LMFDB - Embedded newform 75.4.e.d.68.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,4,Mod(32,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("75.32");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	75.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.42514325043$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 36x^{14} + 562x^{12} - 3672x^{10} + 16413x^{8} - 6588x^{6} + 43024x^{4} + 499896x^{2} + 532900 $ x^16 - 36x^14 + 562x^12 - 3672x^10 + 16413x^8 - 6588x^6 + 43024x^4 + 499896*x^2 + 532900
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{8}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			68.1
Root			$1.55042 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	75.68
Dual form			75.4.e.d.32.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.39887 - 3.39887i) q^{2} +(0.624963 - 5.15843i) q^{3} +15.1047i q^{4} +(-19.6570 + 15.4087i) q^{6} +(-19.7241 + 19.7241i) q^{7} +(24.1479 - 24.1479i) q^{8} +(-26.2188 - 6.44766i) q^{9} +O(q^{10})$	\(q+(-3.39887 - 3.39887i) q^{2} +(0.624963 - 5.15843i) q^{3} +15.1047i q^{4} +(-19.6570 + 15.4087i) q^{6} +(-19.7241 + 19.7241i) q^{7} +(24.1479 - 24.1479i) q^{8} +(-26.2188 - 6.44766i) q^{9} +9.19707i q^{11} +(77.9165 + 9.43987i) q^{12} +(22.4300 + 22.4300i) q^{13} +134.080 q^{14} -43.3141 q^{16} +(-50.6273 - 50.6273i) q^{17} +(67.1998 + 111.029i) q^{18} +16.5813i q^{19} +(89.4187 + 114.072i) q^{21} +(31.2597 - 31.2597i) q^{22} +(-48.2959 + 48.2959i) q^{23} +(-109.474 - 139.657i) q^{24} -152.474i q^{26} +(-49.6456 + 131.219i) q^{27} +(-297.927 - 297.927i) q^{28} -203.298 q^{29} -27.4766 q^{31} +(-45.9644 - 45.9644i) q^{32} +(47.4425 + 5.74783i) q^{33} +344.152i q^{34} +(97.3898 - 396.027i) q^{36} +(-130.592 + 130.592i) q^{37} +(56.3576 - 56.3576i) q^{38} +(129.722 - 101.686i) q^{39} -9.19707i q^{41} +(83.7948 - 691.641i) q^{42} +(-63.3021 - 63.3021i) q^{43} -138.919 q^{44} +328.303 q^{46} +(383.520 + 383.520i) q^{47} +(-27.0697 + 223.433i) q^{48} -435.083i q^{49} +(-292.798 + 229.517i) q^{51} +(-338.799 + 338.799i) q^{52} +(-441.142 + 441.142i) q^{53} +(614.735 - 277.256i) q^{54} +952.594i q^{56} +(85.5333 + 10.3627i) q^{57} +(690.986 + 690.986i) q^{58} -314.626 q^{59} -431.664 q^{61} +(93.3894 + 93.3894i) q^{62} +(644.318 - 389.969i) q^{63} +658.967i q^{64} +(-141.715 - 180.787i) q^{66} +(649.685 - 649.685i) q^{67} +(764.709 - 764.709i) q^{68} +(218.948 + 279.314i) q^{69} -722.186i q^{71} +(-788.828 + 477.433i) q^{72} +(-662.432 - 662.432i) q^{73} +887.733 q^{74} -250.455 q^{76} +(-181.404 - 181.404i) q^{77} +(-786.526 - 95.2905i) q^{78} +206.816i q^{79} +(645.855 + 338.100i) q^{81} +(-31.2597 + 31.2597i) q^{82} +(544.335 - 544.335i) q^{83} +(-1723.03 + 1350.64i) q^{84} +430.312i q^{86} +(-127.054 + 1048.70i) q^{87} +(222.090 + 222.090i) q^{88} -563.910 q^{89} -884.827 q^{91} +(-729.494 - 729.494i) q^{92} +(-17.1718 + 141.736i) q^{93} -2607.07i q^{94} +(-265.830 + 208.378i) q^{96} +(66.0080 - 66.0080i) q^{97} +(-1478.79 + 1478.79i) q^{98} +(59.2996 - 241.137i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 84 q^{6}+O(q^{10}) $ 16 * q - 84 * q^6	$ 16 q - 84 q^{6} - 232 q^{16} + 816 q^{21} - 1208 q^{31} + 252 q^{36} + 1872 q^{46} + 156 q^{51} - 1528 q^{61} - 3420 q^{66} + 1064 q^{76} + 6876 q^{81} - 10008 q^{91} - 8172 q^{96}+O(q^{100}) $ 16 * q - 84 * q^6 - 232 * q^16 + 816 * q^21 - 1208 * q^31 + 252 * q^36 + 1872 * q^46 + 156 * q^51 - 1528 * q^61 - 3420 * q^66 + 1064 * q^76 + 6876 * q^81 - 10008 * q^91 - 8172 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−3.39887	−	3.39887i	−1.20168	−	1.20168i	−0.973654	−	0.228029i	$-0.926772\pi$
$2$	−3.39887	−	3.39887i	−1.20168	−	1.20168i	−0.228029	−	0.973654i	$-0.573228\pi$
$3$	0.624963	−	5.15843i	0.120274	−	0.992741i
$3$	0.624963	−	5.15843i	0.120274	−	0.992741i
$4$			15.1047i			1.88809i
$5$		0			0
$5$		0			0
$6$	−19.6570	+	15.4087i	−1.33749	+	1.04843i
$7$	−19.7241	+	19.7241i	−1.06500	+	1.06500i	−0.0672681	+	0.997735i	$0.521428\pi$
$7$	−19.7241	+	19.7241i	−1.06500	+	1.06500i	−0.997735	+	0.0672681i	$0.978572\pi$
$8$	24.1479	−	24.1479i	1.06720	−	1.06720i
$9$	−26.2188	−	6.44766i	−0.971068	−	0.238802i
$10$		0			0
$11$			9.19707i			0.252093i	0.992024	+	0.126046i	$0.0402288\pi$
$11$			9.19707i			0.252093i	−0.992024	+	0.126046i	$0.959771\pi$
$12$	77.9165	+	9.43987i	1.87438	+	0.227088i
$13$	22.4300	+	22.4300i	0.478537	+	0.478537i	0.904663	−	0.426127i	$-0.140122\pi$
$13$	22.4300	+	22.4300i	0.478537	+	0.478537i	−0.426127	+	0.904663i	$0.640122\pi$
$14$	134.080			2.55959
$15$		0			0
$16$	−43.3141			−0.676782
$17$	−50.6273	−	50.6273i	−0.722290	−	0.722290i	0.246782	−	0.969071i	$-0.420627\pi$
$17$	−50.6273	−	50.6273i	−0.722290	−	0.722290i	−0.969071	+	0.246782i	$0.920627\pi$
$18$	67.1998	+	111.029i	0.879952	+	1.45388i
$19$			16.5813i			0.200211i	0.994977	+	0.100105i	$0.0319180\pi$
$19$			16.5813i			0.200211i	−0.994977	+	0.100105i	$0.968082\pi$
$20$		0			0
$21$	89.4187	+	114.072i	0.929180	+	1.18536i
$22$	31.2597	−	31.2597i	0.302936	−	0.302936i
$23$	−48.2959	+	48.2959i	−0.437843	+	0.437843i	−0.891285	−	0.453443i	$-0.850196\pi$
$23$	−48.2959	+	48.2959i	−0.437843	+	0.437843i	0.453443	+	0.891285i	$0.350196\pi$
$24$	−109.474	−	139.657i	−0.931094	−	1.18781i
$25$		0			0
$26$		−	152.474i		−	1.15010i
$27$	−49.6456	+	131.219i	−0.353863	+	0.935297i
$28$	−297.927	−	297.927i	−2.01082	−	2.01082i
$29$	−203.298			−1.30178			−0.650889	−	0.759173i	$-0.725604\pi$
$29$	−203.298			−1.30178			−0.650889	+	0.759173i	$0.725604\pi$
$30$		0			0
$31$	−27.4766			−0.159192			−0.0795958	−	0.996827i	$-0.525363\pi$
$31$	−27.4766			−0.159192			−0.0795958	+	0.996827i	$0.525363\pi$
$32$	−45.9644	−	45.9644i	−0.253920	−	0.253920i
$33$	47.4425	+	5.74783i	0.250263	+	0.0303203i
$34$			344.152i			1.73593i
$35$		0			0
$36$	97.3898	−	396.027i	0.450879	−	1.83346i
$37$	−130.592	+	130.592i	−0.580250	+	0.580250i	−0.934972	−	0.354722i	$-0.884575\pi$
$37$	−130.592	+	130.592i	−0.580250	+	0.580250i	0.354722	+	0.934972i	$0.384575\pi$
$38$	56.3576	−	56.3576i	0.240590	−	0.240590i
$39$	129.722	−	101.686i	0.532618	−	0.417507i
$40$		0			0
$41$		−	9.19707i		−	0.0350327i	−0.999847	−	0.0175164i	$-0.994424\pi$
$41$		−	9.19707i		−	0.0350327i	0.999847	−	0.0175164i	$-0.00557592\pi$
$42$	83.7948	−	691.641i	0.307853	−	2.54101i
$43$	−63.3021	−	63.3021i	−0.224499	−	0.224499i	0.585891	−	0.810390i	$-0.300745\pi$
$43$	−63.3021	−	63.3021i	−0.224499	−	0.224499i	−0.810390	+	0.585891i	$0.800745\pi$
$44$	−138.919			−0.475973
$45$		0			0
$46$	328.303			1.05230
$47$	383.520	+	383.520i	1.19026	+	1.19026i	0.976994	+	0.213265i	$0.0684098\pi$
$47$	383.520	+	383.520i	1.19026	+	1.19026i	0.213265	+	0.976994i	$0.431590\pi$
$48$	−27.0697	+	223.433i	−0.0813994	+	0.671869i
$49$		−	435.083i		−	1.26846i
$50$		0			0
$51$	−292.798	+	229.517i	−0.803919	+	0.630173i
$52$	−338.799	+	338.799i	−0.903518	+	0.903518i
$53$	−441.142	+	441.142i	−1.14331	+	1.14331i	−0.155471	+	0.987840i	$0.549690\pi$
$53$	−441.142	+	441.142i	−1.14331	+	1.14331i	−0.987840	+	0.155471i	$0.950310\pi$
$54$	614.735	−	277.256i	1.54916	−	0.698700i
$55$		0			0
$56$			952.594i			2.27314i
$57$	85.5333	+	10.3627i	0.198757	+	0.0240802i
$58$	690.986	+	690.986i	1.56433	+	1.56433i
$59$	−314.626			−0.694251			−0.347126	−	0.937819i	$-0.612842\pi$
$59$	−314.626			−0.694251			−0.347126	+	0.937819i	$0.612842\pi$
$60$		0			0
$61$	−431.664			−0.906048			−0.453024	−	0.891498i	$-0.649655\pi$
$61$	−431.664			−0.906048			−0.453024	+	0.891498i	$0.649655\pi$
$62$	93.3894	+	93.3894i	0.191298	+	0.191298i
$63$	644.318	−	389.969i	1.28852	−	0.779866i
$64$			658.967i			1.28705i
$65$		0			0
$66$	−141.715	−	180.787i	−0.264301	−	0.337172i
$67$	649.685	−	649.685i	1.18465	−	1.18465i	0.206126	−	0.978525i	$-0.433914\pi$
$67$	649.685	−	649.685i	1.18465	−	1.18465i	0.978525	−	0.206126i	$-0.0660858\pi$
$68$	764.709	−	764.709i	1.36374	−	1.36374i
$69$	218.948	+	279.314i	0.382003	+	0.487326i
$70$		0			0
$71$		−	722.186i		−	1.20715i	−0.797306	−	0.603575i	$-0.793742\pi$
$71$		−	722.186i		−	1.20715i	0.797306	−	0.603575i	$-0.206258\pi$
$72$	−788.828	+	477.433i	−1.29117	+	0.781473i
$73$	−662.432	−	662.432i	−1.06208	−	1.06208i	−0.997941	−	0.0641383i	$-0.979570\pi$
$73$	−662.432	−	662.432i	−1.06208	−	1.06208i	−0.0641383	−	0.997941i	$-0.520430\pi$
$74$	887.733			1.39455
$75$		0			0
$76$	−250.455			−0.378015
$77$	−181.404	−	181.404i	−0.268480	−	0.268480i
$78$	−786.526	−	95.2905i	−1.14175	−	0.138327i
$79$			206.816i			0.294539i	0.989096	+	0.147269i	$0.0470484\pi$
$79$			206.816i			0.294539i	−0.989096	+	0.147269i	$0.952952\pi$
$80$		0			0
$81$	645.855	+	338.100i	0.885947	+	0.463786i
$82$	−31.2597	+	31.2597i	−0.0420982	+	0.0420982i
$83$	544.335	−	544.335i	0.719862	−	0.719862i	−0.248715	−	0.968577i	$-0.580008\pi$
$83$	544.335	−	544.335i	0.719862	−	0.719862i	0.968577	+	0.248715i	$0.0800083\pi$
$84$	−1723.03	+	1350.64i	−2.23807	+	1.75437i
$85$		0			0
$86$			430.312i			0.539555i
$87$	−127.054	+	1048.70i	−0.156570	+	1.29233i
$88$	222.090	+	222.090i	0.269033	+	0.269033i
$89$	−563.910			−0.671622			−0.335811	−	0.941929i	$-0.609010\pi$
$89$	−563.910			−0.671622			−0.335811	+	0.941929i	$0.609010\pi$
$90$		0			0
$91$	−884.827			−1.01929
$92$	−729.494	−	729.494i	−0.826685	−	0.826685i
$93$	−17.1718	+	141.736i	−0.0191466	+	0.158036i
$94$		−	2607.07i		−	2.86063i
$95$		0			0
$96$	−265.830	+	208.378i	−0.282617	+	0.221537i
$97$	66.0080	−	66.0080i	0.0690938	−	0.0690938i	−0.671715	−	0.740809i	$-0.734442\pi$
$97$	66.0080	−	66.0080i	0.0690938	−	0.0690938i	0.740809	+	0.671715i	$0.234442\pi$
$98$	−1478.79	+	1478.79i	−1.52429	+	1.52429i
$99$	59.2996	−	241.137i	0.0602003	−	0.244799i
$100$		0			0
$101$		−	1108.46i		−	1.09204i	−0.837772	−	0.546021i	$-0.816142\pi$
$101$		−	1108.46i		−	1.09204i	0.837772	−	0.546021i	$-0.183858\pi$
$102$	1775.28	+	215.082i	1.72332	+	0.208787i
$103$	823.002	+	823.002i	0.787308	+	0.787308i	0.981052	−	0.193744i	$-0.0620630\pi$
$103$	823.002	+	823.002i	0.787308	+	0.787308i	−0.193744	+	0.981052i	$0.562063\pi$
$104$	1083.28			1.02139
$105$		0			0
$106$	2998.77			2.74780
$107$	−918.923	−	918.923i	−0.830239	−	0.830239i	0.157310	−	0.987549i	$-0.449718\pi$
$107$	−918.923	−	918.923i	−0.830239	−	0.830239i	−0.987549	+	0.157310i	$0.949718\pi$
$108$	−1982.02	−	749.881i	−1.76592	−	0.668124i
$109$		−	4.75472i		−	0.00417816i	−0.999998	−	0.00208908i	$-0.999335\pi$
$109$		−	4.75472i		−	0.00417816i	0.999998	−	0.00208908i	$-0.000664976\pi$
$110$		0			0
$111$	592.036	+	755.267i	0.506248	+	0.645826i
$112$	854.332	−	854.332i	0.720775	−	0.720775i
$113$	−791.114	+	791.114i	−0.658600	+	0.658600i	−0.955049	−	0.296449i	$-0.904198\pi$
$113$	−791.114	+	791.114i	−0.658600	+	0.658600i	0.296449	+	0.955049i	$0.404198\pi$
$114$	−255.495	−	325.938i	−0.209906	−	0.267780i
$115$		0			0
$116$		−	3070.76i		−	2.45787i
$117$	−443.469	−	732.711i	−0.350416	−	0.578967i
$118$	1069.37	+	1069.37i	0.834270	+	0.834270i
$119$	1997.16			1.53848
$120$		0			0
$121$	1246.41			0.936449
$122$	1467.17	+	1467.17i	1.08878	+	1.08878i
$123$	−47.4425	−	5.74783i	−0.0347784	−	0.00421353i
$124$		−	415.025i		−	0.300567i
$125$		0			0
$126$	−3515.41	−	864.500i	−2.48554	−	0.611236i
$127$	9.96644	−	9.96644i	0.00696361	−	0.00696361i	−0.703616	−	0.710580i	$-0.748433\pi$
$127$	9.96644	−	9.96644i	0.00696361	−	0.00696361i	0.710580	+	0.703616i	$0.248433\pi$
$128$	1872.03	−	1872.03i	1.29270	−	1.29270i
$129$	−366.101	+	286.978i	−0.249871	+	0.195868i
$130$		0			0
$131$			2663.20i			1.77622i	0.459631	+	0.888110i	$0.347982\pi$
$131$			2663.20i			1.77622i	−0.459631	+	0.888110i	$0.652018\pi$
$132$	−86.8192	+	716.604i	−0.0572473	+	0.472518i
$133$	−327.051	−	327.051i	−0.213225	−	0.213225i
$134$	−4416.39			−2.84715
$135$		0			0
$136$	−2445.09			−1.54165
$137$	−351.396	−	351.396i	−0.219137	−	0.219137i	0.588998	−	0.808135i	$-0.299523\pi$
$137$	−351.396	−	351.396i	−0.219137	−	0.219137i	−0.808135	+	0.588998i	$0.799523\pi$
$138$	205.177	−	1693.53i	0.126564	−	1.04466i
$139$			1738.04i			1.06057i	0.847820	+	0.530283i	$0.177914\pi$
$139$			1738.04i			1.06057i	−0.847820	+	0.530283i	$0.822086\pi$
$140$		0			0
$141$	2218.05	−	1738.68i	1.32478	−	1.03846i
$142$	−2454.62	+	2454.62i	−1.45061	+	1.45061i
$143$	−206.291	+	206.291i	−0.120636	+	0.120636i
$144$	1135.64	+	279.274i	0.657202	+	0.161617i
$145$		0			0
$146$			4503.04i			2.55257i
$147$	−2244.34	−	271.911i	−1.25925	−	0.152563i
$148$	−1972.55	−	1972.55i	−1.09556	−	1.09556i
$149$	183.941			0.101135			0.0505674	−	0.998721i	$-0.483897\pi$
$149$	183.941			0.101135			0.0505674	+	0.998721i	$0.483897\pi$
$150$		0			0
$151$	−805.273			−0.433988			−0.216994	−	0.976173i	$-0.569625\pi$
$151$	−805.273			−0.433988			−0.216994	+	0.976173i	$0.569625\pi$
$152$	400.403	+	400.403i	0.213664	+	0.213664i
$153$	1000.96	+	1653.82i	0.528908	+	0.873877i
$154$			1233.14i			0.645255i
$155$		0			0
$156$	1535.93	+	1959.41i	0.788289	+	1.00563i
$157$	1626.56	−	1626.56i	0.826840	−	0.826840i	−0.160239	−	0.987078i	$-0.551226\pi$
$157$	1626.56	−	1626.56i	0.826840	−	0.826840i	0.987078	+	0.160239i	$0.0512264\pi$
$158$	702.940	−	702.940i	0.353942	−	0.353942i
$159$	1999.90	+	2551.30i	0.997501	+	1.27252i
$160$		0			0
$161$		−	1905.19i		−	0.932608i
$162$	−1046.02	−	3344.34i	−0.507304	−	1.62195i
$163$	395.910	+	395.910i	0.190246	+	0.190246i	0.795802	−	0.605556i	$-0.207049\pi$
$163$	395.910	+	395.910i	0.190246	+	0.190246i	−0.605556	+	0.795802i	$0.707049\pi$
$164$	138.919			0.0661448
$165$		0			0
$166$	−3700.25			−1.73009
$167$	875.168	+	875.168i	0.405524	+	0.405524i	0.880174	−	0.474650i	$-0.157426\pi$
$167$	875.168	+	875.168i	0.405524	+	0.405524i	−0.474650	+	0.880174i	$0.657426\pi$
$168$	4913.89	+	595.336i	2.25664	+	0.273400i
$169$		−	1190.79i		−	0.542005i
$170$		0			0
$171$	106.910	−	434.741i	0.0478107	−	0.194418i
$172$	956.158	−	956.158i	0.423874	−	0.423874i
$173$	1048.43	−	1048.43i	0.460753	−	0.460753i	−0.438149	−	0.898902i	$-0.644366\pi$
$173$	1048.43	−	1048.43i	0.460753	−	0.460753i	0.898902	+	0.438149i	$0.144366\pi$
$174$	3996.24	−	3132.56i	1.74112	−	1.36482i
$175$		0			0
$176$		−	398.363i		−	0.170612i
$177$	−196.630	+	1622.98i	−0.0835005	+	0.689212i
$178$	1916.66	+	1916.66i	0.807077	+	0.807077i
$179$	210.570			0.0879259			0.0439629	−	0.999033i	$-0.486002\pi$
$179$	210.570			0.0879259			0.0439629	+	0.999033i	$0.486002\pi$
$180$		0			0
$181$	−128.633			−0.0528244			−0.0264122	−	0.999651i	$-0.508408\pi$
$181$	−128.633			−0.0528244			−0.0264122	+	0.999651i	$0.508408\pi$
$182$	3007.41	+	3007.41i	1.22486	+	1.22486i
$183$	−269.774	+	2226.71i	−0.108974	+	0.899471i
$184$			2332.49i			0.934530i
$185$		0			0
$186$	540.108	−	423.378i	0.212917	−	0.166901i
$187$	465.623	−	465.623i	0.182084	−	0.182084i
$188$	−5792.96	+	5792.96i	−2.24731	+	2.24731i
$189$	−1608.96	−	3567.39i	−0.619229	−	1.37296i
$190$		0			0
$191$			4291.51i			1.62577i	0.582421	+	0.812887i	$0.302106\pi$
$191$			4291.51i			1.62577i	−0.582421	+	0.812887i	$0.697894\pi$
$192$	3399.24	+	411.830i	1.27770	+	0.154798i
$193$	−3567.00	−	3567.00i	−1.33035	−	1.33035i	−0.905051	−	0.425303i	$-0.860168\pi$
$193$	−3567.00	−	3567.00i	−1.33035	−	1.33035i	−0.425303	−	0.905051i	$-0.639832\pi$
$194$	−448.706			−0.166058
$195$		0			0
$196$	6571.79			2.39497
$197$	421.067	+	421.067i	0.152283	+	0.152283i	0.779137	−	0.626854i	$-0.215658\pi$
$197$	421.067	+	421.067i	0.152283	+	0.152283i	−0.626854	+	0.779137i	$0.715658\pi$
$198$	−1021.14	+	618.041i	−0.366513	+	0.221830i
$199$		−	3024.07i		−	1.07724i	−0.842549	−	0.538619i	$-0.818946\pi$
$199$		−	3024.07i		−	1.07724i	0.842549	−	0.538619i	$-0.181054\pi$
$200$		0			0
$201$	−2945.33	−	3757.39i	−1.03357	−	1.31853i
$202$	−3767.53	+	3767.53i	−1.31229	+	1.31229i
$203$	4009.88	−	4009.88i	1.38640	−	1.38640i
$204$	−3466.79	−	4422.62i	−1.18982	−	1.51787i
$205$		0			0
$206$		−	5594.56i		−	1.89219i
$207$	1577.66	−	954.867i	0.529733	−	0.320617i
$208$	−971.537	−	971.537i	−0.323865	−	0.323865i
$209$	−152.499			−0.0504717
$210$		0			0
$211$	−2881.37			−0.940104			−0.470052	−	0.882639i	$-0.655765\pi$
$211$	−2881.37			−0.940104			−0.470052	+	0.882639i	$0.655765\pi$
$212$	−6663.31	−	6663.31i	−2.15867	−	2.15867i
$213$	−3725.35	−	451.339i	−1.19839	−	0.145189i
$214$			6246.60i			1.99537i
$215$		0			0
$216$	1969.82	+	4367.50i	0.620505	+	1.37579i
$217$	541.951	−	541.951i	0.169539	−	0.169539i
$218$	−16.1607	+	16.1607i	−0.00502083	+	0.00502083i
$219$	−3831.11	+	3003.11i	−1.18211	+	0.926629i
$220$		0			0
$221$		−	2271.15i		−	0.691284i
$222$	554.800	−	4579.31i	0.167729	−	1.38443i
$223$	1334.90	+	1334.90i	0.400858	+	0.400858i	0.878535	−	0.477677i	$-0.158521\pi$
$223$	1334.90	+	1334.90i	0.400858	+	0.400858i	−0.477677	+	0.878535i	$0.658521\pi$
$224$	1813.22			0.540851
$225$		0			0
$226$	5377.79			1.58286
$227$	−337.339	−	337.339i	−0.0986342	−	0.0986342i	0.656068	−	0.754702i	$-0.272219\pi$
$227$	−337.339	−	337.339i	−0.0986342	−	0.0986342i	−0.754702	+	0.656068i	$0.772219\pi$
$228$	−156.525	+	1291.95i	−0.0454654	+	0.375271i
$229$			4575.71i			1.32040i	0.751090	+	0.660200i	$0.229529\pi$
$229$			4575.71i			1.32040i	−0.751090	+	0.660200i	$0.770471\pi$
$230$		0			0
$231$	−1049.13	+	822.391i	−0.298822	+	0.234240i
$232$	−4909.24	+	4909.24i	−1.38926	+	1.38926i
$233$	−529.682	+	529.682i	−0.148930	+	0.148930i	−0.777640	−	0.628710i	$-0.783583\pi$
$233$	−529.682	+	529.682i	−0.148930	+	0.148930i	0.628710	+	0.777640i	$0.283583\pi$
$234$	−983.099	+	3997.69i	−0.274646	+	1.11682i
$235$		0			0
$236$		−	4752.33i		−	1.31081i
$237$	1066.84	+	129.252i	0.292401	+	0.0354254i
$238$	−6788.09	−	6788.09i	−1.84877	−	1.84877i
$239$	871.265			0.235805			0.117903	−	0.993025i	$-0.462383\pi$
$239$	871.265			0.235805			0.117903	+	0.993025i	$0.462383\pi$
$240$		0			0
$241$	42.9221			0.0114724			0.00573622	−	0.999984i	$-0.498174\pi$
$241$	42.9221			0.0114724			0.00573622	+	0.999984i	$0.498174\pi$
$242$	−4236.40	−	4236.40i	−1.12532	−	1.12532i
$243$	2147.70	−	3120.30i	0.566976	−	0.823734i
$244$		−	6520.15i		−	1.71070i
$245$		0			0
$246$	141.715	+	180.787i	0.0367293	+	0.0468560i
$247$	−371.918	+	371.918i	−0.0958081	+	0.0958081i
$248$	−663.502	+	663.502i	−0.169889	+	0.169889i
$249$	−2467.73	−	3148.10i	−0.628055	−	0.801217i
$250$		0			0
$251$		−	50.7994i		−	0.0127746i	−0.999980	−	0.00638731i	$-0.997967\pi$
$251$		−	50.7994i		−	0.0127746i	0.999980	−	0.00638731i	$-0.00203316\pi$
$252$	5890.37	+	9732.23i	1.47245	+	2.43283i
$253$	−444.181	−	444.181i	−0.110377	−	0.110377i
$254$	−67.7493			−0.0167361
$255$		0			0
$256$	−7453.85			−1.81979
$257$	4271.29	+	4271.29i	1.03671	+	1.03671i	0.999300	+	0.0374152i	$0.0119124\pi$
$257$	4271.29	+	4271.29i	1.03671	+	1.03671i	0.0374152	+	0.999300i	$0.488088\pi$
$258$	2219.73	+	268.929i	0.535638	+	0.0648945i
$259$		−	5151.64i		−	1.23593i
$260$		0			0
$261$	5330.25	+	1310.80i	1.26412	+	0.310867i
$262$	9051.88	−	9051.88i	2.13445	−	2.13445i
$263$	−1151.74	+	1151.74i	−0.270036	+	0.270036i	−0.829114	−	0.559079i	$-0.811155\pi$
$263$	−1151.74	+	1151.74i	−0.270036	+	0.270036i	0.559079	+	0.829114i	$0.311155\pi$
$264$	1284.44	−	1006.84i	0.299438	−	0.234722i
$265$		0			0
$266$			2223.21i			0.512458i
$267$	−352.423	+	2908.89i	−0.0807787	+	0.666746i
$268$	9813.29	+	9813.29i	2.23672	+	2.23672i
$269$	1684.46			0.381796			0.190898	−	0.981610i	$-0.438860\pi$
$269$	1684.46			0.381796			0.190898	+	0.981610i	$0.438860\pi$
$270$		0			0
$271$	−3308.36			−0.741581			−0.370791	−	0.928717i	$-0.620913\pi$
$271$	−3308.36			−0.741581			−0.370791	+	0.928717i	$0.620913\pi$
$272$	2192.87	+	2192.87i	0.488833	+	0.488833i
$273$	−552.984	+	4564.32i	−0.122594	+	1.01189i
$274$			2388.70i			0.526666i
$275$		0			0
$276$	−4218.95	+	3307.14i	−0.920112	+	0.721255i
$277$	−2178.55	+	2178.55i	−0.472550	+	0.472550i	−0.902739	−	0.430189i	$-0.858447\pi$
$277$	−2178.55	+	2178.55i	−0.472550	+	0.472550i	0.430189	+	0.902739i	$0.358447\pi$
$278$	5907.39	−	5907.39i	1.27447	−	1.27447i
$279$	720.404	+	177.159i	0.154586	+	0.0380153i
$280$		0			0
$281$			4972.10i			1.05555i	0.849383	+	0.527776i	$0.176974\pi$
$281$			4972.10i			1.05555i	−0.849383	+	0.527776i	$0.823026\pi$
$282$	−13448.4	−	1629.32i	−2.83986	−	0.344060i
$283$	3325.61	+	3325.61i	0.698542	+	0.698542i	0.964096	−	0.265554i	$-0.0855550\pi$
$283$	3325.61	+	3325.61i	0.698542	+	0.698542i	−0.265554	+	0.964096i	$0.585555\pi$
$284$	10908.4			2.27920
$285$		0			0
$286$	1402.31			0.289932
$287$	181.404	+	181.404i	0.0373100	+	0.0373100i
$288$	908.771	+	1501.50i	0.185937	+	0.307210i
$289$			213.245i			0.0434043i
$290$		0			0
$291$	−299.245	−	381.750i	−0.0602820	−	0.0769024i
$292$	10005.8	−	10005.8i	2.00530	−	2.00530i
$293$	−3473.24	+	3473.24i	−0.692521	+	0.692521i	−0.962786	−	0.270265i	$-0.912889\pi$
$293$	−3473.24	+	3473.24i	−0.692521	+	0.692521i	0.270265	+	0.962786i	$0.412889\pi$
$294$	6704.06	+	8552.43i	1.32989	+	1.69656i
$295$		0			0
$296$			6307.07i			1.23848i
$297$	−1206.83	−	456.594i	−0.235782	−	0.0892063i
$298$	−625.194	−	625.194i	−0.121532	−	0.121532i
$299$	−2166.56			−0.419048
$300$		0			0
$301$	2497.16			0.478185
$302$	2737.02	+	2737.02i	0.521516	+	0.521516i
$303$	−5717.93	−	692.748i	−1.08411	−	0.131344i
$304$		−	718.201i		−	0.135499i
$305$		0			0
$306$	2218.97	−	9023.26i	0.414543	−	1.68570i
$307$	−4105.90	+	4105.90i	−0.763310	+	0.763310i	−0.976919	−	0.213609i	$-0.931478\pi$
$307$	−4105.90	+	4105.90i	−0.763310	+	0.763310i	0.213609	+	0.976919i	$0.431478\pi$
$308$	2740.05	−	2740.05i	0.506913	−	0.506913i
$309$	4759.74	−	3731.05i	0.876286	−	0.686900i
$310$		0			0
$311$			3937.21i			0.717874i	0.933362	+	0.358937i	$0.116861\pi$
$311$			3937.21i			0.717874i	−0.933362	+	0.358937i	$0.883139\pi$
$312$	677.009	−	5588.02i	0.122846	−	1.01397i
$313$	160.559	+	160.559i	0.0289946	+	0.0289946i	0.721455	−	0.692461i	$-0.243473\pi$
$313$	160.559	+	160.559i	0.0289946	+	0.0289946i	−0.692461	+	0.721455i	$0.743473\pi$
$314$	−11057.0			−1.98720
$315$		0			0
$316$	−3123.88			−0.556115
$317$	−6408.72	−	6408.72i	−1.13549	−	1.13549i	−0.989249	−	0.146239i	$-0.953283\pi$
$317$	−6408.72	−	6408.72i	−1.13549	−	1.13549i	−0.146239	−	0.989249i	$-0.546717\pi$
$318$	1874.12	−	15469.0i	0.330489	−	2.72785i
$319$		−	1869.75i		−	0.328169i
$320$		0			0
$321$	−5314.49	+	4165.91i	−0.924069	+	0.724356i
$322$	−6475.49	+	6475.49i	−1.12070	+	1.12070i
$323$	839.464	−	839.464i	0.144610	−	0.144610i
$324$	−5106.90	+	9755.44i	−0.875668	+	1.67274i
$325$		0			0
$326$		−	2691.30i		−	0.457231i
$327$	−24.5269	−	2.97153i	−0.00414783	−	0.000502525i
$328$	−222.090	−	222.090i	−0.0373868	−	0.0373868i
$329$	−15129.2			−2.53526
$330$		0			0
$331$	8806.84			1.46244			0.731220	−	0.682142i	$-0.238951\pi$
$331$	8806.84			1.46244			0.731220	+	0.682142i	$0.238951\pi$
$332$	8222.01	+	8222.01i	1.35916	+	1.35916i
$333$	4265.99	−	2581.96i	0.702027	−	0.424897i
$334$		−	5949.17i		−	0.974623i
$335$		0			0
$336$	−3873.09	−	4940.94i	−0.628852	−	0.802233i
$337$	−5690.38	+	5690.38i	−0.919806	+	0.919806i	−0.997015	−	0.0772088i	$-0.975399\pi$
$337$	−5690.38	+	5690.38i	−0.919806	+	0.919806i	0.0772088	+	0.997015i	$0.475399\pi$
$338$	−4047.33	+	4047.33i	−0.651319	+	0.651319i
$339$	3586.49	+	4575.33i	0.574606	+	0.733031i
$340$		0			0
$341$		−	252.704i		−	0.0401311i
$342$	−1841.01	+	1114.26i	−0.291082	+	0.176176i
$343$	1816.25	+	1816.25i	0.285914	+	0.285914i
$344$	−3057.23			−0.479171
$345$		0			0
$346$	−7126.93			−1.10736
$347$	4974.95	+	4974.95i	0.769652	+	0.769652i	0.978045	−	0.208393i	$-0.0668234\pi$
$347$	4974.95	+	4974.95i	0.769652	+	0.769652i	−0.208393	+	0.978045i	$0.566823\pi$
$348$	−15840.3	−	1919.11i	−2.44003	−	0.295618i
$349$			6686.71i			1.02559i	0.858511	+	0.512795i	$0.171390\pi$
$349$			6686.71i			1.02559i	−0.858511	+	0.512795i	$0.828610\pi$
$350$		0			0
$351$	−4056.79	+	1829.69i	−0.616910	+	0.278238i
$352$	422.738	−	422.738i	0.0640114	−	0.0640114i
$353$	−2025.97	+	2025.97i	−0.305472	+	0.305472i	−0.843150	−	0.537678i	$-0.819302\pi$
$353$	−2025.97	+	2025.97i	−0.305472	+	0.305472i	0.537678	+	0.843150i	$0.319302\pi$
$354$	6184.61	−	4847.98i	0.928555	−	0.727873i
$355$		0			0
$356$		−	8517.68i		−	1.26808i
$357$	1248.15	−	10302.2i	0.185040	−	1.52731i
$358$	−715.700	−	715.700i	−0.105659	−	0.105659i
$359$	7178.33			1.05531			0.527657	−	0.849458i	$-0.323071\pi$
$359$	7178.33			1.05531			0.527657	+	0.849458i	$0.323071\pi$
$360$		0			0
$361$	6584.06			0.959916
$362$	437.207	+	437.207i	0.0634782	+	0.0634782i
$363$	778.962	−	6429.54i	0.112631	−	0.929651i
$364$		−	13365.0i		−	1.92450i
$365$		0			0
$366$	8485.23	−	6651.38i	1.21183	−	0.949926i
$367$	5129.64	−	5129.64i	0.729605	−	0.729605i	−0.240936	−	0.970541i	$-0.577454\pi$
$367$	5129.64	−	5129.64i	0.729605	−	0.729605i	0.970541	+	0.240936i	$0.0774545\pi$
$368$	2091.89	−	2091.89i	0.296324	−	0.296324i
$369$	−59.2996	+	241.137i	−0.00836589	+	0.0340192i
$370$		0			0
$371$		−	17402.3i		−	2.43526i
$372$	−2140.88	−	259.375i	−0.298385	−	0.0361505i
$373$	1332.77	+	1332.77i	0.185009	+	0.185009i	0.793534	−	0.608525i	$-0.208239\pi$
$373$	1332.77	+	1332.77i	0.185009	+	0.185009i	−0.608525	+	0.793534i	$0.708239\pi$
$374$	−3165.19			−0.437615
$375$		0			0
$376$	18522.4			2.54049
$377$	−4559.99	−	4559.99i	−0.622949	−	0.622949i
$378$	−6656.47	+	17593.7i	−0.905745	+	2.39398i
$379$			5792.28i			0.785039i	0.919744	+	0.392519i	$0.128396\pi$
$379$			5792.28i			0.785039i	−0.919744	+	0.392519i	$0.871604\pi$
$380$		0			0
$381$	−45.1825	−	57.6399i	−0.00607552	−	0.00775060i
$382$	14586.3	−	14586.3i	1.95367	−	1.95367i
$383$	−5023.31	+	5023.31i	−0.670181	+	0.670181i	−0.957758	−	0.287577i	$-0.907150\pi$
$383$	−5023.31	+	5023.31i	−0.670181	+	0.670181i	0.287577	+	0.957758i	$0.407150\pi$
$384$	−8486.79	−	10826.7i	−1.12784	−	1.43880i
$385$		0			0
$386$			24247.6i			3.19733i
$387$	1251.56	+	2067.86i	0.164393	+	0.271615i
$388$	997.030	+	997.030i	0.130455	+	0.130455i
$389$	10198.8			1.32931			0.664654	−	0.747151i	$-0.268579\pi$
$389$	10198.8			1.32931			0.664654	+	0.747151i	$0.268579\pi$
$390$		0			0
$391$	4890.18			0.632498
$392$	−10506.3	−	10506.3i	−1.35370	−	1.35370i
$393$	13737.9	+	1664.40i	1.76333	+	0.213633i
$394$		−	2862.31i		−	0.365993i
$395$		0			0
$396$	3642.29	+	895.701i	0.462202	+	0.113663i
$397$	90.2345	−	90.2345i	0.0114074	−	0.0114074i	−0.701380	−	0.712787i	$-0.747432\pi$
$397$	90.2345	−	90.2345i	0.0114074	−	0.0114074i	0.712787	+	0.701380i	$0.247432\pi$
$398$	−10278.4	+	10278.4i	−1.29450	+	1.29450i
$399$	−1891.46	+	1482.67i	−0.237322	+	0.186032i
$400$		0			0
$401$			597.810i			0.0744469i	0.999307	+	0.0372234i	$0.0118513\pi$
$401$			597.810i			0.0744469i	−0.999307	+	0.0372234i	$0.988149\pi$
$402$	−2760.08	+	22781.7i	−0.342439	+	2.82648i
$403$	−616.301	−	616.301i	−0.0761790	−	0.0761790i
$404$	16743.0			2.06187
$405$		0			0
$406$	−27258.2			−3.33202
$407$	−1201.07	−	1201.07i	−0.146277	−	0.146277i
$408$	−1528.09	+	12612.8i	−0.185421	+	1.53046i
$409$		−	10819.0i		−	1.30799i	−0.756500	−	0.653994i	$-0.773092\pi$
$409$		−	10819.0i		−	1.30799i	0.756500	−	0.653994i	$-0.226908\pi$
$410$		0			0
$411$	−2032.26	+	1593.04i	−0.243903	+	0.191190i
$412$	−12431.2	+	12431.2i	−1.48651	+	1.48651i
$413$	6205.73	−	6205.73i	0.739380	−	0.739380i
$414$	−8607.73	−	2116.79i	−1.02185	−	0.251291i
$415$		0			0
$416$		−	2061.97i		−	0.243020i
$417$	8965.57	+	1086.21i	1.05287	+	0.127559i
$418$	518.325	+	518.325i	0.0606510	+	0.0606510i
$419$	−10849.8			−1.26503			−0.632514	−	0.774549i	$-0.717977\pi$
$419$	−10849.8			−1.26503			−0.632514	+	0.774549i	$0.717977\pi$
$420$		0			0
$421$	−12341.0			−1.42865			−0.714324	−	0.699815i	$-0.753266\pi$
$421$	−12341.0			−1.42865			−0.714324	+	0.699815i	$0.753266\pi$
$422$	9793.43	+	9793.43i	1.12971	+	1.12971i
$423$	−7582.65	−	12528.3i	−0.871587	−	1.44006i
$424$			21305.3i			2.44028i
$425$		0			0
$426$	11127.9	+	14196.0i	1.26561	+	1.61455i
$427$	8514.20	−	8514.20i	0.964944	−	0.964944i
$428$	13880.0	−	13880.0i	1.56756	−	1.56756i
$429$	935.213	+	1193.06i	0.105251	+	0.134269i
$430$		0			0
$431$		−	10648.0i		−	1.19001i	−0.803721	−	0.595006i	$-0.797150\pi$
$431$		−	10648.0i		−	1.19001i	0.803721	−	0.595006i	$-0.202850\pi$
$432$	2150.35	−	5683.61i	0.239488	−	0.632993i
$433$	−10825.2	−	10825.2i	−1.20144	−	1.20144i	−0.973728	−	0.227716i	$-0.926874\pi$
$433$	−10825.2	−	10825.2i	−1.20144	−	1.20144i	−0.227716	−	0.973728i	$-0.573126\pi$
$434$	−3684.05			−0.407465
$435$		0			0
$436$	71.8186			0.00788873
$437$	−800.806	−	800.806i	−0.0876607	−	0.0876607i
$438$	23228.7	+	2814.24i	2.53404	+	0.307008i
$439$		−	1560.21i		−	0.169623i	−0.996397	−	0.0848117i	$-0.972971\pi$
$439$		−	1560.21i		−	0.169623i	0.996397	−	0.0848117i	$-0.0270289\pi$
$440$		0			0
$441$	−2805.26	+	11407.4i	−0.302912	+	1.23176i
$442$	−7719.34	+	7719.34i	−0.830705	+	0.830705i
$443$	−2588.92	+	2588.92i	−0.277660	+	0.277660i	−0.832174	−	0.554514i	$-0.812904\pi$
$443$	−2588.92	+	2588.92i	−0.277660	+	0.277660i	0.554514	+	0.832174i	$0.312904\pi$
$444$	−11408.1	+	8942.52i	−1.21938	+	0.955840i
$445$		0			0
$446$		−	9074.30i		−	0.963409i
$447$	114.957	−	948.850i	0.0121639	−	0.100401i
$448$	−12997.6	−	12997.6i	−1.37071	−	1.37071i
$449$	14291.3			1.50211			0.751057	−	0.660238i	$-0.229544\pi$
$449$	14291.3			1.50211			0.751057	+	0.660238i	$0.229544\pi$
$450$		0			0
$451$	84.5862			0.00883150
$452$	−11949.5	−	11949.5i	−1.24349	−	1.24349i
$453$	−503.266	+	4153.95i	−0.0521976	+	0.430838i
$454$			2293.14i			0.237054i
$455$		0			0
$456$	2315.69	−	1815.21i	0.237812	−	0.186415i
$457$	−7928.59	+	7928.59i	−0.811562	+	0.811562i	−0.984868	−	0.173306i	$-0.944555\pi$
$457$	−7928.59	+	7928.59i	−0.811562	+	0.811562i	0.173306	+	0.984868i	$0.444555\pi$
$458$	15552.3	−	15552.3i	1.58670	−	1.58670i
$459$	9156.66	−	4129.82i	0.931147	−	0.419964i
$460$		0			0
$461$		−	10685.6i		−	1.07957i	−0.841804	−	0.539783i	$-0.818506\pi$
$461$		−	10685.6i		−	1.07957i	0.841804	−	0.539783i	$-0.181494\pi$
$462$	6361.07	+	770.667i	0.640571	+	0.0776075i
$463$	9059.56	+	9059.56i	0.909360	+	0.909360i	0.996220	−	0.0868606i	$-0.0276835\pi$
$463$	9059.56	+	9059.56i	0.909360	+	0.909360i	−0.0868606	+	0.996220i	$0.527683\pi$
$464$	8805.68			0.881020
$465$		0			0
$466$	3600.65			0.357933
$467$	−9692.99	−	9692.99i	−0.960467	−	0.960467i	0.0387806	−	0.999248i	$-0.487653\pi$
$467$	−9692.99	−	9692.99i	−0.960467	−	0.960467i	−0.999248	+	0.0387806i	$0.987653\pi$
$468$	11067.4	−	6698.46i	1.09314	−	0.661616i
$469$			25628.9i			2.52332i
$470$		0			0
$471$	−7373.97	−	9407.05i	−0.721390	−	0.920285i
$472$	−7597.57	+	7597.57i	−0.740904	+	0.740904i
$473$	582.194	−	582.194i	0.0565947	−	0.0565947i
$474$	−3186.76	−	4065.38i	−0.308803	−	0.393943i
$475$		0			0
$476$			30166.5i			2.90478i
$477$	14410.6	−	8721.90i	1.38326	−	0.837208i
$478$	−2961.32	−	2961.32i	−0.283363	−	0.283363i
$479$	−5193.79			−0.495428			−0.247714	−	0.968833i	$-0.579679\pi$
$479$	−5193.79			−0.495428			−0.247714	+	0.968833i	$0.579679\pi$
$480$		0			0
$481$	−5858.38			−0.555341
$482$	−145.887	−	145.887i	−0.0137862	−	0.0137862i
$483$	−9827.78	−	1190.67i	−0.925838	−	0.112169i
$484$			18826.7i			1.76810i
$485$		0			0
$486$	−17905.3	+	3305.74i	−1.67119	+	0.308542i
$487$	1020.47	−	1020.47i	0.0949523	−	0.0949523i	−0.658035	−	0.752987i	$-0.728612\pi$
$487$	1020.47	−	1020.47i	0.0949523	−	0.0949523i	0.752987	+	0.658035i	$0.228612\pi$
$488$	−10423.8	+	10423.8i	−0.966932	+	0.966932i
$489$	2289.70	−	1794.85i	0.211746	−	0.165983i
$490$		0			0
$491$			7350.62i			0.675619i	0.941215	+	0.337809i	$0.109686\pi$
$491$			7350.62i			0.675619i	−0.941215	+	0.337809i	$0.890314\pi$
$492$	86.8192	−	716.604i	0.00795551	−	0.0656646i
$493$	10292.4	+	10292.4i	0.940261	+	0.940261i
$494$	2528.21			0.230262
$495$		0			0
$496$	1190.12			0.107738
$497$	14244.5	+	14244.5i	1.28562	+	1.28562i
$498$	−2312.52	+	19087.5i	−0.208085	+	1.71753i
$499$		−	15309.0i		−	1.37339i	−0.726944	−	0.686697i	$-0.759060\pi$
$499$		−	15309.0i		−	1.37339i	0.726944	−	0.686697i	$-0.240940\pi$
$500$		0			0
$501$	5061.44	−	3967.55i	0.451354	−	0.353806i
$502$	−172.661	+	172.661i	−0.0153511	+	0.0153511i
$503$	738.534	−	738.534i	0.0654664	−	0.0654664i	−0.673616	−	0.739082i	$-0.735260\pi$
$503$	738.534	−	738.534i	0.0654664	−	0.0654664i	0.739082	+	0.673616i	$0.235260\pi$
$504$	6142.00	−	24975.9i	0.542830	−	2.20737i
$505$		0			0
$506$			3019.43i			0.265277i
$507$	−6142.59	−	744.197i	−0.538071	−	0.0651892i
$508$	150.540	+	150.540i	0.0131479	+	0.0131479i
$509$	4477.48			0.389903			0.194952	−	0.980813i	$-0.437545\pi$
$509$	4477.48			0.389903			0.194952	+	0.980813i	$0.437545\pi$
$510$		0			0
$511$	26131.8			2.26224
$512$	10358.5	+	10358.5i	0.894109	+	0.894109i
$513$	−2175.77	−	823.186i	−0.187256	−	0.0708471i
$514$		−	29035.2i		−	2.49161i
$515$		0			0
$516$	−4334.71	−	5529.84i	−0.369816	−	0.471778i
$517$	−3527.27	+	3527.27i	−0.300056	+	0.300056i
$518$	−17509.8	+	17509.8i	−1.48520	+	1.48520i
$519$	−4753.00	−	6063.46i	−0.401992	−	0.512825i
$520$		0			0
$521$			14580.8i			1.22610i	0.790045	+	0.613049i	$0.210057\pi$
$521$			14580.8i			1.22610i	−0.790045	+	0.613049i	$0.789943\pi$
$522$	−13661.6	−	22572.1i	−1.14550	−	1.89263i
$523$	2457.46	+	2457.46i	0.205463	+	0.205463i	0.802336	−	0.596873i	$-0.203590\pi$
$523$	2457.46	+	2457.46i	0.205463	+	0.205463i	−0.596873	+	0.802336i	$0.703590\pi$
$524$	−40226.8			−3.35366
$525$		0			0
$526$	7829.24			0.648994
$527$	1391.06	+	1391.06i	0.114982	+	0.114982i
$528$	−2054.93	−	248.962i	−0.169373	−	0.0205202i
$529$			7502.02i			0.616587i
$530$		0			0
$531$	8249.13	+	2028.60i	0.674165	+	0.165789i
$532$	4940.00	−	4940.00i	0.402587	−	0.402587i
$533$	206.291	−	206.291i	0.0167644	−	0.0167644i
$534$	11084.8	−	8689.11i	0.898288	−	0.704147i
$535$		0			0
$536$		−	31377.1i		−	2.52852i
$537$	131.598	−	1086.21i	0.0105752	−	0.0872876i
$538$	−5725.26	−	5725.26i	−0.458798	−	0.458798i
$539$	4001.49			0.319770
$540$		0			0
$541$	375.804			0.0298652			0.0149326	−	0.999889i	$-0.495247\pi$
$541$	375.804			0.0298652			0.0149326	+	0.999889i	$0.495247\pi$
$542$	11244.7	+	11244.7i	0.891146	+	0.891146i
$543$	−80.3909	+	663.545i	−0.00635341	+	0.0524409i
$544$			4654.11i			0.366808i
$545$		0			0
$546$	17393.1	−	13634.0i	1.36329	−	1.06865i
$547$	3656.92	−	3656.92i	0.285848	−	0.285848i	−0.549588	−	0.835436i	$-0.685215\pi$
$547$	3656.92	−	3656.92i	0.285848	−	0.285848i	0.835436	+	0.549588i	$0.185215\pi$
$548$	5307.72	−	5307.72i	0.413749	−	0.413749i
$549$	11317.7	+	2783.22i	0.879834	+	0.216366i
$550$		0			0
$551$		−	3370.94i		−	0.260630i
$552$	12032.0	+	1457.72i	0.927746	+	0.112400i
$553$	−4079.26	−	4079.26i	−0.313685	−	0.313685i
$554$	14809.2			1.13571
$555$		0			0
$556$	−26252.6			−2.00244
$557$	−4512.51	−	4512.51i	−0.343270	−	0.343270i	0.514325	−	0.857595i	$-0.328042\pi$
$557$	−4512.51	−	4512.51i	−0.343270	−	0.343270i	−0.857595	+	0.514325i	$0.828042\pi$
$558$	−1846.42	−	3050.70i	−0.140081	−	0.231446i
$559$		−	2839.74i		−	0.214862i
$560$		0			0
$561$	−2110.89	−	2692.88i	−0.158862	−	0.202662i
$562$	16899.5	−	16899.5i	1.26844	−	1.26844i
$563$	−15527.9	+	15527.9i	−1.16238	+	1.16238i	−0.178430	+	0.983953i	$0.557102\pi$
$563$	−15527.9	+	15527.9i	−1.16238	+	1.16238i	−0.983953	+	0.178430i	$0.942898\pi$
$564$	26262.2	+	33502.9i	1.96070	+	2.50129i
$565$		0			0
$566$		−	22606.7i		−	1.67885i
$567$	−19407.7	+	6070.20i	−1.43747	+	0.449603i
$568$	−17439.3	−	17439.3i	−1.28827	−	1.28827i
$569$	−12965.1			−0.955230			−0.477615	−	0.878569i	$-0.658499\pi$
$569$	−12965.1			−0.955230			−0.477615	+	0.878569i	$0.658499\pi$
$570$		0			0
$571$	−6452.24			−0.472886			−0.236443	−	0.971645i	$-0.575982\pi$
$571$	−6452.24			−0.472886			−0.236443	+	0.971645i	$0.575982\pi$
$572$	−3115.96	−	3115.96i	−0.227771	−	0.227771i
$573$	22137.5	+	2682.04i	1.61397	+	0.195539i
$574$		−	1233.14i		−	0.0896695i
$575$		0			0
$576$	4248.79	−	17277.4i	0.307349	−	1.24981i
$577$	−11704.9	+	11704.9i	−0.844508	+	0.844508i	−0.989441	−	0.144934i	$-0.953703\pi$
$577$	−11704.9	+	11704.9i	−0.844508	+	0.844508i	0.144934	+	0.989441i	$0.453703\pi$
$578$	724.794	−	724.794i	0.0521582	−	0.0521582i
$579$	−20629.4	+	16170.9i	−1.48070	+	1.16069i
$580$		0			0
$581$			21473.1i			1.53331i
$582$	−280.424	+	2314.62i	−0.0199725	+	0.164852i
$583$	−4057.22	−	4057.22i	−0.288221	−	0.288221i
$584$	−31992.7			−2.26690
$585$		0			0
$586$	23610.2			1.66438
$587$	−6441.65	−	6441.65i	−0.452939	−	0.452939i	0.443390	−	0.896329i	$-0.353776\pi$
$587$	−6441.65	−	6441.65i	−0.452939	−	0.452939i	−0.896329	+	0.443390i	$0.853776\pi$
$588$	4107.12	−	33900.1i	0.288053	−	2.37758i
$589$		−	455.596i		−	0.0318718i
$590$		0			0
$591$	2435.20	−	1908.90i	0.169494	−	0.132862i
$592$	5656.48	−	5656.48i	0.392703	−	0.392703i
$593$	12555.8	−	12555.8i	0.869487	−	0.869487i	−0.122928	−	0.992416i	$-0.539228\pi$
$593$	12555.8	−	12555.8i	0.869487	−	0.869487i	0.992416	+	0.122928i	$0.0392285\pi$
$594$	2549.95	+	5653.76i	0.176137	+	0.390533i
$595$		0			0
$596$			2778.38i			0.190951i
$597$	−15599.4	−	1889.93i	−1.06942	−	0.129564i
$598$	7363.85	+	7363.85i	0.503563	+	0.503563i
$599$	−24700.6			−1.68487			−0.842437	−	0.538795i	$-0.818880\pi$
$599$	−24700.6			−1.68487			−0.842437	+	0.538795i	$0.818880\pi$
$600$		0			0
$601$	−22487.6			−1.52627			−0.763135	−	0.646239i	$-0.776341\pi$
$601$	−22487.6			−1.52627			−0.763135	+	0.646239i	$0.776341\pi$
$602$	−8487.52	−	8487.52i	−0.574627	−	0.574627i
$603$	−21222.9	+	12845.0i	−1.43327	+	0.867480i
$604$		−	12163.4i		−	0.819407i
$605$		0			0
$606$	17080.0	+	21789.1i	1.14493	+	1.46060i
$607$	−13817.0	+	13817.0i	−0.923912	+	0.923912i	−0.997303	−	0.0733910i	$-0.976618\pi$
$607$	−13817.0	+	13817.0i	−0.923912	+	0.923912i	0.0733910	+	0.997303i	$0.476618\pi$
$608$	762.148	−	762.148i	0.0508375	−	0.0508375i
$609$	−18178.7	−	23190.7i	−1.20959	−	1.54308i
$610$		0			0
$611$			17204.8i			1.13917i
$612$	−24980.4	+	15119.2i	−1.64995	+	0.998624i
$613$	−7861.86	−	7861.86i	−0.518005	−	0.518005i	0.398962	−	0.916967i	$-0.369371\pi$
$613$	−7861.86	−	7861.86i	−0.518005	−	0.518005i	−0.916967	+	0.398962i	$0.869371\pi$
$614$	27910.9			1.83451
$615$		0			0
$616$	−8761.08			−0.573042
$617$	17057.5	+	17057.5i	1.11298	+	1.11298i	0.992746	+	0.120233i	$0.0383641\pi$
$617$	17057.5	+	17057.5i	1.11298	+	1.11298i	0.120233	+	0.992746i	$0.461636\pi$
$618$	−28859.1	−	3496.39i	−1.87845	−	0.227582i
$619$		−	24671.5i		−	1.60199i	−0.598671	−	0.800995i	$-0.704304\pi$
$619$		−	24671.5i		−	1.60199i	0.598671	−	0.800995i	$-0.295696\pi$
$620$		0			0
$621$	−3939.64	−	8734.99i	−0.254577	−	0.564450i
$622$	13382.1	−	13382.1i	0.862657	−	0.862657i
$623$	11122.6	−	11122.6i	0.715279	−	0.715279i
$624$	−5618.78	+	4404.43i	−0.360467	+	0.282561i
$625$		0			0
$626$		−	1091.44i		−	0.0696847i
$627$	−95.3062	+	786.656i	−0.00607044	+	0.0501053i
$628$	24568.7	+	24568.7i	1.56114	+	1.56114i
$629$	13223.1			0.838216
$630$		0			0
$631$	13039.4			0.822648			0.411324	−	0.911489i	$-0.365066\pi$
$631$	13039.4			0.822648			0.411324	+	0.911489i	$0.365066\pi$
$632$	4994.17	+	4994.17i	0.314331	+	0.314331i
$633$	−1800.75	+	14863.4i	−0.113070	+	0.933280i
$634$			43564.9i			2.72900i
$635$		0			0
$636$	−38536.6	+	30207.9i	−2.40263	+	1.88337i
$637$	9758.93	−	9758.93i	0.607006	−	0.607006i
$638$	−6355.05	+	6355.05i	−0.394355	+	0.394355i
$639$	−4656.41	+	18934.9i	−0.288270	+	1.17223i
$640$		0			0
$641$			7413.70i			0.456823i	0.973565	+	0.228412i	$0.0733532\pi$
$641$			7413.70i			0.456823i	−0.973565	+	0.228412i	$0.926647\pi$
$642$	32222.7	+	3903.90i	1.98088	+	0.239991i
$643$	−3856.84	−	3856.84i	−0.236546	−	0.236546i	0.578872	−	0.815418i	$-0.303493\pi$
$643$	−3856.84	−	3856.84i	−0.236546	−	0.236546i	−0.815418	+	0.578872i	$0.803493\pi$
$644$	28777.3			1.76084
$645$		0			0
$646$	−5706.46			−0.347551
$647$	−762.540	−	762.540i	−0.0463347	−	0.0463347i	0.683560	−	0.729894i	$-0.260431\pi$
$647$	−762.540	−	762.540i	−0.0463347	−	0.0463347i	−0.729894	+	0.683560i	$0.760431\pi$
$648$	23760.5	−	7431.65i	1.44043	−	0.450529i
$649$		−	2893.64i		−	0.175016i
$650$		0			0
$651$	−2456.92	−	3134.32i	−0.147918	−	0.188700i
$652$	−5980.10	+	5980.10i	−0.359200	+	0.359200i
$653$	18549.1	−	18549.1i	1.11161	−	1.11161i	0.118679	−	0.992933i	$-0.462134\pi$
$653$	18549.1	−	18549.1i	1.11161	−	1.11161i	0.992933	−	0.118679i	$-0.0378661\pi$
$654$	73.2641	+	93.4637i	0.00438051	+	0.00558826i
$655$		0			0
$656$			398.363i			0.0237095i
$657$	13097.1	+	21639.3i	0.777725	+	1.28498i
$658$	51422.3	+	51422.3i	3.04658	+	3.04658i
$659$	27210.3			1.60844			0.804222	−	0.594329i	$-0.202582\pi$
$659$	27210.3			1.60844			0.804222	+	0.594329i	$0.202582\pi$
$660$		0			0
$661$	17912.8			1.05405			0.527026	−	0.849849i	$-0.323307\pi$
$661$	17912.8			1.05405			0.527026	+	0.849849i	$0.323307\pi$
$662$	−29933.3	−	29933.3i	−1.75739	−	1.75739i
$663$	−11715.5	−	1419.38i	−0.686266	−	0.0831436i
$664$		−	26289.1i		−	1.53647i
$665$		0			0
$666$	−23275.3	−	5723.80i	−1.35421	−	0.333022i
$667$	9818.47	−	9818.47i	0.569974	−	0.569974i
$668$	−13219.1	+	13219.1i	−0.765664	+	0.765664i
$669$	7720.24	−	6051.72i	0.446161	−	0.349735i
$670$		0			0
$671$		−	3970.05i		−	0.228408i
$672$	1133.19	−	9353.36i	0.0650504	−	0.536925i
$673$	13447.5	+	13447.5i	0.770225	+	0.770225i	0.978146	−	0.207921i	$-0.0666696\pi$
$673$	13447.5	+	13447.5i	0.770225	+	0.770225i	−0.207921	+	0.978146i	$0.566670\pi$
$674$	38681.8			2.21063
$675$		0			0
$676$	17986.4			1.02335
$677$	−14818.2	−	14818.2i	−0.841228	−	0.841228i	0.147791	−	0.989019i	$-0.452784\pi$
$677$	−14818.2	−	14818.2i	−0.841228	−	0.841228i	−0.989019	+	0.147791i	$0.952784\pi$
$678$	3360.92	−	27741.0i	0.190377	−	1.57137i
$679$			2603.90i			0.147170i
$680$		0			0
$681$	−1950.96	+	1529.32i	−0.109781	+	0.0860550i
$682$	−858.909	+	858.909i	−0.0482248	+	0.0482248i
$683$	−10932.8	+	10932.8i	−0.612493	+	0.612493i	−0.943595	−	0.331102i	$-0.892579\pi$
$683$	−10932.8	+	10932.8i	−0.612493	+	0.612493i	0.331102	+	0.943595i	$0.392579\pi$
$684$	6566.63	+	1614.85i	0.367078	+	0.0902707i
$685$		0			0
$686$		−	12346.4i		−	0.687156i
$687$	23603.5	+	2859.65i	1.31082	+	0.158810i
$688$	2741.87	+	2741.87i	0.151937	+	0.151937i
$689$	−19789.7			−1.09423
$690$		0			0
$691$	−6859.09			−0.377615			−0.188807	−	0.982014i	$-0.560462\pi$
$691$	−6859.09			−0.377615			−0.188807	+	0.982014i	$0.560462\pi$
$692$	15836.1	+	15836.1i	0.869942	+	0.869942i
$693$	3586.58	+	5925.84i	0.196599	+	0.324826i
$694$		−	33818.4i		−	1.84976i
$695$		0			0
$696$	22255.9	+	28392.1i	1.21208	+	1.54626i
$697$	−465.623	+	465.623i	−0.0253038	+	0.0253038i
$698$	22727.3	−	22727.3i	1.23244	−	1.23244i
$699$	2401.30	+	3063.36i	0.129936	+	0.165761i
$700$		0			0
$701$		−	26912.7i		−	1.45004i	−0.688727	−	0.725021i	$-0.741830\pi$
$701$		−	26912.7i		−	1.45004i	0.688727	−	0.725021i	$-0.258170\pi$
$702$	20007.4	+	7569.65i	1.07568	+	0.406977i
$703$	−2165.38	−	2165.38i	−0.116172	−	0.116172i
$704$	−6060.57			−0.324455
$705$		0			0
$706$	13772.1			0.734162
$707$	21863.5	+	21863.5i	1.16303	+	1.16303i
$708$	−24514.6	−	2970.03i	−1.30129	−	0.157656i
$709$			12724.4i			0.674011i	0.941503	+	0.337005i	$0.109414\pi$
$709$			12724.4i			0.674011i	−0.941503	+	0.337005i	$0.890586\pi$
$710$		0			0
$711$	1333.48	−	5422.46i	0.0703365	−	0.286017i
$712$	−13617.3	+	13617.3i	−0.716753	+	0.716753i
$713$	1327.00	−	1327.00i	0.0697009	−	0.0697009i
$714$	−39258.2	+	30773.6i	−2.05771	+	1.61299i
$715$		0			0
$716$			3180.59i			0.166012i
$717$	544.508	−	4494.36i	0.0283613	−	0.234093i
$718$	−24398.2	−	24398.2i	−1.26815	−	1.26815i
$719$	1776.43			0.0921413			0.0460707	−	0.998938i	$-0.485330\pi$
$719$	1776.43			0.0921413			0.0460707	+	0.998938i	$0.485330\pi$
$720$		0			0
$721$	−32466.0			−1.67697
$722$	−22378.4	−	22378.4i	−1.15351	−	1.15351i
$723$	26.8247	−	221.411i	0.00137984	−	0.0113892i
$724$		−	1942.96i		−	0.0997370i
$725$		0			0
$726$	−24500.8	+	19205.6i	−1.25249	+	0.981800i
$727$	11790.0	−	11790.0i	0.601465	−	0.601465i	−0.339236	−	0.940701i	$-0.610169\pi$
$727$	11790.0	−	11790.0i	0.601465	−	0.601465i	0.940701	+	0.339236i	$0.110169\pi$
$728$	−21366.7	+	21366.7i	−1.08778	+	1.08778i
$729$	−14753.6	−	13028.9i	−0.749562	−	0.661934i
$730$		0			0
$731$			6409.63i			0.324307i
$732$	−33633.7	−	4074.85i	−1.69828	−	0.205753i
$733$	−22491.0	−	22491.0i	−1.13332	−	1.13332i	−0.989622	−	0.143696i	$-0.954101\pi$
$733$	−22491.0	−	22491.0i	−1.13332	−	1.13332i	−0.143696	−	0.989622i	$-0.545899\pi$
$734$	−34870.0			−1.75351
$735$		0			0
$736$	4439.78			0.222354
$737$	5975.20	+	5975.20i	0.298642	+	0.298642i
$738$	1021.14	−	618.041i	0.0509334	−	0.0308271i
$739$		−	9723.29i		−	0.484002i	−0.970276	−	0.242001i	$-0.922196\pi$
$739$		−	9723.29i		−	0.484002i	0.970276	−	0.242001i	$-0.0778037\pi$
$740$		0			0
$741$	1686.08	+	2150.95i	0.0835894	+	0.106636i
$742$	−59148.2	+	59148.2i	−2.92641	+	2.92641i
$743$	3640.61	−	3640.61i	0.179759	−	0.179759i	−0.611492	−	0.791251i	$-0.709430\pi$
$743$	3640.61	−	3640.61i	0.179759	−	0.179759i	0.791251	+	0.611492i	$0.209430\pi$
$744$	3007.97	+	3837.30i	0.148222	+	0.189089i
$745$		0			0
$746$		−	9059.85i		−	0.444645i
$747$	−17781.5	+	10762.1i	−0.870939	+	0.527130i
$748$	7033.09	+	7033.09i	0.343790	+	0.343790i
$749$	36249.9			1.76841
$750$		0			0
$751$	−39901.6			−1.93879			−0.969395	−	0.245508i	$-0.921045\pi$
$751$	−39901.6			−1.93879			−0.969395	+	0.245508i	$0.921045\pi$
$752$	−16611.8	−	16611.8i	−0.805546	−	0.805546i
$753$	−262.045	−	31.7477i	−0.0126819	−	0.00153646i
$754$			30997.7i			1.49717i
$755$		0			0
$756$	53884.3	−	24302.8i	2.59227	−	1.16916i
$757$	19152.6	−	19152.6i	0.919568	−	0.919568i	−0.0774296	−	0.996998i	$-0.524671\pi$
$757$	19152.6	−	19152.6i	0.919568	−	0.919568i	0.996998	+	0.0774296i	$0.0246713\pi$
$758$	19687.2	−	19687.2i	0.943368	−	0.943368i
$759$	−2568.87	+	2013.68i	−0.122851	+	0.0963003i
$760$		0			0
$761$			28330.4i			1.34951i	0.738043	+	0.674753i	$0.235750\pi$
$761$			28330.4i			1.34951i	−0.738043	+	0.674753i	$0.764250\pi$
$762$	−42.3408	+	349.480i	−0.00201292	+	0.0166146i
$763$	93.7828	+	93.7828i	0.00444976	+	0.00444976i
$764$	−64821.9			−3.06960
$765$		0			0
$766$	34147.2			1.61069
$767$	−7057.08	−	7057.08i	−0.332225	−	0.332225i
$768$	−4658.38	+	38450.2i	−0.218874	+	1.80658i
$769$			12352.6i			0.579256i	0.957139	+	0.289628i	$0.0935316\pi$
$769$			12352.6i			0.579256i	−0.957139	+	0.289628i	$0.906468\pi$
$770$		0			0
$771$	24702.6	−	19363.8i	1.15388	−	0.904499i
$772$	53878.4	−	53878.4i	2.51182	−	2.51182i
$773$	−12713.0	+	12713.0i	−0.591532	+	0.591532i	−0.938045	−	0.346513i	$-0.887366\pi$
$773$	−12713.0	+	12713.0i	−0.591532	+	0.591532i	0.346513	+	0.938045i	$0.387366\pi$
$774$	2774.50	−	11282.3i	0.128847	−	0.523944i
$775$		0			0
$776$		−	3187.91i		−	0.147474i
$777$	−26574.4	−	3219.58i	−1.22696	−	0.148651i
$778$	−34664.5	−	34664.5i	−1.59741	−	1.59741i
$779$	152.499			0.00701392
$780$		0			0
$781$	6642.00			0.304314
$782$	−16621.1	−	16621.1i	−0.760063	−	0.760063i
$783$	10092.9	−	26676.5i	0.460651	−	1.21755i
$784$			18845.2i			0.858473i
$785$		0			0
$786$	−41036.4	−	52350.6i	−1.86224	−	2.37568i
$787$	11888.6	−	11888.6i	0.538481	−	0.538481i	−0.384602	−	0.923083i	$-0.625661\pi$
$787$	11888.6	−	11888.6i	0.538481	−	0.538481i	0.923083	+	0.384602i	$0.125661\pi$
$788$	−6360.09	+	6360.09i	−0.287524	+	0.287524i
$789$	5221.38	+	6660.97i	0.235597	+	0.300554i
$790$		0			0
$791$		−	31208.1i		−	1.40282i
$792$	−4390.99	−	7254.91i	−0.197004	−	0.325495i
$793$	−9682.25	−	9682.25i	−0.433577	−	0.433577i
$794$	−613.391			−0.0274162
$795$		0			0
$796$	45677.6			2.03392
$797$	8060.57	+	8060.57i	0.358243	+	0.358243i	0.863165	−	0.504922i	$-0.168479\pi$
$797$	8060.57	+	8060.57i	0.358243	+	0.358243i	−0.504922	+	0.863165i	$0.668479\pi$
$798$	11468.3	+	1389.42i	0.508737	+	0.0616354i
$799$		−	38833.2i		−	1.71942i
$800$		0			0
$801$	14785.1	+	3635.90i	0.652191	+	0.160385i
$802$	2031.88	−	2031.88i	0.0894616	−	0.0894616i
$803$	6092.44	−	6092.44i	0.267743	−	0.267743i
$804$	56754.1	−	44488.2i	2.48951	−	1.95147i
$805$		0			0
$806$			4189.46i			0.183086i
$807$	1052.72	−	8689.16i	0.0459202	−	0.379025i
$808$	−26767.1	−	26767.1i	−1.16542	−	1.16542i
$809$	−13824.2			−0.600782			−0.300391	−	0.953816i	$-0.597117\pi$
$809$	−13824.2			−0.600782			−0.300391	+	0.953816i	$0.597117\pi$
$810$		0			0
$811$	−20584.0			−0.891249			−0.445625	−	0.895220i	$-0.647018\pi$
$811$	−20584.0			−0.891249			−0.445625	+	0.895220i	$0.647018\pi$
$812$	60568.1	+	60568.1i	2.61764	+	2.61764i
$813$	−2067.60	+	17065.9i	−0.0891931	+	0.736198i
$814$			8164.55i			0.351557i
$815$		0			0
$816$	12682.3	−	9941.32i	0.544078	−	0.426490i
$817$	1049.63	−	1049.63i	0.0449472	−	0.0449472i
$818$	−36772.6	+	36772.6i	−1.57179	+	1.57179i
$819$	23199.1	+	5705.06i	0.989796	+	0.243408i
$820$		0			0
$821$			7269.14i			0.309007i	0.987992	+	0.154503i	$0.0493778\pi$
$821$			7269.14i			0.309007i	−0.987992	+	0.154503i	$0.950622\pi$
$822$	12321.9	+	1492.85i	0.522843	+	0.0633443i
$823$	22295.9	+	22295.9i	0.944334	+	0.944334i	0.998530	−	0.0541961i	$-0.0172596\pi$
$823$	22295.9	+	22295.9i	0.944334	+	0.944334i	−0.0541961	+	0.998530i	$0.517260\pi$
$824$	39747.6			1.68043
$825$		0			0
$826$	−42185.0			−1.77700
$827$	4878.42	+	4878.42i	0.205126	+	0.205126i	0.802192	−	0.597066i	$-0.203667\pi$
$827$	4878.42	+	4878.42i	0.205126	+	0.205126i	−0.597066	+	0.802192i	$0.703667\pi$
$828$	14423.0	+	23830.0i	0.605353	+	1.00018i
$829$			28818.4i			1.20736i	0.797225	+	0.603682i	$0.206300\pi$
$829$			28818.4i			1.20736i	−0.797225	+	0.603682i	$0.793700\pi$
$830$		0			0
$831$	9876.38	+	12599.4i	0.412284	+	0.525955i
$832$	−14780.7	+	14780.7i	−0.615898	+	0.615898i
$833$	−22027.1	+	22027.1i	−0.916197	+	0.916197i
$834$	−26780.9	−	34164.7i	−1.11193	−	1.41850i
$835$		0			0
$836$		−	2303.45i		−	0.0952948i
$837$	1364.09	−	3605.44i	0.0563320	−	0.148891i
$838$	36877.1	+	36877.1i	1.52016	+	1.52016i
$839$	−19129.2			−0.787144			−0.393572	−	0.919294i	$-0.628761\pi$
$839$	−19129.2			−0.787144			−0.393572	+	0.919294i	$0.628761\pi$
$840$		0			0
$841$	16941.2			0.694627
$842$	41945.3	+	41945.3i	1.71678	+	1.71678i
$843$	25648.2	+	3107.38i	1.04789	+	0.126956i
$844$		−	43522.3i		−	1.77500i
$845$		0			0
$846$	−16809.5	+	68354.5i	−0.683125	+	2.77787i
$847$	−24584.4	+	24584.4i	−0.997321	+	0.997321i
$848$	19107.6	−	19107.6i	0.773773	−	0.773773i
$849$	19233.3	−	15076.6i	0.777487	−	0.609454i
$850$		0			0
$851$		−	12614.1i		−	0.508116i
$852$	6817.34	−	56270.2i	0.274129	−	2.26266i
$853$	−415.608	−	415.608i	−0.0166825	−	0.0166825i	0.698716	−	0.715399i	$-0.253755\pi$
$853$	−415.608	−	415.608i	−0.0166825	−	0.0166825i	−0.715399	+	0.698716i	$0.753755\pi$
$854$	−57877.4			−2.31911
$855$		0			0
$856$	−44380.2			−1.77206
$857$	−21659.9	−	21659.9i	−0.863347	−	0.863347i	0.128378	−	0.991725i	$-0.459023\pi$
$857$	−21659.9	−	21659.9i	−0.863347	−	0.863347i	−0.991725	+	0.128378i	$0.959023\pi$
$858$	876.393	−	7233.74i	0.0348713	−	0.287827i
$859$			20261.0i			0.804769i	0.915471	+	0.402384i	$0.131818\pi$
$859$			20261.0i			0.804769i	−0.915471	+	0.402384i	$0.868182\pi$
$860$		0			0
$861$	1049.13	−	822.391i	0.0415265	−	0.0325517i
$862$	−36191.2	+	36191.2i	−1.43002	+	1.43002i
$863$	23444.8	−	23444.8i	0.924762	−	0.924762i	−0.0725989	−	0.997361i	$-0.523129\pi$
$863$	23444.8	−	23444.8i	0.924762	−	0.924762i	0.997361	+	0.0725989i	$0.0231293\pi$
$864$	8313.32	−	3749.46i	0.327344	−	0.147638i
$865$		0			0
$866$			73586.9i			2.88751i
$867$	1100.01	+	133.270i	0.0430892	+	0.00522041i
$868$	8186.01	+	8186.01i	0.320105	+	0.320105i
$869$	−1902.10			−0.0742512
$870$		0			0
$871$	29144.9			1.13380
$872$	−114.817	−	114.817i	−0.00445893	−	0.00445893i
$873$	−2156.25	+	1305.06i	−0.0835945	+	0.0505950i
$874$			5443.68i			0.210681i
$875$		0			0
$876$	−45361.1	−	57867.6i	−1.74955	−	2.23193i
$877$	11791.4	−	11791.4i	0.454012	−	0.454012i	−0.442672	−	0.896684i	$-0.645969\pi$
$877$	11791.4	−	11791.4i	0.454012	−	0.454012i	0.896684	+	0.442672i	$0.145969\pi$
$878$	−5302.95	+	5302.95i	−0.203834	+	0.203834i
$879$	15745.8	+	20087.1i	0.604201	+	0.770786i
$880$		0			0
$881$		−	30662.9i		−	1.17260i	−0.810095	−	0.586299i	$-0.800584\pi$
$881$		−	30662.9i		−	1.17260i	0.810095	−	0.586299i	$-0.199416\pi$
$882$	48306.9	−	29237.5i	1.84419	−	1.11619i
$883$	−1717.16	−	1717.16i	−0.0654439	−	0.0654439i	0.673627	−	0.739071i	$-0.264735\pi$
$883$	−1717.16	−	1717.16i	−0.0654439	−	0.0654439i	−0.739071	+	0.673627i	$0.764735\pi$
$884$	34304.9			1.30520
$885$		0			0
$886$	17598.8			0.667318
$887$	−13438.0	−	13438.0i	−0.508687	−	0.508687i	0.405436	−	0.914123i	$-0.367120\pi$
$887$	−13438.0	−	13438.0i	−0.508687	−	0.508687i	−0.914123	+	0.405436i	$0.867120\pi$
$888$	32534.6	+	3941.68i	1.22949	+	0.148957i
$889$			393.159i			0.0148325i
$890$		0			0
$891$	−3109.53	+	5939.98i	−0.116917	+	0.223341i
$892$	−20163.2	+	20163.2i	−0.756854	+	0.756854i
$893$	−6359.25	+	6359.25i	−0.238303	+	0.238303i
$894$	−3615.74	+	2834.30i	−0.135267	+	0.106033i
$895$		0			0
$896$			73848.4i			2.75346i
$897$	−1354.02	+	11176.0i	−0.0504006	+	0.416006i
$898$	−48574.4	−	48574.4i	−1.80506	−	1.80506i
$899$	5585.94			0.207232
$900$		0			0
$901$	44667.6			1.65160
$902$	−287.498	−	287.498i	−0.0106127	−	0.0106127i
$903$	1560.63	−	12881.4i	0.0575133	−	0.474714i
$904$			38207.5i			1.40571i
$905$		0			0
$906$	15829.3	−	12408.2i	0.580455	−	0.455006i
$907$	14586.4	−	14586.4i	0.533994	−	0.533994i	−0.387764	−	0.921759i	$-0.626753\pi$
$907$	14586.4	−	14586.4i	0.533994	−	0.533994i	0.921759	+	0.387764i	$0.126753\pi$
$908$	5095.40	−	5095.40i	0.186230	−	0.186230i
$909$	−7146.99	+	29062.6i	−0.260782	+	1.06045i
$910$		0			0
$911$			27679.6i			1.00666i	0.864095	+	0.503329i	$0.167892\pi$
$911$			27679.6i			1.00666i	−0.864095	+	0.503329i	$0.832108\pi$
$912$	−3704.79	−	448.849i	−0.134515	−	0.0162970i
$913$	5006.29	+	5006.29i	0.181472	+	0.181472i
$914$	53896.6			1.95048
$915$		0			0
$916$	−69114.7			−2.49303
$917$	−52529.3	−	52529.3i	−1.89168	−	1.89168i
$918$	−45159.1	−	17085.6i	−1.62361	−	0.614280i
$919$			44894.9i			1.61147i	0.592273	+	0.805737i	$0.298231\pi$
$919$			44894.9i			1.61147i	−0.592273	+	0.805737i	$0.701769\pi$
$920$		0			0
$921$	18614.0	+	23746.1i	0.665963	+	0.849576i
$922$	−36319.1	+	36319.1i	−1.29730	+	1.29730i
$923$	16198.7	−	16198.7i	0.577666	−	0.577666i
$924$	−12422.0	−	15846.8i	−0.442264	−	0.564201i
$925$		0			0
$926$		−	61584.6i		−	2.18553i
$927$	−16271.7	−	26884.6i	−0.576519	−	0.952541i
$928$	9344.50	+	9344.50i	0.330548	+	0.330548i
$929$	−29033.0			−1.02534			−0.512670	−	0.858586i	$-0.671344\pi$
$929$	−29033.0			−1.02534			−0.512670	+	0.858586i	$0.671344\pi$
$930$		0			0
$931$	7214.22			0.253960
$932$	−8000.68	−	8000.68i	−0.281192	−	0.281192i
$933$	20309.8	+	2460.61i	0.712662	+	0.0863416i
$934$			65890.5i			2.30835i
$935$		0			0
$936$	−28402.3	−	6984.61i	−0.991836	−	0.243909i
$937$	−35681.0	+	35681.0i	−1.24402	+	1.24402i	−0.285703	+	0.958318i	$0.592227\pi$
$937$	−35681.0	+	35681.0i	−1.24402	+	1.24402i	−0.958318	+	0.285703i	$0.907773\pi$
$938$	87109.6	−	87109.6i	3.03223	−	3.03223i
$939$	928.574	−	727.888i	0.0322714	−	0.0252968i
$940$		0			0
$941$		−	28986.4i		−	1.00418i	−0.864816	−	0.502089i	$-0.832565\pi$
$941$		−	28986.4i		−	1.00418i	0.864816	−	0.502089i	$-0.167435\pi$
$942$	−6910.19	+	57036.6i	−0.239009	+	1.97277i
$943$	444.181	+	444.181i	0.0153388	+	0.0153388i
$944$	13627.7			0.469857
$945$		0			0
$946$	−3957.61			−0.136018
$947$	10086.1	+	10086.1i	0.346099	+	0.346099i	0.858654	−	0.512555i	$-0.171301\pi$
$947$	10086.1	+	10086.1i	0.346099	+	0.346099i	−0.512555	+	0.858654i	$0.671301\pi$
$948$	−1952.31	+	16114.3i	−0.0668862	+	0.552078i
$949$		−	29716.8i		−	1.01649i
$950$		0			0
$951$	−37064.2	+	29053.8i	−1.26382	+	0.990676i
$952$	48227.3	−	48227.3i	1.64186	−	1.64186i
$953$	−35251.1	+	35251.1i	−1.19821	+	1.19821i	−0.223509	+	0.974702i	$0.571751\pi$
$953$	−35251.1	+	35251.1i	−1.19821	+	1.19821i	−0.974702	+	0.223509i	$0.928249\pi$
$954$	−78624.3	−	19335.1i	−2.66830	−	0.656180i
$955$		0			0
$956$			13160.2i			0.445220i
$957$	−9644.98	−	1168.52i	−0.325787	−	0.0394703i
$958$	17653.0	+	17653.0i	0.595348	+	0.595348i
$959$	13861.9			0.466763
$960$		0			0
$961$	−29036.0			−0.974658
$962$	19911.9	+	19911.9i	0.667344	+	0.667344i
$963$	18168.2	+	30018.0i	0.607956	+	1.00448i
$964$			648.325i			0.0216610i
$965$		0			0
$966$	29356.5	+	37450.3i	0.977773	+	1.24735i
$967$	29437.7	−	29437.7i	0.978958	−	0.978958i	−0.0208251	−	0.999783i	$-0.506629\pi$
$967$	29437.7	−	29437.7i	0.978958	−	0.978958i	0.999783	+	0.0208251i	$0.00662933\pi$
$968$	30098.3	−	30098.3i	0.999377	−	0.999377i
$969$	−3805.68	−	4854.95i	−0.126167	−	0.160953i
$970$		0			0
$971$		−	14117.9i		−	0.466595i	−0.972405	−	0.233298i	$-0.925048\pi$
$971$		−	14117.9i		−	0.466595i	0.972405	−	0.233298i	$-0.0749516\pi$
$972$	47131.2	+	32440.4i	1.55528	+	1.07050i
$973$	−34281.4	−	34281.4i	−1.12951	−	1.12951i
$974$	−6936.87			−0.228205
$975$		0			0
$976$	18697.1			0.613197
$977$	18396.9	+	18396.9i	0.602423	+	0.602423i	0.940955	−	0.338532i	$-0.109930\pi$
$977$	18396.9	+	18396.9i	0.602423	+	0.602423i	−0.338532	+	0.940955i	$0.609930\pi$
$978$	−13882.9	−	1681.96i	−0.453911	−	0.0549930i
$979$		−	5186.32i		−	0.169311i
$980$		0			0
$981$	−30.6568	+	124.663i	−0.000997754	+	0.00405728i
$982$	24983.8	−	24983.8i	0.811880	−	0.811880i
$983$	−37328.5	+	37328.5i	−1.21119	+	1.21119i	−0.240549	+	0.970637i	$0.577327\pi$
$983$	−37328.5	+	37328.5i	−1.21119	+	1.21119i	−0.970637	+	0.240549i	$0.922673\pi$
$984$	−1284.44	+	1006.84i	−0.0416121	+	0.0326188i
$985$		0			0
$986$		−	69965.5i		−	2.25979i
$987$	−9455.20	+	78043.0i	−0.304926	+	2.51686i
$988$	−5617.71	−	5617.71i	−0.180894	−	0.180894i
$989$	6114.46			0.196591
$990$		0			0
$991$	−26565.6			−0.851547			−0.425773	−	0.904830i	$-0.639998\pi$
$991$	−26565.6			−0.851547			−0.425773	+	0.904830i	$0.639998\pi$
$992$	1262.95	+	1262.95i	0.0404219	+	0.0404219i
$993$	5503.95	−	45429.5i	0.175894	−	1.45182i
$994$		−	96830.4i		−	3.08981i
$995$		0			0
$996$	47551.1	−	37274.2i	1.51277	−	1.18582i
$997$	3172.34	−	3172.34i	0.100771	−	0.100771i	−0.654924	−	0.755695i	$-0.727299\pi$
$997$	3172.34	−	3172.34i	0.100771	−	0.100771i	0.755695	+	0.654924i	$0.227299\pi$
$998$	−52033.3	+	52033.3i	−1.65039	+	1.65039i
$999$	−10652.8	−	23619.5i	−0.337377	−	0.748035i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.4.e.d.68.1	yes	16
3.2	odd	2	inner	75.4.e.d.68.7	yes	16
5.2	odd	4	inner	75.4.e.d.32.7	yes	16
5.3	odd	4	inner	75.4.e.d.32.2	yes	16
5.4	even	2	inner	75.4.e.d.68.8	yes	16
15.2	even	4	inner	75.4.e.d.32.1	✓	16
15.8	even	4	inner	75.4.e.d.32.8	yes	16
15.14	odd	2	inner	75.4.e.d.68.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.4.e.d.32.1	✓	16	15.2	even	4	inner
75.4.e.d.32.2	yes	16	5.3	odd	4	inner
75.4.e.d.32.7	yes	16	5.2	odd	4	inner
75.4.e.d.32.8	yes	16	15.8	even	4	inner
75.4.e.d.68.1	yes	16	1.1	even	1	trivial
75.4.e.d.68.2	yes	16	15.14	odd	2	inner
75.4.e.d.68.7	yes	16	3.2	odd	2	inner
75.4.e.d.68.8	yes	16	5.4	even	2	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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	75.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.39887 - 3.39887i) q^{2} +(0.624963 - 5.15843i) q^{3} +15.1047i q^{4} +(-19.6570 + 15.4087i) q^{6} +(-19.7241 + 19.7241i) q^{7} +(24.1479 - 24.1479i) q^{8} +(-26.2188 - 6.44766i) q^{9} +O(q^{10})\)	\(q+(-3.39887 - 3.39887i) q^{2} +(0.624963 - 5.15843i) q^{3} +15.1047i q^{4} +(-19.6570 + 15.4087i) q^{6} +(-19.7241 + 19.7241i) q^{7} +(24.1479 - 24.1479i) q^{8} +(-26.2188 - 6.44766i) q^{9} +9.19707i q^{11} +(77.9165 + 9.43987i) q^{12} +(22.4300 + 22.4300i) q^{13} +134.080 q^{14} -43.3141 q^{16} +(-50.6273 - 50.6273i) q^{17} +(67.1998 + 111.029i) q^{18} +16.5813i q^{19} +(89.4187 + 114.072i) q^{21} +(31.2597 - 31.2597i) q^{22} +(-48.2959 + 48.2959i) q^{23} +(-109.474 - 139.657i) q^{24} -152.474i q^{26} +(-49.6456 + 131.219i) q^{27} +(-297.927 - 297.927i) q^{28} -203.298 q^{29} -27.4766 q^{31} +(-45.9644 - 45.9644i) q^{32} +(47.4425 + 5.74783i) q^{33} +344.152i q^{34} +(97.3898 - 396.027i) q^{36} +(-130.592 + 130.592i) q^{37} +(56.3576 - 56.3576i) q^{38} +(129.722 - 101.686i) q^{39} -9.19707i q^{41} +(83.7948 - 691.641i) q^{42} +(-63.3021 - 63.3021i) q^{43} -138.919 q^{44} +328.303 q^{46} +(383.520 + 383.520i) q^{47} +(-27.0697 + 223.433i) q^{48} -435.083i q^{49} +(-292.798 + 229.517i) q^{51} +(-338.799 + 338.799i) q^{52} +(-441.142 + 441.142i) q^{53} +(614.735 - 277.256i) q^{54} +952.594i q^{56} +(85.5333 + 10.3627i) q^{57} +(690.986 + 690.986i) q^{58} -314.626 q^{59} -431.664 q^{61} +(93.3894 + 93.3894i) q^{62} +(644.318 - 389.969i) q^{63} +658.967i q^{64} +(-141.715 - 180.787i) q^{66} +(649.685 - 649.685i) q^{67} +(764.709 - 764.709i) q^{68} +(218.948 + 279.314i) q^{69} -722.186i q^{71} +(-788.828 + 477.433i) q^{72} +(-662.432 - 662.432i) q^{73} +887.733 q^{74} -250.455 q^{76} +(-181.404 - 181.404i) q^{77} +(-786.526 - 95.2905i) q^{78} +206.816i q^{79} +(645.855 + 338.100i) q^{81} +(-31.2597 + 31.2597i) q^{82} +(544.335 - 544.335i) q^{83} +(-1723.03 + 1350.64i) q^{84} +430.312i q^{86} +(-127.054 + 1048.70i) q^{87} +(222.090 + 222.090i) q^{88} -563.910 q^{89} -884.827 q^{91} +(-729.494 - 729.494i) q^{92} +(-17.1718 + 141.736i) q^{93} -2607.07i q^{94} +(-265.830 + 208.378i) q^{96} +(66.0080 - 66.0080i) q^{97} +(-1478.79 + 1478.79i) q^{98} +(59.2996 - 241.137i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 84 q^{6}+O(q^{10}) \) 16 * q - 84 * q^6	\( 16 q - 84 q^{6} - 232 q^{16} + 816 q^{21} - 1208 q^{31} + 252 q^{36} + 1872 q^{46} + 156 q^{51} - 1528 q^{61} - 3420 q^{66} + 1064 q^{76} + 6876 q^{81} - 10008 q^{91} - 8172 q^{96}+O(q^{100}) \) 16 * q - 84 * q^6 - 232 * q^16 + 816 * q^21 - 1208 * q^31 + 252 * q^36 + 1872 * q^46 + 156 * q^51 - 1528 * q^61 - 3420 * q^66 + 1064 * q^76 + 6876 * q^81 - 10008 * q^91 - 8172 * q^96

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