LMFDB - Embedded newform 750.3.f.b.307.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [750,3,Mod(193,750)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(750, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("750.193"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	750.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,-16,0,0,0,0,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$20.4360198270$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.6879707136000000000000.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 21x^{12} + 86x^{8} + 36x^{4} + 1 $ x^16 + 21x^12 + 86x^8 + 36*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{8}\cdot 5^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.4
Root			$-0.575212 + 0.575212i$ of defining polynomial
Character	$\chi$	$=$	750.307
Dual form			750.3.f.b.193.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +2.44949 q^{6} +(6.47296 + 6.47296i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +0.239358 q^{11} +(-2.44949 - 2.44949i) q^{12} +(3.35623 - 3.35623i) q^{13} -12.9459i q^{14} -4.00000 q^{16} +(14.3569 + 14.3569i) q^{17} +(-3.00000 + 3.00000i) q^{18} +2.54707i q^{19} -15.8554 q^{21} +(-0.239358 - 0.239358i) q^{22} +(26.7643 - 26.7643i) q^{23} +4.89898i q^{24} -6.71247 q^{26} +(3.67423 + 3.67423i) q^{27} +(-12.9459 + 12.9459i) q^{28} -19.8004i q^{29} -33.8737 q^{31} +(4.00000 + 4.00000i) q^{32} +(-0.293153 + 0.293153i) q^{33} -28.7138i q^{34} +6.00000 q^{36} +(25.5735 + 25.5735i) q^{37} +(2.54707 - 2.54707i) q^{38} +8.22106i q^{39} -31.3205 q^{41} +(15.8554 + 15.8554i) q^{42} +(-52.7173 + 52.7173i) q^{43} +0.478717i q^{44} -53.5286 q^{46} +(19.7087 + 19.7087i) q^{47} +(4.89898 - 4.89898i) q^{48} +34.7983i q^{49} -35.1671 q^{51} +(6.71247 + 6.71247i) q^{52} +(32.6096 - 32.6096i) q^{53} -7.34847i q^{54} +25.8918 q^{56} +(-3.11952 - 3.11952i) q^{57} +(-19.8004 + 19.8004i) q^{58} +42.2264i q^{59} +47.6073 q^{61} +(33.8737 + 33.8737i) q^{62} +(19.4189 - 19.4189i) q^{63} -8.00000i q^{64} +0.586306 q^{66} +(86.4226 + 86.4226i) q^{67} +(-28.7138 + 28.7138i) q^{68} +65.5589i q^{69} +128.144 q^{71} +(-6.00000 - 6.00000i) q^{72} +(21.2313 - 21.2313i) q^{73} -51.1470i q^{74} -5.09415 q^{76} +(1.54936 + 1.54936i) q^{77} +(8.22106 - 8.22106i) q^{78} +53.3620i q^{79} -9.00000 q^{81} +(31.3205 + 31.3205i) q^{82} +(-81.9475 + 81.9475i) q^{83} -31.7109i q^{84} +105.435 q^{86} +(24.2505 + 24.2505i) q^{87} +(0.478717 - 0.478717i) q^{88} +1.92704i q^{89} +43.4495 q^{91} +(53.5286 + 53.5286i) q^{92} +(41.4866 - 41.4866i) q^{93} -39.4174i q^{94} -9.79796 q^{96} +(-37.1612 - 37.1612i) q^{97} +(34.7983 - 34.7983i) q^{98} -0.718075i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} + 24 q^{7} + 32 q^{8} - 24 q^{11} - 48 q^{13} - 64 q^{16} - 16 q^{17} - 48 q^{18} - 48 q^{21} + 24 q^{22} + 104 q^{23} + 96 q^{26} - 48 q^{28} + 200 q^{31} + 64 q^{32} - 48 q^{33} + 96 q^{36}+ \cdots - 224 q^{98}+O(q^{100}) $ 16 * q - 16 * q^2 + 24 * q^7 + 32 * q^8 - 24 * q^11 - 48 * q^13 - 64 * q^16 - 16 * q^17 - 48 * q^18 - 48 * q^21 + 24 * q^22 + 104 * q^23 + 96 * q^26 - 48 * q^28 + 200 * q^31 + 64 * q^32 - 48 * q^33 + 96 * q^36 - 128 * q^37 + 56 * q^38 - 192 * q^41 + 48 * q^42 + 88 * q^43 - 208 * q^46 + 16 * q^47 - 48 * q^51 - 96 * q^52 - 160 * q^53 + 96 * q^56 + 48 * q^57 + 24 * q^58 - 24 * q^61 - 200 * q^62 + 72 * q^63 + 96 * q^66 + 264 * q^67 + 32 * q^68 + 176 * q^71 - 96 * q^72 + 32 * q^73 - 112 * q^76 + 32 * q^77 + 96 * q^78 - 144 * q^81 + 192 * q^82 - 288 * q^83 - 176 * q^86 - 168 * q^87 - 48 * q^88 + 32 * q^91 + 208 * q^92 + 144 * q^93 - 48 * q^97 - 224 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$			2.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	2.44949			0.408248
$7$	6.47296	+	6.47296i	0.924708	+	0.924708i	0.997358	−	0.0726496i	$-0.0231455\pi$
$7$	6.47296	+	6.47296i	0.924708	+	0.924708i	−0.0726496	+	0.997358i	$0.523145\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$		0			0
$11$	0.239358			0.0217599			0.0108799	−	0.999941i	$-0.496537\pi$
$11$	0.239358			0.0217599			0.0108799	+	0.999941i	$0.496537\pi$
$12$	−2.44949	−	2.44949i	−0.204124	−	0.204124i
$13$	3.35623	−	3.35623i	0.258172	−	0.258172i	−0.566138	−	0.824310i	$-0.691563\pi$
$13$	3.35623	−	3.35623i	0.258172	−	0.258172i	0.824310	+	0.566138i	$0.191563\pi$
$14$		−	12.9459i		−	0.924708i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	14.3569	+	14.3569i	0.844524	+	0.844524i	0.989443	−	0.144919i	$-0.0462923\pi$
$17$	14.3569	+	14.3569i	0.844524	+	0.844524i	−0.144919	+	0.989443i	$0.546292\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$			2.54707i			0.134057i	0.997751	+	0.0670283i	$0.0213518\pi$
$19$			2.54707i			0.134057i	−0.997751	+	0.0670283i	$0.978648\pi$
$20$		0			0
$21$	−15.8554			−0.755021
$22$	−0.239358	−	0.239358i	−0.0108799	−	0.0108799i
$23$	26.7643	−	26.7643i	1.16367	−	1.16367i	0.179999	−	0.983667i	$-0.442391\pi$
$23$	26.7643	−	26.7643i	1.16367	−	1.16367i	0.983667	−	0.179999i	$-0.0576095\pi$
$24$			4.89898i			0.204124i
$25$		0			0
$26$	−6.71247			−0.258172
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$	−12.9459	+	12.9459i	−0.462354	+	0.462354i
$29$		−	19.8004i		−	0.682774i	−0.939923	−	0.341387i	$-0.889103\pi$
$29$		−	19.8004i		−	0.682774i	0.939923	−	0.341387i	$-0.110897\pi$
$30$		0			0
$31$	−33.8737			−1.09270			−0.546349	−	0.837557i	$-0.683983\pi$
$31$	−33.8737			−1.09270			−0.546349	+	0.837557i	$0.683983\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	−0.293153	+	0.293153i	−0.00888342	+	0.00888342i
$34$		−	28.7138i		−	0.844524i
$35$		0			0
$36$	6.00000			0.166667
$37$	25.5735	+	25.5735i	0.691176	+	0.691176i	0.962491	−	0.271315i	$-0.0874585\pi$
$37$	25.5735	+	25.5735i	0.691176	+	0.691176i	−0.271315	+	0.962491i	$0.587458\pi$
$38$	2.54707	−	2.54707i	0.0670283	−	0.0670283i
$39$			8.22106i			0.210796i
$40$		0			0
$41$	−31.3205			−0.763915			−0.381958	−	0.924180i	$-0.624750\pi$
$41$	−31.3205			−0.763915			−0.381958	+	0.924180i	$0.624750\pi$
$42$	15.8554	+	15.8554i	0.377510	+	0.377510i
$43$	−52.7173	+	52.7173i	−1.22598	+	1.22598i	−0.260514	+	0.965470i	$0.583892\pi$
$43$	−52.7173	+	52.7173i	−1.22598	+	1.22598i	−0.965470	+	0.260514i	$0.916108\pi$
$44$			0.478717i			0.0108799i
$45$		0			0
$46$	−53.5286			−1.16367
$47$	19.7087	+	19.7087i	0.419334	+	0.419334i	0.884974	−	0.465640i	$-0.154176\pi$
$47$	19.7087	+	19.7087i	0.419334	+	0.419334i	−0.465640	+	0.884974i	$0.654176\pi$
$48$	4.89898	−	4.89898i	0.102062	−	0.102062i
$49$			34.7983i			0.710170i
$50$		0			0
$51$	−35.1671			−0.689551
$52$	6.71247	+	6.71247i	0.129086	+	0.129086i
$53$	32.6096	−	32.6096i	0.615276	−	0.615276i	−0.329040	−	0.944316i	$-0.606725\pi$
$53$	32.6096	−	32.6096i	0.615276	−	0.615276i	0.944316	+	0.329040i	$0.106725\pi$
$54$		−	7.34847i		−	0.136083i
$55$		0			0
$56$	25.8918			0.462354
$57$	−3.11952	−	3.11952i	−0.0547283	−	0.0547283i
$58$	−19.8004	+	19.8004i	−0.341387	+	0.341387i
$59$			42.2264i			0.715702i	0.933779	+	0.357851i	$0.116491\pi$
$59$			42.2264i			0.715702i	−0.933779	+	0.357851i	$0.883509\pi$
$60$		0			0
$61$	47.6073			0.780448			0.390224	−	0.920720i	$-0.372398\pi$
$61$	47.6073			0.780448			0.390224	+	0.920720i	$0.372398\pi$
$62$	33.8737	+	33.8737i	0.546349	+	0.546349i
$63$	19.4189	−	19.4189i	0.308236	−	0.308236i
$64$		−	8.00000i		−	0.125000i
$65$		0			0
$66$	0.586306			0.00888342
$67$	86.4226	+	86.4226i	1.28989	+	1.28989i	0.934852	+	0.355038i	$0.115532\pi$
$67$	86.4226	+	86.4226i	1.28989	+	1.28989i	0.355038	+	0.934852i	$0.384468\pi$
$68$	−28.7138	+	28.7138i	−0.422262	+	0.422262i
$69$			65.5589i			0.950129i
$70$		0			0
$71$	128.144			1.80485			0.902425	−	0.430847i	$-0.141785\pi$
$71$	128.144			1.80485			0.902425	+	0.430847i	$0.141785\pi$
$72$	−6.00000	−	6.00000i	−0.0833333	−	0.0833333i
$73$	21.2313	−	21.2313i	0.290840	−	0.290840i	−0.546572	−	0.837412i	$-0.684067\pi$
$73$	21.2313	−	21.2313i	0.290840	−	0.290840i	0.837412	+	0.546572i	$0.184067\pi$
$74$		−	51.1470i		−	0.691176i
$75$		0			0
$76$	−5.09415			−0.0670283
$77$	1.54936	+	1.54936i	0.0201215	+	0.0201215i
$78$	8.22106	−	8.22106i	0.105398	−	0.105398i
$79$			53.3620i			0.675469i	0.941241	+	0.337734i	$0.109661\pi$
$79$			53.3620i			0.675469i	−0.941241	+	0.337734i	$0.890339\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	31.3205	+	31.3205i	0.381958	+	0.381958i
$83$	−81.9475	+	81.9475i	−0.987319	+	0.987319i	−0.999921	−	0.0126012i	$-0.995989\pi$
$83$	−81.9475	+	81.9475i	−0.987319	+	0.987319i	0.0126012	+	0.999921i	$0.495989\pi$
$84$		−	31.7109i		−	0.377510i
$85$		0			0
$86$	105.435			1.22598
$87$	24.2505	+	24.2505i	0.278741	+	0.278741i
$88$	0.478717	−	0.478717i	0.00543996	−	0.00543996i
$89$			1.92704i			0.0216522i	0.999941	+	0.0108261i	$0.00344612\pi$
$89$			1.92704i			0.0216522i	−0.999941	+	0.0108261i	$0.996554\pi$
$90$		0			0
$91$	43.4495			0.477467
$92$	53.5286	+	53.5286i	0.581833	+	0.581833i
$93$	41.4866	−	41.4866i	0.446092	−	0.446092i
$94$		−	39.4174i		−	0.419334i
$95$		0			0
$96$	−9.79796			−0.102062
$97$	−37.1612	−	37.1612i	−0.383105	−	0.383105i	0.489114	−	0.872220i	$-0.337320\pi$
$97$	−37.1612	−	37.1612i	−0.383105	−	0.383105i	−0.872220	+	0.489114i	$0.837320\pi$
$98$	34.7983	−	34.7983i	0.355085	−	0.355085i
$99$		−	0.718075i		−	0.00725329i
$100$		0			0
$101$	−15.1796			−0.150293			−0.0751467	−	0.997172i	$-0.523943\pi$
$101$	−15.1796			−0.150293			−0.0751467	+	0.997172i	$0.523943\pi$
$102$	35.1671	+	35.1671i	0.344776	+	0.344776i
$103$	−25.7548	+	25.7548i	−0.250047	+	0.250047i	−0.820990	−	0.570943i	$-0.806578\pi$
$103$	−25.7548	+	25.7548i	−0.250047	+	0.250047i	0.570943	+	0.820990i	$0.306578\pi$
$104$		−	13.4249i		−	0.129086i
$105$		0			0
$106$	−65.2192			−0.615276
$107$	111.016	+	111.016i	1.03753	+	1.03753i	0.999268	+	0.0382659i	$0.0121834\pi$
$107$	111.016	+	111.016i	1.03753	+	1.03753i	0.0382659	+	0.999268i	$0.487817\pi$
$108$	−7.34847	+	7.34847i	−0.0680414	+	0.0680414i
$109$			162.040i			1.48661i	0.668955	+	0.743303i	$0.266742\pi$
$109$			162.040i			1.48661i	−0.668955	+	0.743303i	$0.733258\pi$
$110$		0			0
$111$	−62.6420			−0.564343
$112$	−25.8918	−	25.8918i	−0.231177	−	0.231177i
$113$	25.6159	−	25.6159i	0.226689	−	0.226689i	−0.584619	−	0.811308i	$-0.698756\pi$
$113$	25.6159	−	25.6159i	0.226689	−	0.226689i	0.811308	+	0.584619i	$0.198756\pi$
$114$			6.23903i			0.0547283i
$115$		0			0
$116$	39.6009			0.341387
$117$	−10.0687	−	10.0687i	−0.0860573	−	0.0860573i
$118$	42.2264	−	42.2264i	0.357851	−	0.357851i
$119$			185.863i			1.56188i
$120$		0			0
$121$	−120.943			−0.999527
$122$	−47.6073	−	47.6073i	−0.390224	−	0.390224i
$123$	38.3596	−	38.3596i	0.311867	−	0.311867i
$124$		−	67.7473i		−	0.546349i
$125$		0			0
$126$	−38.8377			−0.308236
$127$	−1.67000	−	1.67000i	−0.0131496	−	0.0131496i	0.700501	−	0.713651i	$-0.252960\pi$
$127$	−1.67000	−	1.67000i	−0.0131496	−	0.0131496i	−0.713651	+	0.700501i	$0.752960\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$		−	129.131i		−	1.00101i
$130$		0			0
$131$	190.408			1.45349			0.726747	−	0.686905i	$-0.241031\pi$
$131$	190.408			1.45349			0.726747	+	0.686905i	$0.241031\pi$
$132$	−0.586306	−	0.586306i	−0.00444171	−	0.00444171i
$133$	−16.4871	+	16.4871i	−0.123963	+	0.123963i
$134$		−	172.845i		−	1.28989i
$135$		0			0
$136$	57.4276			0.422262
$137$	−26.0666	−	26.0666i	−0.190267	−	0.190267i	0.605545	−	0.795811i	$-0.292955\pi$
$137$	−26.0666	−	26.0666i	−0.190267	−	0.190267i	−0.795811	+	0.605545i	$0.792955\pi$
$138$	65.5589	−	65.5589i	0.475065	−	0.475065i
$139$		−	172.480i		−	1.24086i	−0.784261	−	0.620431i	$-0.786958\pi$
$139$		−	172.480i		−	1.24086i	0.784261	−	0.620431i	$-0.213042\pi$
$140$		0			0
$141$	−48.2762			−0.342385
$142$	−128.144	−	128.144i	−0.902425	−	0.902425i
$143$	0.803343	−	0.803343i	0.00561778	−	0.00561778i
$144$			12.0000i			0.0833333i
$145$		0			0
$146$	−42.4627			−0.290840
$147$	−42.6191	−	42.6191i	−0.289926	−	0.289926i
$148$	−51.1470	+	51.1470i	−0.345588	+	0.345588i
$149$		−	35.7067i		−	0.239642i	−0.992795	−	0.119821i	$-0.961768\pi$
$149$		−	35.7067i		−	0.239642i	0.992795	−	0.119821i	$-0.0382321\pi$
$150$		0			0
$151$	−22.3612			−0.148087			−0.0740436	−	0.997255i	$-0.523590\pi$
$151$	−22.3612			−0.148087			−0.0740436	+	0.997255i	$0.523590\pi$
$152$	5.09415	+	5.09415i	0.0335141	+	0.0335141i
$153$	43.0707	−	43.0707i	0.281508	−	0.281508i
$154$		−	3.09871i		−	0.0201215i
$155$		0			0
$156$	−16.4421			−0.105398
$157$	215.726	+	215.726i	1.37405	+	1.37405i	0.854347	+	0.519703i	$0.173957\pi$
$157$	215.726	+	215.726i	1.37405	+	1.37405i	0.519703	+	0.854347i	$0.326043\pi$
$158$	53.3620	−	53.3620i	0.337734	−	0.337734i
$159$			79.8769i			0.502371i
$160$		0			0
$161$	346.488			2.15210
$162$	9.00000	+	9.00000i	0.0555556	+	0.0555556i
$163$	−95.7668	+	95.7668i	−0.587527	+	0.587527i	−0.936961	−	0.349434i	$-0.886374\pi$
$163$	−95.7668	+	95.7668i	−0.587527	+	0.587527i	0.349434	+	0.936961i	$0.386374\pi$
$164$		−	62.6410i		−	0.381958i
$165$		0			0
$166$	163.895			0.987319
$167$	−181.637	−	181.637i	−1.08765	−	1.08765i	−0.995770	−	0.0918786i	$-0.970713\pi$
$167$	−181.637	−	181.637i	−1.08765	−	1.08765i	−0.0918786	−	0.995770i	$-0.529287\pi$
$168$	−31.7109	+	31.7109i	−0.188755	+	0.188755i
$169$			146.471i			0.866695i
$170$		0			0
$171$	7.64122			0.0446855
$172$	−105.435	−	105.435i	−0.612992	−	0.612992i
$173$	36.4688	−	36.4688i	0.210802	−	0.210802i	−0.593806	−	0.804608i	$-0.702375\pi$
$173$	36.4688	−	36.4688i	0.210802	−	0.210802i	0.804608	+	0.593806i	$0.202375\pi$
$174$		−	48.5010i		−	0.278741i
$175$		0			0
$176$	−0.957434			−0.00543996
$177$	−51.7166	−	51.7166i	−0.292184	−	0.292184i
$178$	1.92704	−	1.92704i	0.0108261	−	0.0108261i
$179$			243.428i			1.35993i	0.733244	+	0.679966i	$0.238005\pi$
$179$			243.428i			1.35993i	−0.733244	+	0.679966i	$0.761995\pi$
$180$		0			0
$181$	−315.333			−1.74217			−0.871085	−	0.491132i	$-0.836583\pi$
$181$	−315.333			−1.74217			−0.871085	+	0.491132i	$0.836583\pi$
$182$	−43.4495	−	43.4495i	−0.238734	−	0.238734i
$183$	−58.3068	+	58.3068i	−0.318616	+	0.318616i
$184$		−	107.057i		−	0.581833i
$185$		0			0
$186$	−82.9732			−0.446092
$187$	3.43645	+	3.43645i	0.0183767	+	0.0183767i
$188$	−39.4174	+	39.4174i	−0.209667	+	0.209667i
$189$			47.5663i			0.251674i
$190$		0			0
$191$	316.969			1.65952			0.829761	−	0.558118i	$-0.188476\pi$
$191$	316.969			1.65952			0.829761	+	0.558118i	$0.188476\pi$
$192$	9.79796	+	9.79796i	0.0510310	+	0.0510310i
$193$	−128.174	+	128.174i	−0.664115	+	0.664115i	−0.956347	−	0.292232i	$-0.905602\pi$
$193$	−128.174	+	128.174i	−0.664115	+	0.664115i	0.292232	+	0.956347i	$0.405602\pi$
$194$			74.3224i			0.383105i
$195$		0			0
$196$	−69.5966			−0.355085
$197$	−168.051	−	168.051i	−0.853052	−	0.853052i	0.137456	−	0.990508i	$-0.456107\pi$
$197$	−168.051	−	168.051i	−0.853052	−	0.853052i	−0.990508	+	0.137456i	$0.956107\pi$
$198$	−0.718075	+	0.718075i	−0.00362664	+	0.00362664i
$199$		−	289.119i		−	1.45286i	−0.687240	−	0.726430i	$-0.741178\pi$
$199$		−	289.119i		−	1.45286i	0.687240	−	0.726430i	$-0.258822\pi$
$200$		0			0
$201$	−211.691			−1.05319
$202$	15.1796	+	15.1796i	0.0751467	+	0.0751467i
$203$	128.167	−	128.167i	0.631367	−	0.631367i
$204$		−	70.3342i		−	0.344776i
$205$		0			0
$206$	51.5096			0.250047
$207$	−80.2929	−	80.2929i	−0.387889	−	0.387889i
$208$	−13.4249	+	13.4249i	−0.0645430	+	0.0645430i
$209$			0.609664i			0.00291705i
$210$		0			0
$211$	−39.5665			−0.187519			−0.0937596	−	0.995595i	$-0.529888\pi$
$211$	−39.5665			−0.187519			−0.0937596	+	0.995595i	$0.529888\pi$
$212$	65.2192	+	65.2192i	0.307638	+	0.307638i
$213$	−156.944	+	156.944i	−0.736827	+	0.736827i
$214$		−	222.032i		−	1.03753i
$215$		0			0
$216$	14.6969			0.0680414
$217$	−219.263	−	219.263i	−1.01043	−	1.01043i
$218$	162.040	−	162.040i	0.743303	−	0.743303i
$219$			52.0059i			0.237470i
$220$		0			0
$221$	96.3703			0.436065
$222$	62.6420	+	62.6420i	0.282171	+	0.282171i
$223$	77.9564	−	77.9564i	0.349580	−	0.349580i	−0.510373	−	0.859953i	$-0.670493\pi$
$223$	77.9564	−	77.9564i	0.349580	−	0.349580i	0.859953	+	0.510373i	$0.170493\pi$
$224$			51.7836i			0.231177i
$225$		0			0
$226$	−51.2318			−0.226689
$227$	−11.0098	−	11.0098i	−0.0485015	−	0.0485015i	0.682440	−	0.730942i	$-0.260919\pi$
$227$	−11.0098	−	11.0098i	−0.0485015	−	0.0485015i	−0.730942	+	0.682440i	$0.760919\pi$
$228$	6.23903	−	6.23903i	0.0273642	−	0.0273642i
$229$			170.347i			0.743874i	0.928258	+	0.371937i	$0.121306\pi$
$229$			170.347i			0.743874i	−0.928258	+	0.371937i	$0.878694\pi$
$230$		0			0
$231$	−3.79513			−0.0164291
$232$	−39.6009	−	39.6009i	−0.170694	−	0.170694i
$233$	−180.554	+	180.554i	−0.774912	+	0.774912i	−0.978961	−	0.204049i	$-0.934590\pi$
$233$	−180.554	+	180.554i	−0.774912	+	0.774912i	0.204049	+	0.978961i	$0.434590\pi$
$234$			20.1374i			0.0860573i
$235$		0			0
$236$	−84.4529			−0.357851
$237$	−65.3549	−	65.3549i	−0.275759	−	0.275759i
$238$	185.863	−	185.863i	0.780938	−	0.780938i
$239$		−	251.741i		−	1.05331i	−0.850079	−	0.526655i	$-0.823446\pi$
$239$		−	251.741i		−	1.05331i	0.850079	−	0.526655i	$-0.176554\pi$
$240$		0			0
$241$	−68.7572			−0.285299			−0.142650	−	0.989773i	$-0.545562\pi$
$241$	−68.7572			−0.285299			−0.142650	+	0.989773i	$0.545562\pi$
$242$	120.943	+	120.943i	0.499763	+	0.499763i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$			95.2146i			0.390224i
$245$		0			0
$246$	−76.7193			−0.311867
$247$	8.54858	+	8.54858i	0.0346096	+	0.0346096i
$248$	−67.7473	+	67.7473i	−0.273175	+	0.273175i
$249$		−	200.730i		−	0.806143i
$250$		0			0
$251$	−256.264			−1.02097			−0.510486	−	0.859886i	$-0.670535\pi$
$251$	−256.264			−1.02097			−0.510486	+	0.859886i	$0.670535\pi$
$252$	38.8377	+	38.8377i	0.154118	+	0.154118i
$253$	6.40626	−	6.40626i	0.0253212	−	0.0253212i
$254$			3.33999i			0.0131496i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−269.228	−	269.228i	−1.04758	−	1.04758i	−0.998810	−	0.0487685i	$-0.984470\pi$
$257$	−269.228	−	269.228i	−1.04758	−	1.04758i	−0.0487685	−	0.998810i	$-0.515530\pi$
$258$	−129.131	+	129.131i	−0.500506	+	0.500506i
$259$			331.072i			1.27827i
$260$		0			0
$261$	−59.4013			−0.227591
$262$	−190.408	−	190.408i	−0.726747	−	0.726747i
$263$	204.354	−	204.354i	0.777011	−	0.777011i	−0.202310	−	0.979321i	$-0.564845\pi$
$263$	204.354	−	204.354i	0.777011	−	0.777011i	0.979321	+	0.202310i	$0.0648450\pi$
$264$			1.17261i			0.00444171i
$265$		0			0
$266$	32.9742			0.123963
$267$	−2.36014	−	2.36014i	−0.00883947	−	0.00883947i
$268$	−172.845	+	172.845i	−0.644945	+	0.644945i
$269$			150.789i			0.560554i	0.959919	+	0.280277i	$0.0904263\pi$
$269$			150.789i			0.560554i	−0.959919	+	0.280277i	$0.909574\pi$
$270$		0			0
$271$	−376.326			−1.38866			−0.694328	−	0.719658i	$-0.744298\pi$
$271$	−376.326			−1.38866			−0.694328	+	0.719658i	$0.744298\pi$
$272$	−57.4276	−	57.4276i	−0.211131	−	0.211131i
$273$	−53.2146	+	53.2146i	−0.194925	+	0.194925i
$274$			52.1331i			0.190267i
$275$		0			0
$276$	−131.118			−0.475065
$277$	−319.711	−	319.711i	−1.15419	−	1.15419i	−0.985704	−	0.168486i	$-0.946112\pi$
$277$	−319.711	−	319.711i	−1.15419	−	1.15419i	−0.168486	−	0.985704i	$-0.553888\pi$
$278$	−172.480	+	172.480i	−0.620431	+	0.620431i
$279$			101.621i			0.364233i
$280$		0			0
$281$	−180.776			−0.643330			−0.321665	−	0.946854i	$-0.604242\pi$
$281$	−180.776			−0.643330			−0.321665	+	0.946854i	$0.604242\pi$
$282$	48.2762	+	48.2762i	0.171192	+	0.171192i
$283$	252.068	−	252.068i	0.890699	−	0.890699i	−0.103890	−	0.994589i	$-0.533129\pi$
$283$	252.068	−	252.068i	0.890699	−	0.890699i	0.994589	+	0.103890i	$0.0331290\pi$
$284$			256.289i			0.902425i
$285$		0			0
$286$	−1.60669			−0.00561778
$287$	−202.736	−	202.736i	−0.706398	−	0.706398i
$288$	12.0000	−	12.0000i	0.0416667	−	0.0416667i
$289$			123.242i			0.426442i
$290$		0			0
$291$	91.0260			0.312804
$292$	42.4627	+	42.4627i	0.145420	+	0.145420i
$293$	−160.974	+	160.974i	−0.549400	+	0.549400i	−0.926267	−	0.376867i	$-0.877001\pi$
$293$	−160.974	+	160.974i	−0.549400	+	0.549400i	0.376867	+	0.926267i	$0.377001\pi$
$294$			85.2381i			0.289926i
$295$		0			0
$296$	102.294			0.345588
$297$	0.879459	+	0.879459i	0.00296114	+	0.00296114i
$298$	−35.7067	+	35.7067i	−0.119821	+	0.119821i
$299$		−	179.655i		−	0.600852i
$300$		0			0
$301$	−682.474			−2.26735
$302$	22.3612	+	22.3612i	0.0740436	+	0.0740436i
$303$	18.5912	−	18.5912i	0.0613570	−	0.0613570i
$304$		−	10.1883i		−	0.0335141i
$305$		0			0
$306$	−86.1415			−0.281508
$307$	265.191	+	265.191i	0.863816	+	0.863816i	0.991779	−	0.127963i	$-0.0408440\pi$
$307$	265.191	+	265.191i	0.863816	+	0.863816i	−0.127963	+	0.991779i	$0.540844\pi$
$308$	−3.09871	+	3.09871i	−0.0100608	+	0.0100608i
$309$		−	63.0861i		−	0.204162i
$310$		0			0
$311$	495.139			1.59209			0.796044	−	0.605239i	$-0.206922\pi$
$311$	495.139			1.59209			0.796044	+	0.605239i	$0.206922\pi$
$312$	16.4421	+	16.4421i	0.0526991	+	0.0526991i
$313$	74.8634	−	74.8634i	0.239180	−	0.239180i	−0.577330	−	0.816511i	$-0.695906\pi$
$313$	74.8634	−	74.8634i	0.239180	−	0.239180i	0.816511	+	0.577330i	$0.195906\pi$
$314$		−	431.452i		−	1.37405i
$315$		0			0
$316$	−106.724			−0.337734
$317$	27.5097	+	27.5097i	0.0867814	+	0.0867814i	0.749165	−	0.662384i	$-0.230455\pi$
$317$	27.5097	+	27.5097i	0.0867814	+	0.0867814i	−0.662384	+	0.749165i	$0.730455\pi$
$318$	79.8769	−	79.8769i	0.251185	−	0.251185i
$319$		−	4.73940i		−	0.0148571i
$320$		0			0
$321$	−271.933			−0.847143
$322$	−346.488	−	346.488i	−1.07605	−	1.07605i
$323$	−36.5681	+	36.5681i	−0.113214	+	0.113214i
$324$		−	18.0000i		−	0.0555556i
$325$		0			0
$326$	191.534			0.587527
$327$	−198.458	−	198.458i	−0.606904	−	0.606904i
$328$	−62.6410	+	62.6410i	−0.190979	+	0.190979i
$329$			255.147i			0.775523i
$330$		0			0
$331$	609.530			1.84148			0.920741	−	0.390175i	$-0.127586\pi$
$331$	609.530			1.84148			0.920741	+	0.390175i	$0.127586\pi$
$332$	−163.895	−	163.895i	−0.493660	−	0.493660i
$333$	76.7205	−	76.7205i	0.230392	−	0.230392i
$334$			363.275i			1.08765i
$335$		0			0
$336$	63.4218			0.188755
$337$	329.028	+	329.028i	0.976344	+	0.976344i	0.999727	−	0.0233824i	$-0.00744353\pi$
$337$	329.028	+	329.028i	0.976344	+	0.976344i	−0.0233824	+	0.999727i	$0.507444\pi$
$338$	146.471	−	146.471i	0.433347	−	0.433347i
$339$			62.7459i			0.185091i
$340$		0			0
$341$	−8.10794			−0.0237770
$342$	−7.64122	−	7.64122i	−0.0223428	−	0.0223428i
$343$	91.9269	−	91.9269i	0.268008	−	0.268008i
$344$			210.869i			0.612992i
$345$		0			0
$346$	−72.9376			−0.210802
$347$	163.107	+	163.107i	0.470050	+	0.470050i	0.901931	−	0.431881i	$-0.142150\pi$
$347$	163.107	+	163.107i	0.470050	+	0.470050i	−0.431881	+	0.901931i	$0.642150\pi$
$348$	−48.5010	+	48.5010i	−0.139371	+	0.139371i
$349$		−	388.612i		−	1.11350i	−0.830679	−	0.556751i	$-0.812048\pi$
$349$		−	388.612i		−	1.11350i	0.830679	−	0.556751i	$-0.187952\pi$
$350$		0			0
$351$	24.6632			0.0702655
$352$	0.957434	+	0.957434i	0.00271998	+	0.00271998i
$353$	42.4982	−	42.4982i	0.120392	−	0.120392i	−0.644344	−	0.764736i	$-0.722870\pi$
$353$	42.4982	−	42.4982i	0.120392	−	0.120392i	0.764736	+	0.644344i	$0.222870\pi$
$354$			103.433i			0.292184i
$355$		0			0
$356$	−3.85409			−0.0108261
$357$	−227.635	−	227.635i	−0.637633	−	0.637633i
$358$	243.428	−	243.428i	0.679966	−	0.679966i
$359$			186.546i			0.519626i	0.965659	+	0.259813i	$0.0836609\pi$
$359$			186.546i			0.519626i	−0.965659	+	0.259813i	$0.916339\pi$
$360$		0			0
$361$	354.512			0.982029
$362$	315.333	+	315.333i	0.871085	+	0.871085i
$363$	148.124	−	148.124i	0.408055	−	0.408055i
$364$			86.8990i			0.238734i
$365$		0			0
$366$	116.614			0.318616
$367$	−70.5464	−	70.5464i	−0.192224	−	0.192224i	0.604432	−	0.796657i	$-0.293400\pi$
$367$	−70.5464	−	70.5464i	−0.192224	−	0.192224i	−0.796657	+	0.604432i	$0.793400\pi$
$368$	−107.057	+	107.057i	−0.290916	+	0.290916i
$369$			93.9615i			0.254638i
$370$		0			0
$371$	422.161			1.13790
$372$	82.9732	+	82.9732i	0.223046	+	0.223046i
$373$	401.472	−	401.472i	1.07633	−	1.07633i	0.0794977	−	0.996835i	$-0.474668\pi$
$373$	401.472	−	401.472i	1.07633	−	1.07633i	0.996835	−	0.0794977i	$-0.0253316\pi$
$374$		−	6.87289i		−	0.0183767i
$375$		0			0
$376$	78.8348			0.209667
$377$	−66.4550	−	66.4550i	−0.176273	−	0.176273i
$378$	47.5663	−	47.5663i	0.125837	−	0.125837i
$379$		−	160.204i		−	0.422702i	−0.977410	−	0.211351i	$-0.932214\pi$
$379$		−	160.204i		−	0.422702i	0.977410	−	0.211351i	$-0.0677863\pi$
$380$		0			0
$381$	4.09064			0.0107366
$382$	−316.969	−	316.969i	−0.829761	−	0.829761i
$383$	−143.952	+	143.952i	−0.375855	+	0.375855i	−0.869604	−	0.493749i	$-0.835626\pi$
$383$	−143.952	+	143.952i	−0.375855	+	0.375855i	0.493749	+	0.869604i	$0.335626\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	256.348			0.664115
$387$	158.152	+	158.152i	0.408661	+	0.408661i
$388$	74.3224	−	74.3224i	0.191553	−	0.191553i
$389$		−	627.721i		−	1.61368i	−0.590771	−	0.806839i	$-0.701176\pi$
$389$		−	627.721i		−	1.61368i	0.590771	−	0.806839i	$-0.298824\pi$
$390$		0			0
$391$	768.506			1.96549
$392$	69.5966	+	69.5966i	0.177542	+	0.177542i
$393$	−233.201	+	233.201i	−0.593386	+	0.593386i
$394$			336.102i			0.853052i
$395$		0			0
$396$	1.43615			0.00362664
$397$	339.239	+	339.239i	0.854506	+	0.854506i	0.990684	−	0.136178i	$-0.0434819\pi$
$397$	339.239	+	339.239i	0.854506	+	0.854506i	−0.136178	+	0.990684i	$0.543482\pi$
$398$	−289.119	+	289.119i	−0.726430	+	0.726430i
$399$		−	40.3850i		−	0.101215i
$400$		0			0
$401$	−639.454			−1.59465			−0.797324	−	0.603552i	$-0.793752\pi$
$401$	−639.454			−1.59465			−0.797324	+	0.603552i	$0.793752\pi$
$402$	211.691	+	211.691i	0.526595	+	0.526595i
$403$	−113.688	+	113.688i	−0.282104	+	0.282104i
$404$		−	30.3593i		−	0.0751467i
$405$		0			0
$406$	−256.335			−0.631367
$407$	6.12123	+	6.12123i	0.0150399	+	0.0150399i
$408$	−70.3342	+	70.3342i	−0.172388	+	0.172388i
$409$		−	648.066i		−	1.58451i	−0.610188	−	0.792257i	$-0.708906\pi$
$409$		−	648.066i		−	1.58451i	0.610188	−	0.792257i	$-0.291094\pi$
$410$		0			0
$411$	63.8498			0.155352
$412$	−51.5096	−	51.5096i	−0.125023	−	0.125023i
$413$	−273.330	+	273.330i	−0.661816	+	0.661816i
$414$			160.586i			0.387889i
$415$		0			0
$416$	26.8499			0.0645430
$417$	211.244	+	211.244i	0.506580	+	0.506580i
$418$	0.609664	−	0.609664i	0.00145853	−	0.00145853i
$419$		−	674.046i		−	1.60870i	−0.594155	−	0.804351i	$-0.702513\pi$
$419$		−	674.046i		−	1.60870i	0.594155	−	0.804351i	$-0.297487\pi$
$420$		0			0
$421$	−251.907			−0.598354			−0.299177	−	0.954198i	$-0.596712\pi$
$421$	−251.907			−0.598354			−0.299177	+	0.954198i	$0.596712\pi$
$422$	39.5665	+	39.5665i	0.0937596	+	0.0937596i
$423$	59.1261	−	59.1261i	0.139778	−	0.139778i
$424$		−	130.438i		−	0.307638i
$425$		0			0
$426$	313.888			0.736827
$427$	308.160	+	308.160i	0.721686	+	0.721686i
$428$	−222.032	+	222.032i	−0.518767	+	0.518767i
$429$			1.96778i			0.00458690i
$430$		0			0
$431$	73.5149			0.170568			0.0852841	−	0.996357i	$-0.472820\pi$
$431$	73.5149			0.170568			0.0852841	+	0.996357i	$0.472820\pi$
$432$	−14.6969	−	14.6969i	−0.0340207	−	0.0340207i
$433$	542.146	−	542.146i	1.25207	−	1.25207i	0.297277	−	0.954791i	$-0.403921\pi$
$433$	542.146	−	542.146i	1.25207	−	1.25207i	0.954791	−	0.297277i	$-0.0960786\pi$
$434$			438.525i			1.01043i
$435$		0			0
$436$	−324.080			−0.743303
$437$	68.1707	+	68.1707i	0.155997	+	0.155997i
$438$	52.0059	−	52.0059i	0.118735	−	0.118735i
$439$		−	347.787i		−	0.792226i	−0.918202	−	0.396113i	$-0.870359\pi$
$439$		−	347.787i		−	0.792226i	0.918202	−	0.396113i	$-0.129641\pi$
$440$		0			0
$441$	104.395			0.236723
$442$	−96.3703	−	96.3703i	−0.218032	−	0.218032i
$443$	−303.258	+	303.258i	−0.684556	+	0.684556i	−0.961023	−	0.276467i	$-0.910836\pi$
$443$	−303.258	+	303.258i	−0.684556	+	0.684556i	0.276467	+	0.961023i	$0.410836\pi$
$444$		−	125.284i		−	0.282171i
$445$		0			0
$446$	−155.913			−0.349580
$447$	43.7316	+	43.7316i	0.0978336	+	0.0978336i
$448$	51.7836	−	51.7836i	0.115588	−	0.115588i
$449$		−	139.114i		−	0.309830i	−0.987928	−	0.154915i	$-0.950490\pi$
$449$		−	139.114i		−	0.309830i	0.987928	−	0.154915i	$-0.0495104\pi$
$450$		0			0
$451$	−7.49683			−0.0166227
$452$	51.2318	+	51.2318i	0.113345	+	0.113345i
$453$	27.3867	−	27.3867i	0.0604563	−	0.0604563i
$454$			22.0197i			0.0485015i
$455$		0			0
$456$	−12.4781			−0.0273642
$457$	547.409	+	547.409i	1.19783	+	1.19783i	0.974814	+	0.223018i	$0.0715910\pi$
$457$	547.409	+	547.409i	1.19783	+	1.19783i	0.223018	+	0.974814i	$0.428409\pi$
$458$	170.347	−	170.347i	0.371937	−	0.371937i
$459$			105.501i			0.229850i
$460$		0			0
$461$	349.358			0.757826			0.378913	−	0.925432i	$-0.376298\pi$
$461$	349.358			0.757826			0.378913	+	0.925432i	$0.376298\pi$
$462$	3.79513	+	3.79513i	0.00821457	+	0.00821457i
$463$	−455.977	+	455.977i	−0.984831	+	0.984831i	−0.999887	−	0.0150559i	$-0.995207\pi$
$463$	−455.977	+	455.977i	−0.984831	+	0.984831i	0.0150559	+	0.999887i	$0.495207\pi$
$464$			79.2018i			0.170694i
$465$		0			0
$466$	361.109			0.774912
$467$	57.4519	+	57.4519i	0.123023	+	0.123023i	0.765938	−	0.642915i	$-0.222275\pi$
$467$	57.4519	+	57.4519i	0.123023	+	0.123023i	−0.642915	+	0.765938i	$0.722275\pi$
$468$	20.1374	−	20.1374i	0.0430287	−	0.0430287i
$469$			1118.82i			2.38554i
$470$		0			0
$471$	−528.418			−1.12191
$472$	84.4529	+	84.4529i	0.178926	+	0.178926i
$473$	−12.6183	+	12.6183i	−0.0266772	+	0.0266772i
$474$			130.710i			0.275759i
$475$		0			0
$476$	−371.727			−0.780938
$477$	−97.8289	−	97.8289i	−0.205092	−	0.205092i
$478$	−251.741	+	251.741i	−0.526655	+	0.526655i
$479$			21.8319i			0.0455780i	0.999740	+	0.0227890i	$0.00725459\pi$
$479$			21.8319i			0.0455780i	−0.999740	+	0.0227890i	$0.992745\pi$
$480$		0			0
$481$	171.661			0.356884
$482$	68.7572	+	68.7572i	0.142650	+	0.142650i
$483$	−424.360	+	424.360i	−0.878592	+	0.878592i
$484$		−	241.885i		−	0.499763i
$485$		0			0
$486$	−22.0454			−0.0453609
$487$	81.7201	+	81.7201i	0.167803	+	0.167803i	0.786013	−	0.618210i	$-0.212142\pi$
$487$	81.7201	+	81.7201i	0.167803	+	0.167803i	−0.618210	+	0.786013i	$0.712142\pi$
$488$	95.2146	−	95.2146i	0.195112	−	0.195112i
$489$		−	234.580i		−	0.479713i
$490$		0			0
$491$	−29.1488			−0.0593663			−0.0296831	−	0.999559i	$-0.509450\pi$
$491$	−29.1488			−0.0593663			−0.0296831	+	0.999559i	$0.509450\pi$
$492$	76.7193	+	76.7193i	0.155934	+	0.155934i
$493$	284.273	−	284.273i	0.576619	−	0.576619i
$494$		−	17.0972i		−	0.0346096i
$495$		0			0
$496$	135.495			0.273175
$497$	829.473	+	829.473i	1.66896	+	1.66896i
$498$	−200.730	+	200.730i	−0.403071	+	0.403071i
$499$		−	379.995i		−	0.761513i	−0.924675	−	0.380756i	$-0.875664\pi$
$499$		−	379.995i		−	0.761513i	0.924675	−	0.380756i	$-0.124336\pi$
$500$		0			0
$501$	444.919			0.888062
$502$	256.264	+	256.264i	0.510486	+	0.510486i
$503$	456.906	−	456.906i	0.908363	−	0.908363i	−0.0877775	−	0.996140i	$-0.527976\pi$
$503$	456.906	−	456.906i	0.908363	−	0.908363i	0.996140	+	0.0877775i	$0.0279764\pi$
$504$		−	77.6755i		−	0.154118i
$505$		0			0
$506$	−12.8125			−0.0253212
$507$	−179.390	−	179.390i	−0.353827	−	0.353827i
$508$	3.33999	−	3.33999i	0.00657479	−	0.00657479i
$509$		−	448.672i		−	0.881477i	−0.897635	−	0.440739i	$-0.854717\pi$
$509$		−	448.672i		−	0.881477i	0.897635	−	0.440739i	$-0.145283\pi$
$510$		0			0
$511$	274.859			0.537885
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	−9.35855	+	9.35855i	−0.0182428	+	0.0182428i
$514$			538.455i			1.04758i
$515$		0			0
$516$	258.261			0.500506
$517$	4.71744	+	4.71744i	0.00912465	+	0.00912465i
$518$	331.072	−	331.072i	0.639136	−	0.639136i
$519$			89.3300i			0.172119i
$520$		0			0
$521$	−743.950			−1.42793			−0.713964	−	0.700183i	$-0.753102\pi$
$521$	−743.950			−1.42793			−0.713964	+	0.700183i	$0.753102\pi$
$522$	59.4013	+	59.4013i	0.113796	+	0.113796i
$523$	−339.868	+	339.868i	−0.649844	+	0.649844i	−0.952955	−	0.303111i	$-0.901975\pi$
$523$	−339.868	+	339.868i	−0.649844	+	0.649844i	0.303111	+	0.952955i	$0.401975\pi$
$524$			380.815i			0.726747i
$525$		0			0
$526$	−408.708			−0.777011
$527$	−486.321	−	486.321i	−0.922810	−	0.922810i
$528$	1.17261	−	1.17261i	0.00222086	−	0.00222086i
$529$		−	903.657i		−	1.70824i
$530$		0			0
$531$	126.679			0.238567
$532$	−32.9742	−	32.9742i	−0.0619816	−	0.0619816i
$533$	−105.119	+	105.119i	−0.197221	+	0.197221i
$534$			4.72028i			0.00883947i
$535$		0			0
$536$	345.691			0.644945
$537$	−298.137	−	298.137i	−0.555190	−	0.555190i
$538$	150.789	−	150.789i	0.280277	−	0.280277i
$539$			8.32927i			0.0154532i
$540$		0			0
$541$	−242.473			−0.448195			−0.224097	−	0.974567i	$-0.571943\pi$
$541$	−242.473			−0.448195			−0.224097	+	0.974567i	$0.571943\pi$
$542$	376.326	+	376.326i	0.694328	+	0.694328i
$543$	386.202	−	386.202i	0.711238	−	0.711238i
$544$			114.855i			0.211131i
$545$		0			0
$546$	106.429			0.194925
$547$	215.569	+	215.569i	0.394094	+	0.394094i	0.876144	−	0.482050i	$-0.160108\pi$
$547$	215.569	+	215.569i	0.394094	+	0.394094i	−0.482050	+	0.876144i	$0.660108\pi$
$548$	52.1331	−	52.1331i	0.0951334	−	0.0951334i
$549$		−	142.822i		−	0.260149i
$550$		0			0
$551$	50.4332			0.0915303
$552$	131.118	+	131.118i	0.237532	+	0.237532i
$553$	−345.410	+	345.410i	−0.624611	+	0.624611i
$554$			639.421i			1.15419i
$555$		0			0
$556$	344.960			0.620431
$557$	−115.397	−	115.397i	−0.207177	−	0.207177i	0.595890	−	0.803066i	$-0.296800\pi$
$557$	−115.397	−	115.397i	−0.207177	−	0.207177i	−0.803066	+	0.595890i	$0.796800\pi$
$558$	101.621	−	101.621i	0.182116	−	0.182116i
$559$			353.863i			0.633029i
$560$		0			0
$561$	−8.41754			−0.0150045
$562$	180.776	+	180.776i	0.321665	+	0.321665i
$563$	−84.8034	+	84.8034i	−0.150628	+	0.150628i	−0.778398	−	0.627771i	$-0.783968\pi$
$563$	−84.8034	+	84.8034i	−0.150628	+	0.150628i	0.627771	+	0.778398i	$0.283968\pi$
$564$		−	96.5525i		−	0.171192i
$565$		0			0
$566$	−504.135			−0.890699
$567$	−58.2566	−	58.2566i	−0.102745	−	0.102745i
$568$	256.289	−	256.289i	0.451212	−	0.451212i
$569$		−	85.6878i		−	0.150594i	−0.997161	−	0.0752969i	$-0.976010\pi$
$569$		−	85.6878i		−	0.150594i	0.997161	−	0.0752969i	$-0.0239904\pi$
$570$		0			0
$571$	811.448			1.42110			0.710549	−	0.703647i	$-0.248446\pi$
$571$	811.448			1.42110			0.710549	+	0.703647i	$0.248446\pi$
$572$	1.60669	+	1.60669i	0.00280889	+	0.00280889i
$573$	−388.206	+	388.206i	−0.677497	+	0.677497i
$574$			405.473i			0.706398i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$	402.333	+	402.333i	0.697284	+	0.697284i	0.963824	−	0.266540i	$-0.0858803\pi$
$577$	402.333	+	402.333i	0.697284	+	0.697284i	−0.266540	+	0.963824i	$0.585880\pi$
$578$	123.242	−	123.242i	0.213221	−	0.213221i
$579$		−	313.961i		−	0.542248i
$580$		0			0
$581$	−1060.89			−1.82596
$582$	−91.0260	−	91.0260i	−0.156402	−	0.156402i
$583$	7.80539	−	7.80539i	0.0133883	−	0.0133883i
$584$		−	84.9254i		−	0.145420i
$585$		0			0
$586$	321.948			0.549400
$587$	−196.739	−	196.739i	−0.335160	−	0.335160i	0.519382	−	0.854542i	$-0.326162\pi$
$587$	−196.739	−	196.739i	−0.335160	−	0.335160i	−0.854542	+	0.519382i	$0.826162\pi$
$588$	85.2381	−	85.2381i	0.144963	−	0.144963i
$589$		−	86.2787i		−	0.146483i
$590$		0			0
$591$	411.640			0.696514
$592$	−102.294	−	102.294i	−0.172794	−	0.172794i
$593$	701.567	−	701.567i	1.18308	−	1.18308i	0.204139	−	0.978942i	$-0.434561\pi$
$593$	701.567	−	701.567i	1.18308	−	1.18308i	0.978942	−	0.204139i	$-0.0654394\pi$
$594$		−	1.75892i		−	0.00296114i
$595$		0			0
$596$	71.4134			0.119821
$597$	354.097	+	354.097i	0.593128	+	0.593128i
$598$	−179.655	+	179.655i	−0.300426	+	0.300426i
$599$			61.8419i			0.103242i	0.998667	+	0.0516210i	$0.0164388\pi$
$599$			61.8419i			0.103242i	−0.998667	+	0.0516210i	$0.983561\pi$
$600$		0			0
$601$	35.2542			0.0586593			0.0293296	−	0.999570i	$-0.490663\pi$
$601$	35.2542			0.0586593			0.0293296	+	0.999570i	$0.490663\pi$
$602$	682.474	+	682.474i	1.13368	+	1.13368i
$603$	259.268	−	259.268i	0.429963	−	0.429963i
$604$		−	44.7223i		−	0.0740436i
$605$		0			0
$606$	−37.1823			−0.0613570
$607$	357.609	+	357.609i	0.589142	+	0.589142i	0.937399	−	0.348257i	$-0.113226\pi$
$607$	357.609	+	357.609i	0.589142	+	0.589142i	−0.348257	+	0.937399i	$0.613226\pi$
$608$	−10.1883	+	10.1883i	−0.0167571	+	0.0167571i
$609$			313.945i			0.515509i
$610$		0			0
$611$	132.294			0.216520
$612$	86.1415	+	86.1415i	0.140754	+	0.140754i
$613$	−617.374	+	617.374i	−1.00714	+	1.00714i	−0.00716146	+	0.999974i	$0.502280\pi$
$613$	−617.374	+	617.374i	−1.00714	+	1.00714i	−0.999974	+	0.00716146i	$0.997720\pi$
$614$		−	530.383i		−	0.863816i
$615$		0			0
$616$	6.19743			0.0100608
$617$	−245.403	−	245.403i	−0.397736	−	0.397736i	0.479698	−	0.877434i	$-0.340746\pi$
$617$	−245.403	−	245.403i	−0.397736	−	0.397736i	−0.877434	+	0.479698i	$0.840746\pi$
$618$	−63.0861	+	63.0861i	−0.102081	+	0.102081i
$619$			361.343i			0.583753i	0.956456	+	0.291877i	$0.0942797\pi$
$619$			361.343i			0.583753i	−0.956456	+	0.291877i	$0.905720\pi$
$620$		0			0
$621$	196.677			0.316710
$622$	−495.139	−	495.139i	−0.796044	−	0.796044i
$623$	−12.4737	+	12.4737i	−0.0200219	+	0.0200219i
$624$		−	32.8843i		−	0.0526991i
$625$		0			0
$626$	−149.727			−0.239180
$627$	−0.746682	−	0.746682i	−0.00119088	−	0.00119088i
$628$	−431.452	+	431.452i	−0.687025	+	0.687025i
$629$			734.313i			1.16743i
$630$		0			0
$631$	89.5750			0.141957			0.0709786	−	0.997478i	$-0.477388\pi$
$631$	89.5750			0.141957			0.0709786	+	0.997478i	$0.477388\pi$
$632$	106.724	+	106.724i	0.168867	+	0.168867i
$633$	48.4589	−	48.4589i	0.0765544	−	0.0765544i
$634$		−	55.0194i		−	0.0867814i
$635$		0			0
$636$	−159.754			−0.251185
$637$	116.791	+	116.791i	0.183346	+	0.183346i
$638$	−4.73940	+	4.73940i	−0.00742853	+	0.00742853i
$639$		−	384.433i		−	0.601617i
$640$		0			0
$641$	−873.858			−1.36327			−0.681636	−	0.731691i	$-0.738731\pi$
$641$	−873.858			−1.36327			−0.681636	+	0.731691i	$0.738731\pi$
$642$	271.933	+	271.933i	0.423571	+	0.423571i
$643$	−427.278	+	427.278i	−0.664507	+	0.664507i	−0.956439	−	0.291932i	$-0.905702\pi$
$643$	−427.278	+	427.278i	−0.664507	+	0.664507i	0.291932	+	0.956439i	$0.405702\pi$
$644$			692.977i			1.07605i
$645$		0			0
$646$	73.1362			0.113214
$647$	786.700	+	786.700i	1.21592	+	1.21592i	0.969048	+	0.246872i	$0.0794027\pi$
$647$	786.700	+	786.700i	1.21592	+	1.21592i	0.246872	+	0.969048i	$0.420597\pi$
$648$	−18.0000	+	18.0000i	−0.0277778	+	0.0277778i
$649$			10.1073i			0.0155736i
$650$		0			0
$651$	537.082			0.825010
$652$	−191.534	−	191.534i	−0.293763	−	0.293763i
$653$	618.390	−	618.390i	0.946999	−	0.946999i	−0.0516653	−	0.998664i	$-0.516453\pi$
$653$	618.390	−	618.390i	0.946999	−	0.946999i	0.998664	+	0.0516653i	$0.0164529\pi$
$654$			396.915i			0.606904i
$655$		0			0
$656$	125.282			0.190979
$657$	−63.6940	−	63.6940i	−0.0969468	−	0.0969468i
$658$	255.147	−	255.147i	0.387761	−	0.387761i
$659$			336.577i			0.510739i	0.966844	+	0.255370i	$0.0821971\pi$
$659$			336.577i			0.510739i	−0.966844	+	0.255370i	$0.917803\pi$
$660$		0			0
$661$	−623.611			−0.943435			−0.471718	−	0.881750i	$-0.656366\pi$
$661$	−623.611			−0.943435			−0.471718	+	0.881750i	$0.656366\pi$
$662$	−609.530	−	609.530i	−0.920741	−	0.920741i
$663$	−118.029	+	118.029i	−0.178023	+	0.178023i
$664$			327.790i			0.493660i
$665$		0			0
$666$	−153.441			−0.230392
$667$	−529.945	−	529.945i	−0.794521	−	0.794521i
$668$	363.275	−	363.275i	0.543824	−	0.543824i
$669$			190.953i			0.285431i
$670$		0			0
$671$	11.3952			0.0169824
$672$	−63.4218	−	63.4218i	−0.0943776	−	0.0943776i
$673$	521.943	−	521.943i	0.775547	−	0.775547i	−0.203523	−	0.979070i	$-0.565239\pi$
$673$	521.943	−	521.943i	0.775547	−	0.775547i	0.979070	+	0.203523i	$0.0652393\pi$
$674$		−	658.056i		−	0.976344i
$675$		0			0
$676$	−292.943			−0.433347
$677$	151.473	+	151.473i	0.223741	+	0.223741i	0.810072	−	0.586331i	$-0.199428\pi$
$677$	151.473	+	151.473i	0.223741	+	0.223741i	−0.586331	+	0.810072i	$0.699428\pi$
$678$	62.7459	−	62.7459i	0.0925456	−	0.0925456i
$679$		−	481.086i		−	0.708521i
$680$		0			0
$681$	26.9685			0.0396013
$682$	8.10794	+	8.10794i	0.0118885	+	0.0118885i
$683$	141.089	−	141.089i	0.206572	−	0.206572i	−0.596237	−	0.802809i	$-0.703338\pi$
$683$	141.089	−	141.089i	0.206572	−	0.206572i	0.802809	+	0.596237i	$0.203338\pi$
$684$			15.2824i			0.0223428i
$685$		0			0
$686$	−183.854			−0.268008
$687$	−208.632	−	208.632i	−0.303685	−	0.303685i
$688$	210.869	−	210.869i	0.306496	−	0.306496i
$689$		−	218.891i		−	0.317694i
$690$		0			0
$691$	−270.741			−0.391811			−0.195905	−	0.980623i	$-0.562765\pi$
$691$	−270.741			−0.391811			−0.195905	+	0.980623i	$0.562765\pi$
$692$	72.9376	+	72.9376i	0.105401	+	0.105401i
$693$	4.64807	−	4.64807i	0.00670717	−	0.00670717i
$694$		−	326.215i		−	0.470050i
$695$		0			0
$696$	97.0020			0.139371
$697$	−449.666	−	449.666i	−0.645145	−	0.645145i
$698$	−388.612	+	388.612i	−0.556751	+	0.556751i
$699$		−	442.266i		−	0.632713i
$700$		0			0
$701$	−954.067			−1.36101			−0.680504	−	0.732744i	$-0.738239\pi$
$701$	−954.067			−1.36101			−0.680504	+	0.732744i	$0.738239\pi$
$702$	−24.6632	−	24.6632i	−0.0351327	−	0.0351327i
$703$	−65.1376	+	65.1376i	−0.0926566	+	0.0926566i
$704$		−	1.91487i		−	0.00271998i
$705$		0			0
$706$	−84.9965			−0.120392
$707$	−98.2571	−	98.2571i	−0.138977	−	0.138977i
$708$	103.433	−	103.433i	0.146092	−	0.146092i
$709$		−	298.144i		−	0.420513i	−0.977646	−	0.210257i	$-0.932570\pi$
$709$		−	298.144i		−	0.420513i	0.977646	−	0.210257i	$-0.0674300\pi$
$710$		0			0
$711$	160.086			0.225156
$712$	3.85409	+	3.85409i	0.00541305	+	0.00541305i
$713$	−906.605	+	906.605i	−1.27154	+	1.27154i
$714$			455.270i			0.637633i
$715$		0			0
$716$	−486.855			−0.679966
$717$	308.318	+	308.318i	0.430012	+	0.430012i
$718$	186.546	−	186.546i	0.259813	−	0.259813i
$719$			248.694i			0.345889i	0.984932	+	0.172944i	$0.0553281\pi$
$719$			248.694i			0.345889i	−0.984932	+	0.172944i	$0.944672\pi$
$720$		0			0
$721$	−333.419			−0.462440
$722$	−354.512	−	354.512i	−0.491014	−	0.491014i
$723$	84.2100	−	84.2100i	0.116473	−	0.116473i
$724$		−	630.665i		−	0.871085i
$725$		0			0
$726$	−296.248			−0.408055
$727$	423.236	+	423.236i	0.582168	+	0.582168i	0.935499	−	0.353331i	$-0.114951\pi$
$727$	423.236	+	423.236i	0.582168	+	0.582168i	−0.353331	+	0.935499i	$0.614951\pi$
$728$	86.8990	−	86.8990i	0.119367	−	0.119367i
$729$			27.0000i			0.0370370i
$730$		0			0
$731$	−1513.72			−2.07075
$732$	−116.614	−	116.614i	−0.159308	−	0.159308i
$733$	502.822	−	502.822i	0.685978	−	0.685978i	−0.275362	−	0.961340i	$-0.588798\pi$
$733$	502.822	−	502.822i	0.685978	−	0.685978i	0.961340	+	0.275362i	$0.0887979\pi$
$734$			141.093i			0.192224i
$735$		0			0
$736$	214.115			0.290916
$737$	20.6860	+	20.6860i	0.0280678	+	0.0280678i
$738$	93.9615	−	93.9615i	0.127319	−	0.127319i
$739$			508.067i			0.687505i	0.939060	+	0.343753i	$0.111698\pi$
$739$			508.067i			0.687505i	−0.939060	+	0.343753i	$0.888302\pi$
$740$		0			0
$741$	−20.9397			−0.0282586
$742$	−422.161	−	422.161i	−0.568950	−	0.568950i
$743$	−100.424	+	100.424i	−0.135160	+	0.135160i	−0.771450	−	0.636290i	$-0.780468\pi$
$743$	−100.424	+	100.424i	−0.135160	+	0.135160i	0.636290	+	0.771450i	$0.280468\pi$
$744$		−	165.946i		−	0.223046i
$745$		0			0
$746$	−802.944			−1.07633
$747$	245.843	+	245.843i	0.329106	+	0.329106i
$748$	−6.87289	+	6.87289i	−0.00918836	+	0.00918836i
$749$			1437.20i			1.91883i
$750$		0			0
$751$	519.697			0.692006			0.346003	−	0.938233i	$-0.387539\pi$
$751$	519.697			0.692006			0.346003	+	0.938233i	$0.387539\pi$
$752$	−78.8348	−	78.8348i	−0.104833	−	0.104833i
$753$	313.858	−	313.858i	0.416810	−	0.416810i
$754$			132.910i			0.176273i
$755$		0			0
$756$	−95.1326			−0.125837
$757$	585.300	+	585.300i	0.773183	+	0.773183i	0.978662	−	0.205478i	$-0.0658750\pi$
$757$	585.300	+	585.300i	0.773183	+	0.773183i	−0.205478	+	0.978662i	$0.565875\pi$
$758$	−160.204	+	160.204i	−0.211351	+	0.211351i
$759$			15.6921i			0.0206747i
$760$		0			0
$761$	−895.742			−1.17706			−0.588529	−	0.808476i	$-0.700293\pi$
$761$	−895.742			−1.17706			−0.588529	+	0.808476i	$0.700293\pi$
$762$	−4.09064	−	4.09064i	−0.00536829	−	0.00536829i
$763$	−1048.88	+	1048.88i	−1.37468	+	1.37468i
$764$			633.938i			0.829761i
$765$		0			0
$766$	287.905			0.375855
$767$	141.722	+	141.722i	0.184774	+	0.184774i
$768$	−19.5959	+	19.5959i	−0.0255155	+	0.0255155i
$769$		−	1173.00i		−	1.52536i	−0.646776	−	0.762680i	$-0.723883\pi$
$769$		−	1173.00i		−	1.52536i	0.646776	−	0.762680i	$-0.276117\pi$
$770$		0			0
$771$	659.470			0.855344
$772$	−256.348	−	256.348i	−0.332058	−	0.332058i
$773$	−246.952	+	246.952i	−0.319472	+	0.319472i	−0.848564	−	0.529092i	$-0.822532\pi$
$773$	−246.952	+	246.952i	−0.319472	+	0.319472i	0.529092	+	0.848564i	$0.322532\pi$
$774$		−	316.304i		−	0.408661i
$775$		0			0
$776$	−148.645			−0.191553
$777$	−405.479	−	405.479i	−0.521852	−	0.521852i
$778$	−627.721	+	627.721i	−0.806839	+	0.806839i
$779$		−	79.7757i		−	0.102408i
$780$		0			0
$781$	30.6724			0.0392733
$782$	−768.506	−	768.506i	−0.982744	−	0.982744i
$783$	72.7515	−	72.7515i	0.0929138	−	0.0929138i
$784$		−	139.193i		−	0.177542i
$785$		0			0
$786$	466.402			0.593386
$787$	−702.103	−	702.103i	−0.892126	−	0.892126i	0.102597	−	0.994723i	$-0.467285\pi$
$787$	−702.103	−	702.103i	−0.892126	−	0.892126i	−0.994723	+	0.102597i	$0.967285\pi$
$788$	336.102	−	336.102i	0.426526	−	0.426526i
$789$			500.563i			0.634427i
$790$		0			0
$791$	331.621			0.419243
$792$	−1.43615	−	1.43615i	−0.00181332	−	0.00181332i
$793$	159.781	−	159.781i	0.201490	−	0.201490i
$794$		−	678.478i		−	0.854506i
$795$		0			0
$796$	578.239			0.726430
$797$	−897.889	−	897.889i	−1.12659	−	1.12659i	−0.990728	−	0.135857i	$-0.956621\pi$
$797$	−897.889	−	897.889i	−1.12659	−	1.12659i	−0.135857	−	0.990728i	$-0.543379\pi$
$798$	−40.3850	+	40.3850i	−0.0506077	+	0.0506077i
$799$			565.912i			0.708275i
$800$		0			0
$801$	5.78113			0.00721740
$802$	639.454	+	639.454i	0.797324	+	0.797324i
$803$	5.08190	−	5.08190i	0.00632864	−	0.00632864i
$804$		−	423.383i		−	0.526595i
$805$		0			0
$806$	227.376			0.282104
$807$	−184.678	−	184.678i	−0.228845	−	0.228845i
$808$	−30.3593	+	30.3593i	−0.0375733	+	0.0375733i
$809$		−	1436.49i		−	1.77563i	−0.460199	−	0.887816i	$-0.652222\pi$
$809$		−	1436.49i		−	1.77563i	0.460199	−	0.887816i	$-0.347778\pi$
$810$		0			0
$811$	−353.032			−0.435304			−0.217652	−	0.976026i	$-0.569840\pi$
$811$	−353.032			−0.435304			−0.217652	+	0.976026i	$0.569840\pi$
$812$	256.335	+	256.335i	0.315683	+	0.315683i
$813$	460.903	−	460.903i	0.566917	−	0.566917i
$814$		−	12.2425i		−	0.0150399i
$815$		0			0
$816$	140.668			0.172388
$817$	−134.275	−	134.275i	−0.164351	−	0.164351i
$818$	−648.066	+	648.066i	−0.792257	+	0.792257i
$819$		−	130.349i		−	0.159156i
$820$		0			0
$821$	838.078			1.02080			0.510401	−	0.859937i	$-0.329497\pi$
$821$	838.078			1.02080			0.510401	+	0.859937i	$0.329497\pi$
$822$	−63.8498	−	63.8498i	−0.0776761	−	0.0776761i
$823$	915.637	−	915.637i	1.11256	−	1.11256i	0.119757	−	0.992803i	$-0.461789\pi$
$823$	915.637	−	915.637i	1.11256	−	1.11256i	0.992803	−	0.119757i	$-0.0382115\pi$
$824$			103.019i			0.125023i
$825$		0			0
$826$	546.660			0.661816
$827$	−844.466	−	844.466i	−1.02112	−	1.02112i	−0.999772	−	0.0213480i	$-0.993204\pi$
$827$	−844.466	−	844.466i	−1.02112	−	1.02112i	−0.0213480	−	0.999772i	$-0.506796\pi$
$828$	160.586	−	160.586i	0.193944	−	0.193944i
$829$			892.513i			1.07661i	0.842749	+	0.538307i	$0.180936\pi$
$829$			892.513i			1.07661i	−0.842749	+	0.538307i	$0.819064\pi$
$830$		0			0
$831$	783.128			0.942392
$832$	−26.8499	−	26.8499i	−0.0322715	−	0.0322715i
$833$	−499.596	+	499.596i	−0.599755	+	0.599755i
$834$		−	422.488i		−	0.506580i
$835$		0			0
$836$	−1.21933			−0.00145853
$837$	−124.460	−	124.460i	−0.148697	−	0.148697i
$838$	−674.046	+	674.046i	−0.804351	+	0.804351i
$839$		−	886.642i		−	1.05678i	−0.849001	−	0.528392i	$-0.822795\pi$
$839$		−	886.642i		−	1.05678i	0.849001	−	0.528392i	$-0.177205\pi$
$840$		0			0
$841$	448.942			0.533820
$842$	251.907	+	251.907i	0.299177	+	0.299177i
$843$	221.404	−	221.404i	0.262638	−	0.262638i
$844$		−	79.1331i		−	0.0937596i
$845$		0			0
$846$	−118.252			−0.139778
$847$	−782.857	−	782.857i	−0.924270	−	0.924270i
$848$	−130.438	+	130.438i	−0.153819	+	0.153819i
$849$			617.437i			0.727252i
$850$		0			0
$851$	1368.91			1.60859
$852$	−313.888	−	313.888i	−0.368413	−	0.368413i
$853$	−380.542	+	380.542i	−0.446122	+	0.446122i	−0.894063	−	0.447941i	$-0.852157\pi$
$853$	−380.542	+	380.542i	−0.446122	+	0.446122i	0.447941	+	0.894063i	$0.352157\pi$
$854$		−	616.320i		−	0.721686i
$855$		0			0
$856$	444.064			0.518767
$857$	−419.114	−	419.114i	−0.489047	−	0.489047i	0.418958	−	0.908006i	$-0.362395\pi$
$857$	−419.114	−	419.114i	−0.489047	−	0.489047i	−0.908006	+	0.418958i	$0.862395\pi$
$858$	1.96778	−	1.96778i	0.00229345	−	0.00229345i
$859$			15.0082i			0.0174717i	0.999962	+	0.00873586i	$0.00278074\pi$
$859$			15.0082i			0.0174717i	−0.999962	+	0.00873586i	$0.997219\pi$
$860$		0			0
$861$	496.601			0.576772
$862$	−73.5149	−	73.5149i	−0.0852841	−	0.0852841i
$863$	710.712	−	710.712i	0.823536	−	0.823536i	−0.163077	−	0.986613i	$-0.552142\pi$
$863$	710.712	−	710.712i	0.823536	−	0.823536i	0.986613	+	0.163077i	$0.0521419\pi$
$864$			29.3939i			0.0340207i
$865$		0			0
$866$	−1084.29			−1.25207
$867$	−150.940	−	150.940i	−0.174094	−	0.174094i
$868$	438.525	−	438.525i	0.505213	−	0.505213i
$869$			12.7727i			0.0146981i
$870$		0			0
$871$	580.109			0.666027
$872$	324.080	+	324.080i	0.371651	+	0.371651i
$873$	−111.484	+	111.484i	−0.127702	+	0.127702i
$874$		−	136.341i		−	0.155997i
$875$		0			0
$876$	−104.012			−0.118735
$877$	−1073.18	−	1073.18i	−1.22369	−	1.22369i	−0.966310	−	0.257381i	$-0.917140\pi$
$877$	−1073.18	−	1073.18i	−1.22369	−	1.22369i	−0.257381	−	0.966310i	$-0.582860\pi$
$878$	−347.787	+	347.787i	−0.396113	+	0.396113i
$879$		−	394.305i		−	0.448583i
$880$		0			0
$881$	326.112			0.370161			0.185081	−	0.982723i	$-0.440745\pi$
$881$	326.112			0.370161			0.185081	+	0.982723i	$0.440745\pi$
$882$	−104.395	−	104.395i	−0.118362	−	0.118362i
$883$	−800.626	+	800.626i	−0.906711	+	0.906711i	−0.996005	−	0.0892945i	$-0.971539\pi$
$883$	−800.626	+	800.626i	−0.906711	+	0.906711i	0.0892945	+	0.996005i	$0.471539\pi$
$884$			192.741i			0.218032i
$885$		0			0
$886$	606.517			0.684556
$887$	−965.885	−	965.885i	−1.08893	−	1.08893i	−0.995638	−	0.0932965i	$-0.970260\pi$
$887$	−965.885	−	965.885i	−1.08893	−	1.08893i	−0.0932965	−	0.995638i	$-0.529740\pi$
$888$	−125.284	+	125.284i	−0.141086	+	0.141086i
$889$		−	21.6196i		−	0.0243190i
$890$		0			0
$891$	−2.15423			−0.00241776
$892$	155.913	+	155.913i	0.174790	+	0.174790i
$893$	−50.1995	+	50.1995i	−0.0562144	+	0.0562144i
$894$		−	87.4632i		−	0.0978336i
$895$		0			0
$896$	−103.567			−0.115588
$897$	220.031	+	220.031i	0.245297	+	0.245297i
$898$	−139.114	+	139.114i	−0.154915	+	0.154915i
$899$			670.713i			0.746066i
$900$		0			0
$901$	936.347			1.03923
$902$	7.49683	+	7.49683i	0.00831134	+	0.00831134i
$903$	835.856	−	835.856i	0.925643	−	0.925643i
$904$		−	102.464i		−	0.113345i
$905$		0			0
$906$	−54.7734			−0.0604563
$907$	−191.581	−	191.581i	−0.211225	−	0.211225i	0.593563	−	0.804788i	$-0.297721\pi$
$907$	−191.581	−	191.581i	−0.211225	−	0.211225i	−0.804788	+	0.593563i	$0.797721\pi$
$908$	22.0197	−	22.0197i	0.0242507	−	0.0242507i
$909$			45.5389i			0.0500978i
$910$		0			0
$911$	−1639.06			−1.79919			−0.899596	−	0.436723i	$-0.856139\pi$
$911$	−1639.06			−1.79919			−0.899596	+	0.436723i	$0.856139\pi$
$912$	12.4781	+	12.4781i	0.0136821	+	0.0136821i
$913$	−19.6148	+	19.6148i	−0.0214839	+	0.0214839i
$914$		−	1094.82i		−	1.19783i
$915$		0			0
$916$	−340.694			−0.371937
$917$	1232.50	+	1232.50i	1.34406	+	1.34406i
$918$	105.501	−	105.501i	0.114925	−	0.114925i
$919$			1038.57i			1.13011i	0.825054	+	0.565053i	$0.191144\pi$
$919$			1038.57i			1.13011i	−0.825054	+	0.565053i	$0.808856\pi$
$920$		0			0
$921$	−649.584			−0.705302
$922$	−349.358	−	349.358i	−0.378913	−	0.378913i
$923$	430.082	−	430.082i	0.465962	−	0.465962i
$924$		−	7.59027i		−	0.00821457i
$925$		0			0
$926$	911.953			0.984831
$927$	77.2644	+	77.2644i	0.0833489	+	0.0833489i
$928$	79.2018	−	79.2018i	0.0853468	−	0.0853468i
$929$		−	527.150i		−	0.567438i	−0.958908	−	0.283719i	$-0.908432\pi$
$929$		−	527.150i		−	0.567438i	0.958908	−	0.283719i	$-0.0915682\pi$
$930$		0			0
$931$	−88.6339			−0.0952029
$932$	−361.109	−	361.109i	−0.387456	−	0.387456i
$933$	−606.419	+	606.419i	−0.649967	+	0.649967i
$934$		−	114.904i		−	0.123023i
$935$		0			0
$936$	−40.2748			−0.0430287
$937$	−157.661	−	157.661i	−0.168262	−	0.168262i	0.617953	−	0.786215i	$-0.287962\pi$
$937$	−157.661	−	157.661i	−0.168262	−	0.168262i	−0.786215	+	0.617953i	$0.787962\pi$
$938$	1118.82	−	1118.82i	1.19277	−	1.19277i
$939$			183.377i			0.195290i
$940$		0			0
$941$	22.4138			0.0238191			0.0119095	−	0.999929i	$-0.496209\pi$
$941$	22.4138			0.0238191			0.0119095	+	0.999929i	$0.496209\pi$
$942$	528.418	+	528.418i	0.560954	+	0.560954i
$943$	−838.272	+	838.272i	−0.888942	+	0.888942i
$944$		−	168.906i		−	0.178926i
$945$		0			0
$946$	25.2367			0.0266772
$947$	200.458	+	200.458i	0.211677	+	0.211677i	0.804979	−	0.593303i	$-0.202176\pi$
$947$	200.458	+	200.458i	0.211677	+	0.211677i	−0.593303	+	0.804979i	$0.702176\pi$
$948$	130.710	−	130.710i	0.137879	−	0.137879i
$949$		−	142.515i		−	0.150174i
$950$		0			0
$951$	−67.3848			−0.0708567
$952$	371.727	+	371.727i	0.390469	+	0.390469i
$953$	−47.5261	+	47.5261i	−0.0498700	+	0.0498700i	−0.731602	−	0.681732i	$-0.761227\pi$
$953$	−47.5261	+	47.5261i	−0.0498700	+	0.0498700i	0.681732	+	0.731602i	$0.261227\pi$
$954$			195.658i			0.205092i
$955$		0			0
$956$	503.482			0.526655
$957$	5.80456	+	5.80456i	0.00606537	+	0.00606537i
$958$	21.8319	−	21.8319i	0.0227890	−	0.0227890i
$959$		−	337.455i		−	0.351883i
$960$		0			0
$961$	186.424			0.193990
$962$	−171.661	−	171.661i	−0.178442	−	0.178442i
$963$	333.048	−	333.048i	0.345844	−	0.345844i
$964$		−	137.514i		−	0.142650i
$965$		0			0
$966$	848.720			0.878592
$967$	−758.498	−	758.498i	−0.784382	−	0.784382i	0.196185	−	0.980567i	$-0.437145\pi$
$967$	−758.498	−	758.498i	−0.784382	−	0.784382i	−0.980567	+	0.196185i	$0.937145\pi$
$968$	−241.885	+	241.885i	−0.249882	+	0.249882i
$969$		−	89.5732i		−	0.0924388i
$970$		0			0
$971$	453.787			0.467340			0.233670	−	0.972316i	$-0.424926\pi$
$971$	453.787			0.467340			0.233670	+	0.972316i	$0.424926\pi$
$972$	22.0454	+	22.0454i	0.0226805	+	0.0226805i
$973$	1116.45	−	1116.45i	1.14743	−	1.14743i
$974$		−	163.440i		−	0.167803i
$975$		0			0
$976$	−190.429			−0.195112
$977$	−1272.97	−	1272.97i	−1.30293	−	1.30293i	−0.926405	−	0.376529i	$-0.877117\pi$
$977$	−1272.97	−	1272.97i	−1.30293	−	1.30293i	−0.376529	−	0.926405i	$-0.622883\pi$
$978$	−234.580	+	234.580i	−0.239857	+	0.239857i
$979$			0.461254i			0.000471149i
$980$		0			0
$981$	486.120			0.495535
$982$	29.1488	+	29.1488i	0.0296831	+	0.0296831i
$983$	463.989	−	463.989i	0.472013	−	0.472013i	−0.430553	−	0.902565i	$-0.641681\pi$
$983$	463.989	−	463.989i	0.472013	−	0.472013i	0.902565	+	0.430553i	$0.141681\pi$
$984$		−	153.439i		−	0.155934i
$985$		0			0
$986$	−568.546			−0.576619
$987$	−312.490	−	312.490i	−0.316606	−	0.316606i
$988$	−17.0972	+	17.0972i	−0.0173048	+	0.0173048i
$989$			2821.89i			2.85327i
$990$		0			0
$991$	386.294			0.389802			0.194901	−	0.980823i	$-0.437561\pi$
$991$	386.294			0.389802			0.194901	+	0.980823i	$0.437561\pi$
$992$	−135.495	−	135.495i	−0.136587	−	0.136587i
$993$	−746.519	+	746.519i	−0.751781	+	0.751781i
$994$		−	1658.95i		−	1.66896i
$995$		0			0
$996$	401.459			0.403071
$997$	207.306	+	207.306i	0.207930	+	0.207930i	0.803387	−	0.595457i	$-0.203029\pi$
$997$	207.306	+	207.306i	0.207930	+	0.207930i	−0.595457	+	0.803387i	$0.703029\pi$
$998$	−379.995	+	379.995i	−0.380756	+	0.380756i
$999$			187.926i			0.188114i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.3.f.b.307.4	yes	16
5.2	odd	4		750.3.f.c.193.5	yes	16
5.3	odd	4	inner	750.3.f.b.193.4	✓	16
5.4	even	2		750.3.f.c.307.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.3.f.b.193.4	✓	16	5.3	odd	4	inner
750.3.f.b.307.4	yes	16	1.1	even	1	trivial
750.3.f.c.193.5	yes	16	5.2	odd	4
750.3.f.c.307.5	yes	16	5.4	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	750.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +2.44949 q^{6} +(6.47296 + 6.47296i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +0.239358 q^{11} +(-2.44949 - 2.44949i) q^{12} +(3.35623 - 3.35623i) q^{13} -12.9459i q^{14} -4.00000 q^{16} +(14.3569 + 14.3569i) q^{17} +(-3.00000 + 3.00000i) q^{18} +2.54707i q^{19} -15.8554 q^{21} +(-0.239358 - 0.239358i) q^{22} +(26.7643 - 26.7643i) q^{23} +4.89898i q^{24} -6.71247 q^{26} +(3.67423 + 3.67423i) q^{27} +(-12.9459 + 12.9459i) q^{28} -19.8004i q^{29} -33.8737 q^{31} +(4.00000 + 4.00000i) q^{32} +(-0.293153 + 0.293153i) q^{33} -28.7138i q^{34} +6.00000 q^{36} +(25.5735 + 25.5735i) q^{37} +(2.54707 - 2.54707i) q^{38} +8.22106i q^{39} -31.3205 q^{41} +(15.8554 + 15.8554i) q^{42} +(-52.7173 + 52.7173i) q^{43} +0.478717i q^{44} -53.5286 q^{46} +(19.7087 + 19.7087i) q^{47} +(4.89898 - 4.89898i) q^{48} +34.7983i q^{49} -35.1671 q^{51} +(6.71247 + 6.71247i) q^{52} +(32.6096 - 32.6096i) q^{53} -7.34847i q^{54} +25.8918 q^{56} +(-3.11952 - 3.11952i) q^{57} +(-19.8004 + 19.8004i) q^{58} +42.2264i q^{59} +47.6073 q^{61} +(33.8737 + 33.8737i) q^{62} +(19.4189 - 19.4189i) q^{63} -8.00000i q^{64} +0.586306 q^{66} +(86.4226 + 86.4226i) q^{67} +(-28.7138 + 28.7138i) q^{68} +65.5589i q^{69} +128.144 q^{71} +(-6.00000 - 6.00000i) q^{72} +(21.2313 - 21.2313i) q^{73} -51.1470i q^{74} -5.09415 q^{76} +(1.54936 + 1.54936i) q^{77} +(8.22106 - 8.22106i) q^{78} +53.3620i q^{79} -9.00000 q^{81} +(31.3205 + 31.3205i) q^{82} +(-81.9475 + 81.9475i) q^{83} -31.7109i q^{84} +105.435 q^{86} +(24.2505 + 24.2505i) q^{87} +(0.478717 - 0.478717i) q^{88} +1.92704i q^{89} +43.4495 q^{91} +(53.5286 + 53.5286i) q^{92} +(41.4866 - 41.4866i) q^{93} -39.4174i q^{94} -9.79796 q^{96} +(-37.1612 - 37.1612i) q^{97} +(34.7983 - 34.7983i) q^{98} -0.718075i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} + 24 q^{7} + 32 q^{8} - 24 q^{11} - 48 q^{13} - 64 q^{16} - 16 q^{17} - 48 q^{18} - 48 q^{21} + 24 q^{22} + 104 q^{23} + 96 q^{26} - 48 q^{28} + 200 q^{31} + 64 q^{32} - 48 q^{33} + 96 q^{36}+ \cdots - 224 q^{98}+O(q^{100}) \) 16 * q - 16 * q^2 + 24 * q^7 + 32 * q^8 - 24 * q^11 - 48 * q^13 - 64 * q^16 - 16 * q^17 - 48 * q^18 - 48 * q^21 + 24 * q^22 + 104 * q^23 + 96 * q^26 - 48 * q^28 + 200 * q^31 + 64 * q^32 - 48 * q^33 + 96 * q^36 - 128 * q^37 + 56 * q^38 - 192 * q^41 + 48 * q^42 + 88 * q^43 - 208 * q^46 + 16 * q^47 - 48 * q^51 - 96 * q^52 - 160 * q^53 + 96 * q^56 + 48 * q^57 + 24 * q^58 - 24 * q^61 - 200 * q^62 + 72 * q^63 + 96 * q^66 + 264 * q^67 + 32 * q^68 + 176 * q^71 - 96 * q^72 + 32 * q^73 - 112 * q^76 + 32 * q^77 + 96 * q^78 - 144 * q^81 + 192 * q^82 - 288 * q^83 - 176 * q^86 - 168 * q^87 - 48 * q^88 + 32 * q^91 + 208 * q^92 + 144 * q^93 - 48 * q^97 - 224 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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