LMFDB - Embedded newform 384.4.k.b.95.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,4,Mod(95,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("384.95");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	384.k (of order $4$, degree $2$, 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:	$22.6567334422$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			95.2
Character	$\chi$	$=$	384.95
Dual form			384.4.k.b.287.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.07063 - 1.13522i) q^{3} +(11.2665 + 11.2665i) q^{5} +30.2121 q^{7} +(24.4225 + 11.5126i) q^{9} +O(q^{10})$	\(q+(-5.07063 - 1.13522i) q^{3} +(11.2665 + 11.2665i) q^{5} +30.2121 q^{7} +(24.4225 + 11.5126i) q^{9} +(14.9799 - 14.9799i) q^{11} +(-10.4733 - 10.4733i) q^{13} +(-44.3383 - 69.9184i) q^{15} +69.5806i q^{17} +(36.4354 - 36.4354i) q^{19} +(-153.194 - 34.2975i) q^{21} +1.28579i q^{23} +128.869i q^{25} +(-110.768 - 86.1012i) q^{27} +(-119.373 + 119.373i) q^{29} -172.615i q^{31} +(-92.9630 + 58.9519i) q^{33} +(340.385 + 340.385i) q^{35} +(235.193 - 235.193i) q^{37} +(41.2167 + 64.9958i) q^{39} -19.9510 q^{41} +(294.812 + 294.812i) q^{43} +(145.450 + 404.864i) q^{45} -69.5052 q^{47} +569.769 q^{49} +(78.9896 - 352.818i) q^{51} +(122.813 + 122.813i) q^{53} +337.543 q^{55} +(-226.113 + 143.388i) q^{57} +(-63.2396 + 63.2396i) q^{59} +(352.521 + 352.521i) q^{61} +(737.855 + 347.819i) q^{63} -235.996i q^{65} +(228.455 - 228.455i) q^{67} +(1.45966 - 6.51976i) q^{69} +524.753i q^{71} +578.802i q^{73} +(146.296 - 653.449i) q^{75} +(452.573 - 452.573i) q^{77} -745.229i q^{79} +(463.920 + 562.334i) q^{81} +(-286.237 - 286.237i) q^{83} +(-783.932 + 783.932i) q^{85} +(740.814 - 469.783i) q^{87} -203.128 q^{89} +(-316.421 - 316.421i) q^{91} +(-195.957 + 875.266i) q^{93} +821.001 q^{95} -39.4244 q^{97} +(538.304 - 193.389i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{3} - 8 q^{7}+O(q^{10}) $ 44 * q + 2 * q^3 - 8 * q^7	$ 44 q + 2 q^{3} - 8 q^{7} + 4 q^{13} - 20 q^{19} + 56 q^{21} + 134 q^{27} - 4 q^{33} + 4 q^{37} + 596 q^{39} + 436 q^{43} + 252 q^{45} + 972 q^{49} + 648 q^{51} + 280 q^{55} + 916 q^{61} + 1636 q^{67} - 52 q^{69} - 1454 q^{75} - 4 q^{81} - 736 q^{85} + 1284 q^{87} - 424 q^{91} + 2084 q^{93} - 8 q^{97} - 1196 q^{99}+O(q^{100}) $ 44 * q + 2 * q^3 - 8 * q^7 + 4 * q^13 - 20 * q^19 + 56 * q^21 + 134 * q^27 - 4 * q^33 + 4 * q^37 + 596 * q^39 + 436 * q^43 + 252 * q^45 + 972 * q^49 + 648 * q^51 + 280 * q^55 + 916 * q^61 + 1636 * q^67 - 52 * q^69 - 1454 * q^75 - 4 * q^81 - 736 * q^85 + 1284 * q^87 - 424 * q^91 + 2084 * q^93 - 8 * q^97 - 1196 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	−5.07063	−	1.13522i	−0.975843	−	0.218474i
$3$	−5.07063	−	1.13522i	−0.975843	−	0.218474i
$4$		0			0
$5$	11.2665	+	11.2665i	1.00771	+	1.00771i	0.999970	+	0.00773900i	$0.00246343\pi$
$5$	11.2665	+	11.2665i	1.00771	+	1.00771i	0.00773900	+	0.999970i	$0.497537\pi$
$6$		0			0
$7$	30.2121			1.63130			0.815649	−	0.578547i	$-0.196380\pi$
$7$	30.2121			1.63130			0.815649	+	0.578547i	$0.196380\pi$
$8$		0			0
$9$	24.4225	+	11.5126i	0.904538	+	0.426393i
$10$		0			0
$11$	14.9799	−	14.9799i	0.410601	−	0.410601i	−0.471347	−	0.881948i	$-0.656232\pi$
$11$	14.9799	−	14.9799i	0.410601	−	0.410601i	0.881948	+	0.471347i	$0.156232\pi$
$12$		0			0
$13$	−10.4733	−	10.4733i	−0.223444	−	0.223444i	0.586503	−	0.809947i	$-0.300504\pi$
$13$	−10.4733	−	10.4733i	−0.223444	−	0.223444i	−0.809947	+	0.586503i	$0.800504\pi$
$14$		0			0
$15$	−44.3383	−	69.9184i	−0.763207	−	1.20352i
$16$		0			0
$17$			69.5806i			0.992693i	0.868124	+	0.496347i	$0.165325\pi$
$17$			69.5806i			0.992693i	−0.868124	+	0.496347i	$0.834675\pi$
$18$		0			0
$19$	36.4354	−	36.4354i	0.439940	−	0.439940i	−0.452052	−	0.891992i	$-0.649308\pi$
$19$	36.4354	−	36.4354i	0.439940	−	0.439940i	0.891992	+	0.452052i	$0.149308\pi$
$20$		0			0
$21$	−153.194	−	34.2975i	−1.59189	−	0.356396i
$22$		0			0
$23$			1.28579i			0.0116568i	0.999983	+	0.00582838i	$0.00185524\pi$
$23$			1.28579i			0.0116568i	−0.999983	+	0.00582838i	$0.998145\pi$
$24$		0			0
$25$			128.869i			1.03096i
$26$		0			0
$27$	−110.768	−	86.1012i	−0.789531	−	0.613710i
$28$		0			0
$29$	−119.373	+	119.373i	−0.764382	+	0.764382i	−0.977111	−	0.212729i	$-0.931765\pi$
$29$	−119.373	+	119.373i	−0.764382	+	0.764382i	0.212729	+	0.977111i	$0.431765\pi$
$30$		0			0
$31$		−	172.615i		−	1.00008i	−0.866002	−	0.500041i	$-0.833318\pi$
$31$		−	172.615i		−	1.00008i	0.866002	−	0.500041i	$-0.166682\pi$
$32$		0			0
$33$	−92.9630	+	58.9519i	−0.490387	+	0.310976i
$34$		0			0
$35$	340.385	+	340.385i	1.64387	+	1.64387i
$36$		0			0
$37$	235.193	−	235.193i	1.04501	−	1.04501i	0.0460739	−	0.998938i	$-0.485329\pi$
$37$	235.193	−	235.193i	1.04501	−	1.04501i	0.998938	−	0.0460739i	$-0.0146710\pi$
$38$		0			0
$39$	41.2167	+	64.9958i	0.169230	+	0.266863i
$40$		0			0
$41$	−19.9510			−0.0759957			−0.0379979	−	0.999278i	$-0.512098\pi$
$41$	−19.9510			−0.0759957			−0.0379979	+	0.999278i	$0.512098\pi$
$42$		0			0
$43$	294.812	+	294.812i	1.04554	+	1.04554i	0.998912	+	0.0466324i	$0.0148489\pi$
$43$	294.812	+	294.812i	1.04554	+	1.04554i	0.0466324	+	0.998912i	$0.485151\pi$
$44$		0			0
$45$	145.450	+	404.864i	0.481832	+	1.34119i
$46$		0			0
$47$	−69.5052			−0.215710			−0.107855	−	0.994167i	$-0.534398\pi$
$47$	−69.5052			−0.215710			−0.107855	+	0.994167i	$0.534398\pi$
$48$		0			0
$49$	569.769			1.66113
$50$		0			0
$51$	78.9896	−	352.818i	0.216878	−	0.968713i
$52$		0			0
$53$	122.813	+	122.813i	0.318295	+	0.318295i	0.848112	−	0.529817i	$-0.177739\pi$
$53$	122.813	+	122.813i	0.318295	+	0.318295i	−0.529817	+	0.848112i	$0.677739\pi$
$54$		0			0
$55$	337.543			0.827532
$56$		0			0
$57$	−226.113	+	143.388i	−0.525427	+	0.333196i
$58$		0			0
$59$	−63.2396	+	63.2396i	−0.139544	+	0.139544i	−0.773428	−	0.633884i	$-0.781460\pi$
$59$	−63.2396	+	63.2396i	−0.139544	+	0.139544i	0.633884	+	0.773428i	$0.281460\pi$
$60$		0			0
$61$	352.521	+	352.521i	0.739928	+	0.739928i	0.972564	−	0.232636i	$-0.0747349\pi$
$61$	352.521	+	352.521i	0.739928	+	0.739928i	−0.232636	+	0.972564i	$0.574735\pi$
$62$		0			0
$63$	737.855	+	347.819i	1.47557	+	0.695574i
$64$		0			0
$65$		−	235.996i		−	0.450334i
$66$		0			0
$67$	228.455	−	228.455i	0.416570	−	0.416570i	−0.467450	−	0.884020i	$-0.654827\pi$
$67$	228.455	−	228.455i	0.416570	−	0.416570i	0.884020	+	0.467450i	$0.154827\pi$
$68$		0			0
$69$	1.45966	−	6.51976i	0.00254670	−	0.0113752i
$70$		0			0
$71$			524.753i			0.877137i	0.898698	+	0.438568i	$0.144514\pi$
$71$			524.753i			0.877137i	−0.898698	+	0.438568i	$0.855486\pi$
$72$		0			0
$73$			578.802i			0.927994i	0.885837	+	0.463997i	$0.153585\pi$
$73$			578.802i			0.927994i	−0.885837	+	0.463997i	$0.846415\pi$
$74$		0			0
$75$	146.296	−	653.449i	0.225237	−	1.00605i
$76$		0			0
$77$	452.573	−	452.573i	0.669812	−	0.669812i
$78$		0			0
$79$		−	745.229i		−	1.06133i	−0.847583	−	0.530664i	$-0.821943\pi$
$79$		−	745.229i		−	1.06133i	0.847583	−	0.530664i	$-0.178057\pi$
$80$		0			0
$81$	463.920	+	562.334i	0.636379	+	0.771377i
$82$		0			0
$83$	−286.237	−	286.237i	−0.378537	−	0.378537i	0.492037	−	0.870574i	$-0.336252\pi$
$83$	−286.237	−	286.237i	−0.378537	−	0.378537i	−0.870574	+	0.492037i	$0.836252\pi$
$84$		0			0
$85$	−783.932	+	783.932i	−1.00035	+	1.00035i
$86$		0			0
$87$	740.814	−	469.783i	0.912914	−	0.578919i
$88$		0			0
$89$	−203.128			−0.241927			−0.120964	−	0.992657i	$-0.538598\pi$
$89$	−203.128			−0.241927			−0.120964	+	0.992657i	$0.538598\pi$
$90$		0			0
$91$	−316.421	−	316.421i	−0.364504	−	0.364504i
$92$		0			0
$93$	−195.957	+	875.266i	−0.218492	+	0.975923i
$94$		0			0
$95$	821.001			0.886662
$96$		0			0
$97$	−39.4244			−0.0412674			−0.0206337	−	0.999787i	$-0.506568\pi$
$97$	−39.4244			−0.0412674			−0.0206337	+	0.999787i	$0.506568\pi$
$98$		0			0
$99$	538.304	−	193.389i	0.546481	−	0.196327i
$100$		0			0
$101$	477.063	+	477.063i	0.469996	+	0.469996i	0.901913	−	0.431917i	$-0.142163\pi$
$101$	477.063	+	477.063i	0.469996	+	0.469996i	−0.431917	+	0.901913i	$0.642163\pi$
$102$		0			0
$103$	−1080.92			−1.03404			−0.517022	−	0.855972i	$-0.672960\pi$
$103$	−1080.92			−1.03404			−0.517022	+	0.855972i	$0.672960\pi$
$104$		0			0
$105$	−1339.55	−	2112.38i	−1.24502	−	1.96331i
$106$		0			0
$107$	−1267.21	+	1267.21i	−1.14491	+	1.14491i	−0.157374	+	0.987539i	$0.550303\pi$
$107$	−1267.21	+	1267.21i	−1.14491	+	1.14491i	−0.987539	+	0.157374i	$0.949697\pi$
$108$		0			0
$109$	−1252.27	−	1252.27i	−1.10042	−	1.10042i	−0.994360	−	0.106058i	$-0.966177\pi$
$109$	−1252.27	−	1252.27i	−1.10042	−	1.10042i	−0.106058	−	0.994360i	$-0.533823\pi$
$110$		0			0
$111$	−1459.57	+	925.578i	−1.24808	+	0.791459i
$112$		0			0
$113$			644.877i			0.536858i	0.963299	+	0.268429i	$0.0865045\pi$
$113$			644.877i			0.536858i	−0.963299	+	0.268429i	$0.913496\pi$
$114$		0			0
$115$	−14.4864	+	14.4864i	−0.0117466	+	0.0117466i
$116$		0			0
$117$	−135.210	−	376.360i	−0.106839	−	0.297389i
$118$		0			0
$119$			2102.18i			1.61938i
$120$		0			0
$121$			882.206i			0.662814i
$122$		0			0
$123$	101.164	+	22.6489i	0.0741599	+	0.0166031i
$124$		0			0
$125$	−43.5945	+	43.5945i	−0.0311937	+	0.0311937i
$126$		0			0
$127$		−	713.342i		−	0.498417i	−0.968450	−	0.249208i	$-0.919830\pi$
$127$		−	713.342i		−	0.498417i	0.968450	−	0.249208i	$-0.0801704\pi$
$128$		0			0
$129$	−1160.20	−	1829.56i	−0.791863	−	1.24871i
$130$		0			0
$131$	342.230	+	342.230i	0.228250	+	0.228250i	0.811961	−	0.583711i	$-0.198400\pi$
$131$	342.230	+	342.230i	0.228250	+	0.228250i	−0.583711	+	0.811961i	$0.698400\pi$
$132$		0			0
$133$	1100.79	−	1100.79i	0.717673	−	0.717673i
$134$		0			0
$135$	−277.912	−	2218.03i	−0.177177	−	1.41406i
$136$		0			0
$137$	3148.95			1.96374			0.981872	−	0.189546i	$-0.0607015\pi$
$137$	3148.95			1.96374			0.981872	+	0.189546i	$0.0607015\pi$
$138$		0			0
$139$	308.310	+	308.310i	0.188133	+	0.188133i	0.794889	−	0.606755i	$-0.207529\pi$
$139$	308.310	+	308.310i	0.188133	+	0.188133i	−0.606755	+	0.794889i	$0.707529\pi$
$140$		0			0
$141$	352.435	+	78.9040i	0.210499	+	0.0471271i
$142$		0			0
$143$	−313.778			−0.183493
$144$		0			0
$145$	−2689.85			−1.54055
$146$		0			0
$147$	−2889.09	−	646.816i	−1.62101	−	0.362915i
$148$		0			0
$149$	397.287	+	397.287i	0.218437	+	0.218437i	0.807839	−	0.589403i	$-0.200637\pi$
$149$	397.287	+	397.287i	0.218437	+	0.218437i	−0.589403	+	0.807839i	$0.700637\pi$
$150$		0			0
$151$	−1028.33			−0.554200			−0.277100	−	0.960841i	$-0.589373\pi$
$151$	−1028.33			−0.554200			−0.277100	+	0.960841i	$0.589373\pi$
$152$		0			0
$153$	−801.054	+	1699.34i	−0.423277	+	0.897929i
$154$		0			0
$155$	1944.77	−	1944.77i	1.00779	−	1.00779i
$156$		0			0
$157$	−154.961	−	154.961i	−0.0787721	−	0.0787721i	0.666623	−	0.745395i	$-0.267739\pi$
$157$	−154.961	−	154.961i	−0.0787721	−	0.0787721i	−0.745395	+	0.666623i	$0.767739\pi$
$158$		0			0
$159$	−483.318	−	762.159i	−0.241067	−	0.380145i
$160$		0			0
$161$			38.8464i			0.0190157i
$162$		0			0
$163$	−1541.10	+	1541.10i	−0.740540	+	0.740540i	−0.972682	−	0.232142i	$-0.925427\pi$
$163$	−1541.10	+	1541.10i	−0.740540	+	0.740540i	0.232142	+	0.972682i	$0.425427\pi$
$164$		0			0
$165$	−1711.55	−	383.187i	−0.807541	−	0.180794i
$166$		0			0
$167$		−	2839.46i		−	1.31571i	−0.753143	−	0.657856i	$-0.771463\pi$
$167$		−	2839.46i		−	1.31571i	0.753143	−	0.657856i	$-0.228537\pi$
$168$		0			0
$169$		−	1977.62i		−	0.900145i
$170$		0			0
$171$	1309.31	−	470.378i	0.585529	−	0.210355i
$172$		0			0
$173$	2220.59	−	2220.59i	0.975885	−	0.975885i	−0.0238309	−	0.999716i	$-0.507586\pi$
$173$	2220.59	−	2220.59i	0.975885	−	0.975885i	0.999716	+	0.0238309i	$0.00758631\pi$
$174$		0			0
$175$			3893.41i			1.68180i
$176$		0			0
$177$	392.456	−	248.873i	0.166660	−	0.105686i
$178$		0			0
$179$	1986.85	+	1986.85i	0.829630	+	0.829630i	0.987465	−	0.157835i	$-0.0504515\pi$
$179$	1986.85	+	1986.85i	0.829630	+	0.829630i	−0.157835	+	0.987465i	$0.550451\pi$
$180$		0			0
$181$	−8.17608	+	8.17608i	−0.00335759	+	0.00335759i	−0.708784	−	0.705426i	$-0.750756\pi$
$181$	−8.17608	+	8.17608i	−0.00335759	+	0.00335759i	0.705426	+	0.708784i	$0.250756\pi$
$182$		0			0
$183$	−1387.31	−	2187.69i	−0.560399	−	0.883709i
$184$		0			0
$185$	5299.61			2.10614
$186$		0			0
$187$	1042.31	+	1042.31i	0.407600	+	0.407600i
$188$		0			0
$189$	−3346.54	−	2601.29i	−1.28796	−	1.00114i
$190$		0			0
$191$	−3114.07			−1.17972			−0.589860	−	0.807506i	$-0.700817\pi$
$191$	−3114.07			−1.17972			−0.589860	+	0.807506i	$0.700817\pi$
$192$		0			0
$193$	4424.82			1.65029			0.825144	−	0.564922i	$-0.191094\pi$
$193$	4424.82			1.65029			0.825144	+	0.564922i	$0.191094\pi$
$194$		0			0
$195$	−267.908	+	1196.65i	−0.0983862	+	0.439455i
$196$		0			0
$197$	−1951.27	−	1951.27i	−0.705697	−	0.705697i	0.259931	−	0.965627i	$-0.416300\pi$
$197$	−1951.27	−	1951.27i	−0.705697	−	0.705697i	−0.965627	+	0.259931i	$0.916300\pi$
$198$		0			0
$199$	2770.53			0.986922			0.493461	−	0.869768i	$-0.335731\pi$
$199$	2770.53			0.986922			0.493461	+	0.869768i	$0.335731\pi$
$200$		0			0
$201$	−1417.76	+	899.062i	−0.497517	+	0.315497i
$202$		0			0
$203$	−3606.52	+	3606.52i	−1.24694	+	1.24694i
$204$		0			0
$205$	−224.779	−	224.779i	−0.0765816	−	0.0765816i
$206$		0			0
$207$	−14.8028	+	31.4022i	−0.00497036	+	0.0105440i
$208$		0			0
$209$		−	1091.60i		−	0.361279i
$210$		0			0
$211$	−3424.36	+	3424.36i	−1.11726	+	1.11726i	−0.125124	+	0.992141i	$0.539933\pi$
$211$	−3424.36	+	3424.36i	−1.11726	+	1.11726i	−0.992141	+	0.125124i	$0.960067\pi$
$212$		0			0
$213$	595.712	−	2660.83i	0.191632	−	0.855947i
$214$		0			0
$215$			6643.02i			2.10721i
$216$		0			0
$217$		−	5215.06i		−	1.63143i
$218$		0			0
$219$	657.070	−	2934.89i	0.202743	−	0.905577i
$220$		0			0
$221$	728.740	−	728.740i	0.221812	−	0.221812i
$222$		0			0
$223$			1568.26i			0.470934i	0.971882	+	0.235467i	$0.0756619\pi$
$223$			1568.26i			0.470934i	−0.971882	+	0.235467i	$0.924338\pi$
$224$		0			0
$225$	−1483.62	+	3147.32i	−0.439592	+	0.932538i
$226$		0			0
$227$	−2298.97	−	2298.97i	−0.672193	−	0.672193i	0.286028	−	0.958221i	$-0.407665\pi$
$227$	−2298.97	−	2298.97i	−0.672193	−	0.672193i	−0.958221	+	0.286028i	$0.907665\pi$
$228$		0			0
$229$	844.364	−	844.364i	0.243656	−	0.243656i	−0.574705	−	0.818361i	$-0.694883\pi$
$229$	844.364	−	844.364i	0.243656	−	0.243656i	0.818361	+	0.574705i	$0.194883\pi$
$230$		0			0
$231$	−2808.60	+	1781.06i	−0.799968	+	0.507295i
$232$		0			0
$233$	−7011.40			−1.97138			−0.985692	−	0.168558i	$-0.946089\pi$
$233$	−7011.40			−1.97138			−0.985692	+	0.168558i	$0.946089\pi$
$234$		0			0
$235$	−783.083	−	783.083i	−0.217373	−	0.217373i
$236$		0			0
$237$	−846.002	+	3778.78i	−0.231872	+	1.03569i
$238$		0			0
$239$	1850.30			0.500779			0.250389	−	0.968145i	$-0.419441\pi$
$239$	1850.30			0.500779			0.250389	+	0.968145i	$0.419441\pi$
$240$		0			0
$241$	−5628.68			−1.50446			−0.752231	−	0.658900i	$-0.771022\pi$
$241$	−5628.68			−1.50446			−0.752231	+	0.658900i	$0.771022\pi$
$242$		0			0
$243$	−1713.99	−	3378.04i	−0.452480	−	0.891775i
$244$		0			0
$245$	6419.32	+	6419.32i	1.67394	+	1.67394i
$246$		0			0
$247$	−763.199			−0.196604
$248$		0			0
$249$	1126.46	+	1776.34i	0.286692	+	0.452093i
$250$		0			0
$251$	−598.579	+	598.579i	−0.150526	+	0.150526i	−0.778353	−	0.627827i	$-0.783944\pi$
$251$	−598.579	+	598.579i	−0.150526	+	0.150526i	0.627827	+	0.778353i	$0.283944\pi$
$252$		0			0
$253$	19.2610	+	19.2610i	0.00478628	+	0.00478628i
$254$		0			0
$255$	4864.97	−	3085.09i	1.19473	−	0.757631i
$256$		0			0
$257$		−	6418.48i		−	1.55787i	−0.627102	−	0.778937i	$-0.715759\pi$
$257$		−	6418.48i		−	1.55787i	0.627102	−	0.778937i	$-0.284241\pi$
$258$		0			0
$259$	7105.66	−	7105.66i	1.70473	−	1.70473i
$260$		0			0
$261$	−4289.70	+	1541.10i	−1.01734	+	0.365486i
$262$		0			0
$263$		−	3467.23i		−	0.812922i	−0.913668	−	0.406461i	$-0.866763\pi$
$263$		−	3467.23i		−	0.812922i	0.913668	−	0.406461i	$-0.133237\pi$
$264$		0			0
$265$			2767.35i			0.641498i
$266$		0			0
$267$	1029.99	+	230.596i	0.236083	+	0.0528548i
$268$		0			0
$269$	2049.90	−	2049.90i	0.464627	−	0.464627i	−0.435542	−	0.900169i	$-0.643443\pi$
$269$	2049.90	−	2049.90i	0.464627	−	0.464627i	0.900169	+	0.435542i	$0.143443\pi$
$270$		0			0
$271$		−	2445.74i		−	0.548223i	−0.961698	−	0.274111i	$-0.911616\pi$
$271$		−	2445.74i		−	0.548223i	0.961698	−	0.274111i	$-0.0883837\pi$
$272$		0			0
$273$	1245.24	+	1963.66i	0.276064	+	0.435334i
$274$		0			0
$275$	1930.45	+	1930.45i	0.423311	+	0.423311i
$276$		0			0
$277$	−4784.71	+	4784.71i	−1.03785	+	1.03785i	−0.0385995	+	0.999255i	$0.512290\pi$
$277$	−4784.71	+	4784.71i	−1.03785	+	1.03785i	−0.999255	+	0.0385995i	$0.987710\pi$
$278$		0			0
$279$	1987.25	−	4215.69i	0.426428	−	0.904613i
$280$		0			0
$281$	1716.06			0.364312			0.182156	−	0.983270i	$-0.441692\pi$
$281$	1716.06			0.364312			0.182156	+	0.983270i	$0.441692\pi$
$282$		0			0
$283$	−4822.50	−	4822.50i	−1.01296	−	1.01296i	−0.999915	−	0.0130454i	$-0.995847\pi$
$283$	−4822.50	−	4822.50i	−1.01296	−	1.01296i	−0.0130454	−	0.999915i	$-0.504153\pi$
$284$		0			0
$285$	−4162.99	−	932.020i	−0.865243	−	0.193713i
$286$		0			0
$287$	−602.761			−0.123972
$288$		0			0
$289$	71.5338			0.0145601
$290$		0			0
$291$	199.906	+	44.7555i	0.0402705	+	0.00901586i
$292$		0			0
$293$	768.551	+	768.551i	0.153240	+	0.153240i	0.779563	−	0.626324i	$-0.215441\pi$
$293$	768.551	+	768.551i	0.153240	+	0.153240i	−0.626324	+	0.779563i	$0.715441\pi$
$294$		0			0
$295$	−1424.98			−0.281239
$296$		0			0
$297$	−2949.08	+	369.509i	−0.576172	+	0.0721923i
$298$		0			0
$299$	13.4665	−	13.4665i	0.00260464	−	0.00260464i
$300$		0			0
$301$	8906.88	+	8906.88i	1.70560	+	1.70560i
$302$		0			0
$303$	−1877.44	−	2960.59i	−0.355960	−	0.561324i
$304$		0			0
$305$			7943.37i			1.49127i
$306$		0			0
$307$	5562.98	−	5562.98i	1.03419	−	1.03419i	0.0347941	−	0.999395i	$-0.488922\pi$
$307$	5562.98	−	5562.98i	1.03419	−	1.03419i	0.999395	−	0.0347941i	$-0.0110775\pi$
$308$		0			0
$309$	5480.96	+	1227.09i	1.00906	+	0.225912i
$310$		0			0
$311$		−	907.726i		−	0.165506i	−0.996570	−	0.0827531i	$-0.973629\pi$
$311$		−	907.726i		−	0.165506i	0.996570	−	0.0827531i	$-0.0263713\pi$
$312$		0			0
$313$			1022.22i			0.184599i	0.995731	+	0.0922993i	$0.0294217\pi$
$313$			1022.22i			0.184599i	−0.995731	+	0.0922993i	$0.970578\pi$
$314$		0			0
$315$	4394.35	+	12231.8i	0.786011	+	2.18788i
$316$		0			0
$317$	−4180.59	+	4180.59i	−0.740711	+	0.740711i	−0.972715	−	0.232004i	$-0.925472\pi$
$317$	−4180.59	+	4180.59i	−0.740711	+	0.740711i	0.232004	+	0.972715i	$0.425472\pi$
$318$		0			0
$319$			3576.40i			0.627712i
$320$		0			0
$321$	7864.11	−	4986.98i	1.36739	−	0.867122i
$322$		0			0
$323$	2535.20	+	2535.20i	0.436725	+	0.436725i
$324$		0			0
$325$	1349.69	−	1349.69i	0.230361	−	0.230361i
$326$		0			0
$327$	4928.18	+	7771.39i	0.833422	+	1.31425i
$328$		0			0
$329$	−2099.90			−0.351888
$330$		0			0
$331$	−1915.71	−	1915.71i	−0.318117	−	0.318117i	0.529926	−	0.848044i	$-0.322220\pi$
$331$	−1915.71	−	1915.71i	−0.318117	−	0.318117i	−0.848044	+	0.529926i	$0.822220\pi$
$332$		0			0
$333$	8451.68	−	3036.32i	1.39084	−	0.499668i
$334$		0			0
$335$	5147.78			0.839563
$336$		0			0
$337$	3088.80			0.499281			0.249641	−	0.968339i	$-0.419687\pi$
$337$	3088.80			0.499281			0.249641	+	0.968339i	$0.419687\pi$
$338$		0			0
$339$	732.080	−	3269.93i	0.117290	−	0.523889i
$340$		0			0
$341$	−2585.75	−	2585.75i	−0.410635	−	0.410635i
$342$		0			0
$343$	6851.17			1.07851
$344$		0			0
$345$	89.9004	−	57.0098i	0.0140292	−	0.00889653i
$346$		0			0
$347$	2015.99	−	2015.99i	0.311884	−	0.311884i	−0.533755	−	0.845639i	$-0.679220\pi$
$347$	2015.99	−	2015.99i	0.311884	−	0.311884i	0.845639	+	0.533755i	$0.179220\pi$
$348$		0			0
$349$	−2106.10	−	2106.10i	−0.323029	−	0.323029i	0.526899	−	0.849928i	$-0.323355\pi$
$349$	−2106.10	−	2106.10i	−0.323029	−	0.323029i	−0.849928	+	0.526899i	$0.823355\pi$
$350$		0			0
$351$	258.346	+	2061.87i	0.0392862	+	0.313546i
$352$		0			0
$353$			6982.94i			1.05287i	0.850214	+	0.526437i	$0.176472\pi$
$353$			6982.94i			1.05287i	−0.850214	+	0.526437i	$0.823528\pi$
$354$		0			0
$355$	−5912.14	+	5912.14i	−0.883898	+	0.883898i
$356$		0			0
$357$	2386.44	−	10659.3i	0.353792	−	1.58026i
$358$		0			0
$359$			8753.09i			1.28683i	0.765519	+	0.643413i	$0.222482\pi$
$359$			8753.09i			1.28683i	−0.765519	+	0.643413i	$0.777518\pi$
$360$		0			0
$361$			4203.93i			0.612906i
$362$		0			0
$363$	1001.50	−	4473.34i	0.144808	−	0.646803i
$364$		0			0
$365$	−6521.08	+	6521.08i	−0.935148	+	0.935148i
$366$		0			0
$367$		−	8242.34i		−	1.17233i	−0.810190	−	0.586167i	$-0.800636\pi$
$367$		−	8242.34i		−	1.17233i	0.810190	−	0.586167i	$-0.199364\pi$
$368$		0			0
$369$	−487.254	−	229.688i	−0.0687410	−	0.0324040i
$370$		0			0
$371$	3710.43	+	3710.43i	0.519234	+	0.519234i
$372$		0			0
$373$	298.350	−	298.350i	0.0414154	−	0.0414154i	−0.686096	−	0.727511i	$-0.740677\pi$
$373$	298.350	−	298.350i	0.0414154	−	0.0414154i	0.727511	+	0.686096i	$0.240677\pi$
$374$		0			0
$375$	270.541	−	171.562i	0.0372552	−	0.0236251i
$376$		0			0
$377$	2500.47			0.341594
$378$		0			0
$379$	1059.78	+	1059.78i	0.143633	+	0.143633i	0.775267	−	0.631634i	$-0.217615\pi$
$379$	1059.78	+	1059.78i	0.143633	+	0.143633i	−0.631634	+	0.775267i	$0.717615\pi$
$380$		0			0
$381$	−809.804	+	3617.09i	−0.108891	+	0.486376i
$382$		0			0
$383$	4404.31			0.587597			0.293799	−	0.955867i	$-0.405080\pi$
$383$	4404.31			0.587597			0.293799	+	0.955867i	$0.405080\pi$
$384$		0			0
$385$	10197.9			1.34995
$386$		0			0
$387$	3806.00	+	10594.1i	0.499923	+	1.39155i
$388$		0			0
$389$	−9687.95	−	9687.95i	−1.26272	−	1.26272i	−0.949769	−	0.312953i	$-0.898682\pi$
$389$	−9687.95	−	9687.95i	−1.26272	−	1.26272i	−0.312953	−	0.949769i	$-0.601318\pi$
$390$		0			0
$391$	−89.4661			−0.0115716
$392$		0			0
$393$	−1346.81	−	2123.83i	−0.172869	−	0.272603i
$394$		0			0
$395$	8396.15	−	8396.15i	1.06951	−	1.06951i
$396$		0			0
$397$	−73.0707	−	73.0707i	−0.00923757	−	0.00923757i	0.702473	−	0.711710i	$-0.252079\pi$
$397$	−73.0707	−	73.0707i	−0.00923757	−	0.00923757i	−0.711710	+	0.702473i	$0.752079\pi$
$398$		0			0
$399$	−6831.33	+	4332.05i	−0.857129	+	0.543543i
$400$		0			0
$401$			340.273i			0.0423751i	0.999776	+	0.0211875i	$0.00674471\pi$
$401$			340.273i			0.0423751i	−0.999776	+	0.0211875i	$0.993255\pi$
$402$		0			0
$403$	−1807.85	+	1807.85i	−0.223463	+	0.223463i
$404$		0			0
$405$	−1108.78	+	11562.3i	−0.136039	+	1.41861i
$406$		0			0
$407$		−	7046.32i		−	0.858165i
$408$		0			0
$409$			10873.6i			1.31458i	0.753636	+	0.657291i	$0.228298\pi$
$409$			10873.6i			1.31458i	−0.753636	+	0.657291i	$0.771702\pi$
$410$		0			0
$411$	−15967.2	−	3574.76i	−1.91631	−	0.429027i
$412$		0			0
$413$	−1910.60	+	1910.60i	−0.227638	+	0.227638i
$414$		0			0
$415$		−	6449.80i		−	0.762911i
$416$		0			0
$417$	−1213.32	−	1913.33i	−0.142486	−	0.224691i
$418$		0			0
$419$	−5701.01	−	5701.01i	−0.664708	−	0.664708i	0.291778	−	0.956486i	$-0.405753\pi$
$419$	−5701.01	−	5701.01i	−0.664708	−	0.664708i	−0.956486	+	0.291778i	$0.905753\pi$
$420$		0			0
$421$	1062.79	−	1062.79i	0.123034	−	0.123034i	−0.642909	−	0.765943i	$-0.722273\pi$
$421$	1062.79	−	1062.79i	0.123034	−	0.123034i	0.765943	+	0.642909i	$0.222273\pi$
$422$		0			0
$423$	−1697.49	−	800.186i	−0.195118	−	0.0919772i
$424$		0			0
$425$	−8966.82			−1.02342
$426$		0			0
$427$	10650.4	+	10650.4i	1.20704	+	1.20704i
$428$		0			0
$429$	1591.05	+	356.209i	0.179060	+	0.0400884i
$430$		0			0
$431$	−2350.06			−0.262641			−0.131321	−	0.991340i	$-0.541922\pi$
$431$	−2350.06			−0.262641			−0.131321	+	0.991340i	$0.541922\pi$
$432$		0			0
$433$	−8617.75			−0.956450			−0.478225	−	0.878237i	$-0.658720\pi$
$433$	−8617.75			−0.956450			−0.478225	+	0.878237i	$0.658720\pi$
$434$		0			0
$435$	13639.2	+	3053.58i	1.50333	+	0.336570i
$436$		0			0
$437$	46.8482	+	46.8482i	0.00512827	+	0.00512827i
$438$		0			0
$439$	−4948.07			−0.537947			−0.268973	−	0.963148i	$-0.586684\pi$
$439$	−4948.07			−0.537947			−0.268973	+	0.963148i	$0.586684\pi$
$440$		0			0
$441$	13915.2	+	6559.52i	1.50256	+	0.708295i
$442$		0			0
$443$	−6128.78	+	6128.78i	−0.657307	+	0.657307i	−0.954742	−	0.297435i	$-0.903869\pi$
$443$	−6128.78	+	6128.78i	−0.657307	+	0.657307i	0.297435	+	0.954742i	$0.403869\pi$
$444$		0			0
$445$	−2288.55	−	2288.55i	−0.243792	−	0.243792i
$446$		0			0
$447$	−1563.49	−	2465.51i	−0.165437	−	0.260882i
$448$		0			0
$449$		−	13057.1i		−	1.37239i	−0.727416	−	0.686197i	$-0.759279\pi$
$449$		−	13057.1i		−	1.37239i	0.727416	−	0.686197i	$-0.240721\pi$
$450$		0			0
$451$	−298.864	+	298.864i	−0.0312039	+	0.0312039i
$452$		0			0
$453$	5214.27	+	1167.38i	0.540812	+	0.121078i
$454$		0			0
$455$		−	7129.92i		−	0.734628i
$456$		0			0
$457$		−	16737.3i		−	1.71321i	−0.515973	−	0.856605i	$-0.672570\pi$
$457$		−	16737.3i		−	1.71321i	0.515973	−	0.856605i	$-0.327430\pi$
$458$		0			0
$459$	5990.97	−	7707.32i	0.609226	−	0.783762i
$460$		0			0
$461$	11008.3	−	11008.3i	1.11216	−	1.11216i	0.119306	−	0.992857i	$-0.461933\pi$
$461$	11008.3	−	11008.3i	1.11216	−	1.11216i	0.992857	−	0.119306i	$-0.0380671\pi$
$462$		0			0
$463$		−	1019.62i		−	0.102345i	−0.998690	−	0.0511723i	$-0.983704\pi$
$463$		−	1019.62i		−	0.102345i	0.998690	−	0.0511723i	$-0.0162958\pi$
$464$		0			0
$465$	−12069.0	+	7653.46i	−1.20362	+	0.763270i
$466$		0			0
$467$	−9386.52	−	9386.52i	−0.930099	−	0.930099i	0.0676128	−	0.997712i	$-0.478462\pi$
$467$	−9386.52	−	9386.52i	−0.930099	−	0.930099i	−0.997712	+	0.0676128i	$0.978462\pi$
$468$		0			0
$469$	6902.09	−	6902.09i	0.679550	−	0.679550i
$470$		0			0
$471$	609.833	+	961.664i	0.0596595	+	0.0940788i
$472$		0			0
$473$	8832.50			0.858602
$474$		0			0
$475$	4695.41	+	4695.41i	0.453558	+	0.453558i
$476$		0			0
$477$	1585.51	+	4413.30i	0.152191	+	0.423629i
$478$		0			0
$479$	−19141.8			−1.82592			−0.912958	−	0.408054i	$-0.866207\pi$
$479$	−19141.8			−1.82592			−0.912958	+	0.408054i	$0.866207\pi$
$480$		0			0
$481$	−4926.49			−0.467004
$482$		0			0
$483$	44.0993	−	196.975i	0.00415443	−	0.0185563i
$484$		0			0
$485$	−444.176	−	444.176i	−0.0415856	−	0.0415856i
$486$		0			0
$487$	9857.78			0.917246			0.458623	−	0.888631i	$-0.348343\pi$
$487$	9857.78			0.917246			0.458623	+	0.888631i	$0.348343\pi$
$488$		0			0
$489$	9563.82	−	6064.84i	0.884440	−	0.560862i
$490$		0			0
$491$	−2235.97	+	2235.97i	−0.205515	+	0.205515i	−0.802358	−	0.596843i	$-0.796422\pi$
$491$	−2235.97	+	2235.97i	−0.205515	+	0.205515i	0.596843	+	0.802358i	$0.296422\pi$
$492$		0			0
$493$	−8306.08	−	8306.08i	−0.758797	−	0.758797i
$494$		0			0
$495$	8243.65	+	3885.99i	0.748534	+	0.352853i
$496$		0			0
$497$			15853.9i			1.43087i
$498$		0			0
$499$	1879.08	−	1879.08i	0.168576	−	0.168576i	−0.617777	−	0.786353i	$-0.711967\pi$
$499$	1879.08	−	1879.08i	0.168576	−	0.168576i	0.786353	+	0.617777i	$0.211967\pi$
$500$		0			0
$501$	−3223.42	+	14397.8i	−0.287449	+	1.28393i
$502$		0			0
$503$		−	18597.9i		−	1.64859i	−0.566161	−	0.824295i	$-0.691572\pi$
$503$		−	18597.9i		−	1.64859i	0.566161	−	0.824295i	$-0.308428\pi$
$504$		0			0
$505$			10749.7i			0.947238i
$506$		0			0
$507$	−2245.04	+	10027.8i	−0.196658	+	0.878400i
$508$		0			0
$509$	−12280.3	+	12280.3i	−1.06938	+	1.06938i	−0.0719701	+	0.997407i	$0.522929\pi$
$509$	−12280.3	+	12280.3i	−1.06938	+	1.06938i	−0.997407	+	0.0719701i	$0.977071\pi$
$510$		0			0
$511$			17486.8i			1.51384i
$512$		0			0
$513$	−7173.01	+	898.753i	−0.617341	+	0.0773507i
$514$		0			0
$515$	−12178.3	−	12178.3i	−1.04202	−	1.04202i
$516$		0			0
$517$	−1041.18	+	1041.18i	−0.0885707	+	0.0885707i
$518$		0			0
$519$	−13780.6	+	8738.91i	−1.16552	+	0.739105i
$520$		0			0
$521$	−9893.24			−0.831921			−0.415961	−	0.909383i	$-0.636555\pi$
$521$	−9893.24			−0.831921			−0.415961	+	0.909383i	$0.636555\pi$
$522$		0			0
$523$	−7608.31	−	7608.31i	−0.636115	−	0.636115i	0.313480	−	0.949595i	$-0.398505\pi$
$523$	−7608.31	−	7608.31i	−0.636115	−	0.636115i	−0.949595	+	0.313480i	$0.898505\pi$
$524$		0			0
$525$	4419.89	−	19742.0i	0.367429	−	1.64117i
$526$		0			0
$527$	12010.7			0.992775
$528$		0			0
$529$	12165.3			0.999864
$530$		0			0
$531$	−2272.52	+	816.419i	−0.185723	+	0.0667223i
$532$		0			0
$533$	208.953	+	208.953i	0.0169808	+	0.0169808i
$534$		0			0
$535$	−28554.1			−2.30748
$536$		0			0
$537$	−7819.04	−	12330.1i	−0.628336	−	0.990841i
$538$		0			0
$539$	8535.08	−	8535.08i	0.682063	−	0.682063i
$540$		0			0
$541$	−9518.30	−	9518.30i	−0.756421	−	0.756421i	0.219248	−	0.975669i	$-0.429639\pi$
$541$	−9518.30	−	9518.30i	−0.756421	−	0.756421i	−0.975669	+	0.219248i	$0.929639\pi$
$542$		0			0
$543$	50.7396	−	32.1762i	0.00401002	−	0.00254293i
$544$		0			0
$545$		−	28217.4i		−	2.21780i
$546$		0			0
$547$	−3126.99	+	3126.99i	−0.244425	+	0.244425i	−0.818678	−	0.574253i	$-0.805293\pi$
$547$	−3126.99	+	3126.99i	−0.244425	+	0.244425i	0.574253	+	0.818678i	$0.305293\pi$
$548$		0			0
$549$	4551.02	+	12667.9i	0.353794	+	0.984794i
$550$		0			0
$551$			8698.83i			0.672564i
$552$		0			0
$553$		−	22514.9i		−	1.73134i
$554$		0			0
$555$	−26872.4	−	6016.25i	−2.05526	−	0.460136i
$556$		0			0
$557$	8497.54	−	8497.54i	0.646414	−	0.646414i	−0.305711	−	0.952124i	$-0.598894\pi$
$557$	8497.54	−	8497.54i	0.646414	−	0.646414i	0.952124	+	0.305711i	$0.0988940\pi$
$558$		0			0
$559$		−	6175.32i		−	0.467242i
$560$		0			0
$561$	−4101.91	−	6468.42i	−0.308704	−	0.486804i
$562$		0			0
$563$	3772.00	+	3772.00i	0.282364	+	0.282364i	0.834051	−	0.551687i	$-0.186016\pi$
$563$	3772.00	+	3772.00i	0.282364	+	0.282364i	−0.551687	+	0.834051i	$0.686016\pi$
$564$		0			0
$565$	−7265.53	+	7265.53i	−0.540997	+	0.540997i
$566$		0			0
$567$	14016.0	+	16989.3i	1.03812	+	1.25835i
$568$		0			0
$569$	−21830.1			−1.60838			−0.804189	−	0.594374i	$-0.797400\pi$
$569$	−21830.1			−1.60838			−0.804189	+	0.594374i	$0.797400\pi$
$570$		0			0
$571$	189.972	+	189.972i	0.0139231	+	0.0139231i	0.714034	−	0.700111i	$-0.246866\pi$
$571$	189.972	+	189.972i	0.0139231	+	0.0139231i	−0.700111	+	0.714034i	$0.746866\pi$
$572$		0			0
$573$	15790.3	+	3535.17i	1.15122	+	0.257738i
$574$		0			0
$575$	−165.699			−0.0120176
$576$		0			0
$577$	−20253.3			−1.46127			−0.730637	−	0.682766i	$-0.760777\pi$
$577$	−20253.3			−1.46127			−0.730637	+	0.682766i	$0.760777\pi$
$578$		0			0
$579$	−22436.6	−	5023.17i	−1.61042	−	0.360545i
$580$		0			0
$581$	−8647.81	−	8647.81i	−0.617507	−	0.617507i
$582$		0			0
$583$	3679.45			0.261384
$584$		0			0
$585$	2716.93	−	5763.62i	0.192019	−	0.407344i
$586$		0			0
$587$	19.1015	−	19.1015i	0.00134311	−	0.00134311i	−0.706435	−	0.707778i	$-0.749698\pi$
$587$	19.1015	−	19.1015i	0.00134311	−	0.00134311i	0.707778	+	0.706435i	$0.249698\pi$
$588$		0			0
$589$	−6289.29	−	6289.29i	−0.439976	−	0.439976i
$590$		0			0
$591$	7679.04	+	12109.3i	0.534473	+	0.842825i
$592$		0			0
$593$			2075.52i			0.143729i	0.997414	+	0.0718646i	$0.0228950\pi$
$593$			2075.52i			0.143729i	−0.997414	+	0.0718646i	$0.977105\pi$
$594$		0			0
$595$	−23684.2	+	23684.2i	−1.63186	+	1.63186i
$596$		0			0
$597$	−14048.3	−	3145.17i	−0.963081	−	0.215617i
$598$		0			0
$599$		−	2373.75i		−	0.161918i	−0.996717	−	0.0809589i	$-0.974202\pi$
$599$		−	2373.75i		−	0.161918i	0.996717	−	0.0809589i	$-0.0257982\pi$
$600$		0			0
$601$			18198.0i			1.23512i	0.786522	+	0.617562i	$0.211880\pi$
$601$			18198.0i			1.23512i	−0.786522	+	0.617562i	$0.788120\pi$
$602$		0			0
$603$	8209.55	−	2949.34i	0.554426	−	0.199181i
$604$		0			0
$605$	−9939.40	+	9939.40i	−0.667924	+	0.667924i
$606$		0			0
$607$			6359.38i			0.425238i	0.977135	+	0.212619i	$0.0681993\pi$
$607$			6359.38i			0.425238i	−0.977135	+	0.212619i	$0.931801\pi$
$608$		0			0
$609$	22381.5	−	14193.1i	1.48924	−	0.944390i
$610$		0			0
$611$	727.950	+	727.950i	0.0481992	+	0.0481992i
$612$		0			0
$613$	14688.4	−	14688.4i	0.967796	−	0.967796i	−0.0317012	−	0.999497i	$-0.510092\pi$
$613$	14688.4	−	14688.4i	0.967796	−	0.967796i	0.999497	+	0.0317012i	$0.0100925\pi$
$614$		0			0
$615$	884.595	+	1394.94i	0.0580005	+	0.0914627i
$616$		0			0
$617$	−8344.93			−0.544496			−0.272248	−	0.962227i	$-0.587767\pi$
$617$	−8344.93			−0.544496			−0.272248	+	0.962227i	$0.587767\pi$
$618$		0			0
$619$	7771.63	+	7771.63i	0.504634	+	0.504634i	0.912874	−	0.408241i	$-0.133858\pi$
$619$	7771.63	+	7771.63i	0.504634	+	0.504634i	−0.408241	+	0.912874i	$0.633858\pi$
$620$		0			0
$621$	110.708	−	142.425i	0.00715388	−	0.00920338i
$622$		0			0
$623$	−6136.91			−0.394655
$624$		0			0
$625$	15126.4			0.968087
$626$		0			0
$627$	−1239.21	+	5535.08i	−0.0789300	+	0.352551i
$628$		0			0
$629$	16364.9	+	16364.9i	1.03738	+	1.03738i
$630$		0			0
$631$	2424.40			0.152954			0.0764768	−	0.997071i	$-0.475633\pi$
$631$	2424.40			0.152954			0.0764768	+	0.997071i	$0.475633\pi$
$632$		0			0
$633$	21251.1	−	13476.3i	1.33437	−	0.846182i
$634$		0			0
$635$	8036.89	−	8036.89i	0.502259	−	0.502259i
$636$		0			0
$637$	−5967.37	−	5967.37i	−0.371171	−	0.371171i
$638$		0			0
$639$	−6041.27	+	12815.8i	−0.374005	+	0.793404i
$640$		0			0
$641$			17744.2i			1.09338i	0.837337	+	0.546688i	$0.184111\pi$
$641$			17744.2i			1.09338i	−0.837337	+	0.546688i	$0.815889\pi$
$642$		0			0
$643$	18580.6	−	18580.6i	1.13958	−	1.13958i	0.151052	−	0.988526i	$-0.451734\pi$
$643$	18580.6	−	18580.6i	1.13958	−	1.13958i	0.988526	−	0.151052i	$-0.0482661\pi$
$644$		0			0
$645$	7541.31	−	33684.3i	0.460370	−	2.05630i
$646$		0			0
$647$		−	32732.6i		−	1.98895i	−0.104958	−	0.994477i	$-0.533471\pi$
$647$		−	32732.6i		−	1.98895i	0.104958	−	0.994477i	$-0.466529\pi$
$648$		0			0
$649$			1894.64i			0.114594i
$650$		0			0
$651$	−5920.26	+	26443.6i	−0.356426	+	1.59202i
$652$		0			0
$653$	10271.0	−	10271.0i	0.615522	−	0.615522i	−0.328858	−	0.944380i	$-0.606664\pi$
$653$	10271.0	−	10271.0i	0.615522	−	0.615522i	0.944380	+	0.328858i	$0.106664\pi$
$654$		0			0
$655$			7711.48i			0.460019i
$656$		0			0
$657$	−6663.51	+	14135.8i	−0.395690	+	0.839406i
$658$		0			0
$659$	2233.64	+	2233.64i	0.132034	+	0.132034i	0.770035	−	0.638001i	$-0.220239\pi$
$659$	2233.64	+	2233.64i	0.132034	+	0.132034i	−0.638001	+	0.770035i	$0.720239\pi$
$660$		0			0
$661$	−15832.2	+	15832.2i	−0.931622	+	0.931622i	−0.997807	−	0.0661854i	$-0.978917\pi$
$661$	−15832.2	+	15832.2i	−0.931622	+	0.931622i	0.0661854	+	0.997807i	$0.478917\pi$
$662$		0			0
$663$	−4522.45	+	2867.89i	−0.264913	+	0.167993i
$664$		0			0
$665$	24804.1			1.44641
$666$		0			0
$667$	−153.489	−	153.489i	−0.00891023	−	0.00891023i
$668$		0			0
$669$	1780.32	−	7952.05i	0.102887	−	0.459557i
$670$		0			0
$671$	10561.4			0.607630
$672$		0			0
$673$	7290.78			0.417591			0.208796	−	0.977959i	$-0.433046\pi$
$673$	7290.78			0.417591			0.208796	+	0.977959i	$0.433046\pi$
$674$		0			0
$675$	11095.8	−	14274.6i	0.632708	−	0.813971i
$676$		0			0
$677$	6254.52	+	6254.52i	0.355067	+	0.355067i	0.861991	−	0.506924i	$-0.169217\pi$
$677$	6254.52	+	6254.52i	0.355067	+	0.355067i	−0.506924	+	0.861991i	$0.669217\pi$
$678$		0			0
$679$	−1191.09			−0.0673195
$680$		0			0
$681$	9047.37	+	14267.1i	0.509098	+	0.802812i
$682$		0			0
$683$	11670.1	−	11670.1i	0.653798	−	0.653798i	−0.300108	−	0.953905i	$-0.597023\pi$
$683$	11670.1	−	11670.1i	0.653798	−	0.653798i	0.953905	+	0.300108i	$0.0970226\pi$
$684$		0			0
$685$	35477.7	+	35477.7i	1.97888	+	1.97888i
$686$		0			0
$687$	−5240.00	+	3322.91i	−0.291002	+	0.184537i
$688$		0			0
$689$		−	2572.52i		−	0.142242i
$690$		0			0
$691$	2970.42	−	2970.42i	0.163531	−	0.163531i	−0.620598	−	0.784129i	$-0.713110\pi$
$691$	2970.42	−	2970.42i	0.163531	−	0.163531i	0.784129	+	0.620598i	$0.213110\pi$
$692$		0			0
$693$	16263.3	−	5842.69i	0.891474	−	0.320268i
$694$		0			0
$695$			6947.17i			0.379167i
$696$		0			0
$697$		−	1388.20i		−	0.0754405i
$698$		0			0
$699$	35552.2	+	7959.52i	1.92376	+	0.430696i
$700$		0			0
$701$	2674.46	−	2674.46i	0.144099	−	0.144099i	−0.631377	−	0.775476i	$-0.717510\pi$
$701$	2674.46	−	2674.46i	0.144099	−	0.144099i	0.775476	+	0.631377i	$0.217510\pi$
$702$		0			0
$703$		−	17138.7i		−	0.919484i
$704$		0			0
$705$	3081.75	+	4859.69i	0.164632	+	0.259612i
$706$		0			0
$707$	14413.1	+	14413.1i	0.766704	+	0.766704i
$708$		0			0
$709$	−14743.1	+	14743.1i	−0.780942	+	0.780942i	−0.979990	−	0.199048i	$-0.936215\pi$
$709$	−14743.1	+	14743.1i	−0.780942	+	0.780942i	0.199048	+	0.979990i	$0.436215\pi$
$710$		0			0
$711$	8579.53	−	18200.4i	0.452542	−	0.960011i
$712$		0			0
$713$	221.947			0.0116577
$714$		0			0
$715$	−3535.19	−	3535.19i	−0.184907	−	0.184907i
$716$		0			0
$717$	−9382.19	−	2100.51i	−0.488681	−	0.109407i
$718$		0			0
$719$	−2860.53			−0.148372			−0.0741861	−	0.997244i	$-0.523636\pi$
$719$	−2860.53			−0.148372			−0.0741861	+	0.997244i	$0.523636\pi$
$720$		0			0
$721$	−32656.9			−1.68684
$722$		0			0
$723$	28540.9	+	6389.82i	1.46812	+	0.328686i
$724$		0			0
$725$	−15383.6	−	15383.6i	−0.788044	−	0.788044i
$726$		0			0
$727$	−4158.25			−0.212133			−0.106067	−	0.994359i	$-0.533826\pi$
$727$	−4158.25			−0.212133			−0.106067	+	0.994359i	$0.533826\pi$
$728$		0			0
$729$	4856.18	+	19074.5i	0.246720	+	0.969087i
$730$		0			0
$731$	−20513.2	+	20513.2i	−1.03790	+	1.03790i
$732$		0			0
$733$	−5464.41	−	5464.41i	−0.275351	−	0.275351i	0.555899	−	0.831250i	$-0.312374\pi$
$733$	−5464.41	−	5464.41i	−0.275351	−	0.275351i	−0.831250	+	0.555899i	$0.812374\pi$
$734$		0			0
$735$	−25262.6	−	39837.4i	−1.26779	−	1.99922i
$736$		0			0
$737$		−	6844.45i		−	0.342088i
$738$		0			0
$739$	−12274.6	+	12274.6i	−0.611002	+	0.611002i	−0.943207	−	0.332205i	$-0.892207\pi$
$739$	−12274.6	+	12274.6i	−0.611002	+	0.611002i	0.332205	+	0.943207i	$0.392207\pi$
$740$		0			0
$741$	3869.90	+	866.402i	0.191854	+	0.0429528i
$742$		0			0
$743$			17013.3i			0.840052i	0.907512	+	0.420026i	$0.137979\pi$
$743$			17013.3i			0.840052i	−0.907512	+	0.420026i	$0.862021\pi$
$744$		0			0
$745$			8952.10i			0.440241i
$746$		0			0
$747$	−3695.30	−	10286.0i	−0.180996	−	0.503807i
$748$		0			0
$749$	−38285.0	+	38285.0i	−1.86770	+	1.86770i
$750$		0			0
$751$		−	28248.5i		−	1.37257i	−0.727332	−	0.686286i	$-0.759240\pi$
$751$		−	28248.5i		−	1.37257i	0.727332	−	0.686286i	$-0.240760\pi$
$752$		0			0
$753$	3714.69	−	2355.65i	0.179775	−	0.114003i
$754$		0			0
$755$	−11585.7	−	11585.7i	−0.558472	−	0.558472i
$756$		0			0
$757$	16064.6	−	16064.6i	0.771306	−	0.771306i	−0.207029	−	0.978335i	$-0.566379\pi$
$757$	16064.6	−	16064.6i	0.771306	−	0.771306i	0.978335	+	0.207029i	$0.0663793\pi$
$758$		0			0
$759$	−75.7997	−	119.531i	−0.00362498	−	0.00571633i
$760$		0			0
$761$	−23115.8			−1.10111			−0.550557	−	0.834798i	$-0.685585\pi$
$761$	−23115.8			−1.10111			−0.550557	+	0.834798i	$0.685585\pi$
$762$		0			0
$763$	−37833.6	−	37833.6i	−1.79511	−	1.79511i
$764$		0			0
$765$	−28170.7	+	10120.5i	−1.33139	+	0.478311i
$766$		0			0
$767$	1324.66			0.0623606
$768$		0			0
$769$	−6409.50			−0.300562			−0.150281	−	0.988643i	$-0.548018\pi$
$769$	−6409.50			−0.300562			−0.150281	+	0.988643i	$0.548018\pi$
$770$		0			0
$771$	−7286.41	+	32545.7i	−0.340355	+	1.52024i
$772$		0			0
$773$	−15617.9	−	15617.9i	−0.726699	−	0.726699i	0.243262	−	0.969961i	$-0.421782\pi$
$773$	−15617.9	−	15617.9i	−0.726699	−	0.726699i	−0.969961	+	0.243262i	$0.921782\pi$
$774$		0			0
$775$	22244.8			1.03104
$776$		0			0
$777$	−44096.7	+	27963.6i	−2.03598	+	1.29111i
$778$		0			0
$779$	−726.923	+	726.923i	−0.0334335	+	0.0334335i
$780$		0			0
$781$	7860.74	+	7860.74i	0.360153	+	0.360153i
$782$		0			0
$783$	23501.0	−	2944.59i	1.07261	−	0.134395i
$784$		0			0
$785$		−	3491.74i		−	0.158759i
$786$		0			0
$787$	24107.2	−	24107.2i	1.09190	−	1.09190i	0.0965795	−	0.995325i	$-0.469210\pi$
$787$	24107.2	−	24107.2i	1.09190	−	1.09190i	0.995325	−	0.0965795i	$-0.0307902\pi$
$788$		0			0
$789$	−3936.08	+	17581.0i	−0.177602	+	0.793284i
$790$		0			0
$791$			19483.1i			0.875776i
$792$		0			0
$793$		−	7384.12i		−	0.330666i
$794$		0			0
$795$	3141.56	−	14032.2i	0.140151	−	0.626001i
$796$		0			0
$797$	10177.6	−	10177.6i	0.452335	−	0.452335i	−0.443794	−	0.896129i	$-0.646368\pi$
$797$	10177.6	−	10177.6i	0.452335	−	0.452335i	0.896129	+	0.443794i	$0.146368\pi$
$798$		0			0
$799$		−	4836.22i		−	0.214134i
$800$		0			0
$801$	−4960.90	−	2338.53i	−0.218832	−	0.103156i
$802$		0			0
$803$	8670.38	+	8670.38i	0.381035	+	0.381035i
$804$		0			0
$805$	−437.664	+	437.664i	−0.0191623	+	0.0191623i
$806$		0			0
$807$	−12721.4	+	8067.18i	−0.554912	+	0.351894i
$808$		0			0
$809$	15986.6			0.694759			0.347380	−	0.937725i	$-0.387072\pi$
$809$	15986.6			0.694759			0.347380	+	0.937725i	$0.387072\pi$
$810$		0			0
$811$	13233.6	+	13233.6i	0.572990	+	0.572990i	0.932963	−	0.359973i	$-0.117214\pi$
$811$	13233.6	+	13233.6i	0.572990	+	0.572990i	−0.359973	+	0.932963i	$0.617214\pi$
$812$		0			0
$813$	−2776.47	+	12401.5i	−0.119772	+	0.534979i
$814$		0			0
$815$	−34725.6			−1.49250
$816$		0			0
$817$	21483.2			0.919953
$818$		0			0
$819$	−4084.97	−	11370.6i	−0.174286	−	0.485130i
$820$		0			0
$821$	6092.12	+	6092.12i	0.258972	+	0.258972i	0.824636	−	0.565664i	$-0.191380\pi$
$821$	6092.12	+	6092.12i	0.258972	+	0.258972i	−0.565664	+	0.824636i	$0.691380\pi$
$822$		0			0
$823$	28908.7			1.22442			0.612208	−	0.790697i	$-0.290281\pi$
$823$	28908.7			1.22442			0.612208	+	0.790697i	$0.290281\pi$
$824$		0			0
$825$	−7597.10	−	11980.1i	−0.320602	−	0.505567i
$826$		0			0
$827$	−8950.54	+	8950.54i	−0.376349	+	0.376349i	−0.869783	−	0.493434i	$-0.835741\pi$
$827$	−8950.54	+	8950.54i	−0.376349	+	0.376349i	0.493434	+	0.869783i	$0.335741\pi$
$828$		0			0
$829$	5252.07	+	5252.07i	0.220038	+	0.220038i	0.808515	−	0.588476i	$-0.200272\pi$
$829$	5252.07	+	5252.07i	0.220038	+	0.220038i	−0.588476	+	0.808515i	$0.700272\pi$
$830$		0			0
$831$	29693.2	−	18829.8i	1.23953	−	0.786038i
$832$		0			0
$833$			39644.9i			1.64900i
$834$		0			0
$835$	31990.9	−	31990.9i	1.32586	−	1.32586i
$836$		0			0
$837$	−14862.3	+	19120.2i	−0.613761	+	0.789597i
$838$		0			0
$839$			26507.2i			1.09074i	0.838195	+	0.545370i	$0.183611\pi$
$839$			26507.2i			1.09074i	−0.838195	+	0.545370i	$0.816389\pi$
$840$		0			0
$841$		−	4111.02i		−	0.168560i
$842$		0			0
$843$	−8701.50	−	1948.11i	−0.355511	−	0.0795926i
$844$		0			0
$845$	22280.9	−	22280.9i	0.907085	−	0.907085i
$846$		0			0
$847$			26653.3i			1.08125i
$848$		0			0
$849$	18978.5	+	29927.7i	0.767184	+	1.20980i
$850$		0			0
$851$	302.408	+	302.408i	0.0121815	+	0.0121815i
$852$		0			0
$853$	11291.0	−	11291.0i	0.453222	−	0.453222i	−0.443201	−	0.896422i	$-0.646157\pi$
$853$	11291.0	−	11291.0i	0.453222	−	0.453222i	0.896422	+	0.443201i	$0.146157\pi$
$854$		0			0
$855$	20050.9	+	9451.85i	0.802020	+	0.378066i
$856$		0			0
$857$	37764.6			1.50527			0.752634	−	0.658439i	$-0.228783\pi$
$857$	37764.6			1.50527			0.752634	+	0.658439i	$0.228783\pi$
$858$		0			0
$859$	10557.9	+	10557.9i	0.419359	+	0.419359i	0.884983	−	0.465624i	$-0.154170\pi$
$859$	10557.9	+	10557.9i	0.419359	+	0.419359i	−0.465624	+	0.884983i	$0.654170\pi$
$860$		0			0
$861$	3056.38	+	684.269i	0.120977	+	0.0270846i
$862$		0			0
$863$	42832.2			1.68949			0.844743	−	0.535173i	$-0.179753\pi$
$863$	42832.2			1.68949			0.844743	+	0.535173i	$0.179753\pi$
$864$		0			0
$865$	50036.6			1.96682
$866$		0			0
$867$	−362.721	−	81.2069i	−0.0142084	−	0.00318100i
$868$		0			0
$869$	−11163.5	−	11163.5i	−0.435782	−	0.435782i
$870$		0			0
$871$	−4785.36			−0.186160
$872$		0			0
$873$	−962.844	−	453.877i	−0.0373280	−	0.0175961i
$874$		0			0
$875$	−1317.08	+	1317.08i	−0.0508863	+	0.0508863i
$876$		0			0
$877$	−2791.16	−	2791.16i	−0.107469	−	0.107469i	0.651327	−	0.758797i	$-0.274212\pi$
$877$	−2791.16	−	2791.16i	−0.107469	−	0.107469i	−0.758797	+	0.651327i	$0.774212\pi$
$878$		0			0
$879$	−3024.56	−	4769.51i	−0.116059	−	0.183017i
$880$		0			0
$881$			8537.89i			0.326503i	0.986585	+	0.163251i	$0.0521981\pi$
$881$			8537.89i			0.326503i	−0.986585	+	0.163251i	$0.947802\pi$
$882$		0			0
$883$	−28914.0	+	28914.0i	−1.10196	+	1.10196i	−0.107791	+	0.994174i	$0.534378\pi$
$883$	−28914.0	+	28914.0i	−1.10196	+	1.10196i	−0.994174	+	0.107791i	$0.965622\pi$
$884$		0			0
$885$	7225.55	+	1617.67i	0.274445	+	0.0614435i
$886$		0			0
$887$		−	3233.15i		−	0.122389i	−0.998126	−	0.0611943i	$-0.980509\pi$
$887$		−	3233.15i		−	0.122389i	0.998126	−	0.0611943i	$-0.0194909\pi$
$888$		0			0
$889$		−	21551.5i		−	0.813066i
$890$		0			0
$891$	15373.2	+	1474.22i	0.578025	+	0.0554302i
$892$		0			0
$893$	−2532.45	+	2532.45i	−0.0948994	+	0.0948994i
$894$		0			0
$895$			44769.7i			1.67205i
$896$		0			0
$897$	−83.5710	+	52.9960i	−0.00311076	+	0.00197267i
$898$		0			0
$899$	20605.6	+	20605.6i	0.764445	+	0.764445i
$900$		0			0
$901$	−8545.40	+	8545.40i	−0.315970	+	0.315970i
$902$		0			0
$903$	−35052.2	−	55274.8i	−1.29176	−	2.03702i
$904$		0			0
$905$	−184.232			−0.00676694
$906$		0			0
$907$	24455.2	+	24455.2i	0.895284	+	0.895284i	0.995014	−	0.0997307i	$-0.0317981\pi$
$907$	24455.2	+	24455.2i	0.895284	+	0.895284i	−0.0997307	+	0.995014i	$0.531798\pi$
$908$		0			0
$909$	6158.86	+	17143.3i	0.224727	+	0.625532i
$910$		0			0
$911$	−26302.8			−0.956589			−0.478294	−	0.878200i	$-0.658745\pi$
$911$	−26302.8			−0.956589			−0.478294	+	0.878200i	$0.658745\pi$
$912$		0			0
$913$	−8575.60			−0.310855
$914$		0			0
$915$	9017.50	−	40277.9i	0.325803	−	1.45524i
$916$		0			0
$917$	10339.5	+	10339.5i	0.372344	+	0.372344i
$918$		0			0
$919$	14271.1			0.512252			0.256126	−	0.966643i	$-0.417554\pi$
$919$	14271.1			0.512252			0.256126	+	0.966643i	$0.417554\pi$
$920$		0			0
$921$	−34523.0	+	21892.6i	−1.23515	+	0.783262i
$922$		0			0
$923$	5495.90	−	5495.90i	0.195991	−	0.195991i
$924$		0			0
$925$	30309.1	+	30309.1i	1.07736	+	1.07736i
$926$		0			0
$927$	−26398.9	−	12444.2i	−0.935333	−	0.440909i
$928$		0			0
$929$		−	14189.2i		−	0.501113i	−0.968102	−	0.250556i	$-0.919386\pi$
$929$		−	14189.2i		−	0.501113i	0.968102	−	0.250556i	$-0.0806135\pi$
$930$		0			0
$931$	20759.8	−	20759.8i	0.730799	−	0.730799i
$932$		0			0
$933$	−1030.47	+	4602.74i	−0.0361588	+	0.161508i
$934$		0			0
$935$			23486.4i			0.821485i
$936$		0			0
$937$			37715.2i			1.31494i	0.753479	+	0.657472i	$0.228374\pi$
$937$			37715.2i			1.31494i	−0.753479	+	0.657472i	$0.771626\pi$
$938$		0			0
$939$	1160.45	−	5183.30i	0.0403300	−	0.180139i
$940$		0			0
$941$	20871.8	−	20871.8i	0.723062	−	0.723062i	−0.246166	−	0.969228i	$-0.579171\pi$
$941$	20871.8	−	20871.8i	0.723062	−	0.723062i	0.969228	+	0.246166i	$0.0791709\pi$
$942$		0			0
$943$		−	25.6528i		−	0.000885865i
$944$		0			0
$945$	−8396.29	−	67011.4i	−0.289028	−	2.30675i
$946$		0			0
$947$	−35217.3	−	35217.3i	−1.20846	−	1.20846i	−0.971526	−	0.236931i	$-0.923858\pi$
$947$	−35217.3	−	35217.3i	−1.20846	−	1.20846i	−0.236931	−	0.971526i	$-0.576142\pi$
$948$		0			0
$949$	6061.97	−	6061.97i	0.207355	−	0.207355i
$950$		0			0
$951$	25944.1	−	16452.3i	0.884644	−	0.560991i
$952$		0			0
$953$	−8998.22			−0.305856			−0.152928	−	0.988237i	$-0.548870\pi$
$953$	−8998.22			−0.305856			−0.152928	+	0.988237i	$0.548870\pi$
$954$		0			0
$955$	−35084.8	−	35084.8i	−1.18881	−	1.18881i
$956$		0			0
$957$	4060.02	−	18134.6i	0.137139	−	0.612548i
$958$		0			0
$959$	95136.3			3.20345
$960$		0			0
$961$	−4.92611			−0.000165356
$962$		0			0
$963$	−45537.3	+	16359.6i	−1.52380	+	0.547435i
$964$		0			0
$965$	49852.4	+	49852.4i	1.66301	+	1.66301i
$966$		0			0
$967$	27956.6			0.929702			0.464851	−	0.885389i	$-0.346108\pi$
$967$	27956.6			0.929702			0.464851	+	0.885389i	$0.346108\pi$
$968$		0			0
$969$	−9977.03	−	15733.1i	−0.330762	−	0.521588i
$970$		0			0
$971$	−10274.5	+	10274.5i	−0.339571	+	0.339571i	−0.856206	−	0.516635i	$-0.827184\pi$
$971$	−10274.5	+	10274.5i	−0.339571	+	0.339571i	0.516635	+	0.856206i	$0.327184\pi$
$972$		0			0
$973$	9314.69	+	9314.69i	0.306901	+	0.306901i
$974$		0			0
$975$	−8375.97	+	5311.57i	−0.275124	+	0.174468i
$976$		0			0
$977$		−	50724.0i		−	1.66101i	−0.557013	−	0.830504i	$-0.688053\pi$
$977$		−	50724.0i		−	1.66101i	0.557013	−	0.830504i	$-0.311947\pi$
$978$		0			0
$979$	−3042.83	+	3042.83i	−0.0993354	+	0.0993354i
$980$		0			0
$981$	−16166.7	−	45000.4i	−0.526160	−	1.46458i
$982$		0			0
$983$		−	8090.00i		−	0.262493i	−0.991350	−	0.131247i	$-0.958102\pi$
$983$		−	8090.00i		−	0.262493i	0.991350	−	0.131247i	$-0.0418980\pi$
$984$		0			0
$985$		−	43968.1i		−	1.42227i
$986$		0			0
$987$	10647.8	+	2383.85i	0.343387	+	0.0768783i
$988$		0			0
$989$	−379.066	+	379.066i	−0.0121877	+	0.0121877i
$990$		0			0
$991$			35268.5i			1.13052i	0.824914	+	0.565258i	$0.191223\pi$
$991$			35268.5i			1.13052i	−0.824914	+	0.565258i	$0.808777\pi$
$992$		0			0
$993$	7539.08	+	11888.6i	0.240932	+	0.379933i
$994$		0			0
$995$	31214.2	+	31214.2i	0.994531	+	0.994531i
$996$		0			0
$997$	−17738.4	+	17738.4i	−0.563473	+	0.563473i	−0.930292	−	0.366820i	$-0.880447\pi$
$997$	−17738.4	+	17738.4i	−0.563473	+	0.563473i	0.366820	+	0.930292i	$0.380447\pi$
$998$		0			0
$999$	−46302.2	+	5801.51i	−1.46640	+	0.183735i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.4.k.b.95.2		44
3.2	odd	2	inner	384.4.k.b.95.13		44
4.3	odd	2		384.4.k.a.95.21		44
8.3	odd	2		192.4.k.a.47.2		44
8.5	even	2		48.4.k.a.35.15	yes	44
12.11	even	2		384.4.k.a.95.10		44
16.3	odd	4		48.4.k.a.11.8	✓	44
16.5	even	4		384.4.k.a.287.10		44
16.11	odd	4	inner	384.4.k.b.287.13		44
16.13	even	4		192.4.k.a.143.13		44
24.5	odd	2		48.4.k.a.35.8	yes	44
24.11	even	2		192.4.k.a.47.13		44
48.5	odd	4		384.4.k.a.287.21		44
48.11	even	4	inner	384.4.k.b.287.2		44
48.29	odd	4		192.4.k.a.143.2		44
48.35	even	4		48.4.k.a.11.15	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.k.a.11.8	✓	44	16.3	odd	4
48.4.k.a.11.15	yes	44	48.35	even	4
48.4.k.a.35.8	yes	44	24.5	odd	2
48.4.k.a.35.15	yes	44	8.5	even	2
192.4.k.a.47.2		44	8.3	odd	2
192.4.k.a.47.13		44	24.11	even	2
192.4.k.a.143.2		44	48.29	odd	4
192.4.k.a.143.13		44	16.13	even	4
384.4.k.a.95.10		44	12.11	even	2
384.4.k.a.95.21		44	4.3	odd	2
384.4.k.a.287.10		44	16.5	even	4
384.4.k.a.287.21		44	48.5	odd	4
384.4.k.b.95.2		44	1.1	even	1	trivial
384.4.k.b.95.13		44	3.2	odd	2	inner
384.4.k.b.287.2		44	48.11	even	4	inner
384.4.k.b.287.13		44	16.11	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	384.k (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-5.07063 - 1.13522i) q^{3} +(11.2665 + 11.2665i) q^{5} +30.2121 q^{7} +(24.4225 + 11.5126i) q^{9} +O(q^{10})\)	\(q+(-5.07063 - 1.13522i) q^{3} +(11.2665 + 11.2665i) q^{5} +30.2121 q^{7} +(24.4225 + 11.5126i) q^{9} +(14.9799 - 14.9799i) q^{11} +(-10.4733 - 10.4733i) q^{13} +(-44.3383 - 69.9184i) q^{15} +69.5806i q^{17} +(36.4354 - 36.4354i) q^{19} +(-153.194 - 34.2975i) q^{21} +1.28579i q^{23} +128.869i q^{25} +(-110.768 - 86.1012i) q^{27} +(-119.373 + 119.373i) q^{29} -172.615i q^{31} +(-92.9630 + 58.9519i) q^{33} +(340.385 + 340.385i) q^{35} +(235.193 - 235.193i) q^{37} +(41.2167 + 64.9958i) q^{39} -19.9510 q^{41} +(294.812 + 294.812i) q^{43} +(145.450 + 404.864i) q^{45} -69.5052 q^{47} +569.769 q^{49} +(78.9896 - 352.818i) q^{51} +(122.813 + 122.813i) q^{53} +337.543 q^{55} +(-226.113 + 143.388i) q^{57} +(-63.2396 + 63.2396i) q^{59} +(352.521 + 352.521i) q^{61} +(737.855 + 347.819i) q^{63} -235.996i q^{65} +(228.455 - 228.455i) q^{67} +(1.45966 - 6.51976i) q^{69} +524.753i q^{71} +578.802i q^{73} +(146.296 - 653.449i) q^{75} +(452.573 - 452.573i) q^{77} -745.229i q^{79} +(463.920 + 562.334i) q^{81} +(-286.237 - 286.237i) q^{83} +(-783.932 + 783.932i) q^{85} +(740.814 - 469.783i) q^{87} -203.128 q^{89} +(-316.421 - 316.421i) q^{91} +(-195.957 + 875.266i) q^{93} +821.001 q^{95} -39.4244 q^{97} +(538.304 - 193.389i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{3} - 8 q^{7}+O(q^{10}) \) 44 * q + 2 * q^3 - 8 * q^7	\( 44 q + 2 q^{3} - 8 q^{7} + 4 q^{13} - 20 q^{19} + 56 q^{21} + 134 q^{27} - 4 q^{33} + 4 q^{37} + 596 q^{39} + 436 q^{43} + 252 q^{45} + 972 q^{49} + 648 q^{51} + 280 q^{55} + 916 q^{61} + 1636 q^{67} - 52 q^{69} - 1454 q^{75} - 4 q^{81} - 736 q^{85} + 1284 q^{87} - 424 q^{91} + 2084 q^{93} - 8 q^{97} - 1196 q^{99}+O(q^{100}) \) 44 * q + 2 * q^3 - 8 * q^7 + 4 * q^13 - 20 * q^19 + 56 * q^21 + 134 * q^27 - 4 * q^33 + 4 * q^37 + 596 * q^39 + 436 * q^43 + 252 * q^45 + 972 * q^49 + 648 * q^51 + 280 * q^55 + 916 * q^61 + 1636 * q^67 - 52 * q^69 - 1454 * q^75 - 4 * q^81 - 736 * q^85 + 1284 * q^87 - 424 * q^91 + 2084 * q^93 - 8 * q^97 - 1196 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more