431089	−	0.0431089i
$568$	−90.0083	+	90.0083i	−0.158465	+	0.158465i
$569$			485.455i			0.853172i	0.904447	+	0.426586i	$0.140284\pi$
$569$			485.455i			0.853172i	−0.904447	+	0.426586i	$0.859716\pi$
$570$	−227.063	−	91.3801i	−0.398356	−	0.160316i
$571$	159.599			0.279508			0.139754	−	0.990186i	$-0.455369\pi$
$571$	159.599			0.279508			0.139754	+	0.990186i	$0.455369\pi$
$572$	−30.1621	−	30.1621i	−0.0527310	−	0.0527310i
$573$	309.419	−	309.419i	0.539999	−	0.539999i
$574$		−	310.744i		−	0.541366i
$575$	119.871	−	2.41871i	0.208472	−	0.00420645i
$576$	−24.0000			−0.0416667
$577$	676.144	+	676.144i	1.17183	+	1.17183i	0.981774	+	0.190052i	$0.0608658\pi$
$577$	676.144	+	676.144i	1.17183	+	1.17183i	0.190052	+	0.981774i	$0.439134\pi$
$578$	−288.382	+	288.382i	−0.498930	+	0.498930i
$579$			77.2260i			0.133378i
$580$	−182.327	+	453.050i	−0.314357	+	0.781120i
$581$	282.301			0.485889
$582$	−268.360	−	268.360i	−0.461099	−	0.461099i
$583$	−567.129	+	567.129i	−0.972776	+	0.972776i
$584$			79.6858i			0.136448i
$585$	14.5742	−	6.20982i	0.0249132	−	0.0106151i
$586$	−294.748			−0.502984
$587$	−9.46267	−	9.46267i	−0.0161204	−	0.0161204i	0.699001	−	0.715121i	$-0.253628\pi$
$587$	−9.46267	−	9.46267i	−0.0161204	−	0.0161204i	−0.715121	+	0.699001i	$0.753628\pi$
$588$	83.8905	−	83.8905i	0.142671	−	0.142671i
$589$		−	1003.80i		−	1.70424i
$590$	128.296	+	301.107i	0.217451	+	0.510351i
$591$	308.165			0.521429
$592$	66.2114	+	66.2114i	0.111844	+	0.111844i
$593$	464.745	−	464.745i	0.783719	−	0.783719i	−0.196738	−	0.980456i	$-0.563035\pi$
$593$	464.745	−	464.745i	0.783719	−	0.783719i	0.980456	+	0.196738i	$0.0630347\pi$
$594$		−	148.396i		−	0.249826i
$595$	−14.0091	−	5.63786i	−0.0235446	−	0.00947540i
$596$	−52.2903			−0.0877355
$597$	260.953	+	260.953i	0.437108	+	0.437108i
$598$	5.06505	−	5.06505i	0.00846999	−	0.00846999i
$599$		−	711.019i		−	1.18701i	−0.804830	−	0.593505i	$-0.797744\pi$
$599$		−	711.019i		−	1.18701i	0.804830	−	0.593505i	$-0.202256\pi$
$600$	−84.8378	+	88.3320i	−0.141396	+	0.147220i
$601$	−103.335			−0.171938			−0.0859689	−	0.996298i	$-0.527399\pi$
$601$	−103.335			−0.171938			−0.0859689	+	0.996298i	$0.527399\pi$
$602$	−318.399	−	318.399i	−0.528902	−	0.528902i
$603$	11.1138	−	11.1138i	0.0184309	−	0.0184309i
$604$			298.736i			0.494596i
$605$	−535.387	+	1330.34i	−0.884937	+	2.19891i
$606$	456.137			0.752701
$607$	−12.5607	−	12.5607i	−0.0206931	−	0.0206931i	0.696685	−	0.717378i	$-0.254658\pi$
$607$	−12.5607	−	12.5607i	−0.0206931	−	0.0206931i	−0.717378	+	0.696685i	$0.754658\pi$
$608$	79.9385	−	79.9385i	0.131478	−	0.131478i
$609$		−	324.882i		−	0.533467i
$610$	−524.831	+	223.621i	−0.860378	+	0.366591i
$611$	−61.7222			−0.101018
$612$	3.33617	+	3.33617i	0.00545126	+	0.00545126i
$613$	−227.704	+	227.704i	−0.371459	+	0.371459i	−0.868008	−	0.496550i	$-0.834600\pi$
$613$	−227.704	+	227.704i	−0.371459	+	0.371459i	0.496550	+	0.868008i	$0.334600\pi$
$614$			599.408i			0.976234i
$615$	194.206	+	455.796i	0.315783	+	0.741131i
$616$	−219.379			−0.356134
$617$	−735.380	−	735.380i	−1.19186	−	1.19186i	−0.976543	−	0.215320i	$-0.930920\pi$
$617$	−735.380	−	735.380i	−1.19186	−	1.19186i	−0.215320	−	0.976543i	$-0.569080\pi$
$618$	169.419	−	169.419i	0.274142	−	0.274142i
$619$			216.723i			0.350118i	0.984558	+	0.175059i	$0.0560116\pi$
$619$			216.723i			0.350118i	−0.984558	+	0.175059i	$0.943988\pi$
$620$	−465.966	−	187.525i	−0.751558	−	0.302460i
$621$	24.9199			0.0401286
$622$	259.066	+	259.066i	0.416504	+	0.416504i
$623$	−415.667	+	415.667i	−0.667203	+	0.667203i
$624$			7.31713i			0.0117262i
$625$	25.2117	+	624.491i	0.0403387	+	0.999186i
$626$	326.128			0.520972
$627$	494.275	+	494.275i	0.788317	+	0.788317i
$628$	186.266	−	186.266i	0.296603	−	0.296603i
$629$		−	18.4077i		−	0.0292650i
$630$	30.4186	−	75.5846i	0.0482835	−	0.119976i
$631$	−702.127			−1.11272			−0.556361	−	0.830941i	$-0.687803\pi$
$631$	−702.127			−1.11272			−0.556361	+	0.830941i	$0.687803\pi$
$632$	−23.8286	−	23.8286i	−0.0377034	−	0.0377034i
$633$	467.224	−	467.224i	0.738110	−	0.738110i
$634$			294.192i			0.464025i
$635$	1074.17	−	457.685i	1.69161	−	0.720764i
$636$	137.582			0.216323
$637$	−25.5766	−	25.5766i	−0.0401516	−	0.0401516i
$638$	986.207	−	986.207i	1.54578	−	1.54578i
$639$			135.013i			0.211287i
$640$	−22.1739	−	52.0415i	−0.0346468	−	0.0813148i
$641$	−121.421			−0.189424			−0.0947122	−	0.995505i	$-0.530193\pi$
$641$	−121.421			−0.189424			−0.0947122	+	0.995505i	$0.530193\pi$
$642$	233.664	+	233.664i	0.363963	+	0.363963i
$643$	−219.567	+	219.567i	−0.341473	+	0.341473i	−0.856921	−	0.515448i	$-0.827626\pi$
$643$	−219.567	+	219.567i	−0.341473	+	0.341473i	0.515448	+	0.856921i	$0.327626\pi$
$644$		−	36.8398i		−	0.0572046i
$645$	666.015	+	268.034i	1.03258	+	0.415556i
$646$	−22.2240			−0.0344025
$647$	−460.289	−	460.289i	−0.711420	−	0.711420i	0.255412	−	0.966832i	$-0.417789\pi$
$647$	−460.289	−	460.289i	−0.711420	−	0.711420i	−0.966832	+	0.255412i	$0.917789\pi$
$648$	−18.0000	+	18.0000i	−0.0277778	+	0.0277778i
$649$		−	934.734i		−	1.44027i
$650$	26.9307	+	25.8654i	0.0414318	+	0.0397929i
$651$	334.144			0.513278
$652$	321.130	+	321.130i	0.492531	+	0.492531i
$653$	−444.922	+	444.922i	−0.681351	+	0.681351i	−0.960304	−	0.278954i	$-0.910012\pi$
$653$	−444.922	+	444.922i	−0.681351	+	0.681351i	0.278954	+	0.960304i	$0.410012\pi$
$654$			212.369i			0.324724i
$655$	183.625	−	456.275i	0.280344	−	0.696603i
$656$	−228.836			−0.348836
$657$	59.7644	+	59.7644i	0.0909655	+	0.0909655i
$658$	−224.463	+	224.463i	−0.341129	+	0.341129i
$659$			215.293i			0.326697i	0.986568	+	0.163348i	$0.0522295\pi$
$659$			215.293i			0.326697i	−0.986568	+	0.163348i	$0.947771\pi$
$660$	321.782	−	137.106i	0.487549	−	0.207736i
$661$	460.077			0.696032			0.348016	−	0.937489i	$-0.386855\pi$
$661$	460.077			0.696032			0.348016	+	0.937489i	$0.386855\pi$
$662$	−354.624	−	354.624i	−0.535686	−	0.535686i
$663$	1.01713	−	1.01713i	0.00153414	−	0.00153414i
$664$		−	207.891i		−	0.313088i
$665$	150.438	+	353.072i	0.226222	+	0.530936i
$666$	99.3171			0.149125
$667$	165.611	+	165.611i	0.248293	+	0.248293i
$668$	394.177	−	394.177i	0.590086	−	0.590086i
$669$			106.916i			0.159814i
$670$	34.3674	+	13.8309i	0.0512946	+	0.0206432i
$671$	1629.24			2.42808
$672$	26.6099	+	26.6099i	0.0395981	+	0.0395981i
$673$	−380.727	+	380.727i	−0.565716	+	0.565716i	−0.930925	−	0.365210i	$-0.880997\pi$
$673$	−380.727	+	380.727i	−0.565716	+	0.565716i	0.365210	+	0.930925i	$0.380997\pi$
$674$			140.249i			0.208084i
$675$	2.62061	+	129.877i	0.00388238	+	0.192411i
$676$	−335.769			−0.496700
$677$	88.2870	+	88.2870i	0.130409	+	0.130409i	0.769299	−	0.638889i	$-0.220606\pi$
$677$	88.2870	+	88.2870i	0.130409	+	0.130409i	−0.638889	+	0.769299i	$0.720606\pi$
$678$	260.868	−	260.868i	0.384762	−	0.384762i
$679$			595.086i			0.876415i
$680$	−4.15180	+	10.3165i	−0.00610559	+	0.0151713i
$681$	363.821			0.534246
$682$	1014.32	+	1014.32i	1.48728	+	1.48728i
$683$	367.133	−	367.133i	0.537530	−	0.537530i	−0.385273	−	0.922803i	$-0.625893\pi$
$683$	367.133	−	367.133i	0.537530	−	0.537530i	0.922803	+	0.385273i	$0.125893\pi$
$684$		−	119.908i		−	0.175304i
$685$	985.953	−	420.097i	1.43935	−	0.613280i
$686$	−452.181			−0.659156
$687$	216.321	+	216.321i	0.314877	+	0.314877i
$688$	−234.474	+	234.474i	−0.340805	+	0.340805i
$689$		−	41.9459i		−	0.0608794i
$690$	23.0238	+	54.0361i	0.0333678	+	0.0783132i
$691$	557.637			0.807001			0.403500	−	0.914979i	$-0.367793\pi$
$691$	557.637			0.807001			0.403500	+	0.914979i	$0.367793\pi$
$692$	34.2775	+	34.2775i	0.0495339	+	0.0495339i
$693$	−164.534	+	164.534i	−0.237423	+	0.237423i
$694$			140.407i			0.202316i
$695$	114.565	+	46.1058i	0.164841	+	0.0663393i
$696$	−239.247			−0.343746
$697$	31.8099	+	31.8099i	0.0456382	+	0.0456382i
$698$	−361.402	+	361.402i	−0.517769	+	0.517769i
$699$			210.843i			0.301635i
$700$	192.001	−	3.87412i	0.274288	−	0.00553445i
$701$	780.433			1.11331			0.556657	−	0.830742i	$-0.312084\pi$
$701$	780.433			1.11331			0.556657	+	0.830742i	$0.312084\pi$
$702$	5.48785	+	5.48785i	0.00781744	+	0.00781744i
$703$	−330.803	+	330.803i	−0.470558	+	0.470558i
$704$			161.554i			0.229480i
$705$	188.956	−	469.522i	0.268023	−	0.665989i
$706$	−353.630			−0.500892
$707$	−505.740	−	505.740i	−0.715332	−	0.715332i
$708$	−113.380	+	113.380i	−0.160141	+	0.160141i
$709$			954.304i			1.34599i	0.739649	+	0.672993i	$0.234992\pi$
$709$			954.304i			1.34599i	−0.739649	+	0.672993i	$0.765008\pi$
$710$	−292.761	+	124.740i	−0.412339	+	0.175690i
$711$	−35.7429			−0.0502712
$712$	306.103	+	306.103i	0.429920	+	0.429920i
$713$	−170.333	+	170.333i	−0.238896	+	0.238896i
$714$		−	7.39793i		−	0.0103612i
$715$	−41.8008	−	98.1051i	−0.0584626	−	0.137210i
$716$	237.468			0.331659
$717$	−101.771	−	101.771i	−0.141940	−	0.141940i
$718$	247.653	−	247.653i	0.344921	−	0.344921i
$719$			898.190i			1.24922i	0.780937	+	0.624610i	$0.214742\pi$
$719$			898.190i			1.24922i	−0.780937	+	0.624610i	$0.785258\pi$
$720$	−55.6616	−	22.4007i	−0.0773077	−	0.0311120i
$721$	−375.687			−0.521063
$722$	38.3856	+	38.3856i	0.0531656	+	0.0531656i
$723$	−561.693	+	561.693i	−0.776892	+	0.776892i
$724$		−	41.7244i		−	0.0576303i
$725$	−845.718	+	880.550i	−1.16651	+	1.21455i
$726$	−702.528			−0.967669
$727$	112.049	+	112.049i	0.154125	+	0.154125i	0.779958	−	0.625832i	$-0.215241\pi$
$727$	112.049	+	112.049i	0.154125	+	0.154125i	−0.625832	+	0.779958i	$0.715241\pi$
$728$	8.11284	−	8.11284i	0.0111440	−	0.0111440i
$729$			27.0000i			0.0370370i
$730$	−74.3757	+	184.810i	−0.101884	+	0.253164i
$731$	65.1870			0.0891750
$732$	−197.622	−	197.622i	−0.269975	−	0.269975i
$733$	−717.264	+	717.264i	−0.978532	+	0.978532i	−0.999774	−	0.0212427i	$-0.993238\pi$
$733$	−717.264	+	717.264i	−0.978532	+	0.978532i	0.0212427	+	0.999774i	$0.493238\pi$
$734$		−	455.883i		−	0.621094i
$735$	272.862	−	116.261i	0.371241	−	0.158179i
$736$	−27.1293			−0.0368605
$737$	−74.8115	−	74.8115i	−0.101508	−	0.101508i
$738$	−171.627	+	171.627i	−0.232557	+	0.232557i
$739$		−	756.398i		−	1.02354i	−0.859122	−	0.511772i	$-0.828989\pi$
$739$		−	756.398i		−	1.02354i	0.859122	−	0.511772i	$-0.171011\pi$
$740$	91.7604	+	215.359i	0.124001	+	0.291025i
$741$	−36.5575			−0.0493354
$742$	−152.543	−	152.543i	−0.205584	−	0.205584i
$743$	611.505	−	611.505i	0.823022	−	0.823022i	−0.163518	−	0.986540i	$-0.552284\pi$
$743$	611.505	−	611.505i	0.823022	−	0.823022i	0.986540	+	0.163518i	$0.0522843\pi$
$744$		−	246.068i		−	0.330737i
$745$	−121.273	−	48.8058i	−0.162783	−	0.0655111i
$746$	−193.832			−0.259829
$747$	−155.918	−	155.918i	−0.208726	−	0.208726i
$748$	22.4571	−	22.4571i	0.0300228	−	0.0300228i
$749$		−	518.149i		−	0.691788i
$750$	−279.204	+	125.678i	−0.372272	+	0.167571i
$751$	720.817			0.959809			0.479905	−	0.877321i	$-0.340671\pi$
$751$	720.817			0.959809			0.479905	+	0.877321i	$0.340671\pi$
$752$	165.297	+	165.297i	0.219810	+	0.219810i
$753$	364.758	−	364.758i	0.484407	−	0.484407i
$754$			72.9418i			0.0967398i
$755$	−278.828	+	692.838i	−0.369309	+	0.917666i
$756$	39.9149			0.0527975
$757$	−704.669	−	704.669i	−0.930870	−	0.930870i	0.0668903	−	0.997760i	$-0.478692\pi$
$757$	−704.669	−	704.669i	−0.930870	−	0.930870i	−0.997760	+	0.0668903i	$0.978692\pi$
$758$	233.612	−	233.612i	0.308195	−	0.308195i
$759$		−	167.746i		−	0.221009i
$760$	260.008	−	110.784i	0.342115	−	0.145769i
$761$	522.214			0.686221			0.343111	−	0.939295i	$-0.388519\pi$
$761$	522.214			0.686221			0.343111	+	0.939295i	$0.388519\pi$
$762$	404.473	+	404.473i	0.530805	+	0.530805i
$763$	235.464	−	235.464i	0.308602	−	0.308602i
$764$			505.280i			0.661361i
$765$	4.62350	+	10.8512i	0.00604379	+	0.0141846i
$766$	−319.948			−0.417687
$767$	34.5674	+	34.5674i	0.0450683	+	0.0450683i
$768$	19.5959	−	19.5959i	0.0255155	−	0.0255155i
$769$		−	478.937i		−	0.622805i	−0.950278	−	0.311403i	$-0.899201\pi$
$769$		−	478.937i		−	0.622805i	0.950278	−	0.311403i	$-0.100799\pi$
$770$	−508.790	−	204.760i	−0.660766	−	0.265922i
$771$	−326.027			−0.422862
$772$	−63.0548	−	63.0548i	−0.0816772	−	0.0816772i
$773$	−149.986	+	149.986i	−0.194031	+	0.194031i	−0.797435	−	0.603405i	$-0.793810\pi$
$773$	−149.986	+	149.986i	−0.194031	+	0.194031i	0.603405	+	0.797435i	$0.293810\pi$
$774$			351.710i			0.454406i
$775$	−905.654	−	869.829i	−1.16859	−	1.12236i
$776$	438.229			0.564729
$777$	−110.117	−	110.117i	−0.141721	−	0.141721i
$778$	218.431	−	218.431i	0.280760	−	0.280760i
$779$		−	1143.30i		−	1.46765i
$780$	−6.82952	+	16.9701i	−0.00875580	+	0.0217566i
$781$	908.823			1.16367
$782$	3.77117	+	3.77117i	0.00482246	+	0.00482246i
$783$	−179.436	+	179.436i	−0.229164	+	0.229164i
$784$			136.993i			0.174736i
$785$	605.849	−	258.141i	0.771782	−	0.328842i
$786$	240.951			0.306553
$787$	−301.772	−	301.772i	−0.383446	−	0.383446i	0.488896	−	0.872342i	$-0.337400\pi$
$787$	−301.772	−	301.772i	−0.383446	−	0.383446i	−0.872342	+	0.488896i	$0.837400\pi$
$788$	−251.615	+	251.615i	−0.319309	+	0.319309i
$789$		−	262.750i		−	0.333016i
$790$	−33.0233	−	77.5046i	−0.0418017	−	0.0981071i
$791$	−578.474			−0.731320
$792$	121.165	+	121.165i	0.152986	+	0.152986i
$793$	−60.2510	+	60.2510i	−0.0759786	+	0.0759786i
$794$			698.509i			0.879735i
$795$	319.084	+	128.413i	0.401363	+	0.161526i
$796$	−426.135			−0.535346
$797$	486.804	+	486.804i	0.610796	+	0.610796i	0.943153	−	0.332358i	$-0.107844\pi$
$797$	486.804	+	486.804i	0.610796	+	0.610796i	−0.332358	+	0.943153i	$0.607844\pi$
$798$	−132.947	+	132.947i	−0.166601	+	0.166601i
$799$		−	45.9550i		−	0.0575157i
$800$	−2.85295	−	141.393i	−0.00356619	−	0.176741i
$801$	459.155			0.573227
$802$	−18.8951	−	18.8951i	−0.0235599	−	0.0235599i
$803$	402.298	−	402.298i	0.500994	−	0.500994i
$804$			18.1488i			0.0225731i
$805$	34.3848	−	85.4399i	0.0427141	−	0.106137i
$806$	−75.0213			−0.0930786
$807$	−83.5815	−	83.5815i	−0.103571	−	0.103571i
$808$	−372.434	+	372.434i	−0.460933	+	0.460933i
$809$		−	664.708i		−	0.821642i	−0.911716	−	0.410821i	$-0.865242\pi$
$809$		−	664.708i		−	0.821642i	0.911716	−	0.410821i	$-0.134758\pi$
$810$	−58.5467	+	24.9457i	−0.0722799	+	0.0307971i
$811$	1068.85			1.31795			0.658973	−	0.752167i	$-0.270991\pi$
$811$	1068.85			1.31795			0.658973	+	0.752167i	$0.270991\pi$
$812$	265.265	+	265.265i	0.326681	+	0.326681i
$813$	−203.312	+	203.312i	−0.250077	+	0.250077i
$814$		−	668.543i		−	0.821306i
$815$	445.045	+	1044.51i	0.546067	+	1.28160i
$816$	−5.44794			−0.00667640
$817$	−1171.47	−	1171.47i	−1.43386	−	1.43386i
$818$	−455.514	+	455.514i	−0.556863	+	0.556863i
$819$		−	12.1693i		−	0.0148587i
$820$	−530.724	−	213.587i	−0.647225	−	0.260472i
$821$	−1574.87			−1.91824			−0.959118	−	0.283007i	$-0.908668\pi$
$821$	−1574.87			−1.91824			−0.959118	+	0.283007i	$0.908668\pi$
$822$	371.255	+	371.255i	0.451648	+	0.451648i
$823$	−859.404	+	859.404i	−1.04423	+	1.04423i	−0.0452577	+	0.998975i	$0.514411\pi$
$823$	−859.404	+	859.404i	−1.04423	+	1.04423i	−0.998975	+	0.0452577i	$0.985589\pi$
$824$			276.661i			0.335753i
$825$	874.257	−	17.6403i	1.05970	−	0.0213822i
$826$	251.420			0.304382
$827$	924.916	+	924.916i	1.11840	+	1.11840i	0.991976	+	0.126423i	$0.0403496\pi$
$827$	924.916	+	924.916i	1.11840	+	1.11840i	0.126423	+	0.991976i	$0.459650\pi$
$828$	−20.3470	+	20.3470i	−0.0245737	+	0.0245737i
$829$			658.286i			0.794072i	0.917803	+	0.397036i	$0.129961\pi$
$829$			658.286i			0.794072i	−0.917803	+	0.397036i	$0.870039\pi$
$830$	194.037	−	482.147i	0.233780	−	0.580900i
$831$	409.058			0.492248
$832$	−5.97441	−	5.97441i	−0.00718078	−	0.00718078i
$833$	19.0429	−	19.0429i	0.0228607	−	0.0228607i
$834$			60.4995i			0.0725413i
$835$	1282.10	−	546.279i	1.53545	−	0.654226i
$836$	−807.147			−0.965487
$837$	−184.551	−	184.551i	−0.220491	−	0.220491i
$838$	348.362	−	348.362i	0.415707	−	0.415707i
$839$		−	160.645i		−	0.191472i	−0.995407	−	0.0957359i	$-0.969480\pi$
$839$		−	160.645i		−	0.191472i	0.995407	−	0.0957359i	$-0.0305204\pi$
$840$	36.8779	+	86.5512i	0.0439023	+	0.103037i
$841$	−1543.97			−1.83587
$842$	394.574	+	394.574i	0.468615	+	0.468615i
$843$	−169.255	+	169.255i	−0.200777	+	0.200777i
$844$			762.973i			0.903996i
$845$	−778.727	−	313.394i	−0.921570	−	0.370880i
$846$	247.946			0.293081
$847$	778.925	+	778.925i	0.919628	+	0.919628i
$848$	−112.335	+	112.335i	−0.132470	+	0.132470i
$849$			136.360i			0.160613i
$850$	−19.2580	+	20.0511i	−0.0226564	+	0.0235896i
$851$	112.267			0.131923
$852$	−110.237	−	110.237i	−0.129386	−	0.129386i
$853$	−483.525	+	483.525i	−0.566852	+	0.566852i	−0.931245	−	0.364393i	$-0.881276\pi$
$853$	−483.525	+	483.525i	−0.566852	+	0.566852i	0.364393	+	0.931245i	$0.381276\pi$
$854$			438.225i			0.513144i
$855$	111.917	−	278.094i	0.130897	−	0.325256i
$856$	−381.572			−0.445762
$857$	57.8997	+	57.8997i	0.0675610	+	0.0675610i	0.740080	−	0.672519i	$-0.234788\pi$
$857$	57.8997	+	57.8997i	0.0675610	+	0.0675610i	−0.672519	+	0.740080i	$0.734788\pi$
$858$	36.9409	−	36.9409i	0.0430546	−	0.0430546i
$859$			263.557i			0.306819i	0.988163	+	0.153409i	$0.0490253\pi$
$859$			263.557i			0.306819i	−0.988163	+	0.153409i	$0.950975\pi$
$860$	−762.647	+	324.950i	−0.886799	+	0.377849i
$861$	380.582			0.442023
$862$	−719.875	−	719.875i	−0.835122	−	0.835122i
$863$	654.119	−	654.119i	0.757960	−	0.757960i	−0.217991	−	0.975951i	$-0.569950\pi$
$863$	654.119	−	654.119i	0.757960	−	0.757960i	0.975951	+	0.217991i	$0.0699503\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	47.5041	+	111.491i	0.0549181	+	0.128891i
$866$	1087.58			1.25586
$867$	−353.194	−	353.194i	−0.407375	−	0.407375i
$868$	−272.827	+	272.827i	−0.314317	+	0.314317i
$869$			240.599i			0.276869i
$870$	−554.870	−	223.304i	−0.637782	−	0.256672i
$871$	5.53321			0.00635271
$872$	−173.399	−	173.399i	−0.198852	−	0.198852i
$873$	328.672	−	328.672i	0.376486	−	0.376486i
$874$		−	135.542i		−	0.155083i
$875$	448.912	+	170.222i	0.513042	+	0.194539i
$876$	−97.5948			−0.111410
$877$	238.188	+	238.188i	0.271594	+	0.271594i	0.829742	−	0.558148i	$-0.188488\pi$
$877$	238.188	+	238.188i	0.271594	+	0.271594i	−0.558148	+	0.829742i	$0.688488\pi$
$878$	478.471	−	478.471i	0.544956	−	0.544956i
$879$		−	360.992i		−	0.410684i
$880$	−150.788	+	374.680i	−0.171350	+	0.425773i
$881$	1379.20			1.56550			0.782748	−	0.622339i	$-0.213817\pi$
$881$	1379.20			1.56550			0.782748	+	0.622339i	$0.213817\pi$
$882$	102.745	+	102.745i	0.116490	+	0.116490i
$883$	241.453	−	241.453i	0.273446	−	0.273446i	−0.557040	−	0.830486i	$-0.688063\pi$
$883$	241.453	−	241.453i	0.273446	−	0.273446i	0.830486	+	0.557040i	$0.188063\pi$
$884$			1.66097i			0.00187893i
$885$	−368.779	+	157.130i	−0.416700	+	0.177548i
$886$	−648.323			−0.731741
$887$	−283.313	−	283.313i	−0.319406	−	0.319406i	0.529133	−	0.848539i	$-0.322517\pi$
$887$	−283.313	−	283.313i	−0.319406	−	0.319406i	−0.848539	+	0.529133i	$0.822517\pi$
$888$	−81.0921	+	81.0921i	−0.0913199	+	0.0913199i
$889$		−	896.916i		−	1.00890i
$890$	424.219	+	995.629i	0.476651	+	1.11868i
$891$	181.748			0.203982
$892$	−87.2963	−	87.2963i	−0.0978658	−	0.0978658i
$893$	−825.852	+	825.852i	−0.924807	+	0.924807i
$894$		−	64.0423i		−	0.0716357i
$895$	550.743	+	221.643i	0.615355	+	0.247646i
$896$	−43.4538			−0.0484976
$897$	6.20340	+	6.20340i	0.00691572	+	0.00691572i
$898$	−316.099	+	316.099i	−0.352003	+	0.352003i
$899$		−	2452.96i		−	2.72855i
$900$	−108.184	−	103.905i	−0.120205	−	0.115450i
$901$	31.2307			0.0346623
$902$	1155.29	+	1155.29i	1.28081	+	1.28081i
$903$	389.958	−	389.958i	0.431847	−	0.431847i
$904$			425.996i			0.471235i
$905$	38.9439	−	96.7684i	0.0430319	−	0.106926i
$906$	−365.875			−0.403836
$907$	348.978	+	348.978i	0.384760	+	0.384760i	0.872814	−	0.488053i	$-0.162293\pi$
$907$	348.978	+	348.978i	0.384760	+	0.384760i	−0.488053	+	0.872814i	$0.662293\pi$
$908$	−297.059	+	297.059i	−0.327157	+	0.327157i
$909$			558.651i			0.614577i
$910$	26.3878	−	11.2433i	0.0289975	−	0.0123553i
$911$	−619.609			−0.680142			−0.340071	−	0.940400i	$-0.610451\pi$
$911$	−619.609			−0.680142			−0.340071	+	0.940400i	$0.610451\pi$
$912$	97.9043	+	97.9043i	0.107351	+	0.107351i
$913$	−1049.55	+	1049.55i	−1.14956	+	1.14956i
$914$			1145.34i			1.25311i
$915$	−273.878	−	642.784i	−0.299321	−	0.702496i
$916$	−353.250			−0.385645
$917$	−267.153	−	267.153i	−0.291334	−	0.291334i
$918$	−4.08596	+	4.08596i	−0.00445093	+	0.00445093i
$919$		−	130.957i		−	0.142499i	−0.997459	−	0.0712496i	$-0.977301\pi$
$919$		−	130.957i		−	0.142499i	0.997459	−	0.0712496i	$-0.0226987\pi$
$920$	−62.9192	−	25.3215i	−0.0683904	−	0.0275233i
$921$	−734.121			−0.797092
$922$	−664.538	−	664.538i	−0.720757	−	0.720757i
$923$	−33.6092	+	33.6092i	−0.0364130	+	0.0364130i
$924$		−	268.683i		−	0.290782i
$925$	11.8061	+	585.112i	0.0127634	+	0.632554i
$926$	64.5936			0.0697555
$927$	207.496	+	207.496i	0.223836	+	0.223836i
$928$	195.345	−	195.345i	0.210501	−	0.210501i
$929$			1236.97i			1.33151i	0.746171	+	0.665754i	$0.231890\pi$
$929$			1236.97i			1.33151i	−0.746171	+	0.665754i	$0.768110\pi$
$930$	229.671	−	570.689i	0.246958	−	0.613644i
$931$	−684.437			−0.735163
$932$	−172.153	−	172.153i	−0.184713	−	0.184713i
$933$	−317.289	+	317.289i	−0.340074	+	0.340074i
$934$		−	214.545i		−	0.229705i
$935$	73.0438	−	31.1226i	0.0781217	−	0.0332862i
$936$	−8.96161			−0.00957437
$937$	84.3352	+	84.3352i	0.0900055	+	0.0900055i	0.750676	−	0.660671i	$-0.229728\pi$
$937$	84.3352	+	84.3352i	0.0900055	+	0.0900055i	−0.660671	+	0.750676i	$0.729728\pi$
$938$	20.1224	−	20.1224i	0.0214525	−	0.0214525i
$939$			399.424i			0.425372i
$940$	229.081	+	537.645i	0.243703	+	0.571963i
$941$	−1058.56			−1.12493			−0.562466	−	0.826820i	$-0.690147\pi$
$941$	−1058.56			−1.12493			−0.562466	+	0.826820i	$0.690147\pi$
$942$	228.129	+	228.129i	0.242175	+	0.242175i
$943$	−194.005	+	194.005i	−0.205732	+	0.205732i
$944$		−	185.149i		−	0.196132i
$945$	92.5719	+	37.2550i	0.0979596	+	0.0394233i
$946$	2367.50			2.50265
$947$	515.115	+	515.115i	0.543944	+	0.543944i	0.924683	−	0.380739i	$-0.124330\pi$
$947$	515.115	+	515.115i	0.543944	+	0.543944i	−0.380739	+	0.924683i	$0.624330\pi$
$948$	29.1839	−	29.1839i	0.0307847	−	0.0307847i
$949$			29.7547i			0.0313538i
$950$	706.420	−	14.2538i	0.743600	−	0.0150040i
$951$	−360.310			−0.378875
$952$	6.04039	+	6.04039i	0.00634494	+	0.00634494i
$953$	710.013	−	710.013i	0.745030	−	0.745030i	−0.228511	−	0.973541i	$-0.573386\pi$
$953$	710.013	−	710.013i	0.745030	−	0.745030i	0.973541	+	0.228511i	$0.0733858\pi$
$954$			168.502i			0.176627i
$955$	−471.608	+	1171.86i	−0.493831	+	1.22708i
$956$	166.191			0.173840
$957$	1207.85	+	1207.85i	1.26212	+	1.26212i
$958$	199.437	−	199.437i	0.208180	−	0.208180i
$959$		−	823.255i		−	0.858451i
$960$	63.7376	−	27.1574i	0.0663933	−	0.0282890i
$961$	1561.90			1.62528
$962$	24.7234	+	24.7234i	0.0257000	+	0.0257000i
$963$	−286.179	+	286.179i	−0.297175	+	0.297175i
$964$		−	917.240i		−	0.951494i
$965$	−87.3858	−	205.092i	−0.0905552	−	0.212530i
$966$	45.1193			0.0467074
$967$	1217.27	+	1217.27i	1.25881	+	1.25881i	0.951664	+	0.307142i	$0.0993728\pi$
$967$	1217.27	+	1217.27i	1.25881	+	1.25881i	0.307142	+	0.951664i	$0.400627\pi$
$968$	573.611	−	573.611i	0.592574	−	0.592574i
$969$		−	27.2188i		−	0.0280896i
$970$	1016.36	+	409.026i	1.04779	+	0.421677i
$971$	1768.43			1.82125			0.910625	−	0.413235i	$-0.135601\pi$
$971$	1768.43			1.82125			0.910625	+	0.413235i	$0.135601\pi$
$972$	−22.0454	−	22.0454i	−0.0226805	−	0.0226805i
$973$	67.0786	−	67.0786i	0.0689400	−	0.0689400i
$974$			404.056i			0.414842i
$975$	−31.6785	+	32.9832i	−0.0324908	+	0.0338289i
$976$	322.715			0.330651
$977$	303.722	+	303.722i	0.310873	+	0.310873i	0.845248	−	0.534375i	$-0.179453\pi$
$977$	303.722	+	303.722i	0.310873	+	0.310873i	−0.534375	+	0.845248i	$0.679453\pi$
$978$	−393.302	+	393.302i	−0.402150	+	0.402150i
$979$		−	3090.76i		−	3.15705i
$980$	−127.864	+	317.718i	−0.130473	+	0.324202i
$981$	−260.098			−0.265136
$982$	−642.465	−	642.465i	−0.654241	−	0.654241i
$983$	319.956	−	319.956i	0.325489	−	0.325489i	−0.525379	−	0.850868i	$-0.676076\pi$
$983$	319.956	−	319.956i	0.325489	−	0.325489i	0.850868	+	0.525379i	$0.176076\pi$
$984$		−	280.266i		−	0.284823i
$985$	−818.403	+	348.706i	−0.830866	+	0.354017i
$986$	−54.3086			−0.0550797
$987$	−274.909	−	274.909i	−0.278530	−	0.278530i
$988$	29.8491	−	29.8491i	0.0302116	−	0.0302116i
$989$			397.569i			0.401991i
$990$	167.919	+	394.101i	0.169615	+	0.398082i
$991$	−1114.72			−1.12484			−0.562420	−	0.826851i	$-0.690130\pi$
$991$	−1114.72			−1.12484			−0.562420	+	0.826851i	$0.690130\pi$
$992$	200.914	+	200.914i	0.202534	+	0.202534i
$993$	434.324	−	434.324i	0.437386	−	0.437386i
$994$			244.450i			0.245926i
$995$	−988.306	−	397.738i	−0.993272	−	0.399737i
$996$	254.613			0.255636
$997$	−82.8225	−	82.8225i	−0.0830717	−	0.0830717i	0.664350	−	0.747422i	$-0.268708\pi$
$997$	−82.8225	−	82.8225i	−0.0830717	−	0.0830717i	−0.747422	+	0.664350i	$0.768708\pi$
$998$	−745.571	+	745.571i	−0.747065	+	0.747065i
$999$			121.638i			0.121760i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.b.277.14	✓	48
5.3	odd	4	inner	690.3.k.b.553.14	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.b.277.14	✓	48	1.1	even	1	trivial
690.3.k.b.553.14	yes	48	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)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-1.86672 + 4.63846i) q^{5} -2.44949 q^{6} +(2.71586 + 2.71586i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-1.86672 + 4.63846i) q^{5} -2.44949 q^{6} +(2.71586 + 2.71586i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(6.50519 - 2.77174i) q^{10} -20.1942 q^{11} +(2.44949 + 2.44949i) q^{12} +(0.746801 - 0.746801i) q^{13} -5.43173i q^{14} +(3.39468 + 7.96719i) q^{15} -4.00000 q^{16} +(0.556028 + 0.556028i) q^{17} +(-3.00000 + 3.00000i) q^{18} -19.9846i q^{19} +(-9.27693 - 3.73345i) q^{20} +6.65248 q^{21} +(20.1942 + 20.1942i) q^{22} +(-3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(-18.0307 - 17.3175i) q^{25} -1.49360 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-5.43173 + 5.43173i) q^{28} -48.8362i q^{29} +(4.57252 - 11.3619i) q^{30} +50.2284 q^{31} +(4.00000 + 4.00000i) q^{32} +(-24.7327 + 24.7327i) q^{33} -1.11206i q^{34} +(-17.6672 + 7.52767i) q^{35} +6.00000 q^{36} +(-16.5528 - 16.5528i) q^{37} +(-19.9846 + 19.9846i) q^{38} -1.82928i q^{39} +(5.54348 + 13.0104i) q^{40} +57.2091 q^{41} +(-6.65248 - 6.65248i) q^{42} +(58.6184 - 58.6184i) q^{43} -40.3884i q^{44} +(13.9154 + 5.60017i) q^{45} +6.78233 q^{46} +(-41.3244 - 41.3244i) q^{47} +(-4.89898 + 4.89898i) q^{48} -34.2482i q^{49} +(0.713239 + 35.3481i) q^{50} +1.36199 q^{51} +(1.49360 + 1.49360i) q^{52} +(28.0837 - 28.0837i) q^{53} +7.34847i q^{54} +(37.6970 - 93.6701i) q^{55} +10.8635 q^{56} +(-24.4761 - 24.4761i) q^{57} +(-48.8362 + 48.8362i) q^{58} +46.2872i q^{59} +(-15.9344 + 6.78935i) q^{60} -80.6788 q^{61} +(-50.2284 - 50.2284i) q^{62} +(8.14759 - 8.14759i) q^{63} -8.00000i q^{64} +(2.06994 + 4.85808i) q^{65} +49.4655 q^{66} +(3.70461 + 3.70461i) q^{67} +(-1.11206 + 1.11206i) q^{68} +8.30662i q^{69} +(25.1949 + 10.1395i) q^{70} -45.0042 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-19.9215 + 19.9215i) q^{73} +33.1057i q^{74} +(-43.2925 + 0.873535i) q^{75} +39.9693 q^{76} +(-54.8447 - 54.8447i) q^{77} +(-1.82928 + 1.82928i) q^{78} -11.9143i q^{79} +(7.46689 - 18.5539i) q^{80} -9.00000 q^{81} +(-57.2091 - 57.2091i) q^{82} +(51.9727 - 51.9727i) q^{83} +13.3050i q^{84} +(-3.61707 + 1.54117i) q^{85} -117.237 q^{86} +(-59.8118 - 59.8118i) q^{87} +(-40.3884 + 40.3884i) q^{88} +153.052i q^{89} +(-8.31522 - 19.5156i) q^{90} +4.05642 q^{91} +(-6.78233 - 6.78233i) q^{92} +(61.5170 - 61.5170i) q^{93} +82.6487i q^{94} +(92.6980 + 37.3058i) q^{95} +9.79796 q^{96} +(109.557 + 109.557i) q^{97} +(-34.2482 + 34.2482i) q^{98} +60.5826i 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

Related objects

Downloads

Learn more