LMFDB - Embedded newform 375.3.k.a.343.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,3,Mod(7,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 17]))

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

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

chi := DirichletCharacter("375.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	375.k (of order $20$, degree $8$, not 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:	$10.2180099135$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			343.7
Character	$\chi$	$=$	375.343
Dual form			375.3.k.a.82.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.202100 - 1.27601i) q^{2} +(-1.54327 + 0.786335i) q^{3} +(2.21687 + 0.720305i) q^{4} +(0.691476 + 2.12814i) q^{6} +(-1.27981 + 1.27981i) q^{7} +(3.71321 - 7.28759i) q^{8} +(1.76336 - 2.42705i) q^{9} +O(q^{10})$	\(q+(0.202100 - 1.27601i) q^{2} +(-1.54327 + 0.786335i) q^{3} +(2.21687 + 0.720305i) q^{4} +(0.691476 + 2.12814i) q^{6} +(-1.27981 + 1.27981i) q^{7} +(3.71321 - 7.28759i) q^{8} +(1.76336 - 2.42705i) q^{9} +(-2.26637 + 1.64661i) q^{11} +(-3.98763 + 0.631578i) q^{12} +(-2.80131 - 17.6867i) q^{13} +(1.37440 + 1.89170i) q^{14} +(-1.00546 - 0.730511i) q^{16} +(24.2628 + 12.3625i) q^{17} +(-2.74057 - 2.74057i) q^{18} +(8.64024 - 2.80738i) q^{19} +(0.968731 - 2.98145i) q^{21} +(1.64306 + 3.22469i) q^{22} +(24.8036 + 3.92850i) q^{23} +14.1665i q^{24} -23.1346 q^{26} +(-0.812857 + 5.13218i) q^{27} +(-3.75903 + 1.91532i) q^{28} +(27.5633 + 8.95587i) q^{29} +(-14.3903 - 44.2887i) q^{31} +(21.9985 - 21.9985i) q^{32} +(2.20283 - 4.32329i) q^{33} +(20.6782 - 28.4611i) q^{34} +(5.65735 - 4.11030i) q^{36} +(31.3477 - 4.96498i) q^{37} +(-1.83606 - 11.5924i) q^{38} +(18.2309 + 25.0926i) q^{39} +(11.2150 + 8.14820i) q^{41} +(-3.60858 - 1.83866i) q^{42} +(-27.8178 - 27.8178i) q^{43} +(-6.21031 + 2.01785i) q^{44} +(10.0256 - 30.8556i) q^{46} +(-18.8125 - 36.9215i) q^{47} +(2.12612 + 0.336745i) q^{48} +45.7242i q^{49} -47.1651 q^{51} +(6.52972 - 41.2270i) q^{52} +(-28.1946 + 14.3659i) q^{53} +(6.38443 + 2.07443i) q^{54} +(4.57452 + 14.0789i) q^{56} +(-11.1267 + 11.1267i) q^{57} +(16.9983 - 33.3611i) q^{58} +(18.6844 - 25.7169i) q^{59} +(36.7017 - 26.6654i) q^{61} +(-59.4210 + 9.41137i) q^{62} +(0.849404 + 5.36292i) q^{63} +(-26.5465 - 36.5381i) q^{64} +(-5.07137 - 3.68456i) q^{66} +(86.9965 + 44.3269i) q^{67} +(44.8827 + 44.8827i) q^{68} +(-41.3677 + 13.4412i) q^{69} +(-1.13108 + 3.48112i) q^{71} +(-11.1396 - 21.8628i) q^{72} +(-76.0348 - 12.0427i) q^{73} -41.0033i q^{74} +21.1765 q^{76} +(0.793169 - 5.00787i) q^{77} +(35.7029 - 18.1915i) q^{78} +(-133.301 - 43.3122i) q^{79} +(-2.78115 - 8.55951i) q^{81} +(12.6637 - 12.6637i) q^{82} +(-9.52910 + 18.7019i) q^{83} +(4.29510 - 5.91170i) q^{84} +(-41.1177 + 29.8738i) q^{86} +(-49.5799 + 7.85269i) q^{87} +(3.58433 + 22.6306i) q^{88} +(98.0657 + 134.976i) q^{89} +(26.2208 + 19.0505i) q^{91} +(52.1566 + 26.5751i) q^{92} +(57.0338 + 57.0338i) q^{93} +(-50.9142 + 16.5430i) q^{94} +(-16.6514 + 51.2478i) q^{96} +(-16.0242 - 31.4493i) q^{97} +(58.3445 + 9.24086i) q^{98} +8.40416i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{2} + 4 q^{7} + 12 q^{8}+O(q^{10}) $ 80 * q - 4 * q^2 + 4 * q^7 + 12 * q^8	$ 80 q - 4 q^{2} + 4 q^{7} + 12 q^{8} + 24 q^{12} - 32 q^{13} + 80 q^{16} + 100 q^{17} + 48 q^{18} - 100 q^{19} + 100 q^{22} + 96 q^{23} - 40 q^{26} - 196 q^{28} + 200 q^{29} - 636 q^{32} - 216 q^{33} + 100 q^{34} - 120 q^{36} + 184 q^{37} + 564 q^{38} + 160 q^{41} + 12 q^{42} + 472 q^{43} - 700 q^{44} + 288 q^{47} + 48 q^{48} - 620 q^{52} - 304 q^{53} - 72 q^{57} - 1272 q^{58} + 800 q^{59} - 240 q^{61} - 1212 q^{62} + 12 q^{63} + 100 q^{64} + 80 q^{67} - 104 q^{68} - 36 q^{72} + 116 q^{73} + 88 q^{77} + 120 q^{78} + 200 q^{79} + 180 q^{81} + 168 q^{82} + 1264 q^{83} - 1200 q^{84} + 876 q^{87} + 212 q^{88} - 1500 q^{89} + 1504 q^{92} + 648 q^{93} - 200 q^{94} + 60 q^{96} + 260 q^{97} + 92 q^{98}+O(q^{100}) $ 80 * q - 4 * q^2 + 4 * q^7 + 12 * q^8 + 24 * q^12 - 32 * q^13 + 80 * q^16 + 100 * q^17 + 48 * q^18 - 100 * q^19 + 100 * q^22 + 96 * q^23 - 40 * q^26 - 196 * q^28 + 200 * q^29 - 636 * q^32 - 216 * q^33 + 100 * q^34 - 120 * q^36 + 184 * q^37 + 564 * q^38 + 160 * q^41 + 12 * q^42 + 472 * q^43 - 700 * q^44 + 288 * q^47 + 48 * q^48 - 620 * q^52 - 304 * q^53 - 72 * q^57 - 1272 * q^58 + 800 * q^59 - 240 * q^61 - 1212 * q^62 + 12 * q^63 + 100 * q^64 + 80 * q^67 - 104 * q^68 - 36 * q^72 + 116 * q^73 + 88 * q^77 + 120 * q^78 + 200 * q^79 + 180 * q^81 + 168 * q^82 + 1264 * q^83 - 1200 * q^84 + 876 * q^87 + 212 * q^88 - 1500 * q^89 + 1504 * q^92 + 648 * q^93 - 200 * q^94 + 60 * q^96 + 260 * q^97 + 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{11}{20}\right)$	$1$

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 $

$2$	0.202100	−	1.27601i	0.101050	−	0.638005i	−0.884229	−	0.467053i	$-0.845316\pi$
$2$	0.202100	−	1.27601i	0.101050	−	0.638005i	0.985279	−	0.170952i	$-0.0546842\pi$
$3$	−1.54327	+	0.786335i	−0.514423	+	0.262112i
$3$	−1.54327	+	0.786335i	−0.514423	+	0.262112i
$4$	2.21687	+	0.720305i	0.554218	+	0.180076i
$5$		0			0
$5$		0			0
$6$	0.691476	+	2.12814i	0.115246	+	0.354691i
$7$	−1.27981	+	1.27981i	−0.182830	+	0.182830i	−0.792588	−	0.609758i	$-0.791267\pi$
$7$	−1.27981	+	1.27981i	−0.182830	+	0.182830i	0.609758	+	0.792588i	$0.291267\pi$
$8$	3.71321	−	7.28759i	0.464152	−	0.910949i
$9$	1.76336	−	2.42705i	0.195928	−	0.269672i
$10$		0			0
$11$	−2.26637	+	1.64661i	−0.206033	+	0.149692i	−0.686017	−	0.727585i	$-0.740643\pi$
$11$	−2.26637	+	1.64661i	−0.206033	+	0.149692i	0.479984	+	0.877277i	$0.340643\pi$
$12$	−3.98763	+	0.631578i	−0.332302	+	0.0526315i
$13$	−2.80131	−	17.6867i	−0.215485	−	1.36052i	−0.823826	−	0.566843i	$-0.808165\pi$
$13$	−2.80131	−	17.6867i	−0.215485	−	1.36052i	0.608341	−	0.793676i	$-0.291835\pi$
$14$	1.37440	+	1.89170i	0.0981714	+	0.135121i
$15$		0			0
$16$	−1.00546	−	0.730511i	−0.0628414	−	0.0456569i
$17$	24.2628	+	12.3625i	1.42722	+	0.727206i	0.985457	−	0.169924i	$-0.0543523\pi$
$17$	24.2628	+	12.3625i	1.42722	+	0.727206i	0.441766	+	0.897131i	$0.354352\pi$
$18$	−2.74057	−	2.74057i	−0.152254	−	0.152254i
$19$	8.64024	−	2.80738i	0.454749	−	0.147757i	−0.0726811	−	0.997355i	$-0.523156\pi$
$19$	8.64024	−	2.80738i	0.454749	−	0.147757i	0.527430	+	0.849598i	$0.323156\pi$
$20$		0			0
$21$	0.968731	−	2.98145i	0.0461301	−	0.141974i
$22$	1.64306	+	3.22469i	0.0746846	+	0.146577i
$23$	24.8036	+	3.92850i	1.07842	+	0.170804i	0.670274	−	0.742114i	$-0.266177\pi$
$23$	24.8036	+	3.92850i	1.07842	+	0.170804i	0.408142	+	0.912918i	$0.366177\pi$
$24$			14.1665i			0.590273i
$25$		0			0
$26$	−23.1346			−0.889792
$27$	−0.812857	+	5.13218i	−0.0301058	+	0.190081i
$28$	−3.75903	+	1.91532i	−0.134251	+	0.0684043i
$29$	27.5633	+	8.95587i	0.950459	+	0.308823i	0.742902	−	0.669400i	$-0.233449\pi$
$29$	27.5633	+	8.95587i	0.950459	+	0.308823i	0.207557	+	0.978223i	$0.433449\pi$
$30$		0			0
$31$	−14.3903	−	44.2887i	−0.464202	−	1.42867i	−0.859983	−	0.510322i	$-0.829526\pi$
$31$	−14.3903	−	44.2887i	−0.464202	−	1.42867i	0.395781	−	0.918345i	$-0.370474\pi$
$32$	21.9985	−	21.9985i	0.687454	−	0.687454i
$33$	2.20283	−	4.32329i	0.0667523	−	0.131009i
$34$	20.6782	−	28.4611i	0.608182	−	0.837090i
$35$		0			0
$36$	5.65735	−	4.11030i	0.157149	−	0.114175i
$37$	31.3477	−	4.96498i	0.847234	−	0.134189i	0.282302	−	0.959326i	$-0.408902\pi$
$37$	31.3477	−	4.96498i	0.847234	−	0.134189i	0.564933	+	0.825137i	$0.308902\pi$
$38$	−1.83606	−	11.5924i	−0.0483172	−	0.305063i
$39$	18.2309	+	25.0926i	0.467458	+	0.643401i
$40$		0			0
$41$	11.2150	+	8.14820i	0.273537	+	0.198737i	0.716094	−	0.698004i	$-0.245928\pi$
$41$	11.2150	+	8.14820i	0.273537	+	0.198737i	−0.442556	+	0.896741i	$0.645928\pi$
$42$	−3.60858	−	1.83866i	−0.0859185	−	0.0437776i
$43$	−27.8178	−	27.8178i	−0.646925	−	0.646925i	0.305324	−	0.952249i	$-0.401235\pi$
$43$	−27.8178	−	27.8178i	−0.646925	−	0.646925i	−0.952249	+	0.305324i	$0.901235\pi$
$44$	−6.21031	+	2.01785i	−0.141143	+	0.0458603i
$45$		0			0
$46$	10.0256	−	30.8556i	0.217948	−	0.670774i
$47$	−18.8125	−	36.9215i	−0.400265	−	0.785564i	0.599627	−	0.800280i	$-0.295316\pi$
$47$	−18.8125	−	36.9215i	−0.400265	−	0.785564i	−0.999892	+	0.0147156i	$0.995316\pi$
$48$	2.12612	+	0.336745i	0.0442943	+	0.00701552i
$49$			45.7242i			0.933146i
$50$		0			0
$51$	−47.1651			−0.924805
$52$	6.52972	−	41.2270i	0.125572	−	0.792828i
$53$	−28.1946	+	14.3659i	−0.531974	+	0.271054i	−0.699277	−	0.714851i	$-0.746494\pi$
$53$	−28.1946	+	14.3659i	−0.531974	+	0.271054i	0.167302	+	0.985906i	$0.446494\pi$
$54$	6.38443	+	2.07443i	0.118230	+	0.0384153i
$55$		0			0
$56$	4.57452	+	14.0789i	0.0816879	+	0.251410i
$57$	−11.1267	+	11.1267i	−0.195205	+	0.195205i
$58$	16.9983	−	33.3611i	0.293074	−	0.575191i
$59$	18.6844	−	25.7169i	0.316685	−	0.435879i	−0.620767	−	0.783995i	$-0.713179\pi$
$59$	18.6844	−	25.7169i	0.316685	−	0.435879i	0.937451	+	0.348116i	$0.113179\pi$
$60$		0			0
$61$	36.7017	−	26.6654i	0.601667	−	0.437137i	−0.244803	−	0.969573i	$-0.578723\pi$
$61$	36.7017	−	26.6654i	0.601667	−	0.437137i	0.846470	+	0.532436i	$0.178723\pi$
$62$	−59.4210	+	9.41137i	−0.958404	+	0.151796i
$63$	0.849404	+	5.36292i	0.0134826	+	0.0851258i
$64$	−26.5465	−	36.5381i	−0.414788	−	0.570907i
$65$		0			0
$66$	−5.07137	−	3.68456i	−0.0768389	−	0.0558267i
$67$	86.9965	+	44.3269i	1.29846	+	0.661596i	0.960162	−	0.279444i	$-0.0901502\pi$
$67$	86.9965	+	44.3269i	1.29846	+	0.661596i	0.338294	+	0.941041i	$0.390150\pi$
$68$	44.8827	+	44.8827i	0.660040	+	0.660040i
$69$	−41.3677	+	13.4412i	−0.599531	+	0.194800i
$70$		0			0
$71$	−1.13108	+	3.48112i	−0.0159308	+	0.0490299i	−0.958706	−	0.284399i	$-0.908206\pi$
$71$	−1.13108	+	3.48112i	−0.0159308	+	0.0490299i	0.942775	+	0.333429i	$0.108206\pi$
$72$	−11.1396	−	21.8628i	−0.154717	−	0.303650i
$73$	−76.0348	−	12.0427i	−1.04157	−	0.164969i	−0.387865	−	0.921716i	$-0.626787\pi$
$73$	−76.0348	−	12.0427i	−1.04157	−	0.164969i	−0.653707	+	0.756747i	$0.726787\pi$
$74$		−	41.0033i		−	0.554099i
$75$		0			0
$76$	21.1765			0.278638
$77$	0.793169	−	5.00787i	0.0103009	−	0.0650373i
$78$	35.7029	−	18.1915i	0.457729	−	0.233225i
$79$	−133.301	−	43.3122i	−1.68736	−	0.548256i	−0.701042	−	0.713120i	$-0.747281\pi$
$79$	−133.301	−	43.3122i	−1.68736	−	0.548256i	−0.986316	+	0.164864i	$0.947281\pi$
$80$		0			0
$81$	−2.78115	−	8.55951i	−0.0343352	−	0.105673i
$82$	12.6637	−	12.6637i	0.154436	−	0.154436i
$83$	−9.52910	+	18.7019i	−0.114808	+	0.225324i	−0.941259	−	0.337685i	$-0.890356\pi$
$83$	−9.52910	+	18.7019i	−0.114808	+	0.225324i	0.826451	+	0.563009i	$0.190356\pi$
$84$	4.29510	−	5.91170i	0.0511322	−	0.0703774i
$85$		0			0
$86$	−41.1177	+	29.8738i	−0.478113	+	0.347369i
$87$	−49.5799	+	7.85269i	−0.569884	+	0.0902608i
$88$	3.58433	+	22.6306i	0.0407311	+	0.257166i
$89$	98.0657	+	134.976i	1.10186	+	1.51658i	0.832894	+	0.553433i	$0.186682\pi$
$89$	98.0657	+	134.976i	1.10186	+	1.51658i	0.268967	+	0.963149i	$0.413318\pi$
$90$		0			0
$91$	26.2208	+	19.0505i	0.288141	+	0.209347i
$92$	52.1566	+	26.5751i	0.566919	+	0.288860i
$93$	57.0338	+	57.0338i	0.613266	+	0.613266i
$94$	−50.9142	+	16.5430i	−0.541640	+	0.175990i
$95$		0			0
$96$	−16.6514	+	51.2478i	−0.173452	+	0.533832i
$97$	−16.0242	−	31.4493i	−0.165198	−	0.324220i	0.793536	−	0.608523i	$-0.208238\pi$
$97$	−16.0242	−	31.4493i	−0.165198	−	0.324220i	−0.958734	+	0.284303i	$0.908238\pi$
$98$	58.3445	+	9.24086i	0.595352	+	0.0942944i
$99$			8.40416i			0.0848905i
$100$		0			0
$101$	8.47158			0.0838770			0.0419385	−	0.999120i	$-0.486647\pi$
$101$	8.47158			0.0838770			0.0419385	+	0.999120i	$0.486647\pi$
$102$	−9.53206	+	60.1831i	−0.0934516	+	0.590030i
$103$	−132.641	+	67.5842i	−1.28778	+	0.656157i	−0.957693	−	0.287793i	$-0.907079\pi$
$103$	−132.641	+	67.5842i	−1.28778	+	0.656157i	−0.330088	+	0.943950i	$0.607079\pi$
$104$	−139.296	−	45.2599i	−1.33938	−	0.435191i
$105$		0			0
$106$	12.6329	+	38.8800i	0.119178	+	0.366792i
$107$	−107.492	+	107.492i	−1.00460	+	1.00460i	−0.00460610	+	0.999989i	$0.501466\pi$
$107$	−107.492	+	107.492i	−1.00460	+	1.00460i	−0.999989	+	0.00460610i	$0.998534\pi$
$108$	−5.49873	+	10.7919i	−0.0509142	+	0.0999248i
$109$	65.8481	−	90.6322i	0.604111	−	0.831488i	−0.391966	−	0.919980i	$-0.628205\pi$
$109$	65.8481	−	90.6322i	0.604111	−	0.831488i	0.996077	+	0.0884922i	$0.0282048\pi$
$110$		0			0
$111$	−44.4737	+	32.3121i	−0.400664	+	0.291100i
$112$	2.22172	−	0.351885i	0.0198367	−	0.00314183i
$113$	−1.99324	−	12.5848i	−0.0176393	−	0.111370i	0.977298	−	0.211871i	$-0.0679556\pi$
$113$	−1.99324	−	12.5848i	−0.0176393	−	0.111370i	−0.994937	+	0.100501i	$0.967956\pi$
$114$	11.9490	+	16.4464i	0.104816	+	0.144267i
$115$		0			0
$116$	54.6534	+	39.7080i	0.471150	+	0.342310i
$117$	−47.8663	−	24.3891i	−0.409114	−	0.208454i
$118$	−29.0388	−	29.0388i	−0.246092	−	0.246092i
$119$	−46.8734	+	15.2301i	−0.393894	+	0.127984i
$120$		0			0
$121$	−34.9660	+	107.614i	−0.288975	+	0.889373i
$122$	−26.6078	−	52.2208i	−0.218097	−	0.428039i
$123$	−23.7150	−	3.75609i	−0.192805	−	0.0305373i
$124$		−	108.548i		−	0.875384i
$125$		0			0
$126$	7.01480			0.0556730
$127$	−26.8016	+	169.219i	−0.211036	+	1.33243i	0.623649	+	0.781704i	$0.285649\pi$
$127$	−26.8016	+	169.219i	−0.211036	+	1.33243i	−0.834686	+	0.550727i	$0.814351\pi$
$128$	58.8911	−	30.0065i	0.460086	−	0.234426i
$129$	64.8044	+	21.0562i	0.502359	+	0.163226i
$130$		0			0
$131$	8.07464	+	24.8512i	0.0616385	+	0.189704i	0.977134	−	0.212624i	$-0.0682011\pi$
$131$	8.07464	+	24.8512i	0.0616385	+	0.189704i	−0.915495	+	0.402328i	$0.868201\pi$
$132$	7.99747	−	7.99747i	0.0605869	−	0.0605869i
$133$	−7.46494	+	14.6508i	−0.0561274	+	0.110156i
$134$	74.1436	−	102.050i	0.553310	−	0.761566i
$135$		0			0
$136$	180.186	−	130.913i	1.32490	−	0.962593i
$137$	−209.827	+	33.2334i	−1.53159	+	0.242579i	−0.864588	−	0.502481i	$-0.832421\pi$
$137$	−209.827	+	33.2334i	−1.53159	+	0.242579i	−0.666997	+	0.745060i	$0.732421\pi$
$138$	8.79065	+	55.5020i	0.0637004	+	0.402188i
$139$	23.5058	+	32.3529i	0.169106	+	0.232755i	0.885156	−	0.465295i	$-0.154052\pi$
$139$	23.5058	+	32.3529i	0.169106	+	0.232755i	−0.716050	+	0.698049i	$0.754052\pi$
$140$		0			0
$141$	58.0653	+	42.1869i	0.411811	+	0.299198i
$142$	4.21335	+	2.14681i	0.0296715	+	0.0151184i
$143$	35.4720	+	35.4720i	0.248056	+	0.248056i
$144$	−3.54598	+	1.15216i	−0.0246248	+	0.00800109i
$145$		0			0
$146$	−30.7333	+	94.5873i	−0.210502	+	0.647858i
$147$	−35.9545	−	70.5647i	−0.244588	−	0.480032i
$148$	73.0700	+	11.5732i	0.493717	+	0.0781970i
$149$			196.500i			1.31879i	0.751797	+	0.659394i	$0.229187\pi$
$149$			196.500i			1.31879i	−0.751797	+	0.659394i	$0.770813\pi$
$150$		0			0
$151$	171.438			1.13535			0.567677	−	0.823251i	$-0.307842\pi$
$151$	171.438			1.13535			0.567677	+	0.823251i	$0.307842\pi$
$152$	11.6240	−	73.3910i	0.0764736	−	0.482835i
$153$	72.7884	−	37.0875i	0.475741	−	0.242402i
$154$	−6.22979	−	2.02418i	−0.0404532	−	0.0131440i
$155$		0			0
$156$	22.3411	+	68.7589i	0.143212	+	0.440762i
$157$	120.559	−	120.559i	0.767894	−	0.767894i	−0.209841	−	0.977735i	$-0.567295\pi$
$157$	120.559	−	120.559i	0.767894	−	0.767894i	0.977735	+	0.209841i	$0.0672947\pi$
$158$	−82.2070	+	161.340i	−0.520297	+	1.02114i
$159$	32.2155	−	44.3408i	0.202613	−	0.278873i
$160$		0			0
$161$	−36.7716	+	26.7161i	−0.228395	+	0.165939i
$162$	−11.4841	+	1.81890i	−0.0708894	+	0.0112278i
$163$	11.0686	+	69.8841i	0.0679053	+	0.428737i	0.998097	+	0.0616630i	$0.0196404\pi$
$163$	11.0686	+	69.8841i	0.0679053	+	0.428737i	−0.930192	+	0.367074i	$0.880360\pi$
$164$	18.9931	+	26.1418i	0.115812	+	0.159401i
$165$		0			0
$166$	21.9380	+	15.9389i	0.132157	+	0.0960173i
$167$	104.454	+	53.2219i	0.625473	+	0.318694i	0.737843	−	0.674972i	$-0.235844\pi$
$167$	104.454	+	53.2219i	0.625473	+	0.318694i	−0.112371	+	0.993666i	$0.535844\pi$
$168$	−18.1305	−	18.1305i	−0.107919	−	0.107919i
$169$	−144.245	+	46.8681i	−0.853522	+	0.277326i
$170$		0			0
$171$	8.42215	−	25.9207i	0.0492523	−	0.151583i
$172$	−41.6311	−	81.7057i	−0.242041	−	0.475033i
$173$	22.3007	+	3.53209i	0.128906	+	0.0204167i	0.220554	−	0.975375i	$-0.429213\pi$
$173$	22.3007	+	3.53209i	0.128906	+	0.0204167i	−0.0916480	+	0.995791i	$0.529213\pi$
$174$			64.8515i			0.372710i
$175$		0			0
$176$	3.48162			0.0197819
$177$	−8.61298	+	54.3802i	−0.0486609	+	0.307233i
$178$	192.049	−	97.8541i	1.07893	−	0.549742i
$179$	−239.985	−	77.9757i	−1.34070	−	0.435619i	−0.451144	−	0.892451i	$-0.648984\pi$
$179$	−239.985	−	77.9757i	−1.34070	−	0.435619i	−0.889553	+	0.456833i	$0.848984\pi$
$180$		0			0
$181$	−81.2286	−	249.996i	−0.448777	−	1.38119i	−0.878288	−	0.478131i	$-0.841314\pi$
$181$	−81.2286	−	249.996i	−0.448777	−	1.38119i	0.429512	−	0.903061i	$-0.358686\pi$
$182$	29.6079	−	29.6079i	0.162681	−	0.162681i
$183$	−35.6727	+	70.0116i	−0.194933	+	0.382577i
$184$	120.730	−	166.171i	0.656142	−	0.903103i
$185$		0			0
$186$	84.3021	−	61.2491i	0.453237	−	0.329296i
$187$	−75.3447	+	11.9334i	−0.402913	+	0.0638151i
$188$	−15.1100	−	95.4009i	−0.0803725	−	0.507452i
$189$	−5.52791	−	7.60851i	−0.0292482	−	0.0402567i
$190$		0			0
$191$	−285.982	−	207.778i	−1.49729	−	1.08784i	−0.971445	−	0.237264i	$-0.923749\pi$
$191$	−285.982	−	207.778i	−1.49729	−	1.08784i	−0.525844	−	0.850581i	$-0.676251\pi$
$192$	69.6995	+	35.5136i	0.363018	+	0.184967i
$193$	−123.500	−	123.500i	−0.639896	−	0.639896i	0.310633	−	0.950530i	$-0.399459\pi$
$193$	−123.500	−	123.500i	−0.639896	−	0.639896i	−0.950530	+	0.310633i	$0.899459\pi$
$194$	−43.3681	+	14.0912i	−0.223547	+	0.0726348i
$195$		0			0
$196$	−32.9354	+	101.365i	−0.168038	+	0.517166i
$197$	35.4963	+	69.6653i	0.180184	+	0.353631i	0.963378	−	0.268146i	$-0.0864110\pi$
$197$	35.4963	+	69.6653i	0.180184	+	0.353631i	−0.783194	+	0.621777i	$0.786411\pi$
$198$	10.7238	+	1.69848i	0.0541605	+	0.00857818i
$199$		−	123.408i		−	0.620143i	−0.950713	−	0.310071i	$-0.899647\pi$
$199$		−	123.408i		−	0.620143i	0.950713	−	0.310071i	$-0.100353\pi$
$200$		0			0
$201$	−169.115			−0.841367
$202$	1.71211	−	10.8098i	0.00847577	−	0.0535139i
$203$	−46.7376	+	23.8140i	−0.230235	+	0.117310i
$204$	−104.559	−	33.9732i	−0.512543	−	0.166535i
$205$		0			0
$206$	59.4312	+	182.910i	0.288501	+	0.887915i
$207$	53.2722	−	53.2722i	0.257353	−	0.257353i
$208$	−10.1038	+	19.8297i	−0.0485758	+	0.0953353i
$209$	−14.9593	+	20.5897i	−0.0715755	+	0.0985153i
$210$		0			0
$211$	−302.644	+	219.884i	−1.43433	+	1.04210i	−0.445141	+	0.895461i	$0.646846\pi$
$211$	−302.644	+	219.884i	−1.43433	+	1.04210i	−0.989190	+	0.146641i	$0.953154\pi$
$212$	−72.8517	+	11.5386i	−0.343640	+	0.0544272i
$213$	−0.991758	−	6.26171i	−0.00465614	−	0.0293977i
$214$	115.436	+	158.885i	0.539422	+	0.742451i
$215$		0			0
$216$	34.3829	+	24.9807i	0.159180	+	0.115651i
$217$	75.0979	+	38.2643i	0.346073	+	0.176333i
$218$	−102.340	−	102.340i	−0.469448	−	0.469448i
$219$	126.812	−	41.2036i	0.579049	−	0.188144i
$220$		0			0
$221$	150.685	−	463.761i	0.681833	−	2.09847i
$222$	32.2423	+	63.2792i	0.145236	+	0.285041i
$223$	−99.0917	−	15.6946i	−0.444357	−	0.0703793i	−0.0697536	−	0.997564i	$-0.522221\pi$
$223$	−99.0917	−	15.6946i	−0.444357	−	0.0703793i	−0.374604	+	0.927185i	$0.622221\pi$
$224$			56.3078i			0.251374i
$225$		0			0
$226$	−16.4612			−0.0728371
$227$	−3.69131	+	23.3060i	−0.0162613	+	0.102670i	−0.994484	−	0.104888i	$-0.966552\pi$
$227$	−3.69131	+	23.3060i	−0.0162613	+	0.102670i	0.978223	+	0.207558i	$0.0665515\pi$
$228$	−32.6810	+	16.6518i	−0.143338	+	0.0730342i
$229$	−67.7925	−	22.0271i	−0.296037	−	0.0961883i	0.157233	−	0.987562i	$-0.449743\pi$
$229$	−67.7925	−	22.0271i	−0.296037	−	0.0961883i	−0.453270	+	0.891373i	$0.649743\pi$
$230$		0			0
$231$	2.71379	+	8.35219i	0.0117480	+	0.0361566i
$232$	167.615	−	167.615i	0.722479	−	0.722479i
$233$	104.284	−	204.669i	0.447571	−	0.878407i	−0.551452	−	0.834207i	$-0.685926\pi$
$233$	104.284	−	204.669i	0.447571	−	0.878407i	0.999023	−	0.0442006i	$-0.0140741\pi$
$234$	−40.7945	+	56.1489i	−0.174336	+	0.239952i
$235$		0			0
$236$	59.9449	−	43.5525i	0.254004	−	0.184544i
$237$	239.778	−	37.9770i	1.01172	−	0.160241i
$238$	9.96062	+	62.8889i	0.0418514	+	0.264239i
$239$	178.631	+	245.864i	0.747410	+	1.02872i	0.998158	+	0.0606692i	$0.0193235\pi$
$239$	178.631	+	245.864i	0.747410	+	1.02872i	−0.250748	+	0.968052i	$0.580677\pi$
$240$		0			0
$241$	−62.1539	−	45.1575i	−0.257900	−	0.187375i	0.451321	−	0.892362i	$-0.350953\pi$
$241$	−62.1539	−	45.1575i	−0.257900	−	0.187375i	−0.709221	+	0.704986i	$0.750953\pi$
$242$	130.250	+	66.3657i	0.538223	+	0.274239i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$	100.570	−	32.6772i	0.412173	−	0.133923i
$245$		0			0
$246$	−9.58561	+	29.5015i	−0.0389659	+	0.119925i
$247$	−73.8574	−	144.953i	−0.299018	−	0.586856i
$248$	−376.192	−	59.5830i	−1.51690	−	0.240254i
$249$		−	36.3551i		−	0.146005i
$250$		0			0
$251$	−3.29750			−0.0131375			−0.00656873	−	0.999978i	$-0.502091\pi$
$251$	−3.29750			−0.0131375			−0.00656873	+	0.999978i	$0.502091\pi$
$252$	−1.97992	+	12.5007i	−0.00785683	+	0.0496061i
$253$	−62.6827	+	31.9384i	−0.247758	+	0.126239i
$254$	210.508	+	68.3982i	0.828772	+	0.269284i
$255$		0			0
$256$	−82.2119	−	253.022i	−0.321140	−	0.988368i
$257$	168.641	−	168.641i	0.656192	−	0.656192i	−0.298285	−	0.954477i	$-0.596415\pi$
$257$	168.641	−	168.641i	0.656192	−	0.656192i	0.954477	+	0.298285i	$0.0964146\pi$
$258$	39.9649	−	78.4355i	0.154903	−	0.304014i
$259$	−33.7648	+	46.4733i	−0.130366	+	0.179434i
$260$		0			0
$261$	70.3403	−	51.1052i	0.269503	−	0.195805i
$262$	33.3422	−	5.28089i	0.127260	−	0.0201561i
$263$	−16.3632	−	103.313i	−0.0622174	−	0.392825i	−0.999071	−	0.0431023i	$-0.986276\pi$
$263$	−16.3632	−	103.313i	−0.0622174	−	0.392825i	0.936853	−	0.349723i	$-0.113724\pi$
$264$	−23.3268	−	32.1066i	−0.0883591	−	0.121616i
$265$		0			0
$266$	17.1859	+	12.4863i	0.0646085	+	0.0469408i
$267$	−257.478	−	131.191i	−0.964336	−	0.491354i
$268$	160.931	+	160.931i	0.600489	+	0.600489i
$269$	315.804	−	102.611i	1.17399	−	0.381453i	0.343860	−	0.939021i	$-0.388265\pi$
$269$	315.804	−	102.611i	1.17399	−	0.381453i	0.830131	+	0.557568i	$0.188265\pi$
$270$		0			0
$271$	−48.6583	+	149.755i	−0.179551	+	0.552601i	−0.999812	−	0.0193883i	$-0.993828\pi$
$271$	−48.6583	+	149.755i	−0.179551	+	0.552601i	0.820261	+	0.571989i	$0.193828\pi$
$272$	−15.3644	−	30.1543i	−0.0564866	−	0.110861i
$273$	−55.4458	−	8.78176i	−0.203098	−	0.0321676i
$274$			274.458i			1.00167i
$275$		0			0
$276$	−101.389			−0.367350
$277$	−78.0548	+	492.819i	−0.281786	+	1.77913i	0.288295	+	0.957541i	$0.406911\pi$
$277$	−78.0548	+	492.819i	−0.281786	+	1.77913i	−0.570082	+	0.821588i	$0.693089\pi$
$278$	46.0331	−	23.4551i	0.165587	−	0.0843707i
$279$	−132.866	−	43.1708i	−0.476222	−	0.154734i
$280$		0			0
$281$	11.1228	+	34.2324i	0.0395828	+	0.121823i	0.968895	−	0.247471i	$-0.0795994\pi$
$281$	11.1228	+	34.2324i	0.0395828	+	0.121823i	−0.929313	+	0.369294i	$0.879599\pi$
$282$	65.5659	−	65.5659i	0.232503	−	0.232503i
$283$	193.095	−	378.969i	0.682313	−	1.33911i	−0.246709	−	0.969090i	$-0.579349\pi$
$283$	193.095	−	378.969i	0.682313	−	1.33911i	0.929022	−	0.370025i	$-0.120651\pi$
$284$	−5.01494	+	6.90247i	−0.0176582	+	0.0243045i
$285$		0			0
$286$	52.4315	−	38.0937i	0.183327	−	0.133195i
$287$	−24.7813	+	3.92497i	−0.0863458	+	0.0136758i
$288$	−14.6003	−	92.1828i	−0.0506955	−	0.320079i
$289$	265.981	+	366.092i	0.920350	+	1.26675i
$290$		0			0
$291$	49.4594	+	35.9343i	0.169964	+	0.123486i
$292$	−159.885	−	81.4654i	−0.547551	−	0.278991i
$293$	−14.8732	−	14.8732i	−0.0507618	−	0.0507618i	0.681270	−	0.732032i	$-0.261428\pi$
$293$	−14.8732	−	14.8732i	−0.0507618	−	0.0507618i	−0.732032	+	0.681270i	$0.761428\pi$
$294$	−97.3076	+	31.6172i	−0.330978	+	0.107541i
$295$		0			0
$296$	80.2178	−	246.885i	0.271006	−	0.834071i
$297$	−6.60848	−	12.9699i	−0.0222508	−	0.0436696i
$298$	250.735	+	39.7126i	0.841393	+	0.133264i
$299$		−	449.699i		−	1.50401i
$300$		0			0
$301$	71.2029			0.236554
$302$	34.6477	−	218.757i	0.114728	−	0.724361i
$303$	−13.0739	+	6.66150i	−0.0431483	+	0.0219851i
$304$	−10.7383	−	3.48907i	−0.0353232	−	0.0114772i
$305$		0			0
$306$	−32.6135	−	100.374i	−0.106580	−	0.328020i
$307$	53.7073	−	53.7073i	0.174942	−	0.174942i	−0.614205	−	0.789147i	$-0.710523\pi$
$307$	53.7073	−	53.7073i	0.174942	−	0.174942i	0.789147	+	0.614205i	$0.210523\pi$
$308$	5.36555	−	10.5305i	0.0174206	−	0.0341899i
$309$	151.558	−	208.601i	0.490478	−	0.675085i
$310$		0			0
$311$	−161.560	+	117.380i	−0.519485	+	0.377428i	−0.816410	−	0.577473i	$-0.804039\pi$
$311$	−161.560	+	117.380i	−0.519485	+	0.377428i	0.296925	+	0.954901i	$0.404039\pi$
$312$	250.560	−	39.6848i	0.803077	−	0.127195i
$313$	26.3462	+	166.343i	0.0841730	+	0.531447i	0.993359	+	0.115057i	$0.0367051\pi$
$313$	26.3462	+	166.343i	0.0841730	+	0.531447i	−0.909186	+	0.416390i	$0.863295\pi$
$314$	−129.470	−	178.200i	−0.412324	−	0.567516i
$315$		0			0
$316$	−264.314	−	192.035i	−0.836436	−	0.607706i
$317$	270.200	+	137.674i	0.852366	+	0.434302i	0.824872	−	0.565320i	$-0.191247\pi$
$317$	270.200	+	137.674i	0.852366	+	0.434302i	0.0274941	+	0.999622i	$0.491247\pi$
$318$	−50.0686	−	50.0686i	−0.157448	−	0.157448i
$319$	−77.2155	+	25.0888i	−0.242055	+	0.0786484i
$320$		0			0
$321$	81.3641	−	250.413i	0.253471	−	0.780103i
$322$	26.6585	+	52.3202i	0.0827903	+	0.162485i
$323$	244.343	+	38.7001i	0.756478	+	0.119814i
$324$		−	20.9786i		−	0.0647488i
$325$		0			0
$326$	91.4098			0.280398
$327$	−30.3541	+	191.648i	−0.0928261	+	0.586081i
$328$	101.025	−	51.4746i	0.308002	−	0.156935i
$329$	71.3289	+	23.1762i	0.216805	+	0.0704442i
$330$		0			0
$331$	134.681	+	414.505i	0.406890	+	1.25228i	0.919306	+	0.393543i	$0.128751\pi$
$331$	134.681	+	414.505i	0.406890	+	1.25228i	−0.512416	+	0.858737i	$0.671249\pi$
$332$	−34.5959	+	34.5959i	−0.104204	+	0.104204i
$333$	43.2268	−	84.8374i	0.129810	−	0.254767i
$334$	89.0218	−	122.528i	0.266532	−	0.366850i
$335$		0			0
$336$	−3.15200	+	2.29007i	−0.00938096	+	0.00681567i
$337$	166.306	−	26.3402i	0.493488	−	0.0781609i	0.0952699	−	0.995451i	$-0.469629\pi$
$337$	166.306	−	26.3402i	0.493488	−	0.0781609i	0.398218	+	0.917291i	$0.369629\pi$
$338$	30.6522	+	193.530i	0.0906869	+	0.572575i
$339$	12.9720	+	17.8544i	0.0382654	+	0.0526678i
$340$		0			0
$341$	105.540	+	76.6793i	0.309501	+	0.224866i
$342$	−31.3730	−	15.9853i	−0.0917338	−	0.0467407i
$343$	−121.229	−	121.229i	−0.353437	−	0.353437i
$344$	−306.018	+	99.4312i	−0.889587	+	0.289044i
$345$		0			0
$346$	9.01396	−	27.7421i	0.0260519	−	0.0801795i
$347$	17.6279	+	34.5967i	0.0508008	+	0.0997022i	0.915011	−	0.403428i	$-0.132182\pi$
$347$	17.6279	+	34.5967i	0.0508008	+	0.0997022i	−0.864210	+	0.503131i	$0.832182\pi$
$348$	−115.569	−	18.3043i	−0.332094	−	0.0525985i
$349$			220.279i			0.631173i	0.948897	+	0.315586i	$0.102201\pi$
$349$			220.279i			0.631173i	−0.948897	+	0.315586i	$0.897799\pi$
$350$		0			0
$351$	93.0486			0.265096
$352$	−13.6337	+	86.0798i	−0.0387321	+	0.244545i
$353$	268.455	−	136.785i	0.760495	−	0.387492i	−0.0303249	−	0.999540i	$-0.509654\pi$
$353$	268.455	−	136.785i	0.760495	−	0.387492i	0.790820	+	0.612048i	$0.209654\pi$
$354$	67.6490	+	21.9805i	0.191099	+	0.0620917i
$355$		0			0
$356$	120.175	+	369.861i	0.337571	+	1.03894i
$357$	60.3623	−	60.3623i	0.169082	−	0.169082i
$358$	−147.999	+	290.464i	−0.413404	+	0.811351i
$359$	140.056	−	192.770i	0.390127	−	0.536964i	−0.568105	−	0.822956i	$-0.692323\pi$
$359$	140.056	−	192.770i	0.390127	−	0.536964i	0.958232	+	0.285992i	$0.0923232\pi$
$360$		0			0
$361$	−225.283	+	163.678i	−0.624052	+	0.453400i
$362$	−335.413	+	53.1243i	−0.926556	+	0.146752i
$363$	−30.6589	−	193.573i	−0.0844597	−	0.533258i
$364$	44.4060	+	61.1196i	0.121994	+	0.167911i
$365$		0			0
$366$	82.1260	+	59.6680i	0.224388	+	0.163027i
$367$	−624.401	−	318.148i	−1.70136	−	0.866888i	−0.985714	−	0.168430i	$-0.946130\pi$
$367$	−624.401	−	318.148i	−1.70136	−	0.866888i	−0.715650	−	0.698459i	$-0.753870\pi$
$368$	−22.0692	−	22.0692i	−0.0599707	−	0.0599707i
$369$	39.5522	−	12.8513i	0.107188	−	0.0348273i
$370$		0			0
$371$	17.6982	−	54.4693i	0.0477039	−	0.146818i
$372$	85.3548	+	167.518i	0.229448	+	0.450318i
$373$	544.089	+	86.1752i	1.45868	+	0.231033i	0.834830	−	0.550508i	$-0.185566\pi$
$373$	544.089	+	86.1752i	1.45868	+	0.231033i	0.623854	+	0.781541i	$0.285566\pi$
$374$			98.5522i			0.263509i
$375$		0			0
$376$	−338.924			−0.901393
$377$	81.1869	−	512.594i	0.215350	−	1.35966i
$378$	−10.8257	+	5.51598i	−0.0286395	+	0.0145925i
$379$	322.888	+	104.913i	0.851946	+	0.276814i	0.702261	−	0.711920i	$-0.252174\pi$
$379$	322.888	+	104.913i	0.851946	+	0.276814i	0.149685	+	0.988734i	$0.452174\pi$
$380$		0			0
$381$	−91.7004	−	282.225i	−0.240684	−	0.740748i
$382$	−322.924	+	322.924i	−0.845351	+	0.845351i
$383$	−107.231	+	210.453i	−0.279977	+	0.549486i	−0.987579	−	0.157126i	$-0.949777\pi$
$383$	−107.231	+	210.453i	−0.279977	+	0.549486i	0.707601	+	0.706612i	$0.249777\pi$
$384$	−67.2896	+	92.6162i	−0.175233	+	0.241188i
$385$		0			0
$386$	−182.547	+	132.628i	−0.472918	+	0.343595i
$387$	−116.568	+	18.4625i	−0.301209	+	0.0477068i
$388$	−12.8705	−	81.2614i	−0.0331715	−	0.209437i
$389$	−415.555	−	571.963i	−1.06827	−	1.47034i	−0.871820	−	0.489827i	$-0.837060\pi$
$389$	−415.555	−	571.963i	−1.06827	−	1.47034i	−0.196446	−	0.980515i	$-0.562940\pi$
$390$		0			0
$391$	553.237	+	401.950i	1.41493	+	1.02801i
$392$	333.219	+	169.784i	0.850049	+	0.433122i
$393$	−32.0027	−	32.0027i	−0.0814318	−	0.0814318i
$394$	96.0674	−	31.2142i	0.243826	−	0.0792238i
$395$		0			0
$396$	−6.05356	+	18.6309i	−0.0152868	+	0.0470478i
$397$	83.9994	+	164.858i	0.211585	+	0.415260i	0.972270	−	0.233862i	$-0.0751365\pi$
$397$	83.9994	+	164.858i	0.211585	+	0.415260i	−0.760684	+	0.649122i	$0.775136\pi$
$398$	−157.470	−	24.9408i	−0.395654	−	0.0626654i
$399$		−	28.4800i		−	0.0713785i
$400$		0			0
$401$	652.180			1.62639			0.813193	−	0.581995i	$-0.197728\pi$
$401$	652.180			1.62639			0.813193	+	0.581995i	$0.197728\pi$
$402$	−34.1781	+	215.792i	−0.0850202	+	0.536796i
$403$	−743.011	+	378.583i	−1.84370	+	0.939412i
$404$	18.7804	+	6.10212i	0.0464861	+	0.0151043i
$405$		0			0
$406$	20.9412	+	64.4504i	0.0515793	+	0.158745i
$407$	−62.8700	+	62.8700i	−0.154472	+	0.154472i
$408$	−175.134	+	343.720i	−0.429250	+	0.842450i
$409$	−355.310	+	489.043i	−0.868730	+	1.19570i	0.110687	+	0.993855i	$0.464695\pi$
$409$	−355.310	+	489.043i	−0.868730	+	1.19570i	−0.979417	+	0.201849i	$0.935305\pi$
$410$		0			0
$411$	297.687	−	216.282i	0.724300	−	0.526235i
$412$	−342.730	+	54.2831i	−0.831869	+	0.131755i
$413$	9.00022	+	56.8251i	0.0217923	+	0.137591i
$414$	−57.2095	−	78.7421i	−0.138187	−	0.190198i
$415$		0			0
$416$	−450.707	−	327.458i	−1.08343	−	0.787158i
$417$	−61.7159	−	31.4458i	−0.148000	−	0.0754097i
$418$	23.2494	+	23.2494i	0.0556205	+	0.0556205i
$419$	−282.385	+	91.7525i	−0.673950	+	0.218980i	−0.625945	−	0.779867i	$-0.715286\pi$
$419$	−282.385	+	91.7525i	−0.673950	+	0.218980i	−0.0480053	+	0.998847i	$0.515286\pi$
$420$		0			0
$421$	−170.801	+	525.672i	−0.405704	+	1.24863i	0.514602	+	0.857429i	$0.327940\pi$
$421$	−170.801	+	525.672i	−0.405704	+	1.24863i	−0.920306	+	0.391199i	$0.872060\pi$
$422$	219.409	+	430.615i	0.519927	+	1.02041i
$423$	−122.783	−	19.4470i	−0.290268	−	0.0459740i
$424$			258.815i			0.610412i
$425$		0			0
$426$	−8.19044			−0.0192264
$427$	−12.8446	+	81.0978i	−0.0300811	+	0.189925i
$428$	−315.722	+	160.868i	−0.737668	+	0.375861i
$429$	−82.6357	−	26.8500i	−0.192624	−	0.0625874i
$430$		0			0
$431$	69.6929	+	214.493i	0.161700	+	0.497663i	0.998778	−	0.0494214i	$-0.0157377\pi$
$431$	69.6929	+	214.493i	0.161700	+	0.497663i	−0.837078	+	0.547084i	$0.815738\pi$
$432$	4.56641	−	4.56641i	0.0105704	−	0.0105704i
$433$	87.9085	−	172.530i	0.203022	−	0.398453i	−0.766937	−	0.641723i	$-0.778220\pi$
$433$	87.9085	−	172.530i	0.203022	−	0.398453i	0.969959	+	0.243270i	$0.0782200\pi$
$434$	64.0028	−	88.0924i	0.147472	−	0.202978i
$435$		0			0
$436$	211.260	−	153.489i	0.484540	−	0.352039i
$437$	225.337	−	35.6899i	0.515646	−	0.0816704i
$438$	−26.9476	−	170.140i	−0.0615241	−	0.388448i
$439$	−424.325	−	584.033i	−0.966571	−	1.33037i	−0.943760	−	0.330631i	$-0.892738\pi$
$439$	−424.325	−	584.033i	−0.966571	−	1.33037i	−0.0228109	−	0.999740i	$-0.507262\pi$
$440$		0			0
$441$	110.975	+	80.6280i	0.251644	+	0.182830i
$442$	−561.310	−	286.002i	−1.26993	−	0.647063i
$443$	324.984	+	324.984i	0.733599	+	0.733599i	0.971331	−	0.237732i	$-0.0764040\pi$
$443$	324.984	+	324.984i	0.733599	+	0.733599i	−0.237732	+	0.971331i	$0.576404\pi$
$444$	−121.867	+	39.5970i	−0.274475	+	0.0891825i
$445$		0			0
$446$	−40.0529	+	123.270i	−0.0898046	+	0.276390i
$447$	−154.514	−	303.252i	−0.345670	−	0.678415i
$448$	80.7362	+	12.7874i	0.180215	+	0.0285432i
$449$			76.3546i			0.170055i	0.996379	+	0.0850274i	$0.0270978\pi$
$449$			76.3546i			0.170055i	−0.996379	+	0.0850274i	$0.972902\pi$
$450$		0			0
$451$	−38.8343			−0.0861072
$452$	4.64615	−	29.3347i	0.0102791	−	0.0648997i
$453$	−264.576	+	134.808i	−0.584052	+	0.297589i
$454$	28.9927	+	9.42030i	0.0638606	+	0.0207496i
$455$		0			0
$456$	39.7709	+	122.402i	0.0872169	+	0.268426i
$457$	−307.229	+	307.229i	−0.672273	+	0.672273i	−0.958240	−	0.285967i	$-0.907685\pi$
$457$	−307.229	+	307.229i	−0.672273	+	0.672273i	0.285967	+	0.958240i	$0.407685\pi$
$458$	−41.8077	+	82.0522i	−0.0912831	+	0.179153i
$459$	−83.1688	+	114.472i	−0.181196	+	0.249394i
$460$		0			0
$461$	−338.793	+	246.148i	−0.734909	+	0.533943i	−0.891113	−	0.453782i	$-0.850074\pi$
$461$	−338.793	+	246.148i	−0.734909	+	0.533943i	0.156204	+	0.987725i	$0.450074\pi$
$462$	11.2059	−	1.77484i	0.0242552	−	0.00384165i
$463$	53.8967	+	340.290i	0.116408	+	0.734969i	0.974983	+	0.222281i	$0.0713502\pi$
$463$	53.8967	+	340.290i	0.116408	+	0.734969i	−0.858575	+	0.512688i	$0.828650\pi$
$464$	−21.1715	−	29.1401i	−0.0456283	−	0.0628019i
$465$		0			0
$466$	−240.084	−	174.431i	−0.515201	−	0.374315i
$467$	−157.765	−	80.3853i	−0.337827	−	0.172131i	0.276845	−	0.960915i	$-0.410711\pi$
$467$	−157.765	−	80.3853i	−0.337827	−	0.172131i	−0.614671	+	0.788783i	$0.710711\pi$
$468$	−88.5459	−	88.5459i	−0.189201	−	0.189201i
$469$	−168.069	+	54.6089i	−0.358356	+	0.116437i
$470$		0			0
$471$	−91.2555	+	280.856i	−0.193748	+	0.596296i
$472$	−118.035	−	231.656i	−0.250074	−	0.490797i
$473$	108.850	+	17.2402i	0.230128	+	0.0364486i
$474$		−	313.634i		−	0.661674i
$475$		0			0
$476$	−114.883			−0.241350
$477$	−14.8504	+	93.7620i	−0.0311330	+	0.196566i
$478$	349.827	−	178.246i	0.731855	−	0.372899i
$479$	−342.771	−	111.373i	−0.715597	−	0.232512i	−0.0714837	−	0.997442i	$-0.522773\pi$
$479$	−342.771	−	111.373i	−0.715597	−	0.232512i	−0.644113	+	0.764930i	$0.722773\pi$
$480$		0			0
$481$	−175.629	−	540.530i	−0.365133	−	1.12376i
$482$	−70.1827	+	70.1827i	−0.145607	+	0.145607i
$483$	35.7406	−	70.1449i	0.0739971	−	0.145227i
$484$	−155.030	+	213.381i	−0.320310	+	0.440869i
$485$		0			0
$486$	16.2928	−	11.8374i	0.0335242	−	0.0243568i
$487$	432.824	−	68.5526i	0.888756	−	0.140765i	0.304671	−	0.952458i	$-0.401453\pi$
$487$	432.824	−	68.5526i	0.888756	−	0.140765i	0.584085	+	0.811692i	$0.301453\pi$
$488$	−58.0449	−	366.481i	−0.118945	−	0.750986i
$489$	−72.0341	−	99.1464i	−0.147309	−	0.202753i
$490$		0			0
$491$	480.359	+	349.001i	0.978328	+	0.710797i	0.957334	−	0.288983i	$-0.0933170\pi$
$491$	480.359	+	349.001i	0.978328	+	0.710797i	0.0209938	+	0.999780i	$0.493317\pi$
$492$	−49.8676	−	25.4088i	−0.101357	−	0.0516439i
$493$	558.046	+	558.046i	1.13194	+	1.13194i
$494$	−199.888	+	64.9477i	−0.404632	+	0.131473i
$495$		0			0
$496$	−17.8845	+	55.0428i	−0.0360575	+	0.110973i
$497$	−3.00760	−	5.90274i	−0.00605151	−	0.0118767i
$498$	−46.3895	−	7.34737i	−0.0931516	−	0.0147538i
$499$		−	471.200i		−	0.944289i	−0.881521	−	0.472145i	$-0.843480\pi$
$499$		−	471.200i		−	0.944289i	0.881521	−	0.472145i	$-0.156520\pi$
$500$		0			0
$501$	−203.051			−0.405291
$502$	−0.666426	+	4.20765i	−0.00132754	+	0.00838177i
$503$	−245.179	+	124.925i	−0.487434	+	0.248360i	−0.680394	−	0.732847i	$-0.738191\pi$
$503$	−245.179	+	124.925i	−0.487434	+	0.248360i	0.192960	+	0.981207i	$0.438191\pi$
$504$	42.2368	+	13.7236i	0.0838032	+	0.0272293i
$505$		0			0
$506$	28.0856	+	86.4385i	0.0555051	+	0.170827i
$507$	185.755	−	185.755i	0.366381	−	0.366381i
$508$	−181.305	+	355.831i	−0.356899	+	0.700454i
$509$	−99.5633	+	137.037i	−0.195606	+	0.269228i	−0.895542	−	0.444977i	$-0.853212\pi$
$509$	−99.5633	+	137.037i	−0.195606	+	0.269228i	0.699936	+	0.714205i	$0.253212\pi$
$510$		0			0
$511$	112.722	−	81.8977i	0.220592	−	0.160269i
$512$	−78.3486	+	12.4092i	−0.153025	+	0.0242367i
$513$	7.38471	+	46.6253i	0.0143952	+	0.0908874i
$514$	−181.105	−	249.270i	−0.352345	−	0.484961i
$515$		0			0
$516$	128.496	+	93.3578i	0.249023	+	0.180926i
$517$	103.431	+	52.7009i	0.200061	+	0.101936i
$518$	52.4765	+	52.4765i	0.101306	+	0.101306i
$519$	−37.1934	+	12.0849i	−0.0716637	+	0.0232849i
$520$		0			0
$521$	222.241	−	683.987i	0.426566	−	1.31284i	−0.474920	−	0.880029i	$-0.657523\pi$
$521$	222.241	−	683.987i	0.426566	−	1.31284i	0.901487	−	0.432807i	$-0.142477\pi$
$522$	−50.9949	−	100.083i	−0.0976915	−	0.191730i
$523$	−154.804	−	24.5185i	−0.295991	−	0.0468804i	0.00667264	−	0.999978i	$-0.497876\pi$
$523$	−154.804	−	24.5185i	−0.295991	−	0.0468804i	−0.302664	+	0.953097i	$0.597876\pi$
$524$			60.9081i			0.116237i
$525$		0			0
$526$	−135.135			−0.256911
$527$	198.371	−	1252.47i	0.376416	−	2.37660i
$528$	−5.37307	+	2.73772i	−0.0101763	+	0.00518507i
$529$	96.6746	+	31.4115i	0.182750	+	0.0593790i
$530$		0			0
$531$	−29.4689	−	90.6959i	−0.0554970	−	0.170802i
$532$	−27.1018	+	27.1018i	−0.0509433	+	0.0509433i
$533$	112.698	−	221.183i	0.211442	−	0.414978i
$534$	−219.438	+	302.030i	−0.410932	+	0.565600i
$535$		0			0
$536$	646.073	−	469.400i	1.20536	−	0.875746i
$537$	431.676	−	68.3707i	0.803866	−	0.127320i
$538$	−67.1084	−	423.706i	−0.124737	−	0.787558i
$539$	−75.2900	−	103.628i	−0.139685	−	0.192259i
$540$		0			0
$541$	−16.6570	−	12.1020i	−0.0307893	−	0.0223698i	0.572284	−	0.820055i	$-0.306057\pi$
$541$	−16.6570	−	12.1020i	−0.0307893	−	0.0223698i	−0.603073	+	0.797686i	$0.706057\pi$
$542$	181.255	+	92.3539i	0.334418	+	0.170395i
$543$	321.938	+	321.938i	0.592888	+	0.592888i
$544$	805.702	−	261.789i	1.48107	−	0.481229i
$545$		0			0
$546$	−22.4112	+	68.9746i	−0.0410462	+	0.126327i
$547$	114.427	+	224.575i	0.209190	+	0.410558i	0.971632	−	0.236499i	$-0.0759999\pi$
$547$	114.427	+	224.575i	0.209190	+	0.410558i	−0.762442	+	0.647056i	$0.776000\pi$
$548$	−489.098	−	77.4655i	−0.892515	−	0.141360i
$549$		−	136.097i		−	0.247901i
$550$		0			0
$551$	263.296			0.477852
$552$	−55.6532	+	351.381i	−0.100821	+	0.636559i
$553$	226.032	−	115.169i	0.408737	−	0.208262i
$554$	613.067	+	199.197i	1.10662	+	0.359562i
$555$		0			0
$556$	28.8053	+	88.6536i	0.0518081	+	0.159449i
$557$	−587.229	+	587.229i	−1.05427	+	1.05427i	−0.0558301	+	0.998440i	$0.517781\pi$
$557$	−587.229	+	587.229i	−1.05427	+	1.05427i	−0.998440	+	0.0558301i	$0.982219\pi$
$558$	−81.9386	+	160.813i	−0.146843	+	0.288196i
$559$	−414.080	+	569.932i	−0.740751	+	1.01956i
$560$		0			0
$561$	106.893	−	77.6626i	0.190541	−	0.138436i
$562$	45.9287	−	7.27440i	0.0817237	−	0.0129438i
$563$	142.523	+	899.852i	0.253148	+	1.59832i	0.706983	+	0.707230i	$0.250056\pi$
$563$	142.523	+	899.852i	0.253148	+	1.59832i	−0.453835	+	0.891086i	$0.649944\pi$
$564$	98.3359	+	135.348i	0.174354	+	0.239978i
$565$		0			0
$566$	−444.544	−	322.980i	−0.785414	−	0.570636i
$567$	14.5139	+	7.39519i	0.0255977	+	0.0130427i
$568$	21.1690	+	21.1690i	0.0372694	+	0.0372694i
$569$	882.800	−	286.839i	1.55149	−	0.504111i	0.596974	−	0.802260i	$-0.296369\pi$
$569$	882.800	−	286.839i	1.55149	−	0.504111i	0.954519	+	0.298150i	$0.0963695\pi$
$570$		0			0
$571$	−93.5955	+	288.057i	−0.163915	+	0.504479i	−0.998955	−	0.0457110i	$-0.985445\pi$
$571$	−93.5955	+	288.057i	−0.163915	+	0.504479i	0.835040	+	0.550190i	$0.185445\pi$
$572$	53.0862	+	104.188i	0.0928081	+	0.182146i
$573$	604.731	+	95.7799i	1.05538	+	0.167155i
$574$			32.4143i			0.0564710i
$575$		0			0
$576$	−135.491			−0.235227
$577$	96.9341	−	612.018i	0.167997	−	1.06069i	−0.749226	−	0.662314i	$-0.769574\pi$
$577$	96.9341	−	612.018i	0.167997	−	1.06069i	0.917223	−	0.398375i	$-0.130426\pi$
$578$	520.891	−	265.407i	0.901196	−	0.459182i
$579$	287.706	+	93.4814i	0.496902	+	0.161453i
$580$		0			0
$581$	−11.7395	−	36.1303i	−0.0202056	−	0.0621864i
$582$	55.8483	−	55.8483i	0.0959593	−	0.0959593i
$583$	40.2444	−	78.9840i	0.0690298	−	0.135479i
$584$	−370.096	+	509.393i	−0.633726	+	0.872249i
$585$		0			0
$586$	−21.9842	+	15.9725i	−0.0375157	+	0.0272568i
$587$	−1039.32	+	164.612i	−1.77056	+	0.280429i	−0.954646	−	0.297743i	$-0.903766\pi$
$587$	−1039.32	+	164.612i	−1.77056	+	0.280429i	−0.815915	+	0.578173i	$0.803766\pi$
$588$	−28.8784	−	182.331i	−0.0491129	−	0.310087i
$589$	−248.671	−	342.266i	−0.422191	−	0.581096i
$590$		0			0
$591$	−109.561	−	79.6004i	−0.185382	−	0.134688i
$592$	−35.1459	−	17.9077i	−0.0593680	−	0.0302495i
$593$	−707.610	−	707.610i	−1.19327	−	1.19327i	−0.976143	−	0.217129i	$-0.930331\pi$
$593$	−707.610	−	707.610i	−1.19327	−	1.19327i	−0.217129	−	0.976143i	$-0.569669\pi$
$594$	−17.8852	+	5.81127i	−0.0301098	+	0.00978328i
$595$		0			0
$596$	−141.540	+	435.614i	−0.237483	+	0.730896i
$597$	97.0403	+	190.452i	0.162547	+	0.319016i
$598$	−573.820	−	90.8842i	−0.959566	−	0.151980i
$599$			170.870i			0.285259i	0.989776	+	0.142630i	$0.0455558\pi$
$599$			170.870i			0.285259i	−0.989776	+	0.142630i	$0.954444\pi$
$600$		0			0
$601$	236.135			0.392903			0.196452	−	0.980513i	$-0.437058\pi$
$601$	236.135			0.392903			0.196452	+	0.980513i	$0.437058\pi$
$602$	14.3901	−	90.8555i	0.0239038	−	0.150923i
$603$	260.990	−	132.981i	0.432819	−	0.220532i
$604$	380.057	+	123.488i	0.629233	+	0.204450i
$605$		0			0
$606$	5.85789	+	18.0287i	0.00966649	+	0.0297504i
$607$	295.001	−	295.001i	0.485998	−	0.485998i	−0.421042	−	0.907041i	$-0.638336\pi$
$607$	295.001	−	295.001i	0.485998	−	0.485998i	0.907041	+	0.421042i	$0.138336\pi$
$608$	128.314	−	251.831i	0.211043	−	0.414195i
$609$	53.4029	−	73.5028i	0.0876895	−	0.120694i
$610$		0			0
$611$	−600.322	+	436.160i	−0.982524	+	0.713845i
$612$	188.077	−	29.7884i	0.307315	−	0.0486739i
$613$	−112.568	−	710.725i	−0.183634	−	1.15942i	−0.891482	−	0.453056i	$-0.850334\pi$
$613$	−112.568	−	710.725i	−0.183634	−	1.15942i	0.707848	−	0.706365i	$-0.249666\pi$
$614$	−57.6768	−	79.3852i	−0.0939361	−	0.129292i
$615$		0			0
$616$	−33.5501	−	24.3756i	−0.0544645	−	0.0395708i
$617$	732.469	+	373.211i	1.18715	+	0.604881i	0.932154	−	0.362062i	$-0.117927\pi$
$617$	732.469	+	373.211i	1.18715	+	0.604881i	0.254992	+	0.966943i	$0.417927\pi$
$618$	−235.547	−	235.547i	−0.381144	−	0.381144i
$619$	360.303	−	117.070i	0.582073	−	0.189127i	−0.00315628	−	0.999995i	$-0.501005\pi$
$619$	360.303	−	117.070i	0.582073	−	0.189127i	0.585229	+	0.810868i	$0.301005\pi$
$620$		0			0
$621$	−40.3235	+	124.103i	−0.0649332	+	0.199844i
$622$	117.127	+	229.874i	0.188307	+	0.369573i
$623$	−298.249	−	47.2379i	−0.478730	−	0.0758234i
$624$		−	38.5476i		−	0.0617749i
$625$		0			0
$626$	217.580			0.347572
$627$	6.89581	−	43.5384i	0.0109981	−	0.0694393i
$628$	354.104	−	180.425i	0.563860	−	0.287301i
$629$	821.961	+	267.071i	1.30678	+	0.424597i
$630$		0			0
$631$	−102.961	−	316.882i	−0.163171	−	0.502190i	0.835725	−	0.549148i	$-0.185048\pi$
$631$	−102.961	−	316.882i	−0.163171	−	0.502190i	−0.998897	+	0.0469574i	$0.985048\pi$
$632$	−810.618	+	810.618i	−1.28262	+	1.28262i
$633$	294.158	−	577.319i	0.464705	−	0.912036i
$634$	230.280	−	316.954i	0.363218	−	0.499927i
$635$		0			0
$636$	103.357	−	75.0929i	0.162510	−	0.118071i
$637$	808.712	−	128.087i	1.26956	−	0.201079i
$638$	16.4083	+	103.598i	0.0257184	+	0.162380i
$639$	6.45435	+	8.88365i	0.0101007	+	0.0139024i
$640$		0			0
$641$	−340.793	−	247.601i	−0.531659	−	0.386273i	0.289319	−	0.957233i	$-0.406571\pi$
$641$	−340.793	−	247.601i	−0.531659	−	0.386273i	−0.820978	+	0.570960i	$0.806571\pi$
$642$	−303.086	−	154.430i	−0.472096	−	0.240545i
$643$	−456.781	−	456.781i	−0.710391	−	0.710391i	0.256226	−	0.966617i	$-0.417521\pi$
$643$	−456.781	−	456.781i	−0.710391	−	0.710391i	−0.966617	+	0.256226i	$0.917521\pi$
$644$	−100.762	+	32.7394i	−0.156462	+	0.0508376i
$645$		0			0
$646$	98.7633	−	303.962i	0.152884	−	0.470530i
$647$	19.6573	+	38.5797i	0.0303823	+	0.0596286i	0.905699	−	0.423922i	$-0.139347\pi$
$647$	19.6573	+	38.5797i	0.0303823	+	0.0596286i	−0.875316	+	0.483551i	$0.839347\pi$
$648$	−72.7052	−	11.5154i	−0.112199	−	0.0177706i
$649$			89.0498i			0.137211i
$650$		0			0
$651$	−145.985			−0.224247
$652$	−25.8003	+	162.897i	−0.0395710	+	0.249842i
$653$	−41.4282	+	21.1087i	−0.0634428	+	0.0323257i	−0.485424	−	0.874279i	$-0.661335\pi$
$653$	−41.4282	+	21.1087i	−0.0634428	+	0.0323257i	0.421981	+	0.906605i	$0.361335\pi$
$654$	238.411	+	77.4643i	0.364542	+	0.118447i
$655$		0			0
$656$	−5.32394	−	16.3854i	−0.00811577	−	0.0249778i
$657$	−163.305	+	163.305i	−0.248561	+	0.248561i
$658$	43.9886	−	86.3324i	0.0668519	−	0.131204i
$659$	−92.1880	+	126.886i	−0.139891	+	0.192543i	−0.873214	−	0.487337i	$-0.837968\pi$
$659$	−92.1880	+	126.886i	−0.139891	+	0.192543i	0.733323	+	0.679880i	$0.237968\pi$
$660$		0			0
$661$	397.805	−	289.023i	0.601824	−	0.437251i	−0.244702	−	0.969598i	$-0.578690\pi$
$661$	397.805	−	289.023i	0.601824	−	0.437251i	0.846526	+	0.532348i	$0.178690\pi$
$662$	556.131	−	88.0825i	0.840077	−	0.133055i
$663$	132.124	+	834.197i	0.199282	+	1.25822i
$664$	100.908	+	138.888i	0.151970	+	0.209169i
$665$		0			0
$666$	−99.5172	−	72.3035i	−0.149425	−	0.108564i
$667$	648.485	+	330.420i	0.972242	+	0.495382i
$668$	193.225	+	193.225i	0.289259	+	0.289259i
$669$	165.266	−	53.6983i	0.247035	−	0.0802665i
$670$		0			0
$671$	−39.2721	+	120.867i	−0.0585277	+	0.180130i
$672$	−44.2768	−	86.8981i	−0.0658881	−	0.129313i
$673$	−135.747	−	21.5002i	−0.201705	−	0.0319469i	0.0547645	−	0.998499i	$-0.482559\pi$
$673$	−135.747	−	21.5002i	−0.201705	−	0.0319469i	−0.256469	+	0.966552i	$0.582559\pi$
$674$		−	217.531i		−	0.322746i
$675$		0			0
$676$	−353.532			−0.522977
$677$	116.940	−	738.328i	0.172732	−	1.09059i	−0.737153	−	0.675726i	$-0.763830\pi$
$677$	116.940	−	738.328i	0.172732	−	1.09059i	0.909885	−	0.414861i	$-0.136170\pi$
$678$	25.4040	−	12.9440i	0.0374690	−	0.0190914i
$679$	60.7571	+	19.7412i	0.0894803	+	0.0290739i
$680$		0			0
$681$	−12.6297	−	38.8701i	−0.0185457	−	0.0570779i
$682$	119.173	−	119.173i	0.174741	−	0.174741i
$683$	76.7144	−	150.561i	0.112320	−	0.220440i	−0.828003	−	0.560724i	$-0.810523\pi$
$683$	76.7144	−	150.561i	0.112320	−	0.220440i	0.940323	+	0.340284i	$0.110523\pi$
$684$	37.3416	−	51.3964i	0.0545930	−	0.0751409i
$685$		0			0
$686$	−179.190	+	130.189i	−0.261209	+	0.189780i
$687$	121.943	−	19.3138i	0.177500	−	0.0281133i
$688$	7.64853	+	48.2909i	0.0111170	+	0.0701903i
$689$	333.068	+	458.428i	0.483407	+	0.665353i
$690$		0			0
$691$	805.662	+	585.348i	1.16594	+	0.847103i	0.990517	−	0.137391i	$-0.0438717\pi$
$691$	805.662	+	585.348i	1.16594	+	0.847103i	0.175420	+	0.984494i	$0.443872\pi$
$692$	46.8937	+	23.8935i	0.0677655	+	0.0345282i
$693$	−10.7557	−	10.7557i	−0.0155205	−	0.0155205i
$694$	47.7083	−	15.5014i	0.0687439	−	0.0223363i
$695$		0			0
$696$	−126.874	+	390.477i	−0.182290	+	0.561030i
$697$	171.376	+	336.344i	0.245876	+	0.482560i
$698$	281.078	+	44.5185i	0.402691	+	0.0637800i
$699$			397.861i			0.569186i
$700$		0			0
$701$	−444.962			−0.634753			−0.317376	−	0.948300i	$-0.602802\pi$
$701$	−444.962			−0.634753			−0.317376	+	0.948300i	$0.602802\pi$
$702$	18.8051	−	118.731i	0.0267879	−	0.169132i
$703$	256.913	−	130.904i	0.365452	−	0.186207i
$704$	120.328	+	39.0970i	0.170921	+	0.0555355i
$705$		0			0
$706$	−120.284	−	370.195i	−0.170373	−	0.524356i
$707$	−10.8420	+	10.8420i	−0.0153352	+	0.0153352i
$708$	−58.2642	+	114.350i	−0.0822941	+	0.161511i
$709$	−110.671	+	152.325i	−0.156094	+	0.214845i	−0.879900	−	0.475158i	$-0.842391\pi$
$709$	−110.671	+	152.325i	−0.156094	+	0.214845i	0.723806	+	0.690003i	$0.242391\pi$
$710$		0			0
$711$	−340.179	+	247.154i	−0.478451	+	0.347615i
$712$	1347.79	−	213.469i	1.89296	−	0.299815i
$713$	−182.942	−	1155.05i	−0.256580	−	1.61998i
$714$	−64.8236	−	89.2221i	−0.0907894	−	0.124961i
$715$		0			0
$716$	−475.849	−	345.724i	−0.664593	−	0.482855i
$717$	−469.007	−	238.971i	−0.654125	−	0.333293i
$718$	−217.671	−	217.671i	−0.303163	−	0.303163i
$719$	40.6847	−	13.2193i	0.0565852	−	0.0183856i	−0.280588	−	0.959828i	$-0.590529\pi$
$719$	40.6847	−	13.2193i	0.0565852	−	0.0183856i	0.337173	+	0.941443i	$0.390529\pi$
$720$		0			0
$721$	83.2609	−	256.251i	0.115480	−	0.355410i
$722$	163.324	+	320.542i	0.226211	+	0.443964i
$723$	131.429	+	20.8163i	0.181783	+	0.0287916i
$724$		−	612.718i		−	0.846296i
$725$		0			0
$726$	−253.196			−0.348755
$727$	−59.7654	+	377.344i	−0.0822082	+	0.519042i	0.911879	+	0.410459i	$0.134631\pi$
$727$	−59.7654	+	377.344i	−0.0822082	+	0.519042i	−0.994087	+	0.108583i	$0.965369\pi$
$728$	236.196	−	120.348i	0.324445	−	0.165313i
$729$	−25.6785	−	8.34346i	−0.0352243	−	0.0114451i
$730$		0			0
$731$	−331.039	−	1018.83i	−0.452858	−	1.39375i
$732$	−129.512	+	129.512i	−0.176928	+	0.176928i
$733$	−119.985	+	235.483i	−0.163690	+	0.321260i	−0.958253	−	0.285922i	$-0.907700\pi$
$733$	−119.985	+	235.483i	−0.163690	+	0.321260i	0.794563	+	0.607182i	$0.207700\pi$
$734$	−532.151	+	732.443i	−0.725002	+	0.997879i
$735$		0			0
$736$	632.063	−	459.220i	0.858781	−	0.623941i
$737$	−270.155	+	42.7884i	−0.366561	+	0.0580576i
$738$	−8.40486	−	53.0662i	−0.0113887	−	0.0719054i
$739$	−283.341	−	389.986i	−0.383412	−	0.527721i	0.573073	−	0.819505i	$-0.305751\pi$
$739$	−283.341	−	389.986i	−0.383412	−	0.527721i	−0.956484	+	0.291784i	$0.905751\pi$
$740$		0			0
$741$	227.964	+	165.625i	0.307643	+	0.223516i
$742$	−65.9266	−	33.5913i	−0.0888499	−	0.0452713i
$743$	−265.405	−	265.405i	−0.357207	−	0.357207i	0.505575	−	0.862783i	$-0.331280\pi$
$743$	−265.405	−	265.405i	−0.357207	−	0.357207i	−0.862783	+	0.505575i	$0.831280\pi$
$744$	627.417	−	203.860i	0.843303	−	0.274006i
$745$		0			0
$746$	219.921	−	676.847i	0.294800	−	0.907301i
$747$	28.5873	+	56.1057i	0.0382695	+	0.0751081i
$748$	−175.625	−	27.8163i	−0.234793	−	0.0371875i
$749$		−	275.138i		−	0.367340i
$750$		0			0
$751$	−518.509			−0.690425			−0.345213	−	0.938525i	$-0.612193\pi$
$751$	−518.509			−0.690425			−0.345213	+	0.938525i	$0.612193\pi$
$752$	−8.05637	+	50.8659i	−0.0107133	+	0.0676408i
$753$	5.08894	−	2.59294i	0.00675821	−	0.00344348i
$754$	−637.666	−	207.190i	−0.845711	−	0.274788i
$755$		0			0
$756$	−6.77421	−	20.8489i	−0.00896060	−	0.0275779i
$757$	378.952	−	378.952i	0.500598	−	0.500598i	−0.411026	−	0.911624i	$-0.634829\pi$
$757$	378.952	−	378.952i	0.500598	−	0.500598i	0.911624	+	0.411026i	$0.134829\pi$
$758$	199.125	−	390.805i	0.262698	−	0.515574i
$759$	71.6220	−	98.5792i	0.0943636	−	0.129880i
$760$		0			0
$761$	−280.723	+	203.957i	−0.368886	+	0.268012i	−0.756749	−	0.653706i	$-0.773214\pi$
$761$	−280.723	+	203.957i	−0.368886	+	0.268012i	0.387863	+	0.921717i	$0.373214\pi$
$762$	−378.654	+	59.9729i	−0.496922	+	0.0787047i
$763$	31.7189	+	200.265i	0.0415712	+	0.262470i
$764$	−484.322	−	666.612i	−0.633929	−	0.872529i
$765$		0			0
$766$	246.869	+	179.361i	0.322283	+	0.234152i
$767$	−507.188	−	258.425i	−0.661262	−	0.336930i
$768$	325.835	+	325.835i	0.424264	+	0.424264i
$769$	−359.323	+	116.751i	−0.467260	+	0.151822i	−0.533178	−	0.846003i	$-0.679002\pi$
$769$	−359.323	+	116.751i	−0.467260	+	0.151822i	0.0659183	+	0.997825i	$0.479002\pi$
$770$		0			0
$771$	−127.650	+	392.867i	−0.165565	+	0.509555i
$772$	−184.826	−	362.741i	−0.239412	−	0.469872i
$773$	1356.16	+	214.795i	1.75441	+	0.277871i	0.949099	−	0.314979i	$-0.101997\pi$
$773$	1356.16	+	214.795i	1.75441	+	0.277871i	0.805313	+	0.592850i	$0.201997\pi$
$774$			152.473i			0.196993i
$775$		0			0
$776$	−288.691			−0.372025
$777$	15.5646	−	98.2712i	0.0200317	−	0.126475i
$778$	−813.814	+	414.659i	−1.04603	+	0.532980i
$779$	119.776	+	38.9175i	0.153756	+	0.0499583i
$780$		0			0
$781$	−3.16860	−	9.75196i	−0.00405711	−	0.0124865i
$782$	624.702	−	624.702i	0.798851	−	0.798851i
$783$	−68.3682	+	134.180i	−0.0873157	+	0.171367i
$784$	33.4020	−	45.9739i	0.0426046	−	0.0586402i
$785$		0			0
$786$	−47.3035	+	34.3680i	−0.0601826	+	0.0437252i
$787$	−121.855	+	19.2999i	−0.154835	+	0.0245234i	−0.233370	−	0.972388i	$-0.574975\pi$
$787$	−121.855	+	19.2999i	−0.154835	+	0.0245234i	0.0785359	+	0.996911i	$0.474975\pi$
$788$	28.5103	+	180.007i	0.0361806	+	0.228435i
$789$	106.491	+	146.573i	0.134970	+	0.185770i
$790$		0			0
$791$	18.6571	+	13.5552i	0.0235868	+	0.0171368i
$792$	61.2461	+	31.2064i	0.0773309	+	0.0394021i
$793$	−574.436	−	574.436i	−0.724383	−	0.724383i
$794$	227.337	−	73.8662i	0.286318	−	0.0930305i
$795$		0			0
$796$	88.8917	−	273.580i	0.111673	−	0.343694i
$797$	132.075	+	259.211i	0.165715	+	0.325234i	0.958899	−	0.283748i	$-0.0915781\pi$
$797$	132.075	+	259.211i	0.165715	+	0.325234i	−0.793184	+	0.608982i	$0.791578\pi$
$798$	−36.3408	−	5.75581i	−0.0455398	−	0.00721280i
$799$		−	1128.39i		−	1.41225i
$800$		0			0
$801$	500.518			0.624866
$802$	131.806	−	832.188i	0.164346	−	1.03764i
$803$	192.153	−	97.9066i	0.239293	−	0.121926i
$804$	−374.906	−	121.814i	−0.466301	−	0.151510i
$805$		0			0
$806$	332.913	+	1024.60i	0.413043	+	1.27122i
$807$	−406.683	+	406.683i	−0.503945	+	0.503945i
$808$	31.4568	−	61.7374i	0.0389317	−	0.0764077i
$809$	−791.643	+	1089.60i	−0.978545	+	1.34685i	−0.0409347	+	0.999162i	$0.513034\pi$
$809$	−791.643	+	1089.60i	−0.978545	+	1.34685i	−0.937610	+	0.347689i	$0.886966\pi$
$810$		0			0
$811$	351.764	−	255.572i	0.433742	−	0.315132i	−0.349402	−	0.936973i	$-0.613615\pi$
$811$	351.764	−	255.572i	0.433742	−	0.315132i	0.783143	+	0.621841i	$0.213615\pi$
$812$	−120.765	+	19.1272i	−0.148725	+	0.0235557i
$813$	−42.6646	−	269.374i	−0.0524780	−	0.331333i
$814$	67.5166	+	92.9287i	0.0829443	+	0.114163i
$815$		0			0
$816$	47.4227	+	34.4546i	0.0581160	+	0.0422238i
$817$	−318.447	−	162.257i	−0.389776	−	0.198601i
$818$	552.215	+	552.215i	0.675079	+	0.675079i
$819$	92.4732	−	30.0464i	0.112910	−	0.0366867i
$820$		0			0
$821$	−86.2266	+	265.378i	−0.105026	+	0.323238i	−0.989737	−	0.142903i	$-0.954356\pi$
$821$	−86.2266	+	265.378i	−0.105026	+	0.323238i	0.884710	+	0.466141i	$0.154356\pi$
$822$	−215.816	−	423.562i	−0.262550	−	0.515283i
$823$	−821.134	−	130.055i	−0.997733	−	0.158025i	−0.363853	−	0.931457i	$-0.618539\pi$
$823$	−821.134	−	130.055i	−0.997733	−	0.158025i	−0.633880	+	0.773431i	$0.718539\pi$
$824$			1217.59i			1.47766i
$825$		0			0
$826$	74.3284			0.0899859
$827$	76.1777	−	480.967i	0.0921133	−	0.581580i	−0.897855	−	0.440291i	$-0.854875\pi$
$827$	76.1777	−	480.967i	0.0921133	−	0.581580i	0.989968	−	0.141289i	$-0.0451248\pi$
$828$	156.470	−	79.7253i	0.188973	−	0.0962866i
$829$	718.878	+	233.578i	0.867163	+	0.281758i	0.708617	−	0.705593i	$-0.249319\pi$
$829$	718.878	+	233.578i	0.867163	+	0.281758i	0.158546	+	0.987352i	$0.449319\pi$
$830$		0			0
$831$	−267.061	−	821.929i	−0.321373	−	0.989084i
$832$	−571.875	+	571.875i	−0.687350	+	0.687350i
$833$	−565.265	+	1109.40i	−0.678590	+	1.33181i
$834$	−52.5980	+	72.3949i	−0.0630671	+	0.0868044i
$835$		0			0
$836$	−47.9937	+	34.8694i	−0.0574087	+	0.0417099i
$837$	238.995	−	37.8530i	0.285537	−	0.0452247i
$838$	60.0070	+	378.869i	0.0716074	+	0.452111i
$839$	170.239	+	234.314i	0.202907	+	0.279278i	0.898328	−	0.439325i	$-0.144782\pi$
$839$	170.239	+	234.314i	0.202907	+	0.279278i	−0.695421	+	0.718602i	$0.744782\pi$
$840$		0			0
$841$	−0.854051	−	0.620504i	−0.00101552	−	0.000737817i
$842$	636.244	+	324.182i	0.755634	+	0.385015i
$843$	−44.0835	−	44.0835i	−0.0522936	−	0.0522936i
$844$	−829.305	+	269.458i	−0.982589	+	0.319263i
$845$		0			0
$846$	−49.6291	+	152.743i	−0.0586632	+	0.180547i
$847$	−92.9759	−	182.475i	−0.109771	−	0.215437i
$848$	38.8431	+	6.15214i	0.0458055	+	0.00725488i
$849$			736.689i			0.867713i
$850$		0			0
$851$	797.039			0.936591
$852$	2.31174	−	14.5958i	0.00271332	−	0.0171312i
$853$	−458.038	+	233.382i	−0.536973	+	0.273601i	−0.701375	−	0.712792i	$-0.747430\pi$
$853$	−458.038	+	233.382i	−0.536973	+	0.273601i	0.164403	+	0.986393i	$0.447430\pi$
$854$	100.886	+	32.7797i	0.118133	+	0.0383837i
$855$		0			0
$856$	384.216	+	1182.50i	0.448851	+	1.38142i
$857$	−794.073	+	794.073i	−0.926572	+	0.926572i	−0.997483	−	0.0709103i	$-0.977410\pi$
$857$	−794.073	+	794.073i	−0.926572	+	0.926572i	0.0709103	+	0.997483i	$0.477410\pi$
$858$	−50.9615	+	100.018i	−0.0593957	+	0.116571i
$859$	439.811	−	605.348i	0.512004	−	0.704713i	−0.472252	−	0.881464i	$-0.656559\pi$
$859$	439.811	−	605.348i	0.512004	−	0.704713i	0.984256	+	0.176751i	$0.0565587\pi$
$860$		0			0
$861$	35.1578	−	25.5436i	0.0408337	−	0.0296674i
$862$	287.780	−	45.5798i	0.333851	−	0.0528768i
$863$	145.813	+	920.624i	0.168960	+	1.06677i	0.915761	+	0.401724i	$0.131589\pi$
$863$	145.813	+	920.624i	0.168960	+	1.06677i	−0.746801	+	0.665048i	$0.768411\pi$
$864$	95.0187	+	130.782i	0.109975	+	0.151368i
$865$		0			0
$866$	−202.384	−	147.040i	−0.233700	−	0.169793i
$867$	−698.351	−	355.828i	−0.805480	−	0.410413i
$868$	138.920	+	138.920i	0.160046	+	0.160046i
$869$	373.428	−	121.334i	0.429722	−	0.139625i
$870$		0			0
$871$	540.296	−	1662.86i	0.620317	−	1.90914i
$872$	−415.982	−	816.411i	−0.477044	−	0.936251i
$873$	−104.586	−	16.5647i	−0.119800	−	0.0189745i
$874$		−	294.746i		−	0.337238i
$875$		0			0
$876$	310.804			0.354800
$877$	20.3449	−	128.453i	0.0231983	−	0.146468i	−0.973370	−	0.229238i	$-0.926377\pi$
$877$	20.3449	−	128.453i	0.0231983	−	0.146468i	0.996569	+	0.0827696i	$0.0263766\pi$
$878$	−830.987	+	423.409i	−0.946455	+	0.482243i
$879$	34.6487	+	11.2580i	0.0394183	+	0.0128078i
$880$		0			0
$881$	−51.9927	−	160.017i	−0.0590155	−	0.181631i	0.917203	−	0.398420i	$-0.130442\pi$
$881$	−51.9927	−	160.017i	−0.0590155	−	0.181631i	−0.976218	+	0.216789i	$0.930442\pi$
$882$	125.310	−	125.310i	0.142075	−	0.142075i
$883$	1.80087	−	3.53441i	0.00203949	−	0.00400272i	−0.889985	−	0.455991i	$-0.849285\pi$
$883$	1.80087	−	3.53441i	0.00203949	−	0.00400272i	0.892024	+	0.451988i	$0.149285\pi$
$884$	668.099	−	919.559i	0.755768	−	1.04023i
$885$		0			0
$886$	480.362	−	349.004i	0.542170	−	0.393909i
$887$	−702.101	+	111.202i	−0.791546	+	0.125369i	−0.539099	−	0.842242i	$-0.681235\pi$
$887$	−702.101	+	111.202i	−0.791546	+	0.125369i	−0.252447	+	0.967611i	$0.581235\pi$
$888$	70.3366	+	444.088i	0.0792079	+	0.500099i
$889$	−182.267	−	250.869i	−0.205024	−	0.282192i
$890$		0			0
$891$	20.3973	+	14.8195i	0.0228926	+	0.0166325i
$892$	−208.369	−	106.169i	−0.233597	−	0.119024i
$893$	−266.197	−	266.197i	−0.298093	−	0.298093i
$894$	−418.179	+	135.875i	−0.467762	+	0.151985i
$895$		0			0
$896$	−36.9667	+	113.772i	−0.0412575	+	0.126978i
$897$	353.614	+	694.007i	0.394219	+	0.773698i
$898$	97.4292	+	15.4313i	0.108496	+	0.0171840i
$899$		−	1349.62i		−	1.50125i
$900$		0			0
$901$	−861.679			−0.956358
$902$	−7.84842	+	49.5530i	−0.00870113	+	0.0549368i
$903$	−109.885	+	55.9893i	−0.121689	+	0.0620037i
$904$	−99.1143	−	32.2042i	−0.109640	−	0.0356241i
$905$		0			0
$906$	118.546	+	364.846i	0.130845	+	0.402699i
$907$	126.631	−	126.631i	0.139615	−	0.139615i	−0.633845	−	0.773460i	$-0.718524\pi$
$907$	126.631	−	126.631i	0.139615	−	0.139615i	0.773460	+	0.633845i	$0.218524\pi$
$908$	−24.9706	+	49.0076i	−0.0275007	+	0.0539731i
$909$	14.9384	−	20.5610i	0.0164339	−	0.0226193i
$910$		0			0
$911$	−877.720	+	637.701i	−0.963469	+	0.700001i	−0.953954	−	0.299954i	$-0.903029\pi$
$911$	−877.720	+	637.701i	−0.963469	+	0.700001i	−0.00951505	+	0.999955i	$0.503029\pi$
$912$	19.3156	−	3.05929i	0.0211794	−	0.00335448i
$913$	−9.19836	−	58.0762i	−0.0100749	−	0.0636102i
$914$	329.936	+	454.118i	0.360980	+	0.496846i
$915$		0			0
$916$	−134.421	−	97.6626i	−0.146748	−	0.106619i
$917$	−42.1388	−	21.4708i	−0.0459529	−	0.0234142i
$918$	129.259	+	129.259i	0.140805	+	0.140805i
$919$	−863.424	+	280.543i	−0.939526	+	0.305270i	−0.738452	−	0.674306i	$-0.764443\pi$
$919$	−863.424	+	280.543i	−0.939526	+	0.305270i	−0.201073	+	0.979576i	$0.564443\pi$
$920$		0			0
$921$	−40.6529	+	125.117i	−0.0441399	+	0.135849i
$922$	245.617	+	482.050i	0.266395	+	0.522830i
$923$	64.7382	+	10.2535i	0.0701389	+	0.0111089i
$924$			20.4705i			0.0221542i
$925$		0			0
$926$	445.106			0.480676
$927$	−69.8638	+	441.103i	−0.0753655	+	0.475839i
$928$	803.368	−	409.337i	0.865698	−	0.441095i
$929$	−1502.39	−	488.157i	−1.61721	−	0.525465i	−0.645932	−	0.763395i	$-0.723531\pi$
$929$	−1502.39	−	488.157i	−1.61721	−	0.525465i	−0.971282	+	0.237930i	$0.923531\pi$
$930$		0			0
$931$	128.365	+	395.068i	0.137879	+	0.424348i
$932$	378.608	−	378.608i	0.406232	−	0.406232i
$933$	157.030	−	308.189i	0.168307	−	0.330321i
$934$	−134.457	+	185.064i	−0.143958	+	0.198141i
$935$		0			0
$936$	−355.476	+	258.268i	−0.379782	+	0.275928i
$937$	−1561.57	+	247.329i	−1.66657	+	0.263959i	−0.917268	−	0.398271i	$-0.869610\pi$
$937$	−1561.57	+	247.329i	−1.66657	+	0.263959i	−0.749301	+	0.662230i	$0.769610\pi$
$938$	35.7148	+	225.494i	0.0380754	+	0.240399i
$939$	−171.460	−	235.995i	−0.182599	−	0.251326i
$940$		0			0
$941$	911.873	+	662.515i	0.969047	+	0.704054i	0.955234	−	0.295851i	$-0.0956031\pi$
$941$	911.873	+	662.515i	0.969047	+	0.704054i	0.0138127	+	0.999905i	$0.495603\pi$
$942$	339.931	+	173.204i	0.360861	+	0.183868i
$943$	246.163	+	246.163i	0.261042	+	0.261042i
$944$	−37.5729	+	12.2082i	−0.0398018	+	0.0129324i
$945$		0			0
$946$	43.9973	−	135.410i	0.0465088	−	0.143139i
$947$	165.795	+	325.391i	0.175074	+	0.343602i	0.961824	−	0.273670i	$-0.0882377\pi$
$947$	165.795	+	325.391i	0.175074	+	0.343602i	−0.786750	+	0.617272i	$0.788238\pi$
$948$	558.911	+	88.5228i	0.589569	+	0.0933785i
$949$			1378.54i			1.45263i
$950$		0			0
$951$	−525.249			−0.552312
$952$	−63.0603	+	398.147i	−0.0662398	+	0.418221i
$953$	−444.297	+	226.381i	−0.466209	+	0.237545i	−0.671283	−	0.741201i	$-0.734257\pi$
$953$	−444.297	+	226.381i	−0.466209	+	0.237545i	0.205074	+	0.978746i	$0.434257\pi$
$954$	116.640	+	37.8986i	0.122264	+	0.0397260i
$955$		0			0
$956$	218.904	+	673.719i	0.228980	+	0.704727i
$957$	99.4360	−	99.4360i	0.103904	−	0.103904i
$958$	−211.387	+	414.870i	−0.220654	+	0.433059i
$959$	226.007	−	311.071i	0.235669	−	0.324370i
$960$		0			0
$961$	−976.942	+	709.790i	−1.01659	+	0.738595i
$962$	−725.216	+	114.863i	−0.753863	+	0.119400i
$963$	71.3417	+	450.434i	0.0740828	+	0.467740i
$964$	−105.260	−	144.878i	−0.109191	−	0.150288i
$965$		0			0
$966$	−82.2823	−	59.7816i	−0.0851784	−	0.0618857i
$967$	1282.13	+	653.279i	1.32589	+	0.675573i	0.966271	−	0.257527i	$-0.0829077\pi$
$967$	1282.13	+	653.279i	1.32589	+	0.675573i	0.359616	+	0.933100i	$0.382908\pi$
$968$	654.412	+	654.412i	0.676046	+	0.676046i
$969$	−407.517	+	132.410i	−0.420555	+	0.136646i
$970$		0			0
$971$	−415.272	+	1278.08i	−0.427675	+	1.31625i	0.472735	+	0.881204i	$0.343267\pi$
$971$	−415.272	+	1278.08i	−0.427675	+	1.31625i	−0.900410	+	0.435043i	$0.856733\pi$
$972$	16.4962	+	32.3756i	0.0169714	+	0.0333083i
$973$	−71.4885	−	11.3227i	−0.0734722	−	0.0116369i
$974$		−	566.142i		−	0.581255i
$975$		0			0
$976$	−56.3815			−0.0577680
$977$	−147.737	+	932.776i	−0.151215	+	0.954735i	0.789059	+	0.614317i	$0.210568\pi$
$977$	−147.737	+	932.776i	−0.151215	+	0.954735i	−0.940274	+	0.340418i	$0.889432\pi$
$978$	−141.070	+	71.8787i	−0.144243	+	0.0734956i
$979$	−444.506	−	144.429i	−0.454041	−	0.147527i
$980$		0			0
$981$	−103.855	−	319.633i	−0.105867	−	0.325824i
$982$	542.409	−	542.409i	0.552352	−	0.552352i
$983$	0.210533	−	0.413194i	0.000214174	−	0.000420339i	−0.890899	−	0.454201i	$-0.849925\pi$
$983$	0.210533	−	0.413194i	0.000214174	−	0.000420339i	0.891114	+	0.453780i	$0.149925\pi$
$984$	−115.432	+	158.878i	−0.117309	+	0.161462i
$985$		0			0
$986$	824.853	−	599.291i	0.836565	−	0.607800i
$987$	−128.304	+	20.3213i	−0.129994	+	0.0205890i
$988$	−59.3218	−	374.543i	−0.0600423	−	0.379092i
$989$	−580.698	−	799.262i	−0.587156	−	0.808151i
$990$		0			0
$991$	293.072	+	212.929i	0.295734	+	0.214863i	0.725751	−	0.687958i	$-0.241492\pi$
$991$	293.072	+	212.929i	0.295734	+	0.214863i	−0.430017	+	0.902821i	$0.641492\pi$
$992$	−1290.85	−	657.721i	−1.30126	−	0.663025i
$993$	−533.788	−	533.788i	−0.537551	−	0.537551i
$994$	−8.13979	+	2.64478i	−0.00818892	+	0.00266074i
$995$		0			0
$996$	26.1868	−	80.5946i	0.0262920	−	0.0809183i
$997$	−160.391	−	314.785i	−0.160874	−	0.315732i	0.796473	−	0.604674i	$-0.206697\pi$
$997$	−160.391	−	314.785i	−0.160874	−	0.315732i	−0.957347	+	0.288942i	$0.906697\pi$
$998$	−601.256	−	95.2296i	−0.602461	−	0.0954205i
$999$			164.918i			0.165083i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.3.k.a.343.7		80
5.2	odd	4		375.3.k.b.157.7		80
5.3	odd	4		375.3.k.c.157.4		80
5.4	even	2		75.3.k.a.73.4	yes	80
15.14	odd	2		225.3.r.b.73.7		80
25.9	even	10		375.3.k.c.43.4		80
25.12	odd	20	inner	375.3.k.a.82.7		80
25.13	odd	20		75.3.k.a.37.4	✓	80
25.16	even	5		375.3.k.b.43.7		80
75.38	even	20		225.3.r.b.37.7		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.37.4	✓	80	25.13	odd	20
75.3.k.a.73.4	yes	80	5.4	even	2
225.3.r.b.37.7		80	75.38	even	20
225.3.r.b.73.7		80	15.14	odd	2
375.3.k.a.82.7		80	25.12	odd	20	inner
375.3.k.a.343.7		80	1.1	even	1	trivial
375.3.k.b.43.7		80	25.16	even	5
375.3.k.b.157.7		80	5.2	odd	4
375.3.k.c.43.4		80	25.9	even	10
375.3.k.c.157.4		80	5.3	odd	4

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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	375.k (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.202100 - 1.27601i) q^{2} +(-1.54327 + 0.786335i) q^{3} +(2.21687 + 0.720305i) q^{4} +(0.691476 + 2.12814i) q^{6} +(-1.27981 + 1.27981i) q^{7} +(3.71321 - 7.28759i) q^{8} +(1.76336 - 2.42705i) q^{9} +O(q^{10})\)	\(q+(0.202100 - 1.27601i) q^{2} +(-1.54327 + 0.786335i) q^{3} +(2.21687 + 0.720305i) q^{4} +(0.691476 + 2.12814i) q^{6} +(-1.27981 + 1.27981i) q^{7} +(3.71321 - 7.28759i) q^{8} +(1.76336 - 2.42705i) q^{9} +(-2.26637 + 1.64661i) q^{11} +(-3.98763 + 0.631578i) q^{12} +(-2.80131 - 17.6867i) q^{13} +(1.37440 + 1.89170i) q^{14} +(-1.00546 - 0.730511i) q^{16} +(24.2628 + 12.3625i) q^{17} +(-2.74057 - 2.74057i) q^{18} +(8.64024 - 2.80738i) q^{19} +(0.968731 - 2.98145i) q^{21} +(1.64306 + 3.22469i) q^{22} +(24.8036 + 3.92850i) q^{23} +14.1665i q^{24} -23.1346 q^{26} +(-0.812857 + 5.13218i) q^{27} +(-3.75903 + 1.91532i) q^{28} +(27.5633 + 8.95587i) q^{29} +(-14.3903 - 44.2887i) q^{31} +(21.9985 - 21.9985i) q^{32} +(2.20283 - 4.32329i) q^{33} +(20.6782 - 28.4611i) q^{34} +(5.65735 - 4.11030i) q^{36} +(31.3477 - 4.96498i) q^{37} +(-1.83606 - 11.5924i) q^{38} +(18.2309 + 25.0926i) q^{39} +(11.2150 + 8.14820i) q^{41} +(-3.60858 - 1.83866i) q^{42} +(-27.8178 - 27.8178i) q^{43} +(-6.21031 + 2.01785i) q^{44} +(10.0256 - 30.8556i) q^{46} +(-18.8125 - 36.9215i) q^{47} +(2.12612 + 0.336745i) q^{48} +45.7242i q^{49} -47.1651 q^{51} +(6.52972 - 41.2270i) q^{52} +(-28.1946 + 14.3659i) q^{53} +(6.38443 + 2.07443i) q^{54} +(4.57452 + 14.0789i) q^{56} +(-11.1267 + 11.1267i) q^{57} +(16.9983 - 33.3611i) q^{58} +(18.6844 - 25.7169i) q^{59} +(36.7017 - 26.6654i) q^{61} +(-59.4210 + 9.41137i) q^{62} +(0.849404 + 5.36292i) q^{63} +(-26.5465 - 36.5381i) q^{64} +(-5.07137 - 3.68456i) q^{66} +(86.9965 + 44.3269i) q^{67} +(44.8827 + 44.8827i) q^{68} +(-41.3677 + 13.4412i) q^{69} +(-1.13108 + 3.48112i) q^{71} +(-11.1396 - 21.8628i) q^{72} +(-76.0348 - 12.0427i) q^{73} -41.0033i q^{74} +21.1765 q^{76} +(0.793169 - 5.00787i) q^{77} +(35.7029 - 18.1915i) q^{78} +(-133.301 - 43.3122i) q^{79} +(-2.78115 - 8.55951i) q^{81} +(12.6637 - 12.6637i) q^{82} +(-9.52910 + 18.7019i) q^{83} +(4.29510 - 5.91170i) q^{84} +(-41.1177 + 29.8738i) q^{86} +(-49.5799 + 7.85269i) q^{87} +(3.58433 + 22.6306i) q^{88} +(98.0657 + 134.976i) q^{89} +(26.2208 + 19.0505i) q^{91} +(52.1566 + 26.5751i) q^{92} +(57.0338 + 57.0338i) q^{93} +(-50.9142 + 16.5430i) q^{94} +(-16.6514 + 51.2478i) q^{96} +(-16.0242 - 31.4493i) q^{97} +(58.3445 + 9.24086i) q^{98} +8.40416i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{2} + 4 q^{7} + 12 q^{8}+O(q^{10}) \) 80 * q - 4 * q^2 + 4 * q^7 + 12 * q^8	\( 80 q - 4 q^{2} + 4 q^{7} + 12 q^{8} + 24 q^{12} - 32 q^{13} + 80 q^{16} + 100 q^{17} + 48 q^{18} - 100 q^{19} + 100 q^{22} + 96 q^{23} - 40 q^{26} - 196 q^{28} + 200 q^{29} - 636 q^{32} - 216 q^{33} + 100 q^{34} - 120 q^{36} + 184 q^{37} + 564 q^{38} + 160 q^{41} + 12 q^{42} + 472 q^{43} - 700 q^{44} + 288 q^{47} + 48 q^{48} - 620 q^{52} - 304 q^{53} - 72 q^{57} - 1272 q^{58} + 800 q^{59} - 240 q^{61} - 1212 q^{62} + 12 q^{63} + 100 q^{64} + 80 q^{67} - 104 q^{68} - 36 q^{72} + 116 q^{73} + 88 q^{77} + 120 q^{78} + 200 q^{79} + 180 q^{81} + 168 q^{82} + 1264 q^{83} - 1200 q^{84} + 876 q^{87} + 212 q^{88} - 1500 q^{89} + 1504 q^{92} + 648 q^{93} - 200 q^{94} + 60 q^{96} + 260 q^{97} + 92 q^{98}+O(q^{100}) \) 80 * q - 4 * q^2 + 4 * q^7 + 12 * q^8 + 24 * q^12 - 32 * q^13 + 80 * q^16 + 100 * q^17 + 48 * q^18 - 100 * q^19 + 100 * q^22 + 96 * q^23 - 40 * q^26 - 196 * q^28 + 200 * q^29 - 636 * q^32 - 216 * q^33 + 100 * q^34 - 120 * q^36 + 184 * q^37 + 564 * q^38 + 160 * q^41 + 12 * q^42 + 472 * q^43 - 700 * q^44 + 288 * q^47 + 48 * q^48 - 620 * q^52 - 304 * q^53 - 72 * q^57 - 1272 * q^58 + 800 * q^59 - 240 * q^61 - 1212 * q^62 + 12 * q^63 + 100 * q^64 + 80 * q^67 - 104 * q^68 - 36 * q^72 + 116 * q^73 + 88 * q^77 + 120 * q^78 + 200 * q^79 + 180 * q^81 + 168 * q^82 + 1264 * q^83 - 1200 * q^84 + 876 * q^87 + 212 * q^88 - 1500 * q^89 + 1504 * q^92 + 648 * q^93 - 200 * q^94 + 60 * q^96 + 260 * q^97 + 92 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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