LMFDB - Embedded newform 25.7.c.d.18.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,7,Mod(7,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("25.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	25.c (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:	$5.75135209050$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.333061916000256.23
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 90x^{6} - 12x^{5} + 3011x^{4} + 528x^{3} + 41202x^{2} + 17580x + 243850 $ x^8 + 90x^6 - 12x^5 + 3011x^4 + 528x^3 + 41202x^2 + 17580x + 243850
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			18.3
Root			$-1.22474 - 2.99225i$ of defining polynomial
Character	$\chi$	$=$	25.18
Dual form			25.7.c.d.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.71525 - 2.71525i) q^{2} +(16.9847 + 16.9847i) q^{3} +49.2549i q^{4} +92.2354 q^{6} +(-383.600 + 383.600i) q^{7} +(307.515 + 307.515i) q^{8} -152.039i q^{9} +O(q^{10})$	\(q+(2.71525 - 2.71525i) q^{2} +(16.9847 + 16.9847i) q^{3} +49.2549i q^{4} +92.2354 q^{6} +(-383.600 + 383.600i) q^{7} +(307.515 + 307.515i) q^{8} -152.039i q^{9} +2402.10 q^{11} +(-836.580 + 836.580i) q^{12} +(332.065 + 332.065i) q^{13} +2083.14i q^{14} -1482.35 q^{16} +(373.542 - 373.542i) q^{17} +(-412.823 - 412.823i) q^{18} -7032.37i q^{19} -13030.7 q^{21} +(6522.29 - 6522.29i) q^{22} +(-2610.56 - 2610.56i) q^{23} +10446.1i q^{24} +1803.28 q^{26} +(14964.2 - 14964.2i) q^{27} +(-18894.1 - 18894.1i) q^{28} -13628.5i q^{29} +10751.8 q^{31} +(-23705.9 + 23705.9i) q^{32} +(40798.9 + 40798.9i) q^{33} -2028.52i q^{34} +7488.65 q^{36} +(-29901.9 + 29901.9i) q^{37} +(-19094.6 - 19094.6i) q^{38} +11280.1i q^{39} +60337.8 q^{41} +(-35381.5 + 35381.5i) q^{42} +(63899.3 + 63899.3i) q^{43} +118315. i q^{44} -14176.6 q^{46} +(74307.8 - 74307.8i) q^{47} +(-25177.3 - 25177.3i) q^{48} -176648. i q^{49} +12689.0 q^{51} +(-16355.8 + 16355.8i) q^{52} +(-125220. - 125220. i) q^{53} -81263.0i q^{54} -235925. q^{56} +(119443. - 119443. i) q^{57} +(-37004.8 - 37004.8i) q^{58} +152944. i q^{59} -134851. q^{61} +(29193.8 - 29193.8i) q^{62} +(58322.1 + 58322.1i) q^{63} +33864.3i q^{64} +221558. q^{66} +(69010.1 - 69010.1i) q^{67} +(18398.8 + 18398.8i) q^{68} -88679.1i q^{69} -96191.6 q^{71} +(46754.2 - 46754.2i) q^{72} +(231651. + 231651. i) q^{73} +162382. i q^{74} +346378. q^{76} +(-921444. + 921444. i) q^{77} +(30628.2 + 30628.2i) q^{78} -28114.8i q^{79} +397489. q^{81} +(163832. - 163832. i) q^{82} +(-549687. - 549687. i) q^{83} -641823. i q^{84} +347005. q^{86} +(231476. - 231476. i) q^{87} +(738681. + 738681. i) q^{88} +1.19284e6i q^{89} -254760. q^{91} +(128583. - 128583. i) q^{92} +(182616. + 182616. i) q^{93} -403528. i q^{94} -805276. q^{96} +(469094. - 469094. i) q^{97} +(-479644. - 479644. i) q^{98} -365212. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2436 q^{6}+O(q^{10}) $ 8 * q + 2436 * q^6	$ 8 q + 2436 q^{6} + 7896 q^{11} + 28 q^{16} - 27264 q^{21} - 192744 q^{26} + 108656 q^{31} + 391608 q^{36} + 392136 q^{41} + 16776 q^{46} - 1182264 q^{51} - 1156080 q^{56} + 392896 q^{61} + 1332 q^{66} + 815376 q^{71} + 2759140 q^{76} + 2731608 q^{81} - 2130384 q^{86} - 3423744 q^{91} + 3595356 q^{96}+O(q^{100}) $ 8 * q + 2436 * q^6 + 7896 * q^11 + 28 * q^16 - 27264 * q^21 - 192744 * q^26 + 108656 * q^31 + 391608 * q^36 + 392136 * q^41 + 16776 * q^46 - 1182264 * q^51 - 1156080 * q^56 + 392896 * q^61 + 1332 * q^66 + 815376 * q^71 + 2759140 * q^76 + 2731608 * q^81 - 2130384 * q^86 - 3423744 * q^91 + 3595356 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	2.71525	−	2.71525i	0.339406	−	0.339406i	−0.516738	−	0.856144i	$-0.672854\pi$
$2$	2.71525	−	2.71525i	0.339406	−	0.339406i	0.856144	+	0.516738i	$0.172854\pi$
$3$	16.9847	+	16.9847i	0.629064	+	0.629064i	0.947832	−	0.318769i	$-0.103269\pi$
$3$	16.9847	+	16.9847i	0.629064	+	0.629064i	−0.318769	+	0.947832i	$0.603269\pi$
$4$			49.2549i			0.769607i
$5$		0			0
$5$		0			0
$6$	92.2354			0.427016
$7$	−383.600	+	383.600i	−1.11837	+	1.11837i	−0.126385	+	0.991981i	$0.540337\pi$
$7$	−383.600	+	383.600i	−1.11837	+	1.11837i	−0.991981	+	0.126385i	$0.959663\pi$
$8$	307.515	+	307.515i	0.600615	+	0.600615i
$9$		−	152.039i		−	0.208558i
$10$		0			0
$11$	2402.10			1.80473			0.902366	−	0.430971i	$-0.141829\pi$
$11$	2402.10			1.80473			0.902366	+	0.430971i	$0.141829\pi$
$12$	−836.580	+	836.580i	−0.484132	+	0.484132i
$13$	332.065	+	332.065i	0.151145	+	0.151145i	0.778629	−	0.627484i	$-0.215915\pi$
$13$	332.065	+	332.065i	0.151145	+	0.151145i	−0.627484	+	0.778629i	$0.715915\pi$
$14$			2083.14i			0.759160i
$15$		0			0
$16$	−1482.35			−0.361902
$17$	373.542	−	373.542i	0.0760314	−	0.0760314i	−0.668068	−	0.744100i	$-0.732879\pi$
$17$	373.542	−	373.542i	0.0760314	−	0.0760314i	0.744100	+	0.668068i	$0.232879\pi$
$18$	−412.823	−	412.823i	−0.0707859	−	0.0707859i
$19$		−	7032.37i		−	1.02528i	−0.858605	−	0.512638i	$-0.828668\pi$
$19$		−	7032.37i		−	1.02528i	0.858605	−	0.512638i	$-0.171332\pi$
$20$		0			0
$21$	−13030.7			−1.40705
$22$	6522.29	−	6522.29i	0.612537	−	0.612537i
$23$	−2610.56	−	2610.56i	−0.214560	−	0.214560i	0.591641	−	0.806201i	$-0.298480\pi$
$23$	−2610.56	−	2610.56i	−0.214560	−	0.214560i	−0.806201	+	0.591641i	$0.798480\pi$
$24$			10446.1i			0.755650i
$25$		0			0
$26$	1803.28			0.102599
$27$	14964.2	−	14964.2i	0.760260	−	0.760260i
$28$	−18894.1	−	18894.1i	−0.860703	−	0.860703i
$29$		−	13628.5i		−	0.558797i	−0.960175	−	0.279399i	$-0.909865\pi$
$29$		−	13628.5i		−	0.558797i	0.960175	−	0.279399i	$-0.0901351\pi$
$30$		0			0
$31$	10751.8			0.360908			0.180454	−	0.983583i	$-0.442243\pi$
$31$	10751.8			0.360908			0.180454	+	0.983583i	$0.442243\pi$
$32$	−23705.9	+	23705.9i	−0.723447	+	0.723447i
$33$	40798.9	+	40798.9i	1.13529	+	1.13529i
$34$		−	2028.52i		−	0.0516110i
$35$		0			0
$36$	7488.65			0.160508
$37$	−29901.9	+	29901.9i	−0.590327	+	0.590327i	−0.937720	−	0.347392i	$-0.887067\pi$
$37$	−29901.9	+	29901.9i	−0.590327	+	0.590327i	0.347392	+	0.937720i	$0.387067\pi$
$38$	−19094.6	−	19094.6i	−0.347985	−	0.347985i
$39$			11280.1i			0.190159i
$40$		0			0
$41$	60337.8			0.875463			0.437731	−	0.899106i	$-0.355782\pi$
$41$	60337.8			0.875463			0.437731	+	0.899106i	$0.355782\pi$
$42$	−35381.5	+	35381.5i	−0.477560	+	0.477560i
$43$	63899.3	+	63899.3i	0.803695	+	0.803695i	0.983671	−	0.179976i	$-0.0576021\pi$
$43$	63899.3	+	63899.3i	0.803695	+	0.803695i	−0.179976	+	0.983671i	$0.557602\pi$
$44$			118315.i			1.38893i
$45$		0			0
$46$	−14176.6			−0.145646
$47$	74307.8	−	74307.8i	0.715716	−	0.715716i	−0.252009	−	0.967725i	$-0.581091\pi$
$47$	74307.8	−	74307.8i	0.715716	−	0.715716i	0.967725	+	0.252009i	$0.0810913\pi$
$48$	−25177.3	−	25177.3i	−0.227660	−	0.227660i
$49$		−	176648.i		−	1.50149i
$50$		0			0
$51$	12689.0			0.0956572
$52$	−16355.8	+	16355.8i	−0.116322	+	0.116322i
$53$	−125220.	−	125220.i	−0.841095	−	0.841095i	0.147906	−	0.989001i	$-0.452747\pi$
$53$	−125220.	−	125220.i	−0.841095	−	0.841095i	−0.989001	+	0.147906i	$0.952747\pi$
$54$		−	81263.0i		−	0.516073i
$55$		0			0
$56$	−235925.			−1.34342
$57$	119443.	−	119443.i	0.644964	−	0.644964i
$58$	−37004.8	−	37004.8i	−0.189659	−	0.189659i
$59$			152944.i			0.744693i	0.928094	+	0.372346i	$0.121447\pi$
$59$			152944.i			0.744693i	−0.928094	+	0.372346i	$0.878553\pi$
$60$		0			0
$61$	−134851.			−0.594105			−0.297053	−	0.954861i	$-0.596004\pi$
$61$	−134851.			−0.594105			−0.297053	+	0.954861i	$0.596004\pi$
$62$	29193.8	−	29193.8i	0.122494	−	0.122494i
$63$	58322.1	+	58322.1i	0.233244	+	0.233244i
$64$			33864.3i			0.129182i
$65$		0			0
$66$	221558.			0.770649
$67$	69010.1	−	69010.1i	0.229450	−	0.229450i	−0.583013	−	0.812463i	$-0.698126\pi$
$67$	69010.1	−	69010.1i	0.229450	−	0.229450i	0.812463	+	0.583013i	$0.198126\pi$
$68$	18398.8	+	18398.8i	0.0585143	+	0.0585143i
$69$		−	88679.1i		−	0.269944i
$70$		0			0
$71$	−96191.6			−0.268758			−0.134379	−	0.990930i	$-0.542904\pi$
$71$	−96191.6			−0.268758			−0.134379	+	0.990930i	$0.542904\pi$
$72$	46754.2	−	46754.2i	0.125263	−	0.125263i
$73$	231651.	+	231651.i	0.595479	+	0.595479i	0.939106	−	0.343627i	$-0.111656\pi$
$73$	231651.	+	231651.i	0.595479	+	0.595479i	−0.343627	+	0.939106i	$0.611656\pi$
$74$			162382.i			0.400721i
$75$		0			0
$76$	346378.			0.789060
$77$	−921444.	+	921444.i	−2.01835	+	2.01835i
$78$	30628.2	+	30628.2i	0.0645412	+	0.0645412i
$79$		−	28114.8i		−	0.0570235i	−0.999593	−	0.0285118i	$-0.990923\pi$
$79$		−	28114.8i		−	0.0570235i	0.999593	−	0.0285118i	$-0.00907681\pi$
$80$		0			0
$81$	397489.			0.747945
$82$	163832.	−	163832.i	0.297137	−	0.297137i
$83$	−549687.	−	549687.i	−0.961349	−	0.961349i	0.0379309	−	0.999280i	$-0.487923\pi$
$83$	−549687.	−	549687.i	−0.961349	−	0.961349i	−0.999280	+	0.0379309i	$0.987923\pi$
$84$		−	641823.i		−	1.08287i
$85$		0			0
$86$	347005.			0.545557
$87$	231476.	−	231476.i	0.351519	−	0.351519i
$88$	738681.	+	738681.i	1.08395	+	1.08395i
$89$			1.19284e6i			1.69205i	0.533143	+	0.846025i	$0.321011\pi$
$89$			1.19284e6i			1.69205i	−0.533143	+	0.846025i	$0.678989\pi$
$90$		0			0
$91$	−254760.			−0.338070
$92$	128583.	−	128583.i	0.165127	−	0.165127i
$93$	182616.	+	182616.i	0.227034	+	0.227034i
$94$		−	403528.i		−	0.485836i
$95$		0			0
$96$	−805276.			−0.910188
$97$	469094.	−	469094.i	0.513978	−	0.513978i	−0.401765	−	0.915743i	$-0.631603\pi$
$97$	469094.	−	469094.i	0.513978	−	0.513978i	0.915743	+	0.401765i	$0.131603\pi$
$98$	−479644.	−	479644.i	−0.509613	−	0.509613i
$99$		−	365212.i		−	0.376391i
$100$		0			0
$101$	−610039.			−0.592098			−0.296049	−	0.955173i	$-0.595669\pi$
$101$	−610039.			−0.592098			−0.296049	+	0.955173i	$0.595669\pi$
$102$	34453.8	−	34453.8i	0.0324666	−	0.0324666i
$103$	−1.05731e6	−	1.05731e6i	−0.967584	−	0.967584i	0.0319069	−	0.999491i	$-0.489842\pi$
$103$	−1.05731e6	−	1.05731e6i	−0.967584	−	0.967584i	−0.999491	+	0.0319069i	$0.989842\pi$
$104$			204230.i			0.181560i
$105$		0			0
$106$	−680005.			−0.570945
$107$	76525.5	−	76525.5i	0.0624676	−	0.0624676i	−0.675183	−	0.737650i	$-0.735935\pi$
$107$	76525.5	−	76525.5i	0.0624676	−	0.0624676i	0.737650	+	0.675183i	$0.235935\pi$
$108$	737059.	+	737059.i	0.585101	+	0.585101i
$109$		−	441339.i		−	0.340795i	−0.985375	−	0.170397i	$-0.945495\pi$
$109$		−	441339.i		−	0.340795i	0.985375	−	0.170397i	$-0.0545052\pi$
$110$		0			0
$111$	−1.01575e6			−0.742707
$112$	568630.	−	568630.i	0.404739	−	0.404739i
$113$	−756591.	−	756591.i	−0.524356	−	0.524356i	0.394528	−	0.918884i	$-0.370908\pi$
$113$	−756591.	−	756591.i	−0.524356	−	0.524356i	−0.918884	+	0.394528i	$0.870908\pi$
$114$		−	648634.i		−	0.437809i
$115$		0			0
$116$	671270.			0.430054
$117$	50486.8	−	50486.8i	0.0315225	−	0.0315225i
$118$	415282.	+	415282.i	0.252753	+	0.252753i
$119$			286581.i			0.170062i
$120$		0			0
$121$	3.99851e6			2.25705
$122$	−366153.	+	366153.i	−0.201643	+	0.201643i
$123$	1.02482e6	+	1.02482e6i	0.550722	+	0.550722i
$124$			529579.i			0.277757i
$125$		0			0
$126$	316718.			0.158329
$127$	−269108.	+	269108.i	−0.131376	+	0.131376i	−0.769737	−	0.638361i	$-0.779613\pi$
$127$	−269108.	+	269108.i	−0.131376	+	0.131376i	0.638361	+	0.769737i	$0.279613\pi$
$128$	−1.42523e6	−	1.42523e6i	−0.679602	−	0.679602i
$129$			2.17062e6i			1.01115i
$130$		0			0
$131$	−2.45724e6			−1.09304			−0.546518	−	0.837447i	$-0.684047\pi$
$131$	−2.45724e6			−1.09304			−0.546518	+	0.837447i	$0.684047\pi$
$132$	−2.00955e6	+	2.00955e6i	−0.873728	+	0.873728i
$133$	2.69761e6	+	2.69761e6i	1.14663	+	1.14663i
$134$		−	374759.i		−	0.155753i
$135$		0			0
$136$	229740.			0.0913312
$137$	−2.13907e6	+	2.13907e6i	−0.831885	+	0.831885i	−0.987775	−	0.155889i	$-0.950176\pi$
$137$	−2.13907e6	+	2.13907e6i	−0.831885	+	0.831885i	0.155889	+	0.987775i	$0.450176\pi$
$138$	−240786.	−	240786.i	−0.0916207	−	0.0916207i
$139$		−	2.12039e6i		−	0.789534i	−0.918781	−	0.394767i	$-0.870825\pi$
$139$		−	2.12039e6i		−	0.789534i	0.918781	−	0.394767i	$-0.129175\pi$
$140$		0			0
$141$	2.52419e6			0.900462
$142$	−261184.	+	261184.i	−0.0912182	+	0.0912182i
$143$	797653.	+	797653.i	0.272776	+	0.272776i
$144$			225375.i			0.0754777i
$145$		0			0
$146$	1.25798e6			0.404218
$147$	3.00032e6	−	3.00032e6i	0.944530	−	0.944530i
$148$	−1.47281e6	−	1.47281e6i	−0.454320	−	0.454320i
$149$		−	1.39457e6i		−	0.421582i	−0.977531	−	0.210791i	$-0.932396\pi$
$149$		−	1.39457e6i		−	0.421582i	0.977531	−	0.210791i	$-0.0676039\pi$
$150$		0			0
$151$	−5.09334e6			−1.47935			−0.739677	−	0.672962i	$-0.765022\pi$
$151$	−5.09334e6			−1.47935			−0.739677	+	0.672962i	$0.765022\pi$
$152$	2.16256e6	−	2.16256e6i	0.615797	−	0.615797i
$153$	−56792.9	−	56792.9i	−0.0158570	−	0.0158570i
$154$			5.00390e6i			1.37008i
$155$		0			0
$156$	−555598.			−0.146348
$157$	−248449.	+	248449.i	−0.0642006	+	0.0642006i	−0.738478	−	0.674277i	$-0.764455\pi$
$157$	−248449.	+	248449.i	−0.0642006	+	0.0642006i	0.674277	+	0.738478i	$0.264455\pi$
$158$	−76338.7	−	76338.7i	−0.0193541	−	0.0193541i
$159$		−	4.25364e6i		−	1.05820i
$160$		0			0
$161$	2.00282e6			0.479914
$162$	1.07928e6	−	1.07928e6i	0.253857	−	0.253857i
$163$	−4.62194e6	−	4.62194e6i	−1.06724	−	1.06724i	−0.997570	−	0.0696687i	$-0.977806\pi$
$163$	−4.62194e6	−	4.62194e6i	−1.06724	−	1.06724i	−0.0696687	−	0.997570i	$-0.522194\pi$
$164$			2.97193e6i			0.673763i
$165$		0			0
$166$	−2.98507e6			−0.652575
$167$	4.91675e6	−	4.91675e6i	1.05567	−	1.05567i	0.0573154	−	0.998356i	$-0.481746\pi$
$167$	4.91675e6	−	4.91675e6i	1.05567	−	1.05567i	0.998356	−	0.0573154i	$-0.0182541\pi$
$168$	−4.00712e6	−	4.00712e6i	−0.845094	−	0.845094i
$169$		−	4.60627e6i		−	0.954310i
$170$		0			0
$171$	−1.06919e6			−0.213830
$172$	−3.14735e6	+	3.14735e6i	−0.618529	+	0.618529i
$173$	6.18056e6	+	6.18056e6i	1.19368	+	1.19368i	0.976025	+	0.217659i	$0.0698420\pi$
$173$	6.18056e6	+	6.18056e6i	1.19368	+	1.19368i	0.217659	+	0.976025i	$0.430158\pi$
$174$		−	1.25703e6i		−	0.238615i
$175$		0			0
$176$	−3.56075e6			−0.653136
$177$	−2.59771e6	+	2.59771e6i	−0.468459	+	0.468459i
$178$	3.23887e6	+	3.23887e6i	0.574292	+	0.574292i
$179$		−	68910.2i		−	0.0120150i	−0.999982	−	0.00600751i	$-0.998088\pi$
$179$		−	68910.2i		−	0.0120150i	0.999982	−	0.00600751i	$-0.00191226\pi$
$180$		0			0
$181$	−1.75676e6			−0.296263			−0.148132	−	0.988968i	$-0.547326\pi$
$181$	−1.75676e6			−0.296263			−0.148132	+	0.988968i	$0.547326\pi$
$182$	−691737.	+	691737.i	−0.114743	+	0.114743i
$183$	−2.29040e6	−	2.29040e6i	−0.373730	−	0.373730i
$184$		−	1.60557e6i		−	0.257737i
$185$		0			0
$186$	991697.			0.154113
$187$	897285.	−	897285.i	0.137216	−	0.137216i
$188$	3.66002e6	+	3.66002e6i	0.550820	+	0.550820i
$189$			1.14805e7i			1.70050i
$190$		0			0
$191$	1.14917e7			1.64924			0.824621	−	0.565685i	$-0.191388\pi$
$191$	1.14917e7			1.64924			0.824621	+	0.565685i	$0.191388\pi$
$192$	−575176.	+	575176.i	−0.0812638	+	0.0812638i
$193$	−1.34415e6	−	1.34415e6i	−0.186972	−	0.186972i	0.607414	−	0.794386i	$-0.292207\pi$
$193$	−1.34415e6	−	1.34415e6i	−0.186972	−	0.186972i	−0.794386	+	0.607414i	$0.792207\pi$
$194$		−	2.54741e6i		−	0.348894i
$195$		0			0
$196$	8.70079e6			1.15555
$197$	−7.13909e6	+	7.13909e6i	−0.933780	+	0.933780i	−0.997940	−	0.0641600i	$-0.979563\pi$
$197$	−7.13909e6	+	7.13909e6i	−0.933780	+	0.933780i	0.0641600	+	0.997940i	$0.479563\pi$
$198$	−991641.	−	991641.i	−0.127749	−	0.127749i
$199$			6.08275e6i			0.771864i	0.922527	+	0.385932i	$0.126120\pi$
$199$			6.08275e6i			0.771864i	−0.922527	+	0.385932i	$0.873880\pi$
$200$		0			0
$201$	2.34423e6			0.288677
$202$	−1.65641e6	+	1.65641e6i	−0.200962	+	0.200962i
$203$	5.22789e6	+	5.22789e6i	0.624940	+	0.624940i
$204$			624996.i			0.0736184i
$205$		0			0
$206$	−5.74169e6			−0.656808
$207$	−396906.	+	396906.i	−0.0447483	+	0.0447483i
$208$	−492237.	−	492237.i	−0.0546997	−	0.0546997i
$209$		−	1.68924e7i		−	1.85035i
$210$		0			0
$211$	−6.05692e6			−0.644769			−0.322385	−	0.946609i	$-0.604484\pi$
$211$	−6.05692e6			−0.644769			−0.322385	+	0.946609i	$0.604484\pi$
$212$	6.16768e6	−	6.16768e6i	0.647313	−	0.647313i
$213$	−1.63379e6	−	1.63379e6i	−0.169066	−	0.169066i
$214$		−	415571.i		−	0.0424037i
$215$		0			0
$216$	9.20343e6			0.913247
$217$	−4.12439e6	+	4.12439e6i	−0.403627	+	0.403627i
$218$	−1.19835e6	−	1.19835e6i	−0.115668	−	0.115668i
$219$			7.86907e6i			0.749188i
$220$		0			0
$221$	248081.			0.0229835
$222$	−2.75801e6	+	2.75801e6i	−0.252079	+	0.252079i
$223$	−8.33971e6	−	8.33971e6i	−0.752032	−	0.752032i	0.222826	−	0.974858i	$-0.428472\pi$
$223$	−8.33971e6	−	8.33971e6i	−0.752032	−	0.752032i	−0.974858	+	0.222826i	$0.928472\pi$
$224$		−	1.81872e7i		−	1.61816i
$225$		0			0
$226$	−4.10867e6			−0.355939
$227$	1.19794e7	−	1.19794e7i	1.02414	−	1.02414i	0.0244373	−	0.999701i	$-0.492221\pi$
$227$	1.19794e7	−	1.19794e7i	1.02414	−	1.02414i	0.999701	−	0.0244373i	$-0.00777942\pi$
$228$	5.88314e6	+	5.88314e6i	0.496369	+	0.496369i
$229$			2.19074e7i			1.82425i	0.409913	+	0.912125i	$0.365559\pi$
$229$			2.19074e7i			1.82425i	−0.409913	+	0.912125i	$0.634441\pi$
$230$		0			0
$231$	−3.13009e7			−2.53934
$232$	4.19097e6	−	4.19097e6i	0.335622	−	0.335622i
$233$	−3.44419e6	−	3.44419e6i	−0.272282	−	0.272282i	0.557736	−	0.830018i	$-0.311670\pi$
$233$	−3.44419e6	−	3.44419e6i	−0.272282	−	0.272282i	−0.830018	+	0.557736i	$0.811670\pi$
$234$		−	274168.i		−	0.0213978i
$235$		0			0
$236$	−7.53325e6			−0.573121
$237$	477522.	−	477522.i	0.0358714	−	0.0358714i
$238$	778139.	+	778139.i	0.0577200	+	0.0577200i
$239$			1.25160e7i			0.916796i	0.888747	+	0.458398i	$0.151577\pi$
$239$			1.25160e7i			0.916796i	−0.888747	+	0.458398i	$0.848423\pi$
$240$		0			0
$241$	1.42402e7			1.01734			0.508670	−	0.860961i	$-0.330137\pi$
$241$	1.42402e7			1.01734			0.508670	+	0.860961i	$0.330137\pi$
$242$	1.08569e7	−	1.08569e7i	0.766058	−	0.766058i
$243$	−4.15766e6	−	4.15766e6i	−0.289755	−	0.289755i
$244$		−	6.64205e6i		−	0.457228i
$245$		0			0
$246$	5.56528e6			0.373837
$247$	2.33520e6	−	2.33520e6i	0.154965	−	0.154965i
$248$	3.30634e6	+	3.30634e6i	0.216767	+	0.216767i
$249$		−	1.86726e7i		−	1.20950i
$250$		0			0
$251$	6.08845e6			0.385022			0.192511	−	0.981295i	$-0.438337\pi$
$251$	6.08845e6			0.385022			0.192511	+	0.981295i	$0.438337\pi$
$252$	−2.87264e6	+	2.87264e6i	−0.179507	+	0.179507i
$253$	−6.27081e6	−	6.27081e6i	−0.387224	−	0.387224i
$254$			1.46139e6i			0.0891795i
$255$		0			0
$256$	−9.90701e6			−0.590504
$257$	−1.13295e7	+	1.13295e7i	−0.667437	+	0.667437i	−0.957122	−	0.289685i	$-0.906449\pi$
$257$	−1.13295e7	+	1.13295e7i	−0.667437	+	0.667437i	0.289685	+	0.957122i	$0.406449\pi$
$258$	5.89378e6	+	5.89378e6i	0.343190	+	0.343190i
$259$		−	2.29407e7i		−	1.32040i
$260$		0			0
$261$	−2.07206e6			−0.116542
$262$	−6.67203e6	+	6.67203e6i	−0.370983	+	0.370983i
$263$	3.55449e6	+	3.55449e6i	0.195394	+	0.195394i	0.798022	−	0.602628i	$-0.205880\pi$
$263$	3.55449e6	+	3.55449e6i	0.195394	+	0.195394i	−0.602628	+	0.798022i	$0.705880\pi$
$264$			2.50926e7i			1.36375i
$265$		0			0
$266$	1.46494e7			0.778349
$267$	−2.02601e7	+	2.02601e7i	−1.06441	+	1.06441i
$268$	3.39908e6	+	3.39908e6i	0.176586	+	0.176586i
$269$			3.59971e6i			0.184931i	0.995716	+	0.0924657i	$0.0294749\pi$
$269$			3.59971e6i			0.184931i	−0.995716	+	0.0924657i	$0.970525\pi$
$270$		0			0
$271$	2.66998e7			1.34153			0.670764	−	0.741671i	$-0.265966\pi$
$271$	2.66998e7			1.34153			0.670764	+	0.741671i	$0.265966\pi$
$272$	−553721.	+	553721.i	−0.0275159	+	0.0275159i
$273$	−4.32703e6	−	4.32703e6i	−0.212668	−	0.212668i
$274$			1.16162e7i			0.564694i
$275$		0			0
$276$	4.36788e6			0.207751
$277$	1.30361e7	−	1.30361e7i	0.613351	−	0.613351i	−0.330466	−	0.943818i	$-0.607206\pi$
$277$	1.30361e7	−	1.30361e7i	0.613351	−	0.613351i	0.943818	+	0.330466i	$0.107206\pi$
$278$	−5.75738e6	−	5.75738e6i	−0.267973	−	0.267973i
$279$		−	1.63469e6i		−	0.0752703i
$280$		0			0
$281$	−1.39152e6			−0.0627150			−0.0313575	−	0.999508i	$-0.509983\pi$
$281$	−1.39152e6			−0.0627150			−0.0313575	+	0.999508i	$0.509983\pi$
$282$	6.85381e6	−	6.85381e6i	0.305622	−	0.305622i
$283$	1.57473e7	+	1.57473e7i	0.694778	+	0.694778i	0.963279	−	0.268501i	$-0.0865284\pi$
$283$	1.57473e7	+	1.57473e7i	0.694778	+	0.694778i	−0.268501	+	0.963279i	$0.586528\pi$
$284$		−	4.73790e6i		−	0.206838i
$285$		0			0
$286$	4.33165e6			0.185163
$287$	−2.31455e7	+	2.31455e7i	−0.979088	+	0.979088i
$288$	3.60422e6	+	3.60422e6i	0.150881	+	0.150881i
$289$			2.38585e7i			0.988438i
$290$		0			0
$291$	1.59349e7			0.646650
$292$	−1.14100e7	+	1.14100e7i	−0.458285	+	0.458285i
$293$	2.78009e7	+	2.78009e7i	1.10524	+	1.10524i	0.993768	+	0.111472i	$0.0355566\pi$
$293$	2.78009e7	+	2.78009e7i	1.10524	+	1.10524i	0.111472	+	0.993768i	$0.464443\pi$
$294$		−	1.62932e7i		−	0.641158i
$295$		0			0
$296$	−1.83905e7			−0.709119
$297$	3.59454e7	−	3.59454e7i	1.37206	−	1.37206i
$298$	−3.78661e6	−	3.78661e6i	−0.143087	−	0.143087i
$299$		−	1.73375e6i		−	0.0648594i
$300$		0			0
$301$	−4.90235e7			−1.79765
$302$	−1.38297e7	+	1.38297e7i	−0.502102	+	0.502102i
$303$	−1.03613e7	−	1.03613e7i	−0.372467	−	0.372467i
$304$			1.04244e7i			0.371050i
$305$		0			0
$306$	−308414.			−0.0107639
$307$	1.91801e7	−	1.91801e7i	0.662883	−	0.662883i	−0.293176	−	0.956059i	$-0.594712\pi$
$307$	1.91801e7	−	1.91801e7i	0.662883	−	0.662883i	0.956059	+	0.293176i	$0.0947122\pi$
$308$	−4.53856e7	−	4.53856e7i	−1.55334	−	1.55334i
$309$		−	3.59161e7i		−	1.21734i
$310$		0			0
$311$	−672506.			−0.0223571			−0.0111785	−	0.999938i	$-0.503558\pi$
$311$	−672506.			−0.0223571			−0.0111785	+	0.999938i	$0.503558\pi$
$312$	−3.46879e6	+	3.46879e6i	−0.114213	+	0.114213i
$313$	−3.01532e6	−	3.01532e6i	−0.0983331	−	0.0983331i	0.656229	−	0.754562i	$-0.272151\pi$
$313$	−3.01532e6	−	3.01532e6i	−0.0983331	−	0.0983331i	−0.754562	+	0.656229i	$0.772151\pi$
$314$			1.34920e6i			0.0435801i
$315$		0			0
$316$	1.38479e6			0.0438857
$317$	3.55428e6	−	3.55428e6i	0.111577	−	0.111577i	−0.649114	−	0.760691i	$-0.724860\pi$
$317$	3.55428e6	−	3.55428e6i	0.111577	−	0.111577i	0.760691	+	0.649114i	$0.224860\pi$
$318$	−1.15497e7	−	1.15497e7i	−0.359161	−	0.359161i
$319$		−	3.27370e7i		−	1.00848i
$320$		0			0
$321$	2.59953e6			0.0785922
$322$	5.43814e6	−	5.43814e6i	0.162886	−	0.162886i
$323$	−2.62689e6	−	2.62689e6i	−0.0779532	−	0.0779532i
$324$			1.95783e7i			0.575624i
$325$		0			0
$326$	−2.50994e7			−0.724455
$327$	7.49602e6	−	7.49602e6i	0.214382	−	0.214382i
$328$	1.85548e7	+	1.85548e7i	0.525816	+	0.525816i
$329$			5.70089e7i			1.60086i
$330$		0			0
$331$	−1.60494e7			−0.442564			−0.221282	−	0.975210i	$-0.571024\pi$
$331$	−1.60494e7			−0.442564			−0.221282	+	0.975210i	$0.571024\pi$
$332$	2.70748e7	−	2.70748e7i	0.739861	−	0.739861i
$333$	4.54624e6	+	4.54624e6i	0.123118	+	0.123118i
$334$		−	2.67004e7i		−	0.716602i
$335$		0			0
$336$	1.93160e7			0.509214
$337$	2.58165e7	−	2.58165e7i	0.674541	−	0.674541i	−0.284219	−	0.958760i	$-0.591734\pi$
$337$	2.58165e7	−	2.58165e7i	0.674541	−	0.674541i	0.958760	+	0.284219i	$0.0917341\pi$
$338$	−1.25072e7	−	1.25072e7i	−0.323899	−	0.323899i
$339$		−	2.57010e7i		−	0.659706i
$340$		0			0
$341$	2.58269e7			0.651342
$342$	−2.90313e6	+	2.90313e6i	−0.0725751	+	0.0725751i
$343$	2.26321e7	+	2.26321e7i	0.560845	+	0.560845i
$344$			3.93000e7i			0.965422i
$345$		0			0
$346$	3.35635e7			0.810287
$347$	−3.37727e7	+	3.37727e7i	−0.808308	+	0.808308i	−0.984378	−	0.176069i	$-0.943662\pi$
$347$	−3.37727e7	+	3.37727e7i	−0.808308	+	0.808308i	0.176069	+	0.984378i	$0.443662\pi$
$348$	1.14013e7	+	1.14013e7i	0.270532	+	0.270532i
$349$		−	5.15245e7i		−	1.21210i	−0.795427	−	0.606049i	$-0.792754\pi$
$349$		−	5.15245e7i		−	1.21210i	0.795427	−	0.606049i	$-0.207246\pi$
$350$		0			0
$351$	9.93817e6			0.229819
$352$	−5.69439e7	+	5.69439e7i	−1.30563	+	1.30563i
$353$	−2.59077e7	−	2.59077e7i	−0.588986	−	0.588986i	0.348371	−	0.937357i	$-0.386735\pi$
$353$	−2.59077e7	−	2.59077e7i	−0.588986	−	0.588986i	−0.937357	+	0.348371i	$0.886735\pi$
$354$			1.41069e7i			0.317996i
$355$		0			0
$356$	−5.87533e7			−1.30221
$357$	−4.86750e6	+	4.86750e6i	−0.106980	+	0.106980i
$358$	−187108.	−	187108.i	−0.00407797	−	0.00407797i
$359$			6.45192e7i			1.39446i	0.716848	+	0.697229i	$0.245584\pi$
$359$			6.45192e7i			1.39446i	−0.716848	+	0.697229i	$0.754416\pi$
$360$		0			0
$361$	−2.40834e6			−0.0511912
$362$	−4.77005e6	+	4.77005e6i	−0.100554	+	0.100554i
$363$	6.79136e7	+	6.79136e7i	1.41983	+	1.41983i
$364$		−	1.25482e7i		−	0.260181i
$365$		0			0
$366$	−1.24380e7			−0.253692
$367$	−4.17545e7	+	4.17545e7i	−0.844705	+	0.844705i	−0.989467	−	0.144761i	$-0.953759\pi$
$367$	−4.17545e7	+	4.17545e7i	−0.844705	+	0.844705i	0.144761	+	0.989467i	$0.453759\pi$
$368$	3.86976e6	+	3.86976e6i	0.0776499	+	0.0776499i
$369$		−	9.17369e6i		−	0.182585i
$370$		0			0
$371$	9.60685e7			1.88130
$372$	−8.99474e6	+	8.99474e6i	−0.174727	+	0.174727i
$373$	−3.12116e7	−	3.12116e7i	−0.601436	−	0.601436i	0.339258	−	0.940693i	$-0.389824\pi$
$373$	−3.12116e7	−	3.12116e7i	−0.601436	−	0.601436i	−0.940693	+	0.339258i	$0.889824\pi$
$374$		−	4.87270e6i		−	0.0931440i
$375$		0			0
$376$	4.57015e7			0.859740
$377$	4.52555e6	−	4.52555e6i	0.0844593	−	0.0844593i
$378$	3.11725e7	+	3.11725e7i	0.577159	+	0.577159i
$379$			1.15046e7i			0.211326i	0.994402	+	0.105663i	$0.0336965\pi$
$379$			1.15046e7i			0.211326i	−0.994402	+	0.105663i	$0.966304\pi$
$380$		0			0
$381$	−9.14145e6			−0.165287
$382$	3.12028e7	−	3.12028e7i	0.559763	−	0.559763i
$383$	−4.25312e7	−	4.25312e7i	−0.757026	−	0.757026i	0.218754	−	0.975780i	$-0.429801\pi$
$383$	−4.25312e7	−	4.25312e7i	−0.757026	−	0.757026i	−0.975780	+	0.218754i	$0.929801\pi$
$384$		−	4.84142e7i		−	0.855026i
$385$		0			0
$386$	−7.29940e6			−0.126919
$387$	9.71518e6	−	9.71518e6i	0.167617	−	0.167617i
$388$	2.31052e7	+	2.31052e7i	0.395561	+	0.395561i
$389$		−	3.45253e7i		−	0.586528i	−0.956032	−	0.293264i	$-0.905259\pi$
$389$		−	3.45253e7i		−	0.586528i	0.956032	−	0.293264i	$-0.0947415\pi$
$390$		0			0
$391$	−1.95031e6			−0.0326267
$392$	5.43220e7	−	5.43220e7i	0.901815	−	0.901815i
$393$	−4.17356e7	−	4.17356e7i	−0.687589	−	0.687589i
$394$			3.87688e7i			0.633861i
$395$		0			0
$396$	1.79885e7			0.289673
$397$	1.36149e7	−	1.36149e7i	0.217592	−	0.217592i	−0.589891	−	0.807483i	$-0.700829\pi$
$397$	1.36149e7	−	1.36149e7i	0.217592	−	0.217592i	0.807483	+	0.589891i	$0.200829\pi$
$398$	1.65162e7	+	1.65162e7i	0.261975	+	0.261975i
$399$			9.16364e7i			1.44261i
$400$		0			0
$401$	−8.91943e7			−1.38326			−0.691630	−	0.722252i	$-0.743107\pi$
$401$	−8.91943e7			−1.38326			−0.691630	+	0.722252i	$0.743107\pi$
$402$	6.36517e6	−	6.36517e6i	0.0979788	−	0.0979788i
$403$	3.57030e6	+	3.57030e6i	0.0545493	+	0.0545493i
$404$		−	3.00474e7i		−	0.455683i
$405$		0			0
$406$	2.83900e7			0.424217
$407$	−7.18272e7	+	7.18272e7i	−1.06538	+	1.06538i
$408$	3.90206e6	+	3.90206e6i	0.0574532	+	0.0574532i
$409$		−	2.75539e7i		−	0.402729i	−0.979516	−	0.201364i	$-0.935462\pi$
$409$		−	2.75539e7i		−	0.402729i	0.979516	−	0.201364i	$-0.0645375\pi$
$410$		0			0
$411$	−7.26630e7			−1.04662
$412$	5.20774e7	−	5.20774e7i	0.744660	−	0.744660i
$413$	−5.86694e7	−	5.86694e7i	−0.832839	−	0.832839i
$414$			2.15540e6i			0.0303757i
$415$		0			0
$416$	−1.57438e7			−0.218691
$417$	3.60142e7	−	3.60142e7i	0.496667	−	0.496667i
$418$	−4.58671e7	−	4.58671e7i	−0.628019	−	0.628019i
$419$		−	6.47061e7i		−	0.879636i	−0.898087	−	0.439818i	$-0.855043\pi$
$419$		−	6.47061e7i		−	0.879636i	0.898087	−	0.439818i	$-0.144957\pi$
$420$		0			0
$421$	−1.48259e8			−1.98690			−0.993450	−	0.114267i	$-0.963548\pi$
$421$	−1.48259e8			−1.98690			−0.993450	+	0.114267i	$0.963548\pi$
$422$	−1.64460e7	+	1.64460e7i	−0.218839	+	0.218839i
$423$	−1.12977e7	−	1.12977e7i	−0.149268	−	0.149268i
$424$		−	7.70139e7i		−	1.01035i
$425$		0			0
$426$	−8.87227e6			−0.114764
$427$	5.17287e7	−	5.17287e7i	0.664427	−	0.664427i
$428$	3.76925e6	+	3.76925e6i	0.0480755	+	0.0480755i
$429$			2.70958e7i			0.343187i
$430$		0			0
$431$	9.24831e7			1.15513			0.577565	−	0.816345i	$-0.304003\pi$
$431$	9.24831e7			1.15513			0.577565	+	0.816345i	$0.304003\pi$
$432$	−2.21822e7	+	2.21822e7i	−0.275140	+	0.275140i
$433$	9.15871e7	+	9.15871e7i	1.12816	+	1.12816i	0.990476	+	0.137683i	$0.0439657\pi$
$433$	9.15871e7	+	9.15871e7i	1.12816	+	1.12816i	0.137683	+	0.990476i	$0.456034\pi$
$434$			2.23975e7i			0.273987i
$435$		0			0
$436$	2.17381e7			0.262278
$437$	−1.83584e7	+	1.83584e7i	−0.219984	+	0.219984i
$438$	2.13665e7	+	2.13665e7i	0.254279	+	0.254279i
$439$			1.31005e8i			1.54844i	0.632915	+	0.774221i	$0.281858\pi$
$439$			1.31005e8i			1.54844i	−0.632915	+	0.774221i	$0.718142\pi$
$440$		0			0
$441$	−2.68574e7			−0.313147
$442$	673601.	−	673601.i	0.00780074	−	0.00780074i
$443$	5.10135e7	+	5.10135e7i	0.586778	+	0.586778i	0.936757	−	0.349979i	$-0.113811\pi$
$443$	5.10135e7	+	5.10135e7i	0.586778	+	0.586778i	−0.349979	+	0.936757i	$0.613811\pi$
$444$		−	5.00306e7i		−	0.571593i
$445$		0			0
$446$	−4.52888e7			−0.510489
$447$	2.36864e7	−	2.36864e7i	0.265202	−	0.265202i
$448$	−1.29903e7	−	1.29903e7i	−0.144473	−	0.144473i
$449$			6.85143e7i			0.756906i	0.925620	+	0.378453i	$0.123544\pi$
$449$			6.85143e7i			0.756906i	−0.925620	+	0.378453i	$0.876456\pi$
$450$		0			0
$451$	1.44937e8			1.57998
$452$	3.72658e7	−	3.72658e7i	0.403548	−	0.403548i
$453$	−8.65090e7	−	8.65090e7i	−0.930608	−	0.930608i
$454$		−	6.50543e7i		−	0.695198i
$455$		0			0
$456$	7.34609e7			0.774750
$457$	−9.03199e7	+	9.03199e7i	−0.946313	+	0.946313i	−0.998631	−	0.0523174i	$-0.983339\pi$
$457$	−9.03199e7	+	9.03199e7i	−0.946313	+	0.946313i	0.0523174	+	0.998631i	$0.483339\pi$
$458$	5.94840e7	+	5.94840e7i	0.619161	+	0.619161i
$459$		−	1.11795e7i		−	0.115607i
$460$		0			0
$461$	1.44157e8			1.47141			0.735705	−	0.677303i	$-0.236851\pi$
$461$	1.44157e8			1.47141			0.735705	+	0.677303i	$0.236851\pi$
$462$	−8.49897e7	+	8.49897e7i	−0.861868	+	0.861868i
$463$	−1.29520e8	−	1.29520e8i	−1.30495	−	1.30495i	−0.925013	−	0.379934i	$-0.875947\pi$
$463$	−1.29520e8	−	1.29520e8i	−1.30495	−	1.30495i	−0.379934	−	0.925013i	$-0.624053\pi$
$464$			2.02022e7i			0.202230i
$465$		0			0
$466$	−1.87037e7			−0.184829
$467$	−6.96344e6	+	6.96344e6i	−0.0683712	+	0.0683712i	−0.740466	−	0.672094i	$-0.765395\pi$
$467$	−6.96344e6	+	6.96344e6i	−0.0683712	+	0.0683712i	0.672094	+	0.740466i	$0.265395\pi$
$468$	2.48672e6	+	2.48672e6i	0.0242599	+	0.0242599i
$469$			5.29445e7i			0.513218i
$470$		0			0
$471$	−8.43969e6			−0.0807725
$472$	−4.70327e7	+	4.70327e7i	−0.447274	+	0.447274i
$473$	1.53492e8	+	1.53492e8i	1.45045	+	1.45045i
$474$		−	2.59318e6i		−	0.0243500i
$475$		0			0
$476$	−1.41155e7			−0.130881
$477$	−1.90383e7	+	1.90383e7i	−0.175417	+	0.175417i
$478$	3.39841e7	+	3.39841e7i	0.311166	+	0.311166i
$479$		−	1.79225e8i		−	1.63077i	−0.578919	−	0.815385i	$-0.696525\pi$
$479$		−	1.79225e8i		−	1.63077i	0.578919	−	0.815385i	$-0.303475\pi$
$480$		0			0
$481$	−1.98587e7			−0.178450
$482$	3.86658e7	−	3.86658e7i	0.345291	−	0.345291i
$483$	3.40173e7	+	3.40173e7i	0.301897	+	0.301897i
$484$			1.96946e8i			1.73705i
$485$		0			0
$486$	−2.25782e7			−0.196689
$487$	−2.11900e7	+	2.11900e7i	−0.183461	+	0.183461i	−0.792862	−	0.609401i	$-0.791410\pi$
$487$	−2.11900e7	+	2.11900e7i	−0.183461	+	0.183461i	0.609401	+	0.792862i	$0.291410\pi$
$488$	−4.14686e7	−	4.14686e7i	−0.356829	−	0.356829i
$489$		−	1.57005e8i		−	1.34272i
$490$		0			0
$491$	−6.72686e7			−0.568288			−0.284144	−	0.958782i	$-0.591709\pi$
$491$	−6.72686e7			−0.568288			−0.284144	+	0.958782i	$0.591709\pi$
$492$	−5.04774e7	+	5.04774e7i	−0.423839	+	0.423839i
$493$	−5.09082e6	−	5.09082e6i	−0.0424861	−	0.0424861i
$494$		−	1.26813e7i		−	0.105192i
$495$		0			0
$496$	−1.59380e7			−0.130613
$497$	3.68991e7	−	3.68991e7i	0.300570	−	0.300570i
$498$	−5.07006e7	−	5.07006e7i	−0.410511	−	0.410511i
$499$			6.42641e6i			0.0517210i	0.999666	+	0.0258605i	$0.00823257\pi$
$499$			6.42641e6i			0.0517210i	−0.999666	+	0.0258605i	$0.991767\pi$
$500$		0			0
$501$	1.67019e8			1.32817
$502$	1.65317e7	−	1.65317e7i	0.130679	−	0.130679i
$503$	7.98868e7	+	7.98868e7i	0.627727	+	0.627727i	0.947496	−	0.319768i	$-0.103605\pi$
$503$	7.98868e7	+	7.98868e7i	0.627727	+	0.627727i	−0.319768	+	0.947496i	$0.603605\pi$
$504$			3.58698e7i			0.280180i
$505$		0			0
$506$	−3.40536e7			−0.262852
$507$	7.82363e7	−	7.82363e7i	0.600322	−	0.600322i
$508$	−1.32549e7	−	1.32549e7i	−0.101108	−	0.101108i
$509$			6.08449e7i			0.461393i	0.973026	+	0.230696i	$0.0741004\pi$
$509$			6.08449e7i			0.461393i	−0.973026	+	0.230696i	$0.925900\pi$
$510$		0			0
$511$	−1.77723e8			−1.33193
$512$	6.43146e7	−	6.43146e7i	0.479181	−	0.479181i
$513$	−1.05234e8	−	1.05234e8i	−0.779476	−	0.779476i
$514$			6.15246e7i			0.453064i
$515$		0			0
$516$	−1.06914e8			−0.778188
$517$	1.78494e8	−	1.78494e8i	1.29167	−	1.29167i
$518$	−6.22896e7	−	6.22896e7i	−0.448153	−	0.448153i
$519$			2.09950e8i			1.50181i
$520$		0			0
$521$	−1.51477e8			−1.07111			−0.535555	−	0.844500i	$-0.679898\pi$
$521$	−1.51477e8			−1.07111			−0.535555	+	0.844500i	$0.679898\pi$
$522$	−5.62616e6	+	5.62616e6i	−0.0395549	+	0.0395549i
$523$	3.86508e7	+	3.86508e7i	0.270180	+	0.270180i	0.829173	−	0.558993i	$-0.188812\pi$
$523$	3.86508e7	+	3.86508e7i	0.270180	+	0.270180i	−0.558993	+	0.829173i	$0.688812\pi$
$524$		−	1.21031e8i		−	0.841208i
$525$		0			0
$526$	1.93027e7			0.132635
$527$	4.01625e6	−	4.01625e6i	0.0274403	−	0.0274403i
$528$	−6.04784e7	−	6.04784e7i	−0.410864	−	0.410864i
$529$		−	1.34406e8i		−	0.907928i
$530$		0			0
$531$	2.32535e7			0.155312
$532$	−1.32871e8	+	1.32871e8i	−0.882458	+	0.882458i
$533$	2.00361e7	+	2.00361e7i	0.132322	+	0.132322i
$534$			1.10022e8i			0.722533i
$535$		0			0
$536$	4.24433e7			0.275622
$537$	1.17042e6	−	1.17042e6i	0.00755821	−	0.00755821i
$538$	9.77411e6	+	9.77411e6i	0.0627668	+	0.0627668i
$539$		−	4.24326e8i		−	2.70978i
$540$		0			0
$541$	1.00964e8			0.637637			0.318819	−	0.947816i	$-0.396714\pi$
$541$	1.00964e8			0.637637			0.318819	+	0.947816i	$0.396714\pi$
$542$	7.24965e7	−	7.24965e7i	0.455323	−	0.455323i
$543$	−2.98382e7	−	2.98382e7i	−0.186368	−	0.186368i
$544$			1.77103e7i			0.110009i
$545$		0			0
$546$	−2.34979e7			−0.144361
$547$	−8.80351e6	+	8.80351e6i	−0.0537891	+	0.0537891i	−0.733490	−	0.679701i	$-0.762110\pi$
$547$	−8.80351e6	+	8.80351e6i	−0.0537891	+	0.0537891i	0.679701	+	0.733490i	$0.262110\pi$
$548$	−1.05360e8	−	1.05360e8i	−0.640225	−	0.640225i
$549$			2.05025e7i			0.123905i
$550$		0			0
$551$	−9.58407e7			−0.572921
$552$	2.72702e7	−	2.72702e7i	0.162133	−	0.162133i
$553$	1.07848e7	+	1.07848e7i	0.0637732	+	0.0637732i
$554$		−	7.07926e7i		−	0.416350i
$555$		0			0
$556$	1.04439e8			0.607631
$557$	6.07102e6	−	6.07102e6i	0.0351314	−	0.0351314i	−0.689323	−	0.724454i	$-0.742092\pi$
$557$	6.07102e6	−	6.07102e6i	0.0351314	−	0.0351314i	0.724454	+	0.689323i	$0.242092\pi$
$558$	−4.43859e6	−	4.43859e6i	−0.0255472	−	0.0255472i
$559$			4.24375e7i			0.242949i
$560$		0			0
$561$	3.04803e7			0.172635
$562$	−3.77833e6	+	3.77833e6i	−0.0212858	+	0.0212858i
$563$	1.90242e8	+	1.90242e8i	1.06606	+	1.06606i	0.997658	+	0.0684018i	$0.0217900\pi$
$563$	1.90242e8	+	1.90242e8i	1.06606	+	1.06606i	0.0684018	+	0.997658i	$0.478210\pi$
$564$			1.24329e8i			0.693002i
$565$		0			0
$566$	8.55155e7			0.471624
$567$	−1.52477e8	+	1.52477e8i	−0.836477	+	0.836477i
$568$	−2.95804e7	−	2.95804e7i	−0.161420	−	0.161420i
$569$			2.39087e8i			1.29783i	0.760859	+	0.648917i	$0.224778\pi$
$569$			2.39087e8i			1.29783i	−0.760859	+	0.648917i	$0.775222\pi$
$570$		0			0
$571$	−1.51162e8			−0.811960			−0.405980	−	0.913882i	$-0.633070\pi$
$571$	−1.51162e8			−0.811960			−0.405980	+	0.913882i	$0.633070\pi$
$572$	−3.92883e7	+	3.92883e7i	−0.209930	+	0.209930i
$573$	1.95183e8	+	1.95183e8i	1.03748	+	1.03748i
$574$			1.25692e8i			0.664617i
$575$		0			0
$576$	5.14869e6			0.0269420
$577$	−2.65297e8	+	2.65297e8i	−1.38103	+	1.38103i	−0.538249	+	0.842786i	$0.680914\pi$
$577$	−2.65297e8	+	2.65297e8i	−1.38103	+	1.38103i	−0.842786	+	0.538249i	$0.819086\pi$
$578$	6.47817e7	+	6.47817e7i	0.335482	+	0.335482i
$579$		−	4.56600e7i		−	0.235234i
$580$		0			0
$581$	4.21720e8			2.15028
$582$	4.32671e7	−	4.32671e7i	0.219477	−	0.219477i
$583$	−3.00790e8	−	3.00790e8i	−1.51795	−	1.51795i
$584$			1.42473e8i			0.715308i
$585$		0			0
$586$	1.50973e8			0.750250
$587$	1.66774e8	−	1.66774e8i	0.824544	−	0.824544i	−0.162212	−	0.986756i	$-0.551863\pi$
$587$	1.66774e8	−	1.66774e8i	0.824544	−	0.824544i	0.986756	+	0.162212i	$0.0518630\pi$
$588$	1.47780e8	+	1.47780e8i	0.726917	+	0.726917i
$589$		−	7.56107e7i		−	0.370030i
$590$		0			0
$591$	−2.42511e8			−1.17481
$592$	4.43251e7	−	4.43251e7i	0.213641	−	0.213641i
$593$	9.38190e7	+	9.38190e7i	0.449911	+	0.449911i	0.895325	−	0.445414i	$-0.146943\pi$
$593$	9.38190e7	+	9.38190e7i	0.449911	+	0.449911i	−0.445414	+	0.895325i	$0.646943\pi$
$594$		−	1.95202e8i		−	0.931374i
$595$		0			0
$596$	6.86894e7			0.324452
$597$	−1.03314e8	+	1.03314e8i	−0.485552	+	0.485552i
$598$	−4.70756e6	−	4.70756e6i	−0.0220137	−	0.0220137i
$599$			2.10159e8i			0.977841i	0.872328	+	0.488921i	$0.162609\pi$
$599$			2.10159e8i			0.977841i	−0.872328	+	0.488921i	$0.837391\pi$
$600$		0			0
$601$	1.79076e8			0.824924			0.412462	−	0.910975i	$-0.364669\pi$
$601$	1.79076e8			0.824924			0.412462	+	0.910975i	$0.364669\pi$
$602$	−1.33111e8	+	1.33111e8i	−0.610133	+	0.610133i
$603$	−1.04922e7	−	1.04922e7i	−0.0478537	−	0.0478537i
$604$		−	2.50872e8i		−	1.13852i
$605$		0			0
$606$	−5.62672e7			−0.252835
$607$	7.09085e7	−	7.09085e7i	0.317053	−	0.317053i	−0.530581	−	0.847634i	$-0.678026\pi$
$607$	7.09085e7	−	7.09085e7i	0.317053	−	0.317053i	0.847634	+	0.530581i	$0.178026\pi$
$608$	1.66709e8	+	1.66709e8i	0.741733	+	0.741733i
$609$			1.77588e8i			0.786254i
$610$		0			0
$611$	4.93500e7			0.216353
$612$	2.79733e6	−	2.79733e6i	0.0122036	−	0.0122036i
$613$	1.20399e8	+	1.20399e8i	0.522685	+	0.522685i	0.918381	−	0.395696i	$-0.129497\pi$
$613$	1.20399e8	+	1.20399e8i	0.522685	+	0.522685i	−0.395696	+	0.918381i	$0.629497\pi$
$614$		−	1.04158e8i		−	0.449973i
$615$		0			0
$616$	−5.66715e8			−2.42450
$617$	−9.83715e7	+	9.83715e7i	−0.418807	+	0.418807i	−0.884792	−	0.465985i	$-0.845700\pi$
$617$	−9.83715e7	+	9.83715e7i	−0.418807	+	0.418807i	0.465985	+	0.884792i	$0.345700\pi$
$618$	−9.75210e7	−	9.75210e7i	−0.413174	−	0.413174i
$619$		−	3.07649e8i		−	1.29713i	−0.761159	−	0.648565i	$-0.775369\pi$
$619$		−	3.07649e8i		−	1.29713i	0.761159	−	0.648565i	$-0.224631\pi$
$620$		0			0
$621$	−7.81298e7			−0.326243
$622$	−1.82602e6	+	1.82602e6i	−0.00758812	+	0.00758812i
$623$	−4.57574e8	−	4.57574e8i	−1.89233	−	1.89233i
$624$		−	1.67210e7i		−	0.0688191i
$625$		0			0
$626$	−1.63747e7			−0.0667497
$627$	2.86913e8	−	2.86913e8i	1.16399	−	1.16399i
$628$	−1.22373e7	−	1.22373e7i	−0.0494092	−	0.0494092i
$629$			2.23392e7i			0.0897668i
$630$		0			0
$631$	2.86256e8			1.13938			0.569688	−	0.821861i	$-0.307064\pi$
$631$	2.86256e8			1.13938			0.569688	+	0.821861i	$0.307064\pi$
$632$	8.64573e6	−	8.64573e6i	0.0342492	−	0.0342492i
$633$	−1.02875e8	−	1.02875e8i	−0.405601	−	0.405601i
$634$		−	1.93015e7i		−	0.0757396i
$635$		0			0
$636$	2.09513e8			0.814402
$637$	5.86587e7	−	5.86587e7i	0.226942	−	0.226942i
$638$	−8.88891e7	−	8.88891e7i	−0.342284	−	0.342284i
$639$			1.46249e7i			0.0560518i
$640$		0			0
$641$	−2.23492e8			−0.848572			−0.424286	−	0.905528i	$-0.639475\pi$
$641$	−2.23492e8			−0.848572			−0.424286	+	0.905528i	$0.639475\pi$
$642$	7.05836e6	−	7.05836e6i	0.0266746	−	0.0266746i
$643$	9.04760e7	+	9.04760e7i	0.340330	+	0.340330i	0.856491	−	0.516161i	$-0.172640\pi$
$643$	9.04760e7	+	9.04760e7i	0.340330	+	0.340330i	−0.516161	+	0.856491i	$0.672640\pi$
$644$			9.86485e7i			0.369345i
$645$		0			0
$646$	−1.42653e7			−0.0529156
$647$	1.42334e8	−	1.42334e8i	0.525527	−	0.525527i	−0.393708	−	0.919235i	$-0.628808\pi$
$647$	1.42334e8	−	1.42334e8i	0.525527	−	0.525527i	0.919235	+	0.393708i	$0.128808\pi$
$648$	1.22234e8	+	1.22234e8i	0.449227	+	0.449227i
$649$			3.67387e8i			1.34397i
$650$		0			0
$651$	−1.40103e8			−0.507814
$652$	2.27653e8	−	2.27653e8i	0.821355	−	0.821355i
$653$	−2.75946e8	−	2.75946e8i	−0.991025	−	0.991025i	0.00893507	−	0.999960i	$-0.497156\pi$
$653$	−2.75946e8	−	2.75946e8i	−0.991025	−	0.991025i	−0.999960	+	0.00893507i	$0.997156\pi$
$654$		−	4.07071e7i		−	0.145525i
$655$		0			0
$656$	−8.94418e7			−0.316832
$657$	3.52200e7	−	3.52200e7i	0.124192	−	0.124192i
$658$	1.54793e8	+	1.54793e8i	0.543343	+	0.543343i
$659$			1.82565e8i			0.637913i	0.947769	+	0.318957i	$0.103332\pi$
$659$			1.82565e8i			0.637913i	−0.947769	+	0.318957i	$0.896668\pi$
$660$		0			0
$661$	−4.05107e8			−1.40270			−0.701352	−	0.712816i	$-0.747420\pi$
$661$	−4.05107e8			−1.40270			−0.701352	+	0.712816i	$0.747420\pi$
$662$	−4.35782e7	+	4.35782e7i	−0.150209	+	0.150209i
$663$	4.21358e6	+	4.21358e6i	0.0144581	+	0.0144581i
$664$		−	3.38074e8i		−	1.15480i
$665$		0			0
$666$	2.46884e7			0.0835737
$667$	−3.55780e7	+	3.55780e7i	−0.119896	+	0.119896i
$668$	2.42174e8	+	2.42174e8i	0.812452	+	0.812452i
$669$		−	2.83295e8i		−	0.946152i
$670$		0			0
$671$	−3.23924e8			−1.07220
$672$	3.08904e8	−	3.08904e8i	1.01792	−	1.01792i
$673$	7.51896e7	+	7.51896e7i	0.246668	+	0.246668i	0.819602	−	0.572934i	$-0.194195\pi$
$673$	7.51896e7	+	7.51896e7i	0.246668	+	0.246668i	−0.572934	+	0.819602i	$0.694195\pi$
$674$		−	1.40197e8i		−	0.457886i
$675$		0			0
$676$	2.26881e8			0.734444
$677$	−4.04485e8	+	4.04485e8i	−1.30358	+	1.30358i	−0.377613	+	0.925963i	$0.623255\pi$
$677$	−4.04485e8	+	4.04485e8i	−1.30358	+	1.30358i	−0.925963	+	0.377613i	$0.876745\pi$
$678$	−6.97845e7	−	6.97845e7i	−0.223908	−	0.223908i
$679$			3.59888e8i			1.14963i
$680$		0			0
$681$	4.06935e8			1.28850
$682$	7.01264e7	−	7.01264e7i	0.221069	−	0.221069i
$683$	−1.60273e7	−	1.60273e7i	−0.0503034	−	0.0503034i	0.681508	−	0.731811i	$-0.261325\pi$
$683$	−1.60273e7	−	1.60273e7i	−0.0503034	−	0.0503034i	−0.731811	+	0.681508i	$0.761325\pi$
$684$		−	5.26630e7i		−	0.164565i
$685$		0			0
$686$	1.22904e8			0.380708
$687$	−3.72091e8	+	3.72091e8i	−1.14757	+	1.14757i
$688$	−9.47213e7	−	9.47213e7i	−0.290859	−	0.290859i
$689$		−	8.31622e7i		−	0.254254i
$690$		0			0
$691$	1.78407e8			0.540728			0.270364	−	0.962758i	$-0.412856\pi$
$691$	1.78407e8			0.540728			0.270364	+	0.962758i	$0.412856\pi$
$692$	−3.04422e8	+	3.04422e8i	−0.918668	+	0.918668i
$693$	1.40095e8	+	1.40095e8i	0.420943	+	0.420943i
$694$			1.83402e8i			0.548689i
$695$		0			0
$696$	1.42365e8			0.422255
$697$	2.25387e7	−	2.25387e7i	0.0665627	−	0.0665627i
$698$	−1.39902e8	−	1.39902e8i	−0.411393	−	0.411393i
$699$		−	1.16997e8i		−	0.342566i
$700$		0			0
$701$	−1.67499e8			−0.486249			−0.243125	−	0.969995i	$-0.578172\pi$
$701$	−1.67499e8			−0.486249			−0.243125	+	0.969995i	$0.578172\pi$
$702$	2.69846e7	−	2.69846e7i	0.0780018	−	0.0780018i
$703$	2.10281e8	+	2.10281e8i	0.605249	+	0.605249i
$704$			8.13454e7i			0.233139i
$705$		0			0
$706$	−1.40692e8			−0.399811
$707$	2.34011e8	−	2.34011e8i	0.662182	−	0.662182i
$708$	−1.27950e8	−	1.27950e8i	−0.360529	−	0.360529i
$709$		−	7.42966e7i		−	0.208463i	−0.994553	−	0.104232i	$-0.966762\pi$
$709$		−	7.42966e7i		−	0.208463i	0.994553	−	0.104232i	$-0.0332384\pi$
$710$		0			0
$711$	−4.27455e6			−0.0118927
$712$	−3.66817e8	+	3.66817e8i	−1.01627	+	1.01627i
$713$	−2.80682e7	−	2.80682e7i	−0.0774365	−	0.0774365i
$714$			2.64330e7i			0.0726191i
$715$		0			0
$716$	3.39416e6			0.00924685
$717$	−2.12581e8	+	2.12581e8i	−0.576723	+	0.576723i
$718$	1.75186e8	+	1.75186e8i	0.473288	+	0.473288i
$719$			5.82976e8i			1.56843i	0.620492	+	0.784213i	$0.286933\pi$
$719$			5.82976e8i			1.56843i	−0.620492	+	0.784213i	$0.713067\pi$
$720$		0			0
$721$	8.11164e8			2.16423
$722$	−6.53923e6	+	6.53923e6i	−0.0173746	+	0.0173746i
$723$	2.41867e8	+	2.41867e8i	0.639972	+	0.639972i
$724$		−	8.65292e7i		−	0.228006i
$725$		0			0
$726$	3.68804e8			0.963798
$727$	2.21220e8	−	2.21220e8i	0.575734	−	0.575734i	−0.357991	−	0.933725i	$-0.616538\pi$
$727$	2.21220e8	−	2.21220e8i	0.575734	−	0.575734i	0.933725	+	0.357991i	$0.116538\pi$
$728$	−7.83426e7	−	7.83426e7i	−0.203050	−	0.203050i
$729$		−	4.31003e8i		−	1.11249i
$730$		0			0
$731$	4.77382e7			0.122212
$732$	1.12813e8	−	1.12813e8i	0.287625	−	0.287625i
$733$	−1.51730e6	−	1.51730e6i	−0.00385265	−	0.00385265i	0.705178	−	0.709030i	$-0.250867\pi$
$733$	−1.51730e6	−	1.51730e6i	−0.00385265	−	0.00385265i	−0.709030	+	0.705178i	$0.750867\pi$
$734$			2.26748e8i			0.573396i
$735$		0			0
$736$	1.23771e8			0.310446
$737$	1.65769e8	−	1.65769e8i	0.414096	−	0.414096i
$738$	−2.49088e7	−	2.49088e7i	−0.0619704	−	0.0619704i
$739$		−	3.44636e8i		−	0.853939i	−0.904266	−	0.426969i	$-0.859581\pi$
$739$		−	3.44636e8i		−	0.853939i	0.904266	−	0.426969i	$-0.140419\pi$
$740$		0			0
$741$	7.93256e7			0.194966
$742$	2.60850e8	−	2.60850e8i	0.638526	−	0.638526i
$743$	−2.75120e8	−	2.75120e8i	−0.670743	−	0.670743i	0.287144	−	0.957887i	$-0.407294\pi$
$743$	−2.75120e8	−	2.75120e8i	−0.670743	−	0.670743i	−0.957887	+	0.287144i	$0.907294\pi$
$744$			1.12315e8i			0.272720i
$745$		0			0
$746$	−1.69494e8			−0.408262
$747$	−8.35738e7	+	8.35738e7i	−0.200497	+	0.200497i
$748$	4.41956e7	+	4.41956e7i	0.105603	+	0.105603i
$749$			5.87103e7i			0.139723i
$750$		0			0
$751$	−4.61018e8			−1.08842			−0.544212	−	0.838948i	$-0.683171\pi$
$751$	−4.61018e8			−1.08842			−0.544212	+	0.838948i	$0.683171\pi$
$752$	−1.10150e8	+	1.10150e8i	−0.259019	+	0.259019i
$753$	1.03411e8	+	1.03411e8i	0.242203	+	0.242203i
$754$		−	2.45760e7i		−	0.0573320i
$755$		0			0
$756$	−5.65471e8			−1.30872
$757$	−2.27312e8	+	2.27312e8i	−0.524005	+	0.524005i	−0.918778	−	0.394774i	$-0.870823\pi$
$757$	−2.27312e8	+	2.27312e8i	−0.524005	+	0.524005i	0.394774	+	0.918778i	$0.370823\pi$
$758$	3.12378e7	+	3.12378e7i	0.0717253	+	0.0717253i
$759$		−	2.13016e8i		−	0.487177i
$760$		0			0
$761$	−5.25130e8			−1.19155			−0.595776	−	0.803151i	$-0.703155\pi$
$761$	−5.25130e8			−1.19155			−0.595776	+	0.803151i	$0.703155\pi$
$762$	−2.48213e7	+	2.48213e7i	−0.0560996	+	0.0560996i
$763$	1.69298e8	+	1.69298e8i	0.381133	+	0.381133i
$764$			5.66022e8i			1.26927i
$765$		0			0
$766$	−2.30965e8			−0.513878
$767$	−5.07875e7	+	5.07875e7i	−0.112556	+	0.112556i
$768$	−1.68268e8	−	1.68268e8i	−0.371465	−	0.371465i
$769$		−	3.58307e8i		−	0.787909i	−0.919130	−	0.393955i	$-0.871107\pi$
$769$		−	3.58307e8i		−	0.787909i	0.919130	−	0.393955i	$-0.128893\pi$
$770$		0			0
$771$	−3.84856e8			−0.839721
$772$	6.62059e7	−	6.62059e7i	0.143895	−	0.143895i
$773$	−2.63294e8	−	2.63294e8i	−0.570037	−	0.570037i	0.362101	−	0.932139i	$-0.382059\pi$
$773$	−2.63294e8	−	2.63294e8i	−0.570037	−	0.570037i	−0.932139	+	0.362101i	$0.882059\pi$
$774$		−	5.27583e7i		−	0.113780i
$775$		0			0
$776$	2.88507e8			0.617406
$777$	3.89641e8	−	3.89641e8i	0.830618	−	0.830618i
$778$	−9.37447e7	−	9.37447e7i	−0.199071	−	0.199071i
$779$		−	4.24318e8i		−	0.897591i
$780$		0			0
$781$	−2.31062e8			−0.485037
$782$	−5.29557e6	+	5.29557e6i	−0.0110737	+	0.0110737i
$783$	−2.03940e8	−	2.03940e8i	−0.424831	−	0.424831i
$784$			2.61855e8i			0.543391i
$785$		0			0
$786$	−2.26645e8			−0.466744
$787$	5.46180e8	−	5.46180e8i	1.12050	−	1.12050i	0.128832	−	0.991666i	$-0.458877\pi$
$787$	5.46180e8	−	5.46180e8i	1.12050	−	1.12050i	0.991666	−	0.128832i	$-0.0411228\pi$
$788$	−3.51635e8	−	3.51635e8i	−0.718643	−	0.718643i
$789$			1.20744e8i			0.245830i
$790$		0			0
$791$	5.80456e8			1.17284
$792$	1.12308e8	−	1.12308e8i	0.226066	−	0.226066i
$793$	−4.47792e7	−	4.47792e7i	−0.0897959	−	0.0897959i
$794$		−	7.39355e7i		−	0.147704i
$795$		0			0
$796$	−2.99605e8			−0.594032
$797$	1.48436e8	−	1.48436e8i	0.293201	−	0.293201i	−0.545143	−	0.838343i	$-0.683525\pi$
$797$	1.48436e8	−	1.48436e8i	0.293201	−	0.293201i	0.838343	+	0.545143i	$0.183525\pi$
$798$	2.48816e8	+	2.48816e8i	0.489631	+	0.489631i
$799$		−	5.55142e7i		−	0.108834i
$800$		0			0
$801$	1.81359e8			0.352891
$802$	−2.42185e8	+	2.42185e8i	−0.469487	+	0.469487i
$803$	5.56449e8	+	5.56449e8i	1.07468	+	1.07468i
$804$			1.15465e8i			0.222168i
$805$		0			0
$806$	1.93885e7			0.0370287
$807$	−6.11401e7	+	6.11401e7i	−0.116334	+	0.116334i
$808$	−1.87596e8	−	1.87596e8i	−0.355623	−	0.355623i
$809$		−	2.49688e8i		−	0.471576i	−0.971805	−	0.235788i	$-0.924233\pi$
$809$		−	2.49688e8i		−	0.471576i	0.971805	−	0.235788i	$-0.0757671\pi$
$810$		0			0
$811$	7.41776e8			1.39063			0.695313	−	0.718707i	$-0.255266\pi$
$811$	7.41776e8			1.39063			0.695313	+	0.718707i	$0.255266\pi$
$812$	−2.57499e8	+	2.57499e8i	−0.480958	+	0.480958i
$813$	4.53488e8	+	4.53488e8i	0.843906	+	0.843906i
$814$			3.90057e8i			0.723194i
$815$		0			0
$816$	−1.88096e7			−0.0346186
$817$	4.49364e8	−	4.49364e8i	0.824009	−	0.824009i
$818$	−7.48156e7	−	7.48156e7i	−0.136689	−	0.136689i
$819$			3.87334e7i			0.0705073i
$820$		0			0
$821$	−4.35687e8			−0.787309			−0.393655	−	0.919258i	$-0.628789\pi$
$821$	−4.35687e8			−0.787309			−0.393655	+	0.919258i	$0.628789\pi$
$822$	−1.97298e8	+	1.97298e8i	−0.355228	+	0.355228i
$823$	−4.41351e8	−	4.41351e8i	−0.791743	−	0.791743i	0.190035	−	0.981777i	$-0.439140\pi$
$823$	−4.41351e8	−	4.41351e8i	−0.791743	−	0.791743i	−0.981777	+	0.190035i	$0.939140\pi$
$824$		−	6.50274e8i		−	1.16229i
$825$		0			0
$826$	−3.18604e8			−0.565341
$827$	−9.56220e7	+	9.56220e7i	−0.169060	+	0.169060i	−0.786566	−	0.617506i	$-0.788143\pi$
$827$	−9.56220e7	+	9.56220e7i	−0.169060	+	0.169060i	0.617506	+	0.786566i	$0.288143\pi$
$828$	−1.95496e7	−	1.95496e7i	−0.0344386	−	0.0344386i
$829$			7.80825e8i			1.37054i	0.728291	+	0.685268i	$0.240315\pi$
$829$			7.80825e8i			1.37054i	−0.728291	+	0.685268i	$0.759685\pi$
$830$		0			0
$831$	4.42830e8			0.771674
$832$	−1.12452e7	+	1.12452e7i	−0.0195252	+	0.0195252i
$833$	−6.59856e7	−	6.59856e7i	−0.114160	−	0.114160i
$834$		−	1.95575e8i		−	0.337144i
$835$		0			0
$836$	8.32034e8			1.42404
$837$	1.60892e8	−	1.60892e8i	0.274384	−	0.274384i
$838$	−1.75693e8	−	1.75693e8i	−0.298554	−	0.298554i
$839$			1.44468e8i			0.244616i	0.992492	+	0.122308i	$0.0390296\pi$
$839$			1.44468e8i			0.244616i	−0.992492	+	0.122308i	$0.960970\pi$
$840$		0			0
$841$	4.09087e8			0.687746
$842$	−4.02561e8	+	4.02561e8i	−0.674366	+	0.674366i
$843$	−2.36346e7	−	2.36346e7i	−0.0394517	−	0.0394517i
$844$		−	2.98333e8i		−	0.496219i
$845$		0			0
$846$	−6.13519e7			−0.101325
$847$	−1.53383e9	+	1.53383e9i	−2.52421	+	2.52421i
$848$	1.85620e8	+	1.85620e8i	0.304394	+	0.304394i
$849$			5.34926e8i			0.874119i
$850$		0			0
$851$	1.56121e8			0.253322
$852$	8.04719e7	−	8.04719e7i	0.130115	−	0.130115i
$853$	4.12270e8	+	4.12270e8i	0.664254	+	0.664254i	0.956380	−	0.292126i	$-0.0943626\pi$
$853$	4.12270e8	+	4.12270e8i	0.664254	+	0.664254i	−0.292126	+	0.956380i	$0.594363\pi$
$854$		−	2.80912e8i		−	0.451021i
$855$		0			0
$856$	4.70655e7			0.0750380
$857$	−5.18365e6	+	5.18365e6i	−0.00823556	+	0.00823556i	−0.711213	−	0.702977i	$-0.751854\pi$
$857$	−5.18365e6	+	5.18365e6i	−0.00823556	+	0.00823556i	0.702977	+	0.711213i	$0.251854\pi$
$858$	7.35718e7	+	7.35718e7i	0.116480	+	0.116480i
$859$		−	9.84492e8i		−	1.55322i	−0.629982	−	0.776609i	$-0.716938\pi$
$859$		−	9.84492e8i		−	1.55322i	0.629982	−	0.776609i	$-0.283062\pi$
$860$		0			0
$861$	−7.86241e8			−1.23182
$862$	2.51115e8	−	2.51115e8i	0.392058	−	0.392058i
$863$	7.16892e8	+	7.16892e8i	1.11538	+	1.11538i	0.992411	+	0.122966i	$0.0392406\pi$
$863$	7.16892e8	+	7.16892e8i	1.11538	+	1.11538i	0.122966	+	0.992411i	$0.460759\pi$
$864$			7.09480e8i			1.10002i
$865$		0			0
$866$	4.97363e8			0.765808
$867$	−4.05230e8	+	4.05230e8i	−0.621791	+	0.621791i
$868$	−2.03146e8	−	2.03146e8i	−0.310634	−	0.310634i
$869$		−	6.75346e7i		−	0.102912i
$870$		0			0
$871$	4.58317e7			0.0693604
$872$	1.35718e8	−	1.35718e8i	0.204687	−	0.204687i
$873$	−7.13205e7	−	7.13205e7i	−0.107194	−	0.107194i
$874$			9.96952e7i			0.149328i
$875$		0			0
$876$	−3.87590e8			−0.576581
$877$	3.84095e8	−	3.84095e8i	0.569429	−	0.569429i	−0.362539	−	0.931969i	$-0.618090\pi$
$877$	3.84095e8	−	3.84095e8i	0.569429	−	0.569429i	0.931969	+	0.362539i	$0.118090\pi$
$878$	3.55712e8	+	3.55712e8i	0.525551	+	0.525551i
$879$			9.44382e8i			1.39053i
$880$		0			0
$881$	−9.55741e8			−1.39769			−0.698847	−	0.715271i	$-0.746303\pi$
$881$	−9.55741e8			−1.39769			−0.698847	+	0.715271i	$0.746303\pi$
$882$	−7.29245e7	+	7.29245e7i	−0.106284	+	0.106284i
$883$	3.85519e8	+	3.85519e8i	0.559969	+	0.559969i	0.929299	−	0.369329i	$-0.120413\pi$
$883$	3.85519e8	+	3.85519e8i	0.559969	+	0.559969i	−0.369329	+	0.929299i	$0.620413\pi$
$884$			1.22192e7i			0.0176883i
$885$		0			0
$886$	2.77029e8			0.398312
$887$	6.73645e8	−	6.73645e8i	0.965296	−	0.965296i	−0.0341220	−	0.999418i	$-0.510863\pi$
$887$	6.73645e8	−	6.73645e8i	0.965296	−	0.965296i	0.999418	+	0.0341220i	$0.0108635\pi$
$888$	−3.12358e8	−	3.12358e8i	−0.446081	−	0.446081i
$889$		−	2.06459e8i		−	0.293853i
$890$		0			0
$891$	9.54807e8			1.34984
$892$	4.10771e8	−	4.10771e8i	0.578770	−	0.578770i
$893$	−5.22560e8	−	5.22560e8i	−0.733806	−	0.733806i
$894$		−	1.28629e8i		−	0.180022i
$895$		0			0
$896$	1.09343e9			1.52009
$897$	2.94472e7	−	2.94472e7i	0.0408007	−	0.0408007i
$898$	1.86033e8	+	1.86033e8i	0.256898	+	0.256898i
$899$		−	1.46531e8i		−	0.201674i
$900$		0			0
$901$	−9.35497e7			−0.127899
$902$	3.93540e8	−	3.93540e8i	0.536253	−	0.536253i
$903$	−8.32651e8	−	8.32651e8i	−1.13084	−	1.13084i
$904$		−	4.65326e8i		−	0.629872i
$905$		0			0
$906$	−4.69787e8			−0.631708
$907$	−8.67904e8	+	8.67904e8i	−1.16319	+	1.16319i	−0.179414	+	0.983774i	$0.557420\pi$
$907$	−8.67904e8	+	8.67904e8i	−1.16319	+	1.16319i	−0.983774	+	0.179414i	$0.942580\pi$
$908$	5.90045e8	+	5.90045e8i	0.788184	+	0.788184i
$909$			9.27497e7i			0.123487i
$910$		0			0
$911$	−1.07789e9			−1.42567			−0.712837	−	0.701330i	$-0.752590\pi$
$911$	−1.07789e9			−1.42567			−0.712837	+	0.701330i	$0.752590\pi$
$912$	−1.77056e8	+	1.77056e8i	−0.233414	+	0.233414i
$913$	−1.32040e9	−	1.32040e9i	−1.73498	−	1.73498i
$914$			4.90482e8i			0.642369i
$915$		0			0
$916$	−1.07905e9			−1.40396
$917$	9.42598e8	−	9.42598e8i	1.22241	−	1.22241i
$918$	−3.03552e7	−	3.03552e7i	−0.0392378	−	0.0392378i
$919$			6.68544e8i			0.861357i	0.902505	+	0.430679i	$0.141726\pi$
$919$			6.68544e8i			0.861357i	−0.902505	+	0.430679i	$0.858274\pi$
$920$		0			0
$921$	6.51538e8			0.833991
$922$	3.91422e8	−	3.91422e8i	0.499405	−	0.499405i
$923$	−3.19419e7	−	3.19419e7i	−0.0406214	−	0.0406214i
$924$		−	1.54172e9i		−	1.95430i
$925$		0			0
$926$	−7.03357e8			−0.885814
$927$	−1.60751e8	+	1.60751e8i	−0.201797	+	0.201797i
$928$	3.23076e8	+	3.23076e8i	0.404260	+	0.404260i
$929$		−	1.71956e8i		−	0.214472i	−0.994234	−	0.107236i	$-0.965800\pi$
$929$		−	1.71956e8i		−	0.214472i	0.994234	−	0.107236i	$-0.0342001\pi$
$930$		0			0
$931$	−1.24226e9			−1.53944
$932$	1.69643e8	−	1.69643e8i	0.209551	−	0.209551i
$933$	−1.14223e7	−	1.14223e7i	−0.0140640	−	0.0140640i
$934$			3.78149e7i			0.0464112i
$935$		0			0
$936$	3.10509e7			0.0378658
$937$	−7.39804e8	+	7.39804e8i	−0.899286	+	0.899286i	−0.995373	−	0.0960869i	$-0.969367\pi$
$937$	−7.39804e8	+	7.39804e8i	−0.899286	+	0.899286i	0.0960869	+	0.995373i	$0.469367\pi$
$938$	1.43757e8	+	1.43757e8i	0.174189	+	0.174189i
$939$		−	1.02429e8i		−	0.123716i
$940$		0			0
$941$	9.44325e8			1.13332			0.566660	−	0.823952i	$-0.308235\pi$
$941$	9.44325e8			1.13332			0.566660	+	0.823952i	$0.308235\pi$
$942$	−2.29158e7	+	2.29158e7i	−0.0274147	+	0.0274147i
$943$	−1.57515e8	−	1.57515e8i	−0.187840	−	0.187840i
$944$		−	2.26717e8i		−	0.269506i
$945$		0			0
$946$	8.33540e8			0.984585
$947$	8.16654e8	−	8.16654e8i	0.961586	−	0.961586i	−0.0377034	−	0.999289i	$-0.512004\pi$
$947$	8.16654e8	−	8.16654e8i	0.961586	−	0.961586i	0.999289	+	0.0377034i	$0.0120042\pi$
$948$	2.35203e7	+	2.35203e7i	0.0276069	+	0.0276069i
$949$			1.53847e8i			0.180007i
$950$		0			0
$951$	1.20737e8			0.140378
$952$	−8.81281e7	+	8.81281e7i	−0.102142	+	0.102142i
$953$	−4.40051e8	−	4.40051e8i	−0.508422	−	0.508422i	0.405620	−	0.914042i	$-0.367056\pi$
$953$	−4.40051e8	−	4.40051e8i	−0.508422	−	0.508422i	−0.914042	+	0.405620i	$0.867056\pi$
$954$			1.03387e8i			0.119075i
$955$		0			0
$956$	−6.16475e8			−0.705573
$957$	5.56029e8	−	5.56029e8i	0.634397	−	0.634397i
$958$	−4.86641e8	−	4.86641e8i	−0.553493	−	0.553493i
$959$		−	1.64109e9i		−	1.86071i
$960$		0			0
$961$	−7.71902e8			−0.869746
$962$	−5.39214e7	+	5.39214e7i	−0.0605669	+	0.0605669i
$963$	−1.16348e7	−	1.16348e7i	−0.0130281	−	0.0130281i
$964$			7.01401e8i			0.782953i
$965$		0			0
$966$	1.84731e8			0.204931
$967$	−1.38431e8	+	1.38431e8i	−0.153092	+	0.153092i	−0.779497	−	0.626405i	$-0.784525\pi$
$967$	−1.38431e8	+	1.38431e8i	−0.153092	+	0.153092i	0.626405	+	0.779497i	$0.284525\pi$
$968$	1.22960e9	+	1.22960e9i	1.35562	+	1.35562i
$969$		−	8.92339e7i		−	0.0980750i
$970$		0			0
$971$	4.70863e8			0.514324			0.257162	−	0.966368i	$-0.417213\pi$
$971$	4.70863e8			0.514324			0.257162	+	0.966368i	$0.417213\pi$
$972$	2.04785e8	−	2.04785e8i	0.222997	−	0.222997i
$973$	8.13380e8	+	8.13380e8i	0.882989	+	0.882989i
$974$			1.15072e8i			0.124536i
$975$		0			0
$976$	1.99896e8			0.215008
$977$	−9.36496e8	+	9.36496e8i	−1.00420	+	1.00420i	−0.00421351	+	0.999991i	$0.501341\pi$
$977$	−9.36496e8	+	9.36496e8i	−1.00420	+	1.00420i	−0.999991	+	0.00421351i	$0.998659\pi$
$978$	−4.26307e8	−	4.26307e8i	−0.455728	−	0.455728i
$979$			2.86533e9i			3.05370i
$980$		0			0
$981$	−6.71007e7			−0.0710755
$982$	−1.82651e8	+	1.82651e8i	−0.192880	+	0.192880i
$983$	7.76947e8	+	7.76947e8i	0.817957	+	0.817957i	0.985812	−	0.167854i	$-0.0536838\pi$
$983$	7.76947e8	+	7.76947e8i	0.817957	+	0.817957i	−0.167854	+	0.985812i	$0.553684\pi$
$984$			6.30295e8i			0.661544i
$985$		0			0
$986$	−2.76457e7			−0.0288401
$987$	−9.68279e8	+	9.68279e8i	−1.00705	+	1.00705i
$988$	1.15020e8	+	1.15020e8i	0.119262	+	0.119262i
$989$		−	3.33626e8i		−	0.344882i
$990$		0			0
$991$	1.22547e9			1.25916			0.629579	−	0.776937i	$-0.283228\pi$
$991$	1.22547e9			1.25916			0.629579	+	0.776937i	$0.283228\pi$
$992$	−2.54881e8	+	2.54881e8i	−0.261098	+	0.261098i
$993$	−2.72595e8	−	2.72595e8i	−0.278401	−	0.278401i
$994$		−	2.00380e8i		−	0.204031i
$995$		0			0
$996$	9.19714e8			0.930840
$997$	3.22586e8	−	3.22586e8i	0.325507	−	0.325507i	−0.525368	−	0.850875i	$-0.676072\pi$
$997$	3.22586e8	−	3.22586e8i	0.325507	−	0.325507i	0.850875	+	0.525368i	$0.176072\pi$
$998$	1.74493e7	+	1.74493e7i	0.0175544	+	0.0175544i
$999$			8.94914e8i			0.897604i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.7.c.d.18.3	yes	8
3.2	odd	2		225.7.g.f.118.2		8
5.2	odd	4	inner	25.7.c.d.7.3	yes	8
5.3	odd	4	inner	25.7.c.d.7.2	✓	8
5.4	even	2	inner	25.7.c.d.18.2	yes	8
15.2	even	4		225.7.g.f.82.2		8
15.8	even	4		225.7.g.f.82.3		8
15.14	odd	2		225.7.g.f.118.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.7.c.d.7.2	✓	8	5.3	odd	4	inner
25.7.c.d.7.3	yes	8	5.2	odd	4	inner
25.7.c.d.18.2	yes	8	5.4	even	2	inner
25.7.c.d.18.3	yes	8	1.1	even	1	trivial
225.7.g.f.82.2		8	15.2	even	4
225.7.g.f.82.3		8	15.8	even	4
225.7.g.f.118.2		8	3.2	odd	2
225.7.g.f.118.3		8	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	25.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.71525 - 2.71525i) q^{2} +(16.9847 + 16.9847i) q^{3} +49.2549i q^{4} +92.2354 q^{6} +(-383.600 + 383.600i) q^{7} +(307.515 + 307.515i) q^{8} -152.039i q^{9} +O(q^{10})\)	\(q+(2.71525 - 2.71525i) q^{2} +(16.9847 + 16.9847i) q^{3} +49.2549i q^{4} +92.2354 q^{6} +(-383.600 + 383.600i) q^{7} +(307.515 + 307.515i) q^{8} -152.039i q^{9} +2402.10 q^{11} +(-836.580 + 836.580i) q^{12} +(332.065 + 332.065i) q^{13} +2083.14i q^{14} -1482.35 q^{16} +(373.542 - 373.542i) q^{17} +(-412.823 - 412.823i) q^{18} -7032.37i q^{19} -13030.7 q^{21} +(6522.29 - 6522.29i) q^{22} +(-2610.56 - 2610.56i) q^{23} +10446.1i q^{24} +1803.28 q^{26} +(14964.2 - 14964.2i) q^{27} +(-18894.1 - 18894.1i) q^{28} -13628.5i q^{29} +10751.8 q^{31} +(-23705.9 + 23705.9i) q^{32} +(40798.9 + 40798.9i) q^{33} -2028.52i q^{34} +7488.65 q^{36} +(-29901.9 + 29901.9i) q^{37} +(-19094.6 - 19094.6i) q^{38} +11280.1i q^{39} +60337.8 q^{41} +(-35381.5 + 35381.5i) q^{42} +(63899.3 + 63899.3i) q^{43} +118315. i q^{44} -14176.6 q^{46} +(74307.8 - 74307.8i) q^{47} +(-25177.3 - 25177.3i) q^{48} -176648. i q^{49} +12689.0 q^{51} +(-16355.8 + 16355.8i) q^{52} +(-125220. - 125220. i) q^{53} -81263.0i q^{54} -235925. q^{56} +(119443. - 119443. i) q^{57} +(-37004.8 - 37004.8i) q^{58} +152944. i q^{59} -134851. q^{61} +(29193.8 - 29193.8i) q^{62} +(58322.1 + 58322.1i) q^{63} +33864.3i q^{64} +221558. q^{66} +(69010.1 - 69010.1i) q^{67} +(18398.8 + 18398.8i) q^{68} -88679.1i q^{69} -96191.6 q^{71} +(46754.2 - 46754.2i) q^{72} +(231651. + 231651. i) q^{73} +162382. i q^{74} +346378. q^{76} +(-921444. + 921444. i) q^{77} +(30628.2 + 30628.2i) q^{78} -28114.8i q^{79} +397489. q^{81} +(163832. - 163832. i) q^{82} +(-549687. - 549687. i) q^{83} -641823. i q^{84} +347005. q^{86} +(231476. - 231476. i) q^{87} +(738681. + 738681. i) q^{88} +1.19284e6i q^{89} -254760. q^{91} +(128583. - 128583. i) q^{92} +(182616. + 182616. i) q^{93} -403528. i q^{94} -805276. q^{96} +(469094. - 469094. i) q^{97} +(-479644. - 479644. i) q^{98} -365212. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2436 q^{6}+O(q^{10}) \) 8 * q + 2436 * q^6	\( 8 q + 2436 q^{6} + 7896 q^{11} + 28 q^{16} - 27264 q^{21} - 192744 q^{26} + 108656 q^{31} + 391608 q^{36} + 392136 q^{41} + 16776 q^{46} - 1182264 q^{51} - 1156080 q^{56} + 392896 q^{61} + 1332 q^{66} + 815376 q^{71} + 2759140 q^{76} + 2731608 q^{81} - 2130384 q^{86} - 3423744 q^{91} + 3595356 q^{96}+O(q^{100}) \) 8 * q + 2436 * q^6 + 7896 * q^11 + 28 * q^16 - 27264 * q^21 - 192744 * q^26 + 108656 * q^31 + 391608 * q^36 + 392136 * q^41 + 16776 * q^46 - 1182264 * q^51 - 1156080 * q^56 + 392896 * q^61 + 1332 * q^66 + 815376 * q^71 + 2759140 * q^76 + 2731608 * q^81 - 2130384 * q^86 - 3423744 * q^91 + 3595356 * q^96

Introduction

L-functions

Modular forms

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