LMFDB - Embedded newform 75.4.e.d.68.2

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			68.2
Root			$-1.55042 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	75.68
Dual form			75.4.e.d.32.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.39887 - 3.39887i) q^{2} +(5.15843 - 0.624963i) q^{3} +15.1047i q^{4} +(-19.6570 - 15.4087i) q^{6} +(19.7241 - 19.7241i) q^{7} +(24.1479 - 24.1479i) q^{8} +(26.2188 - 6.44766i) q^{9} +O(q^{10})$	\(q+(-3.39887 - 3.39887i) q^{2} +(5.15843 - 0.624963i) 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} +(9.43987 + 77.9165i) q^{12} +(-22.4300 - 22.4300i) q^{13} -134.080 q^{14} -43.3141 q^{16} +(-50.6273 - 50.6273i) q^{17} +(-111.029 - 67.1998i) 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} +(131.219 - 49.6456i) q^{27} +(297.927 + 297.927i) q^{28} +203.298 q^{29} -27.4766 q^{31} +(-45.9644 - 45.9644i) q^{32} +(-5.74783 - 47.4425i) 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} +(-691.641 + 83.7948i) q^{42} +(63.3021 + 63.3021i) q^{43} +138.919 q^{44} +328.303 q^{46} +(383.520 + 383.520i) q^{47} +(-223.433 + 27.0697i) 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} +(10.3627 + 85.5333i) q^{57} +(-690.986 - 690.986i) q^{58} +314.626 q^{59} -431.664 q^{61} +(93.3894 + 93.3894i) q^{62} +(389.969 - 644.318i) 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} +(477.433 - 788.828i) q^{72} +(662.432 + 662.432i) q^{73} -887.733 q^{74} -250.455 q^{76} +(-181.404 - 181.404i) q^{77} +(95.2905 + 786.526i) 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} +(1048.70 - 127.054i) q^{87} +(-222.090 - 222.090i) q^{88} +563.910 q^{89} -884.827 q^{91} +(-729.494 - 729.494i) q^{92} +(-141.736 + 17.1718i) 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	$-0.573228\pi$
$3$	5.15843	−	0.624963i	0.992741	−	0.120274i
$3$	5.15843	−	0.624963i	0.992741	−	0.120274i
$4$			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	$-0.478572\pi$
$7$	19.7241	−	19.7241i	1.06500	−	1.06500i	0.997735	−	0.0672681i	$-0.0214283\pi$
$8$	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	$-0.959771\pi$
$11$		−	9.19707i		−	0.252093i	0.992024	−	0.126046i	$-0.0402288\pi$
$12$	9.43987	+	77.9165i	0.227088	+	1.87438i
$13$	−22.4300	−	22.4300i	−0.478537	−	0.478537i	0.426127	−	0.904663i	$-0.359878\pi$
$13$	−22.4300	−	22.4300i	−0.478537	−	0.478537i	−0.904663	+	0.426127i	$0.859878\pi$
$14$	−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	$0.920627\pi$
$18$	−111.029	−	67.1998i	−1.45388	−	0.879952i
$19$			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
$27$	131.219	−	49.6456i	0.935297	−	0.353863i
$28$	297.927	+	297.927i	2.01082	+	2.01082i
$29$	203.298			1.30178			0.650889	−	0.759173i	$-0.274396\pi$
$29$	203.298			1.30178			0.650889	+	0.759173i	$0.274396\pi$
$30$		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
$33$	−5.74783	−	47.4425i	−0.0303203	−	0.250263i
$34$			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	−0.354722	−	0.934972i	$-0.615425\pi$
$37$	130.592	−	130.592i	0.580250	−	0.580250i	0.934972	+	0.354722i	$0.115425\pi$
$38$	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	$0.00557592\pi$
$41$			9.19707i			0.0350327i	−0.999847	+	0.0175164i	$0.994424\pi$
$42$	−691.641	+	83.7948i	−2.54101	+	0.307853i
$43$	63.3021	+	63.3021i	0.224499	+	0.224499i	0.810390	−	0.585891i	$-0.199255\pi$
$43$	63.3021	+	63.3021i	0.224499	+	0.224499i	−0.585891	+	0.810390i	$0.699255\pi$
$44$	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	$0.431590\pi$
$48$	−223.433	+	27.0697i	−0.671869	+	0.0813994i
$49$		−	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
$57$	10.3627	+	85.5333i	0.0240802	+	0.198757i
$58$	−690.986	−	690.986i	−1.56433	−	1.56433i
$59$	314.626			0.694251			0.347126	−	0.937819i	$-0.387158\pi$
$59$	314.626			0.694251			0.347126	+	0.937819i	$0.387158\pi$
$60$		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
$63$	389.969	−	644.318i	0.779866	−	1.28852i
$64$			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	$0.566086\pi$
$67$	−649.685	+	649.685i	−1.18465	+	1.18465i	−0.978525	+	0.206126i	$0.933914\pi$
$68$	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	$0.206258\pi$
$71$			722.186i			1.20715i	−0.797306	+	0.603575i	$0.793742\pi$
$72$	477.433	−	788.828i	0.781473	−	1.29117i
$73$	662.432	+	662.432i	1.06208	+	1.06208i	0.997941	+	0.0641383i	$0.0204299\pi$
$73$	662.432	+	662.432i	1.06208	+	1.06208i	0.0641383	+	0.997941i	$0.479570\pi$
$74$	−887.733			−1.39455
$75$		0			0
$76$	−250.455			−0.378015
$77$	−181.404	−	181.404i	−0.268480	−	0.268480i
$78$	95.2905	+	786.526i	0.138327	+	1.14175i
$79$			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
$87$	1048.70	−	127.054i	1.29233	−	0.156570i
$88$	−222.090	−	222.090i	−0.269033	−	0.269033i
$89$	563.910			0.671622			0.335811	−	0.941929i	$-0.390990\pi$
$89$	563.910			0.671622			0.335811	+	0.941929i	$0.390990\pi$
$90$		0			0
$91$	−884.827			−1.01929
$92$	−729.494	−	729.494i	−0.826685	−	0.826685i
$93$	−141.736	+	17.1718i	−0.158036	+	0.0191466i
$94$		−	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	−0.740809	−	0.671715i	$-0.765558\pi$
$97$	−66.0080	+	66.0080i	−0.0690938	+	0.0690938i	0.671715	+	0.740809i	$0.265558\pi$
$98$	−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	$0.183858\pi$
$101$			1108.46i			1.09204i	−0.837772	+	0.546021i	$0.816142\pi$
$102$	215.082	+	1775.28i	0.208787	+	1.72332i
$103$	−823.002	−	823.002i	−0.787308	−	0.787308i	0.193744	−	0.981052i	$-0.437937\pi$
$103$	−823.002	−	823.002i	−0.787308	−	0.787308i	−0.981052	+	0.193744i	$0.937937\pi$
$104$	−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	$0.949718\pi$
$108$	749.881	+	1982.02i	0.668124	+	1.76592i
$109$		−	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
$117$	−732.711	−	443.469i	−0.578967	−	0.350416i
$118$	−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
$123$	5.74783	+	47.4425i	0.00421353	+	0.0347784i
$124$		−	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	−0.710580	−	0.703616i	$-0.751567\pi$
$127$	−9.96644	+	9.96644i	−0.00696361	+	0.00696361i	0.703616	+	0.710580i	$0.251567\pi$
$128$	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	$-0.652018\pi$
$131$		−	2663.20i		−	1.77622i	0.459631	−	0.888110i	$-0.347982\pi$
$132$	716.604	−	86.8192i	0.472518	−	0.0572473i
$133$	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	$0.799523\pi$
$138$	1693.53	−	205.177i	1.04466	−	0.126564i
$139$			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
$147$	−271.911	−	2244.34i	−0.152563	−	1.25925i
$148$	1972.55	+	1972.55i	1.09556	+	1.09556i
$149$	−183.941			−0.101135			−0.0505674	−	0.998721i	$-0.516103\pi$
$149$	−183.941			−0.101135			−0.0505674	+	0.998721i	$0.516103\pi$
$150$		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
$153$	−1653.82	−	1000.96i	−0.873877	−	0.528908i
$154$			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	−0.987078	−	0.160239i	$-0.948774\pi$
$157$	−1626.56	+	1626.56i	−0.826840	+	0.826840i	0.160239	+	0.987078i	$0.448774\pi$
$158$	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
$162$	−3344.34	−	1046.02i	−1.62195	−	0.507304i
$163$	−395.910	−	395.910i	−0.190246	−	0.190246i	0.605556	−	0.795802i	$-0.292951\pi$
$163$	−395.910	−	395.910i	−0.190246	−	0.190246i	−0.795802	+	0.605556i	$0.792951\pi$
$164$	−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	$0.657426\pi$
$168$	−595.336	−	4913.89i	−0.273400	−	2.25664i
$169$		−	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
$177$	1622.98	−	196.630i	0.689212	−	0.0835005i
$178$	−1916.66	−	1916.66i	−0.807077	−	0.807077i
$179$	−210.570			−0.0879259			−0.0439629	−	0.999033i	$-0.513998\pi$
$179$	−210.570			−0.0879259			−0.0439629	+	0.999033i	$0.513998\pi$
$180$		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
$183$	−2226.71	+	269.774i	−0.899471	+	0.108974i
$184$			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	$-0.697894\pi$
$191$		−	4291.51i		−	1.62577i	0.582421	−	0.812887i	$-0.302106\pi$
$192$	411.830	+	3399.24i	0.154798	+	1.27770i
$193$	3567.00	+	3567.00i	1.33035	+	1.33035i	0.905051	+	0.425303i	$0.139832\pi$
$193$	3567.00	+	3567.00i	1.33035	+	1.33035i	0.425303	+	0.905051i	$0.360168\pi$
$194$	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	$0.715658\pi$
$198$	−618.041	+	1021.14i	−0.221830	+	0.366513i
$199$		−	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
$207$	−954.867	+	1577.66i	−0.320617	+	0.529733i
$208$	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
$213$	451.339	+	3725.35i	0.145189	+	1.19839i
$214$			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
$222$	−4579.31	+	554.800i	−1.38443	+	0.167729i
$223$	−1334.90	−	1334.90i	−0.400858	−	0.400858i	0.477677	−	0.878535i	$-0.341479\pi$
$223$	−1334.90	−	1334.90i	−0.400858	−	0.400858i	−0.878535	+	0.477677i	$0.841479\pi$
$224$	−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	$0.772219\pi$
$228$	−1291.95	+	156.525i	−0.375271	+	0.0454654i
$229$			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
$237$	129.252	+	1066.84i	0.0354254	+	0.292401i
$238$	6788.09	+	6788.09i	1.84877	+	1.84877i
$239$	−871.265			−0.235805			−0.117903	−	0.993025i	$-0.537617\pi$
$239$	−871.265			−0.235805			−0.117903	+	0.993025i	$0.537617\pi$
$240$		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
$243$	3120.30	−	2147.70i	0.823734	−	0.566976i
$244$		−	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	$0.00203316\pi$
$251$			50.7994i			0.0127746i	−0.999980	+	0.00638731i	$0.997967\pi$
$252$	9732.23	+	5890.37i	2.43283	+	1.47245i
$253$	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	$0.488088\pi$
$258$	−268.929	−	2219.73i	−0.0648945	−	0.535638i
$259$		−	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
$267$	2908.89	−	352.423i	0.666746	−	0.0807787i
$268$	−9813.29	−	9813.29i	−2.23672	−	2.23672i
$269$	−1684.46			−0.381796			−0.190898	−	0.981610i	$-0.561140\pi$
$269$	−1684.46			−0.381796			−0.190898	+	0.981610i	$0.561140\pi$
$270$		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
$273$	−4564.32	+	552.984i	−1.01189	+	0.122594i
$274$			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	−0.430189	−	0.902739i	$-0.641553\pi$
$277$	2178.55	−	2178.55i	0.472550	−	0.472550i	0.902739	+	0.430189i	$0.141553\pi$
$278$	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	$-0.823026\pi$
$281$		−	4972.10i		−	1.05555i	0.849383	−	0.527776i	$-0.176974\pi$
$282$	−1629.32	−	13448.4i	−0.344060	−	2.83986i
$283$	−3325.61	−	3325.61i	−0.698542	−	0.698542i	0.265554	−	0.964096i	$-0.414445\pi$
$283$	−3325.61	−	3325.61i	−0.698542	−	0.698542i	−0.964096	+	0.265554i	$0.914445\pi$
$284$	−10908.4			−2.27920
$285$		0			0
$286$	1402.31			0.289932
$287$	181.404	+	181.404i	0.0373100	+	0.0373100i
$288$	−1501.50	−	908.771i	−0.307210	−	0.185937i
$289$			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
$297$	−456.594	−	1206.83i	−0.0892063	−	0.235782i
$298$	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
$303$	692.748	+	5717.93i	0.131344	+	1.08411i
$304$		−	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	−0.213609	−	0.976919i	$-0.568522\pi$
$307$	4105.90	−	4105.90i	0.763310	−	0.763310i	0.976919	+	0.213609i	$0.0685218\pi$
$308$	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	$-0.883139\pi$
$311$		−	3937.21i		−	0.717874i	0.933362	−	0.358937i	$-0.116861\pi$
$312$	−5588.02	+	677.009i	−1.01397	+	0.122846i
$313$	−160.559	−	160.559i	−0.0289946	−	0.0289946i	0.692461	−	0.721455i	$-0.256527\pi$
$313$	−160.559	−	160.559i	−0.0289946	−	0.0289946i	−0.721455	+	0.692461i	$0.756527\pi$
$314$	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	$-0.546717\pi$
$318$	15469.0	−	1874.12i	2.72785	−	0.330489i
$319$		−	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
$327$	−2.97153	−	24.5269i	−0.000502525	−	0.00414783i
$328$	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
$333$	2581.96	−	4265.99i	0.424897	−	0.702027i
$334$		−	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	−0.0772088	−	0.997015i	$-0.524601\pi$
$337$	5690.38	−	5690.38i	0.919806	−	0.919806i	0.997015	+	0.0772088i	$0.0246008\pi$
$338$	−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
$342$	1114.26	−	1841.01i	0.176176	−	0.291082i
$343$	−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	$0.566823\pi$
$348$	1919.11	+	15840.3i	0.295618	+	2.44003i
$349$			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
$357$	−10302.2	+	1248.15i	−1.52731	+	0.185040i
$358$	715.700	+	715.700i	0.105659	+	0.105659i
$359$	−7178.33			−1.05531			−0.527657	−	0.849458i	$-0.676929\pi$
$359$	−7178.33			−1.05531			−0.527657	+	0.849458i	$0.676929\pi$
$360$		0			0
$361$	6584.06			0.959916
$362$	437.207	+	437.207i	0.0634782	+	0.0634782i
$363$	6429.54	−	778.962i	0.929651	−	0.112631i
$364$		−	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	−0.970541	−	0.240936i	$-0.922546\pi$
$367$	−5129.64	+	5129.64i	−0.729605	+	0.729605i	0.240936	+	0.970541i	$0.422546\pi$
$368$	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
$372$	−259.375	−	2140.88i	−0.0361505	−	0.298385i
$373$	−1332.77	−	1332.77i	−0.185009	−	0.185009i	0.608525	−	0.793534i	$-0.291761\pi$
$373$	−1332.77	−	1332.77i	−0.185009	−	0.185009i	−0.793534	+	0.608525i	$0.791761\pi$
$374$	3165.19			0.437615
$375$		0			0
$376$	18522.4			2.54049
$377$	−4559.99	−	4559.99i	−0.622949	−	0.622949i
$378$	−17593.7	+	6656.47i	−2.39398	+	0.905745i
$379$			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
$387$	2067.86	+	1251.56i	0.271615	+	0.164393i
$388$	−997.030	−	997.030i	−0.130455	−	0.130455i
$389$	−10198.8			−1.32931			−0.664654	−	0.747151i	$-0.731421\pi$
$389$	−10198.8			−1.32931			−0.664654	+	0.747151i	$0.731421\pi$
$390$		0			0
$391$	4890.18			0.632498
$392$	−10506.3	−	10506.3i	−1.35370	−	1.35370i
$393$	−1664.40	−	13737.9i	−0.213633	−	1.76333i
$394$		−	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	−0.712787	−	0.701380i	$-0.752568\pi$
$397$	−90.2345	+	90.2345i	−0.0114074	+	0.0114074i	0.701380	+	0.712787i	$0.252568\pi$
$398$	−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	$-0.988149\pi$
$401$		−	597.810i		−	0.0744469i	0.999307	−	0.0372234i	$-0.0118513\pi$
$402$	22781.7	−	2760.08i	2.82648	−	0.342439i
$403$	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
$408$	−12612.8	+	1528.09i	−1.53046	+	0.185421i
$409$		−	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
$417$	1086.21	+	8965.57i	0.127559	+	1.05287i
$418$	−518.325	−	518.325i	−0.0606510	−	0.0606510i
$419$	10849.8			1.26503			0.632514	−	0.774549i	$-0.282023\pi$
$419$	10849.8			1.26503			0.632514	+	0.774549i	$0.282023\pi$
$420$		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
$423$	12528.3	+	7582.65i	1.44006	+	0.871587i
$424$			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	$0.202850\pi$
$431$			10648.0i			1.19001i	−0.803721	+	0.595006i	$0.797150\pi$
$432$	−5683.61	+	2150.35i	−0.632993	+	0.239488i
$433$	10825.2	+	10825.2i	1.20144	+	1.20144i	0.973728	+	0.227716i	$0.0731258\pi$
$433$	10825.2	+	10825.2i	1.20144	+	1.20144i	0.227716	+	0.973728i	$0.426874\pi$
$434$	3684.05			0.407465
$435$		0			0
$436$	71.8186			0.00788873
$437$	−800.806	−	800.806i	−0.0876607	−	0.0876607i
$438$	−2814.24	−	23228.7i	−0.307008	−	2.53404i
$439$		−	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
$447$	−948.850	+	114.957i	−0.100401	+	0.0121639i
$448$	12997.6	+	12997.6i	1.37071	+	1.37071i
$449$	−14291.3			−1.50211			−0.751057	−	0.660238i	$-0.770456\pi$
$449$	−14291.3			−1.50211			−0.751057	+	0.660238i	$0.770456\pi$
$450$		0			0
$451$	84.5862			0.00883150
$452$	−11949.5	−	11949.5i	−1.24349	−	1.24349i
$453$	−4153.95	+	503.266i	−0.430838	+	0.0521976i
$454$			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	−0.173306	−	0.984868i	$-0.555445\pi$
$457$	7928.59	−	7928.59i	0.811562	−	0.811562i	0.984868	+	0.173306i	$0.0554450\pi$
$458$	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	$0.181494\pi$
$461$			10685.6i			1.07957i	−0.841804	+	0.539783i	$0.818506\pi$
$462$	770.667	+	6361.07i	0.0776075	+	0.640571i
$463$	−9059.56	−	9059.56i	−0.909360	−	0.909360i	0.0868606	−	0.996220i	$-0.472317\pi$
$463$	−9059.56	−	9059.56i	−0.909360	−	0.909360i	−0.996220	+	0.0868606i	$0.972317\pi$
$464$	−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	$0.987653\pi$
$468$	6698.46	−	11067.4i	0.661616	−	1.09314i
$469$			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
$477$	−8721.90	+	14410.6i	−0.837208	+	1.38326i
$478$	2961.32	+	2961.32i	0.283363	+	0.283363i
$479$	5193.79			0.495428			0.247714	−	0.968833i	$-0.420321\pi$
$479$	5193.79			0.495428			0.247714	+	0.968833i	$0.420321\pi$
$480$		0			0
$481$	−5858.38			−0.555341
$482$	−145.887	−	145.887i	−0.0137862	−	0.0137862i
$483$	1190.67	+	9827.78i	0.112169	+	0.925838i
$484$			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	−0.752987	−	0.658035i	$-0.771388\pi$
$487$	−1020.47	+	1020.47i	−0.0949523	+	0.0949523i	0.658035	+	0.752987i	$0.271388\pi$
$488$	−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	$-0.890314\pi$
$491$		−	7350.62i		−	0.675619i	0.941215	−	0.337809i	$-0.109686\pi$
$492$	−716.604	+	86.8192i	−0.0656646	+	0.00795551i
$493$	−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
$498$	−19087.5	+	2312.52i	−1.71753	+	0.208085i
$499$		−	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
$507$	−744.197	−	6142.59i	−0.0651892	−	0.538071i
$508$	−150.540	−	150.540i	−0.0131479	−	0.0131479i
$509$	−4477.48			−0.389903			−0.194952	−	0.980813i	$-0.562455\pi$
$509$	−4477.48			−0.389903			−0.194952	+	0.980813i	$0.562455\pi$
$510$		0			0
$511$	26131.8			2.26224
$512$	10358.5	+	10358.5i	0.894109	+	0.894109i
$513$	823.186	+	2175.77i	0.0708471	+	0.187256i
$514$		−	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	$-0.789943\pi$
$521$		−	14580.8i		−	1.22610i	0.790045	−	0.613049i	$-0.210057\pi$
$522$	−22572.1	−	13661.6i	−1.89263	−	1.14550i
$523$	−2457.46	−	2457.46i	−0.205463	−	0.205463i	0.596873	−	0.802336i	$-0.296410\pi$
$523$	−2457.46	−	2457.46i	−0.205463	−	0.205463i	−0.802336	+	0.596873i	$0.796410\pi$
$524$	40226.8			3.35366
$525$		0			0
$526$	7829.24			0.648994
$527$	1391.06	+	1391.06i	0.114982	+	0.114982i
$528$	248.962	+	2054.93i	0.0205202	+	0.169373i
$529$			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
$537$	−1086.21	+	131.598i	−0.0872876	+	0.0105752i
$538$	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
$543$	−663.545	+	80.3909i	−0.0524409	+	0.00635341i
$544$			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	−0.835436	−	0.549588i	$-0.814785\pi$
$547$	−3656.92	+	3656.92i	−0.285848	+	0.285848i	0.549588	+	0.835436i	$0.314785\pi$
$548$	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
$552$	1457.72	+	12032.0i	0.112400	+	0.927746i
$553$	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	$0.828042\pi$
$558$	3050.70	+	1846.42i	0.231446	+	0.140081i
$559$		−	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
$567$	6070.20	−	19407.7i	0.449603	−	1.43747i
$568$	17439.3	+	17439.3i	1.28827	+	1.28827i
$569$	12965.1			0.955230			0.477615	−	0.878569i	$-0.341501\pi$
$569$	12965.1			0.955230			0.477615	+	0.878569i	$0.341501\pi$
$570$		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
$573$	−2682.04	−	22137.5i	−0.195539	−	1.61397i
$574$		−	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	−0.144934	−	0.989441i	$-0.546297\pi$
$577$	11704.9	−	11704.9i	0.844508	−	0.844508i	0.989441	+	0.144934i	$0.0462969\pi$
$578$	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
$582$	2314.62	−	280.424i	0.164852	−	0.0199725i
$583$	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	$0.853776\pi$
$588$	33900.1	−	4107.12i	2.37758	−	0.288053i
$589$		−	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
$597$	−1889.93	−	15599.4i	−0.129564	−	1.06942i
$598$	−7363.85	−	7363.85i	−0.503563	−	0.503563i
$599$	24700.6			1.68487			0.842437	−	0.538795i	$-0.181120\pi$
$599$	24700.6			1.68487			0.842437	+	0.538795i	$0.181120\pi$
$600$		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
$603$	−12845.0	+	21222.9i	−0.867480	+	1.43327i
$604$		−	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	−0.0733910	−	0.997303i	$-0.523382\pi$
$607$	13817.0	−	13817.0i	0.923912	−	0.923912i	0.997303	+	0.0733910i	$0.0233821\pi$
$608$	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
$612$	15119.2	−	24980.4i	0.998624	−	1.64995i
$613$	7861.86	+	7861.86i	0.518005	+	0.518005i	0.916967	−	0.398962i	$-0.130629\pi$
$613$	7861.86	+	7861.86i	0.518005	+	0.518005i	−0.398962	+	0.916967i	$0.630629\pi$
$614$	−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	$0.461636\pi$
$618$	3496.39	+	28859.1i	0.227582	+	1.87845i
$619$		−	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
$627$	786.656	−	95.3062i	0.0501053	−	0.00607044i
$628$	−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
$633$	−14863.4	+	1800.75i	−0.933280	+	0.113070i
$634$			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	$-0.926647\pi$
$641$		−	7413.70i		−	0.456823i	0.973565	−	0.228412i	$-0.0733532\pi$
$642$	3903.90	+	32222.7i	0.239991	+	1.98088i
$643$	3856.84	+	3856.84i	0.236546	+	0.236546i	0.815418	−	0.578872i	$-0.196507\pi$
$643$	3856.84	+	3856.84i	0.236546	+	0.236546i	−0.578872	+	0.815418i	$0.696507\pi$
$644$	−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	$0.760431\pi$
$648$	7431.65	−	23760.5i	0.450529	−	1.44043i
$649$		−	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
$657$	21639.3	+	13097.1i	1.28498	+	0.777725i
$658$	−51422.3	−	51422.3i	−3.04658	−	3.04658i
$659$	−27210.3			−1.60844			−0.804222	−	0.594329i	$-0.797418\pi$
$659$	−27210.3			−1.60844			−0.804222	+	0.594329i	$0.797418\pi$
$660$		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
$663$	1419.38	+	11715.5i	0.0831436	+	0.686266i
$664$		−	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
$672$	−9353.36	+	1133.19i	−0.536925	+	0.0650504i
$673$	−13447.5	−	13447.5i	−0.770225	−	0.770225i	0.207921	−	0.978146i	$-0.433330\pi$
$673$	−13447.5	−	13447.5i	−0.770225	−	0.770225i	−0.978146	+	0.207921i	$0.933330\pi$
$674$	−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	$0.952784\pi$
$678$	27741.0	−	3360.92i	1.57137	−	0.190377i
$679$			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
$687$	2859.65	+	23603.5i	0.158810	+	1.31082i
$688$	−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
$693$	−5925.84	−	3586.58i	−0.324826	−	0.196599i
$694$		−	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	$0.258170\pi$
$701$			26912.7i			1.45004i	−0.688727	+	0.725021i	$0.741830\pi$
$702$	7569.65	+	20007.4i	0.406977	+	1.07568i
$703$	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
$708$	2970.03	+	24514.6i	0.157656	+	1.30129i
$709$			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
$717$	−4494.36	+	544.508i	−0.234093	+	0.0283613i
$718$	24398.2	+	24398.2i	1.26815	+	1.26815i
$719$	−1776.43			−0.0921413			−0.0460707	−	0.998938i	$-0.514670\pi$
$719$	−1776.43			−0.0921413			−0.0460707	+	0.998938i	$0.514670\pi$
$720$		0			0
$721$	−32466.0			−1.67697
$722$	−22378.4	−	22378.4i	−1.15351	−	1.15351i
$723$	221.411	−	26.8247i	0.0113892	−	0.00137984i
$724$		−	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	−0.940701	−	0.339236i	$-0.889831\pi$
$727$	−11790.0	+	11790.0i	−0.601465	+	0.601465i	0.339236	+	0.940701i	$0.389831\pi$
$728$	−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
$732$	−4074.85	−	33633.7i	−0.205753	−	1.69828i
$733$	22491.0	+	22491.0i	1.13332	+	1.13332i	0.989622	+	0.143696i	$0.0458989\pi$
$733$	22491.0	+	22491.0i	1.13332	+	1.13332i	0.143696	+	0.989622i	$0.454101\pi$
$734$	34870.0			1.75351
$735$		0			0
$736$	4439.78			0.222354
$737$	5975.20	+	5975.20i	0.298642	+	0.298642i
$738$	618.041	−	1021.14i	0.0308271	−	0.0509334i
$739$		−	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
$747$	10762.1	−	17781.5i	0.527130	−	0.870939i
$748$	−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
$753$	31.7477	+	262.045i	0.00153646	+	0.0126819i
$754$			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	−0.996998	−	0.0774296i	$-0.975329\pi$
$757$	−19152.6	+	19152.6i	−0.919568	+	0.919568i	0.0774296	+	0.996998i	$0.475329\pi$
$758$	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	$-0.764250\pi$
$761$		−	28330.4i		−	1.34951i	0.738043	−	0.674753i	$-0.235750\pi$
$762$	349.480	−	42.3408i	0.0166146	−	0.00201292i
$763$	−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
$768$	−38450.2	+	4658.38i	−1.80658	+	0.218874i
$769$			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
$777$	−3219.58	−	26574.4i	−0.148651	−	1.22696i
$778$	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
$783$	26676.5	−	10092.9i	1.21755	−	0.460651i
$784$			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	−0.923083	−	0.384602i	$-0.874339\pi$
$787$	−11888.6	+	11888.6i	−0.538481	+	0.538481i	0.384602	+	0.923083i	$0.374339\pi$
$788$	−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
$792$	−7254.91	−	4390.99i	−0.325495	−	0.197004i
$793$	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	$0.668479\pi$
$798$	−1389.42	−	11468.3i	−0.0616354	−	0.508737i
$799$		−	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
$807$	−8689.16	+	1052.72i	−0.379025	+	0.0459202i
$808$	26767.1	+	26767.1i	1.16542	+	1.16542i
$809$	13824.2			0.600782			0.300391	−	0.953816i	$-0.402883\pi$
$809$	13824.2			0.600782			0.300391	+	0.953816i	$0.402883\pi$
$810$		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
$813$	−17065.9	+	2067.60i	−0.736198	+	0.0891931i
$814$			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	$-0.950622\pi$
$821$		−	7269.14i		−	0.309007i	0.987992	−	0.154503i	$-0.0493778\pi$
$822$	1492.85	+	12321.9i	0.0633443	+	0.522843i
$823$	−22295.9	−	22295.9i	−0.944334	−	0.944334i	0.0541961	−	0.998530i	$-0.482740\pi$
$823$	−22295.9	−	22295.9i	−0.944334	−	0.944334i	−0.998530	+	0.0541961i	$0.982740\pi$
$824$	−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	$0.703667\pi$
$828$	−23830.0	−	14423.0i	−1.00018	−	0.605353i
$829$			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
$837$	−3605.44	+	1364.09i	−0.148891	+	0.0563320i
$838$	−36877.1	−	36877.1i	−1.52016	−	1.52016i
$839$	19129.2			0.787144			0.393572	−	0.919294i	$-0.371239\pi$
$839$	19129.2			0.787144			0.393572	+	0.919294i	$0.371239\pi$
$840$		0			0
$841$	16941.2			0.694627
$842$	41945.3	+	41945.3i	1.71678	+	1.71678i
$843$	−3107.38	−	25648.2i	−0.126956	−	1.04789i
$844$		−	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
$852$	−56270.2	+	6817.34i	−2.26266	+	0.274129i
$853$	415.608	+	415.608i	0.0166825	+	0.0166825i	0.715399	−	0.698716i	$-0.246245\pi$
$853$	415.608	+	415.608i	0.0166825	+	0.0166825i	−0.698716	+	0.715399i	$0.746245\pi$
$854$	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	$0.959023\pi$
$858$	7233.74	−	876.393i	0.287827	−	0.0348713i
$859$			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
$867$	133.270	+	1100.01i	0.00522041	+	0.0430892i
$868$	−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
$873$	−1305.06	+	2156.25i	−0.0505950	+	0.0835945i
$874$			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	−0.896684	−	0.442672i	$-0.854031\pi$
$877$	−11791.4	+	11791.4i	−0.454012	+	0.454012i	0.442672	+	0.896684i	$0.354031\pi$
$878$	−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	$0.199416\pi$
$881$			30662.9i			1.17260i	−0.810095	+	0.586299i	$0.800584\pi$
$882$	−29237.5	+	48306.9i	−1.11619	+	1.84419i
$883$	1717.16	+	1717.16i	0.0654439	+	0.0654439i	0.739071	−	0.673627i	$-0.235265\pi$
$883$	1717.16	+	1717.16i	0.0654439	+	0.0654439i	−0.673627	+	0.739071i	$0.735265\pi$
$884$	−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	$0.867120\pi$
$888$	−3941.68	−	32534.6i	−0.148957	−	1.22949i
$889$			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
$897$	11176.0	−	1354.02i	0.416006	−	0.0504006i
$898$	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
$903$	12881.4	−	1560.63i	0.474714	−	0.0575133i
$904$			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	−0.921759	−	0.387764i	$-0.873247\pi$
$907$	−14586.4	+	14586.4i	−0.533994	+	0.533994i	0.387764	+	0.921759i	$0.373247\pi$
$908$	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	$-0.832108\pi$
$911$		−	27679.6i		−	1.00666i	0.864095	−	0.503329i	$-0.167892\pi$
$912$	−448.849	−	3704.79i	−0.0162970	−	0.134515i
$913$	−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
$918$	17085.6	+	45159.1i	0.614280	+	1.62361i
$919$			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
$927$	−26884.6	−	16271.7i	−0.952541	−	0.576519i
$928$	−9344.50	−	9344.50i	−0.330548	−	0.330548i
$929$	29033.0			1.02534			0.512670	−	0.858586i	$-0.328656\pi$
$929$	29033.0			1.02534			0.512670	+	0.858586i	$0.328656\pi$
$930$		0			0
$931$	7214.22			0.253960
$932$	−8000.68	−	8000.68i	−0.281192	−	0.281192i
$933$	−2460.61	−	20309.8i	−0.0863416	−	0.712662i
$934$			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	$-0.407773\pi$
$937$	35681.0	−	35681.0i	1.24402	−	1.24402i	0.958318	−	0.285703i	$-0.0922271\pi$
$938$	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	$0.167435\pi$
$941$			28986.4i			1.00418i	−0.864816	+	0.502089i	$0.832565\pi$
$942$	57036.6	−	6910.19i	1.97277	−	0.239009i
$943$	−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	$0.671301\pi$
$948$	−16114.3	+	1952.31i	−0.552078	+	0.0668862i
$949$		−	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
$957$	−1168.52	−	9644.98i	−0.0394703	−	0.325787i
$958$	−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
$963$	−30018.0	−	18168.2i	−1.00448	−	0.607956i
$964$			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	−0.999783	−	0.0208251i	$-0.993371\pi$
$967$	−29437.7	+	29437.7i	−0.978958	+	0.978958i	0.0208251	+	0.999783i	$0.493371\pi$
$968$	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	$0.0749516\pi$
$971$			14117.9i			0.466595i	−0.972405	+	0.233298i	$0.925048\pi$
$972$	32440.4	+	47131.2i	1.07050	+	1.55528i
$973$	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	$0.609930\pi$
$978$	1681.96	+	13882.9i	0.0549930	+	0.453911i
$979$		−	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
$987$	78043.0	−	9455.20i	2.51686	−	0.304926i
$988$	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
$993$	45429.5	−	5503.95i	1.45182	−	0.175894i
$994$		−	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	−0.755695	−	0.654924i	$-0.772701\pi$
$997$	−3172.34	+	3172.34i	−0.100771	+	0.100771i	0.654924	+	0.755695i	$0.272701\pi$
$998$	−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.68.2	yes	16
3.2	odd	2	inner	75.4.e.d.68.8	yes	16
5.2	odd	4	inner	75.4.e.d.32.8	yes	16
5.3	odd	4	inner	75.4.e.d.32.1	✓	16
5.4	even	2	inner	75.4.e.d.68.7	yes	16
15.2	even	4	inner	75.4.e.d.32.2	yes	16
15.8	even	4	inner	75.4.e.d.32.7	yes	16
15.14	odd	2	inner	75.4.e.d.68.1	yes	16

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

\(f(q)\)	\(=\)	\(q+(-3.39887 - 3.39887i) q^{2} +(5.15843 - 0.624963i) q^{3} +15.1047i q^{4} +(-19.6570 - 15.4087i) q^{6} +(19.7241 - 19.7241i) q^{7} +(24.1479 - 24.1479i) q^{8} +(26.2188 - 6.44766i) q^{9} +O(q^{10})\)	\(q+(-3.39887 - 3.39887i) q^{2} +(5.15843 - 0.624963i) 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} +(9.43987 + 77.9165i) q^{12} +(-22.4300 - 22.4300i) q^{13} -134.080 q^{14} -43.3141 q^{16} +(-50.6273 - 50.6273i) q^{17} +(-111.029 - 67.1998i) 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} +(131.219 - 49.6456i) q^{27} +(297.927 + 297.927i) q^{28} +203.298 q^{29} -27.4766 q^{31} +(-45.9644 - 45.9644i) q^{32} +(-5.74783 - 47.4425i) 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} +(-691.641 + 83.7948i) q^{42} +(63.3021 + 63.3021i) q^{43} +138.919 q^{44} +328.303 q^{46} +(383.520 + 383.520i) q^{47} +(-223.433 + 27.0697i) 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} +(10.3627 + 85.5333i) q^{57} +(-690.986 - 690.986i) q^{58} +314.626 q^{59} -431.664 q^{61} +(93.3894 + 93.3894i) q^{62} +(389.969 - 644.318i) 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} +(477.433 - 788.828i) q^{72} +(662.432 + 662.432i) q^{73} -887.733 q^{74} -250.455 q^{76} +(-181.404 - 181.404i) q^{77} +(95.2905 + 786.526i) 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} +(1048.70 - 127.054i) q^{87} +(-222.090 - 222.090i) q^{88} +563.910 q^{89} -884.827 q^{91} +(-729.494 - 729.494i) q^{92} +(-141.736 + 17.1718i) 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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