LMFDB - Embedded newform 25.7.c.d.7.4

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			7.4
Root			$1.22474 - 3.99225i$ of defining polynomial
Character	$\chi$	$=$	25.7
Dual form			25.7.c.d.18.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.83897 + 8.83897i) q^{2} +(29.2322 - 29.2322i) q^{3} +92.2549i q^{4} +516.765 q^{6} +(106.298 + 106.298i) q^{7} +(-249.744 + 249.744i) q^{8} -980.039i q^{9} +O(q^{10})$	\(q+(8.83897 + 8.83897i) q^{2} +(29.2322 - 29.2322i) q^{3} +92.2549i q^{4} +516.765 q^{6} +(106.298 + 106.298i) q^{7} +(-249.744 + 249.744i) q^{8} -980.039i q^{9} -428.097 q^{11} +(2696.81 + 2696.81i) q^{12} +(-2827.78 + 2827.78i) q^{13} +1879.14i q^{14} +1489.35 q^{16} +(-5272.53 - 5272.53i) q^{17} +(8662.54 - 8662.54i) q^{18} -3722.37i q^{19} +6214.66 q^{21} +(-3783.94 - 3783.94i) q^{22} +(1039.18 - 1039.18i) q^{23} +14601.1i q^{24} -49989.3 q^{26} +(-7338.41 - 7338.41i) q^{27} +(-9806.54 + 9806.54i) q^{28} -1088.51i q^{29} +16412.2 q^{31} +(29148.0 + 29148.0i) q^{32} +(-12514.2 + 12514.2i) q^{33} -93207.5i q^{34} +90413.3 q^{36} +(-25835.7 - 25835.7i) q^{37} +(32901.9 - 32901.9i) q^{38} +165324. i q^{39} +37696.2 q^{41} +(54931.2 + 54931.2i) q^{42} +(-49757.0 + 49757.0i) q^{43} -39494.0i q^{44} +18370.6 q^{46} +(112593. + 112593. i) q^{47} +(43537.0 - 43537.0i) q^{48} -95050.3i q^{49} -308255. q^{51} +(-260876. - 260876. i) q^{52} +(-65378.7 + 65378.7i) q^{53} -129728. i q^{54} -53094.7 q^{56} +(-108813. - 108813. i) q^{57} +(9621.27 - 9621.27i) q^{58} +145924. i q^{59} +233075. q^{61} +(145067. + 145067. i) q^{62} +(104176. - 104176. i) q^{63} +419957. i q^{64} -221225. q^{66} +(-79686.2 - 79686.2i) q^{67} +(486417. - 486417. i) q^{68} -60755.1i q^{69} +300036. q^{71} +(244759. + 244759. i) q^{72} +(-145411. + 145411. i) q^{73} -456722. i q^{74} +343407. q^{76} +(-45506.0 - 45506.0i) q^{77} +(-1.46129e6 + 1.46129e6i) q^{78} -462075. i q^{79} +285413. q^{81} +(333196. + 333196. i) q^{82} +(543263. - 543263. i) q^{83} +573333. i q^{84} -879601. q^{86} +(-31819.4 - 31819.4i) q^{87} +(106915. - 106915. i) q^{88} -1.12379e6i q^{89} -601176. q^{91} +(95869.7 + 95869.7i) q^{92} +(479764. - 479764. i) q^{93} +1.99042e6i q^{94} +1.70412e6 q^{96} +(840877. + 840877. i) q^{97} +(840147. - 840147. i) q^{98} +419552. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	8.83897	+	8.83897i	1.10487	+	1.10487i	0.993814	+	0.111058i	$0.0354238\pi$
$2$	8.83897	+	8.83897i	1.10487	+	1.10487i	0.111058	+	0.993814i	$0.464576\pi$
$3$	29.2322	−	29.2322i	1.08267	−	1.08267i	0.0864134	−	0.996259i	$-0.472459\pi$
$3$	29.2322	−	29.2322i	1.08267	−	1.08267i	0.996259	−	0.0864134i	$-0.0275406\pi$
$4$			92.2549i			1.44148i
$5$		0			0
$5$		0			0
$6$	516.765			2.39243
$7$	106.298	+	106.298i	0.309908	+	0.309908i	0.844874	−	0.534966i	$-0.179676\pi$
$7$	106.298	+	106.298i	0.309908	+	0.309908i	−0.534966	+	0.844874i	$0.679676\pi$
$8$	−249.744	+	249.744i	−0.487781	+	0.487781i
$9$		−	980.039i		−	1.34436i
$10$		0			0
$11$	−428.097			−0.321636			−0.160818	−	0.986984i	$-0.551413\pi$
$11$	−428.097			−0.321636			−0.160818	+	0.986984i	$0.551413\pi$
$12$	2696.81	+	2696.81i	1.56065	+	1.56065i
$13$	−2827.78	+	2827.78i	−1.28711	+	1.28711i	−0.350573	+	0.936536i	$0.614013\pi$
$13$	−2827.78	+	2827.78i	−1.28711	+	1.28711i	−0.936536	+	0.350573i	$0.885987\pi$
$14$			1879.14i			0.684816i
$15$		0			0
$16$	1489.35			0.363611
$17$	−5272.53	−	5272.53i	−1.07318	−	1.07318i	−0.997102	−	0.0760778i	$-0.975760\pi$
$17$	−5272.53	−	5272.53i	−1.07318	−	1.07318i	−0.0760778	−	0.997102i	$-0.524240\pi$
$18$	8662.54	−	8662.54i	1.48535	−	1.48535i
$19$		−	3722.37i		−	0.542699i	−0.962481	−	0.271349i	$-0.912530\pi$
$19$		−	3722.37i		−	0.542699i	0.962481	−	0.271349i	$-0.0874698\pi$
$20$		0			0
$21$	6214.66			0.671057
$22$	−3783.94	−	3783.94i	−0.355366	−	0.355366i
$23$	1039.18	−	1039.18i	0.0854100	−	0.0854100i	−0.663111	−	0.748521i	$-0.730764\pi$
$23$	1039.18	−	1039.18i	0.0854100	−	0.0854100i	0.748521	+	0.663111i	$0.230764\pi$
$24$			14601.1i			1.05621i
$25$		0			0
$26$	−49989.3			−2.84418
$27$	−7338.41	−	7338.41i	−0.372830	−	0.372830i
$28$	−9806.54	+	9806.54i	−0.446726	+	0.446726i
$29$		−	1088.51i		−	0.0446310i	−0.999751	−	0.0223155i	$-0.992896\pi$
$29$		−	1088.51i		−	0.0446310i	0.999751	−	0.0223155i	$-0.00710383\pi$
$30$		0			0
$31$	16412.2			0.550911			0.275456	−	0.961314i	$-0.411171\pi$
$31$	16412.2			0.550911			0.275456	+	0.961314i	$0.411171\pi$
$32$	29148.0	+	29148.0i	0.889525	+	0.889525i
$33$	−12514.2	+	12514.2i	−0.348226	+	0.348226i
$34$		−	93207.5i		−	2.37145i
$35$		0			0
$36$	90413.3			1.93787
$37$	−25835.7	−	25835.7i	−0.510053	−	0.510053i	0.404490	−	0.914543i	$-0.367449\pi$
$37$	−25835.7	−	25835.7i	−0.510053	−	0.510053i	−0.914543	+	0.404490i	$0.867449\pi$
$38$	32901.9	−	32901.9i	0.599612	−	0.599612i
$39$			165324.i			2.78703i
$40$		0			0
$41$	37696.2			0.546948			0.273474	−	0.961879i	$-0.411827\pi$
$41$	37696.2			0.546948			0.273474	+	0.961879i	$0.411827\pi$
$42$	54931.2	+	54931.2i	0.741432	+	0.741432i
$43$	−49757.0	+	49757.0i	−0.625819	+	0.625819i	−0.947013	−	0.321194i	$-0.895916\pi$
$43$	−49757.0	+	49757.0i	−0.625819	+	0.625819i	0.321194	+	0.947013i	$0.395916\pi$
$44$		−	39494.0i		−	0.463632i
$45$		0			0
$46$	18370.6			0.188734
$47$	112593.	+	112593.i	1.08447	+	1.08447i	0.996086	+	0.0883873i	$0.0281713\pi$
$47$	112593.	+	112593.i	1.08447	+	1.08447i	0.0883873	+	0.996086i	$0.471829\pi$
$48$	43537.0	−	43537.0i	0.393672	−	0.393672i
$49$		−	95050.3i		−	0.807914i
$50$		0			0
$51$	−308255.			−2.32380
$52$	−260876.	−	260876.i	−1.85534	−	1.85534i
$53$	−65378.7	+	65378.7i	−0.439146	+	0.439146i	−0.891724	−	0.452579i	$-0.850504\pi$
$53$	−65378.7	+	65378.7i	−0.439146	+	0.439146i	0.452579	+	0.891724i	$0.350504\pi$
$54$		−	129728.i		−	0.823858i
$55$		0			0
$56$	−53094.7			−0.302334
$57$	−108813.	−	108813.i	−0.587565	−	0.587565i
$58$	9621.27	−	9621.27i	0.0493115	−	0.0493115i
$59$			145924.i			0.710512i	0.934769	+	0.355256i	$0.115606\pi$
$59$			145924.i			0.710512i	−0.934769	+	0.355256i	$0.884394\pi$
$60$		0			0
$61$	233075.			1.02685			0.513423	−	0.858136i	$-0.328377\pi$
$61$	233075.			1.02685			0.513423	+	0.858136i	$0.328377\pi$
$62$	145067.	+	145067.i	0.608686	+	0.608686i
$63$	104176.	−	104176.i	0.416628	−	0.416628i
$64$			419957.i			1.60201i
$65$		0			0
$66$	−221225.			−0.769491
$67$	−79686.2	−	79686.2i	−0.264947	−	0.264947i	0.562113	−	0.827060i	$-0.309988\pi$
$67$	−79686.2	−	79686.2i	−0.264947	−	0.264947i	−0.827060	+	0.562113i	$0.809988\pi$
$68$	486417.	−	486417.i	1.54697	−	1.54697i
$69$		−	60755.1i		−	0.184942i
$70$		0			0
$71$	300036.			0.838297			0.419148	−	0.907918i	$-0.362329\pi$
$71$	300036.			0.838297			0.419148	+	0.907918i	$0.362329\pi$
$72$	244759.	+	244759.i	0.655754	+	0.655754i
$73$	−145411.	+	145411.i	−0.373790	+	0.373790i	−0.868856	−	0.495065i	$-0.835144\pi$
$73$	−145411.	+	145411.i	−0.373790	+	0.373790i	0.495065	+	0.868856i	$0.335144\pi$
$74$		−	456722.i		−	1.12709i
$75$		0			0
$76$	343407.			0.782290
$77$	−45506.0	−	45506.0i	−0.0996774	−	0.0996774i
$78$	−1.46129e6	+	1.46129e6i	−3.07931	+	3.07931i
$79$		−	462075.i		−	0.937197i	−0.883411	−	0.468599i	$-0.844759\pi$
$79$		−	462075.i		−	0.937197i	0.883411	−	0.468599i	$-0.155241\pi$
$80$		0			0
$81$	285413.			0.537055
$82$	333196.	+	333196.i	0.604308	+	0.604308i
$83$	543263.	−	543263.i	0.950114	−	0.950114i	−0.0486993	−	0.998813i	$-0.515508\pi$
$83$	543263.	−	543263.i	0.950114	−	0.950114i	0.998813	+	0.0486993i	$0.0155076\pi$
$84$			573333.i			0.967317i
$85$		0			0
$86$	−879601.			−1.38290
$87$	−31819.4	−	31819.4i	−0.0483208	−	0.0483208i
$88$	106915.	−	106915.i	0.156888	−	0.156888i
$89$		−	1.12379e6i		−	1.59409i	−0.603917	−	0.797047i	$-0.706394\pi$
$89$		−	1.12379e6i		−	1.59409i	0.603917	−	0.797047i	$-0.293606\pi$
$90$		0			0
$91$	−601176.			−0.797769
$92$	95869.7	+	95869.7i	0.123117	+	0.123117i
$93$	479764.	−	479764.i	0.596457	−	0.596457i
$94$			1.99042e6i			2.39641i
$95$		0			0
$96$	1.70412e6			1.92613
$97$	840877.	+	840877.i	0.921335	+	0.921335i	0.997124	−	0.0757891i	$-0.0241476\pi$
$97$	840877.	+	840877.i	0.921335	+	0.921335i	−0.0757891	+	0.997124i	$0.524148\pi$
$98$	840147.	−	840147.i	0.892642	−	0.892642i
$99$			419552.i			0.432394i
$100$		0			0
$101$	6943.18			0.00673899			0.00336949	−	0.999994i	$-0.498927\pi$
$101$	6943.18			0.00673899			0.00336949	+	0.999994i	$0.498927\pi$
$102$	−2.72466e6	−	2.72466e6i	−2.56751	−	2.56751i
$103$	−482826.	+	482826.i	−0.441854	+	0.441854i	−0.892635	−	0.450780i	$-0.851146\pi$
$103$	−482826.	+	482826.i	−0.441854	+	0.441854i	0.450780	+	0.892635i	$0.351146\pi$
$104$		−	1.41244e6i		−	1.25565i
$105$		0			0
$106$	−1.15576e6			−0.970399
$107$	−932970.	−	932970.i	−0.761582	−	0.761582i	0.215026	−	0.976608i	$-0.431016\pi$
$107$	−932970.	−	932970.i	−0.761582	−	0.761582i	−0.976608	+	0.215026i	$0.931016\pi$
$108$	677004.	−	677004.i	0.537428	−	0.537428i
$109$			1.22134e6i			0.943099i	0.881840	+	0.471550i	$0.156305\pi$
$109$			1.22134e6i			0.943099i	−0.881840	+	0.471550i	$0.843695\pi$
$110$		0			0
$111$	−1.51047e6			−1.10444
$112$	158316.	+	158316.i	0.112686	+	0.112686i
$113$	−680939.	+	680939.i	−0.471925	+	0.471925i	−0.902537	−	0.430612i	$-0.858298\pi$
$113$	−680939.	+	680939.i	−0.471925	+	0.471925i	0.430612	+	0.902537i	$0.358298\pi$
$114$		−	1.92359e6i		−	1.29837i
$115$		0			0
$116$	100420.			0.0643348
$117$	2.77133e6	+	2.77133e6i	1.73034	+	1.73034i
$118$	−1.28982e6	+	1.28982e6i	−0.785025	+	0.785025i
$119$		−	1.12092e6i		−	0.665173i
$120$		0			0
$121$	−1.58829e6			−0.896550
$122$	2.06014e6	+	2.06014e6i	1.13453	+	1.13453i
$123$	1.10194e6	−	1.10194e6i	0.592166	−	0.592166i
$124$			1.51410e6i			0.794129i
$125$		0			0
$126$	1.84163e6			0.920640
$127$	−1.96344e6	−	1.96344e6i	−0.958534	−	0.958534i	0.0406399	−	0.999174i	$-0.487060\pi$
$127$	−1.96344e6	−	1.96344e6i	−0.958534	−	0.958534i	−0.999174	+	0.0406399i	$0.987060\pi$
$128$	−1.84652e6	+	1.84652e6i	−0.880490	+	0.880490i
$129$			2.90901e6i			1.35511i
$130$		0			0
$131$	2.36541e6			1.05218			0.526092	−	0.850427i	$-0.323657\pi$
$131$	2.36541e6			1.05218			0.526092	+	0.850427i	$0.323657\pi$
$132$	−1.15450e6	−	1.15450e6i	−0.501962	−	0.501962i
$133$	395682.	−	395682.i	0.168186	−	0.168186i
$134$		−	1.40869e6i		−	0.585464i
$135$		0			0
$136$	2.63357e6			1.04695
$137$	1.08736e6	+	1.08736e6i	0.422875	+	0.422875i	0.886192	−	0.463318i	$-0.153341\pi$
$137$	1.08736e6	+	1.08736e6i	0.422875	+	0.422875i	−0.463318	+	0.886192i	$0.653341\pi$
$138$	537013.	−	537013.i	0.204337	−	0.204337i
$139$		−	2.38132e6i		−	0.886693i	−0.896350	−	0.443346i	$-0.853791\pi$
$139$		−	2.38132e6i		−	0.886693i	0.896350	−	0.443346i	$-0.146209\pi$
$140$		0			0
$141$	6.58269e6			2.34826
$142$	2.65201e6	+	2.65201e6i	0.926210	+	0.926210i
$143$	1.21056e6	−	1.21056e6i	0.413980	−	0.413980i
$144$		−	1.45962e6i		−	0.488825i
$145$		0			0
$146$	−2.57056e6			−0.825980
$147$	−2.77853e6	−	2.77853e6i	−0.874707	−	0.874707i
$148$	2.38347e6	−	2.38347e6i	0.735232	−	0.735232i
$149$			2.81533e6i			0.851080i	0.904940	+	0.425540i	$0.139916\pi$
$149$			2.81533e6i			0.851080i	−0.904940	+	0.425540i	$0.860084\pi$
$150$		0			0
$151$	−4.36315e6			−1.26727			−0.633636	−	0.773632i	$-0.718438\pi$
$151$	−4.36315e6			−1.26727			−0.633636	+	0.773632i	$0.718438\pi$
$152$	929639.	+	929639.i	0.264718	+	0.264718i
$153$	−5.16729e6	+	5.16729e6i	−1.44274	+	1.44274i
$154$		−	804453.i		−	0.220261i
$155$		0			0
$156$	−1.52519e7			−4.01746
$157$	−2.78134e6	−	2.78134e6i	−0.718713	−	0.718713i	0.249628	−	0.968342i	$-0.419692\pi$
$157$	−2.78134e6	−	2.78134e6i	−0.718713	−	0.718713i	−0.968342	+	0.249628i	$0.919692\pi$
$158$	4.08427e6	−	4.08427e6i	1.03548	−	1.03548i
$159$			3.82232e6i			0.950902i
$160$		0			0
$161$	220927.			0.0529384
$162$	2.52276e6	+	2.52276e6i	0.593377	+	0.593377i
$163$	−3.96649e6	+	3.96649e6i	−0.915892	+	0.915892i	−0.996727	−	0.0808358i	$-0.974241\pi$
$163$	−3.96649e6	+	3.96649e6i	−0.915892	+	0.915892i	0.0808358	+	0.996727i	$0.474241\pi$
$164$			3.47766e6i			0.788416i
$165$		0			0
$166$	9.60377e6			2.09951
$167$	−3.60216e6	−	3.60216e6i	−0.773416	−	0.773416i	0.205286	−	0.978702i	$-0.434188\pi$
$167$	−3.60216e6	−	3.60216e6i	−0.773416	−	0.773416i	−0.978702	+	0.205286i	$0.934188\pi$
$168$	−1.55207e6	+	1.55207e6i	−0.327329	+	0.327329i
$169$		−	1.11658e7i		−	2.31329i
$170$		0			0
$171$	−3.64807e6			−0.729583
$172$	−4.59032e6	−	4.59032e6i	−0.902107	−	0.902107i
$173$	1.01615e6	−	1.01615e6i	0.196255	−	0.196255i	−0.602138	−	0.798392i	$-0.705684\pi$
$173$	1.01615e6	−	1.01615e6i	0.196255	−	0.196255i	0.798392	+	0.602138i	$0.205684\pi$
$174$		−	562501.i		−	0.106776i
$175$		0			0
$176$	−637587.			−0.116950
$177$	4.26568e6	+	4.26568e6i	0.769252	+	0.769252i
$178$	9.93312e6	−	9.93312e6i	1.76127	−	1.76127i
$179$			4.66458e6i			0.813305i	0.913583	+	0.406652i	$0.133304\pi$
$179$			4.66458e6i			0.813305i	−0.913583	+	0.406652i	$0.866696\pi$
$180$		0			0
$181$	5.43193e6			0.916048			0.458024	−	0.888940i	$-0.348557\pi$
$181$	5.43193e6			0.916048			0.458024	+	0.888940i	$0.348557\pi$
$182$	−5.31378e6	−	5.31378e6i	−0.881433	−	0.881433i
$183$	6.81328e6	−	6.81328e6i	1.11174	−	1.11174i
$184$			519059.i			0.0833227i
$185$		0			0
$186$	8.48124e6			1.31802
$187$	2.25716e6	+	2.25716e6i	0.345173	+	0.345173i
$188$	−1.03873e7	+	1.03873e7i	−1.56325	+	1.56325i
$189$		−	1.56012e6i		−	0.231086i
$190$		0			0
$191$	−1.19322e6			−0.171246			−0.0856232	−	0.996328i	$-0.527288\pi$
$191$	−1.19322e6			−0.171246			−0.0856232	+	0.996328i	$0.527288\pi$
$192$	1.22763e7	+	1.22763e7i	1.73445	+	1.73445i
$193$	−6.57252e6	+	6.57252e6i	−0.914240	+	0.914240i	−0.996602	−	0.0823623i	$-0.973754\pi$
$193$	−6.57252e6	+	6.57252e6i	−0.914240	+	0.914240i	0.0823623	+	0.996602i	$0.473754\pi$
$194$			1.48650e7i			2.03591i
$195$		0			0
$196$	8.76885e6			1.16459
$197$	4.32190e6	+	4.32190e6i	0.565296	+	0.565296i	0.930807	−	0.365511i	$-0.119106\pi$
$197$	4.32190e6	+	4.32190e6i	0.565296	+	0.565296i	−0.365511	+	0.930807i	$0.619106\pi$
$198$	−3.70841e6	+	3.70841e6i	−0.477740	+	0.477740i
$199$			5.90595e6i			0.749429i	0.927140	+	0.374715i	$0.122259\pi$
$199$			5.90595e6i			0.749429i	−0.927140	+	0.374715i	$0.877741\pi$
$200$		0			0
$201$	−4.65880e6			−0.573701
$202$	61370.6	+	61370.6i	0.00744571	+	0.00744571i
$203$	115706.	−	115706.i	0.0138315	−	0.0138315i
$204$		−	2.84380e7i		−	3.34972i
$205$		0			0
$206$	−8.53538e6			−0.976385
$207$	−1.01844e6	−	1.01844e6i	−0.114822	−	0.114822i
$208$	−4.21155e6	+	4.21155e6i	−0.468007	+	0.468007i
$209$			1.59354e6i			0.174551i
$210$		0			0
$211$	−1.59541e7			−1.69834			−0.849171	−	0.528118i	$-0.822898\pi$
$211$	−1.59541e7			−1.69834			−0.849171	+	0.528118i	$0.822898\pi$
$212$	−6.03150e6	−	6.03150e6i	−0.633021	−	0.633021i
$213$	8.77069e6	−	8.77069e6i	0.907601	−	0.907601i
$214$		−	1.64930e7i		−	1.68290i
$215$		0			0
$216$	3.66545e6			0.363719
$217$	1.74459e6	+	1.74459e6i	0.170732	+	0.170732i
$218$	−1.07954e7	+	1.07954e7i	−1.04200	+	1.04200i
$219$			8.50134e6i			0.809385i
$220$		0			0
$221$	2.98191e7			2.76260
$222$	−1.33510e7	−	1.33510e7i	−1.22026	−	1.22026i
$223$	7.50393e6	−	7.50393e6i	0.676666	−	0.676666i	−0.282579	−	0.959244i	$-0.591190\pi$
$223$	7.50393e6	−	7.50393e6i	0.676666	−	0.676666i	0.959244	+	0.282579i	$0.0911898\pi$
$224$			6.19676e6i			0.551341i
$225$		0			0
$226$	−1.20376e7			−1.04283
$227$	9.22459e6	+	9.22459e6i	0.788623	+	0.788623i	0.981268	−	0.192645i	$-0.0617066\pi$
$227$	9.22459e6	+	9.22459e6i	0.788623	+	0.788623i	−0.192645	+	0.981268i	$0.561707\pi$
$228$	1.00385e7	−	1.00385e7i	0.846964	−	0.846964i
$229$		−	893767.i		−	0.0744248i	−0.999307	−	0.0372124i	$-0.988152\pi$
$229$		−	893767.i		−	0.0744248i	0.999307	−	0.0372124i	$-0.0118478\pi$
$230$		0			0
$231$	−2.66048e6			−0.215836
$232$	271848.	+	271848.i	0.0217702	+	0.0217702i
$233$	−1.93379e6	+	1.93379e6i	−0.152877	+	0.152877i	−0.779401	−	0.626525i	$-0.784477\pi$
$233$	−1.93379e6	+	1.93379e6i	−0.152877	+	0.152877i	0.626525	+	0.779401i	$0.284477\pi$
$234$			4.89914e7i			3.82360i
$235$		0			0
$236$	−1.34622e7			−1.02419
$237$	−1.35074e7	−	1.35074e7i	−1.01468	−	1.01468i
$238$	9.90780e6	−	9.90780e6i	0.734931	−	0.734931i
$239$		−	1.60640e7i		−	1.17668i	−0.808613	−	0.588341i	$-0.799781\pi$
$239$		−	1.60640e7i		−	1.17668i	0.808613	−	0.588341i	$-0.200219\pi$
$240$		0			0
$241$	−1.71466e7			−1.22497			−0.612487	−	0.790480i	$-0.709831\pi$
$241$	−1.71466e7			−1.22497			−0.612487	+	0.790480i	$0.709831\pi$
$242$	−1.40389e7	−	1.40389e7i	−0.990573	−	0.990573i
$243$	1.36929e7	−	1.36929e7i	0.954285	−	0.954285i
$244$			2.15023e7i			1.48018i
$245$		0			0
$246$	1.94801e7			1.30853
$247$	1.05260e7	+	1.05260e7i	0.698512	+	0.698512i
$248$	−4.09885e6	+	4.09885e6i	−0.268724	+	0.268724i
$249$		−	3.17615e7i		−	2.05733i
$250$		0			0
$251$	215800.			0.0136468			0.00682340	−	0.999977i	$-0.497828\pi$
$251$	215800.			0.0136468			0.00682340	+	0.999977i	$0.497828\pi$
$252$	9.61079e6	+	9.61079e6i	0.600561	+	0.600561i
$253$	−444871.	+	444871.i	−0.0274709	+	0.0274709i
$254$		−	3.47097e7i		−	2.11811i
$255$		0			0
$256$	−5.76545e6			−0.343648
$257$	5.45272e6	+	5.45272e6i	0.321228	+	0.321228i	0.849238	−	0.528010i	$-0.177062\pi$
$257$	5.45272e6	+	5.45272e6i	0.321228	+	0.321228i	−0.528010	+	0.849238i	$0.677062\pi$
$258$	−2.57126e7	+	2.57126e7i	−1.49723	+	1.49723i
$259$		−	5.49258e6i		−	0.316139i
$260$		0			0
$261$	−1.06678e6			−0.0600001
$262$	2.09078e7	+	2.09078e7i	1.16253	+	1.16253i
$263$	−2.14291e7	+	2.14291e7i	−1.17797	+	1.17797i	−0.197715	+	0.980260i	$0.563352\pi$
$263$	−2.14291e7	+	2.14291e7i	−1.17797	+	1.17797i	−0.980260	+	0.197715i	$0.936648\pi$
$264$		−	6.25069e6i		−	0.339716i
$265$		0			0
$266$	6.99484e6			0.371649
$267$	−3.28507e7	−	3.28507e7i	−1.72588	−	1.72588i
$268$	7.35144e6	−	7.35144e6i	0.381916	−	0.381916i
$269$			1.68547e7i			0.865891i	0.901420	+	0.432946i	$0.142526\pi$
$269$			1.68547e7i			0.865891i	−0.901420	+	0.432946i	$0.857474\pi$
$270$		0			0
$271$	4.00727e6			0.201345			0.100673	−	0.994920i	$-0.467901\pi$
$271$	4.00727e6			0.201345			0.100673	+	0.994920i	$0.467901\pi$
$272$	−7.85266e6	−	7.85266e6i	−0.390220	−	0.390220i
$273$	−1.75737e7	+	1.75737e7i	−0.863723	+	0.863723i
$274$			1.92223e7i			0.934444i
$275$		0			0
$276$	5.60496e6			0.266591
$277$	9.66071e6	+	9.66071e6i	0.454537	+	0.454537i	0.896857	−	0.442320i	$-0.145844\pi$
$277$	9.66071e6	+	9.66071e6i	0.454537	+	0.454537i	−0.442320	+	0.896857i	$0.645844\pi$
$278$	2.10484e7	−	2.10484e7i	0.979681	−	0.979681i
$279$		−	1.60846e7i		−	0.740623i
$280$		0			0
$281$	−9.39531e6			−0.423440			−0.211720	−	0.977330i	$-0.567907\pi$
$281$	−9.39531e6			−0.423440			−0.211720	+	0.977330i	$0.567907\pi$
$282$	5.81842e7	+	5.81842e7i	2.59453	+	2.59453i
$283$	−1.23799e7	+	1.23799e7i	−0.546206	+	0.546206i	−0.925341	−	0.379135i	$-0.876222\pi$
$283$	−1.23799e7	+	1.23799e7i	−0.546206	+	0.546206i	0.379135	+	0.925341i	$0.376222\pi$
$284$			2.76797e7i			1.20839i
$285$		0			0
$286$	2.14003e7			0.914789
$287$	4.00705e6	+	4.00705e6i	0.169503	+	0.169503i
$288$	2.85661e7	−	2.85661e7i	1.19584	−	1.19584i
$289$			3.14616e7i			1.30343i
$290$		0			0
$291$	4.91613e7			1.99501
$292$	−1.34148e7	−	1.34148e7i	−0.538812	−	0.538812i
$293$	3.16158e7	−	3.16158e7i	1.25690	−	1.25690i	0.304335	−	0.952565i	$-0.401566\pi$
$293$	3.16158e7	−	3.16158e7i	1.25690	−	1.25690i	0.952565	−	0.304335i	$-0.0984344\pi$
$294$		−	4.91186e7i		−	1.93288i
$295$		0			0
$296$	1.29046e7			0.497588
$297$	3.14155e6	+	3.14155e6i	0.119915	+	0.119915i
$298$	−2.48846e7	+	2.48846e7i	−0.940334	+	0.940334i
$299$			5.87715e6i			0.219864i
$300$		0			0
$301$	−1.05782e7			−0.387892
$302$	−3.85658e7	−	3.85658e7i	−1.40017	−	1.40017i
$303$	202964.	−	202964.i	0.00729612	−	0.00729612i
$304$		−	5.54392e6i		−	0.197331i
$305$		0			0
$306$	−9.13470e7			−3.18809
$307$	−2.19916e7	−	2.19916e7i	−0.760048	−	0.760048i	0.216283	−	0.976331i	$-0.430607\pi$
$307$	−2.19916e7	−	2.19916e7i	−0.760048	−	0.760048i	−0.976331	+	0.216283i	$0.930607\pi$
$308$	4.19815e6	−	4.19815e6i	0.143683	−	0.143683i
$309$			2.82281e7i			0.956767i
$310$		0			0
$311$	7.71053e6			0.256332			0.128166	−	0.991753i	$-0.459091\pi$
$311$	7.71053e6			0.256332			0.128166	+	0.991753i	$0.459091\pi$
$312$	−4.12887e7	−	4.12887e7i	−1.35946	−	1.35946i
$313$	1.70373e7	−	1.70373e7i	0.555608	−	0.555608i	−0.372446	−	0.928054i	$-0.621481\pi$
$313$	1.70373e7	−	1.70373e7i	0.555608	−	0.555608i	0.928054	+	0.372446i	$0.121481\pi$
$314$		−	4.91685e7i		−	1.58817i
$315$		0			0
$316$	4.26286e7			1.35095
$317$	8.22844e6	+	8.22844e6i	0.258309	+	0.258309i	0.824366	−	0.566057i	$-0.191532\pi$
$317$	8.22844e6	+	8.22844e6i	0.258309	+	0.258309i	−0.566057	+	0.824366i	$0.691532\pi$
$318$	−3.37854e7	+	3.37854e7i	−1.05062	+	1.05062i
$319$			465986.i			0.0143549i
$320$		0			0
$321$	−5.45455e7			−1.64909
$322$	1.95277e6	+	1.95277e6i	0.0584901	+	0.0584901i
$323$	−1.96263e7	+	1.96263e7i	−0.582413	+	0.582413i
$324$			2.63307e7i			0.774155i
$325$		0			0
$326$	−7.01195e7			−2.02389
$327$	3.57024e7	+	3.57024e7i	1.02107	+	1.02107i
$328$	−9.41440e6	+	9.41440e6i	−0.266791	+	0.266791i
$329$			2.39370e7i			0.672173i
$330$		0			0
$331$	651545.			0.0179664			0.00898319	−	0.999960i	$-0.497141\pi$
$331$	651545.			0.0179664			0.00898319	+	0.999960i	$0.497141\pi$
$332$	5.01186e7	+	5.01186e7i	1.36957	+	1.36957i
$333$	−2.53200e7	+	2.53200e7i	−0.685695	+	0.685695i
$334$		−	6.36787e7i		−	1.70905i
$335$		0			0
$336$	9.25582e6			0.244004
$337$	−3.63751e7	−	3.63751e7i	−0.950417	−	0.950417i	0.0484108	−	0.998828i	$-0.484584\pi$
$337$	−3.63751e7	−	3.63751e7i	−0.950417	−	0.950417i	−0.998828	+	0.0484108i	$0.984584\pi$
$338$	9.86945e7	−	9.86945e7i	2.55589	−	2.55589i
$339$			3.98106e7i			1.02188i
$340$		0			0
$341$	−7.02601e6			−0.177193
$342$	−3.22452e7	−	3.22452e7i	−0.806095	−	0.806095i
$343$	2.26096e7	−	2.26096e7i	0.560287	−	0.560287i
$344$		−	2.48530e7i		−	0.610525i
$345$		0			0
$346$	1.79635e7			0.433672
$347$	4.15542e7	+	4.15542e7i	0.994549	+	0.994549i	0.999985	−	0.00543630i	$-0.00173044\pi$
$347$	4.15542e7	+	4.15542e7i	0.994549	+	0.994549i	−0.00543630	+	0.999985i	$0.501730\pi$
$348$	2.93549e6	−	2.93549e6i	0.0696535	−	0.0696535i
$349$			4.34019e7i			1.02102i	0.859873	+	0.510508i	$0.170542\pi$
$349$			4.34019e7i			1.02102i	−0.859873	+	0.510508i	$0.829458\pi$
$350$		0			0
$351$	4.15028e7			0.959745
$352$	−1.24782e7	−	1.24782e7i	−0.286103	−	0.286103i
$353$	−2.94566e7	+	2.94566e7i	−0.669666	+	0.669666i	−0.957639	−	0.287973i	$-0.907019\pi$
$353$	−2.94566e7	+	2.94566e7i	−0.669666	+	0.669666i	0.287973	+	0.957639i	$0.407019\pi$
$354$			7.54085e7i			1.69985i
$355$		0			0
$356$	1.03675e8			2.29786
$357$	−3.27670e7	−	3.27670e7i	−0.720165	−	0.720165i
$358$	−4.12301e7	+	4.12301e7i	−0.898598	+	0.898598i
$359$		−	5.21467e7i		−	1.12705i	−0.826099	−	0.563526i	$-0.809445\pi$
$359$		−	5.21467e7i		−	1.12705i	0.826099	−	0.563526i	$-0.190555\pi$
$360$		0			0
$361$	3.31898e7			0.705478
$362$	4.80127e7	+	4.80127e7i	1.01212	+	1.01212i
$363$	−4.64293e7	+	4.64293e7i	−0.970671	+	0.970671i
$364$		−	5.54614e7i		−	1.14997i
$365$		0			0
$366$	1.20445e8			2.45666
$367$	−1.85103e7	−	1.85103e7i	−0.374468	−	0.374468i	0.494634	−	0.869102i	$-0.335302\pi$
$367$	−1.85103e7	−	1.85103e7i	−0.374468	−	0.374468i	−0.869102	+	0.494634i	$0.835302\pi$
$368$	1.54771e6	−	1.54771e6i	0.0310560	−	0.0310560i
$369$		−	3.69438e7i		−	0.735296i
$370$		0			0
$371$	−1.38993e7			−0.272189
$372$	4.42606e7	+	4.42606e7i	0.859781	+	0.859781i
$373$	4.10657e7	−	4.10657e7i	0.791322	−	0.791322i	−0.190387	−	0.981709i	$-0.560974\pi$
$373$	4.10657e7	−	4.10657e7i	0.791322	−	0.791322i	0.981709	+	0.190387i	$0.0609743\pi$
$374$			3.99019e7i			0.762743i
$375$		0			0
$376$	−5.62390e7			−1.05797
$377$	3.07805e6	+	3.07805e6i	0.0574449	+	0.0574449i
$378$	1.37899e7	−	1.37899e7i	0.255320	−	0.255320i
$379$		−	6.43505e7i		−	1.18205i	−0.806655	−	0.591023i	$-0.798724\pi$
$379$		−	6.43505e7i		−	1.18205i	0.806655	−	0.591023i	$-0.201276\pi$
$380$		0			0
$381$	−1.14791e8			−2.07556
$382$	−1.05469e7	−	1.05469e7i	−0.189205	−	0.189205i
$383$	5.20577e6	−	5.20577e6i	0.0926591	−	0.0926591i	−0.659258	−	0.751917i	$-0.729129\pi$
$383$	5.20577e6	−	5.20577e6i	0.0926591	−	0.0926591i	0.751917	+	0.659258i	$0.229129\pi$
$384$			1.07956e8i			1.90657i
$385$		0			0
$386$	−1.16189e8			−2.02024
$387$	4.87638e7	+	4.87638e7i	0.841326	+	0.841326i
$388$	−7.75750e7	+	7.75750e7i	−1.32809	+	1.32809i
$389$		−	1.07113e8i		−	1.81968i	−0.414958	−	0.909841i	$-0.636204\pi$
$389$		−	1.07113e8i		−	1.81968i	0.414958	−	0.909841i	$-0.363796\pi$
$390$		0			0
$391$	−1.09582e7			−0.183320
$392$	2.37382e7	+	2.37382e7i	0.394085	+	0.394085i
$393$	6.91460e7	−	6.91460e7i	1.13917	−	1.13917i
$394$			7.64023e7i			1.24916i
$395$		0			0
$396$	−3.87057e7			−0.623289
$397$	−2.93451e7	−	2.93451e7i	−0.468990	−	0.468990i	0.432597	−	0.901587i	$-0.357597\pi$
$397$	−2.93451e7	−	2.93451e7i	−0.468990	−	0.468990i	−0.901587	+	0.432597i	$0.857597\pi$
$398$	−5.22025e7	+	5.22025e7i	−0.828023	+	0.828023i
$399$		−	2.31333e7i		−	0.364182i
$400$		0			0
$401$	8.66570e7			1.34391			0.671955	−	0.740592i	$-0.265455\pi$
$401$	8.66570e7			1.34391			0.671955	+	0.740592i	$0.265455\pi$
$402$	−4.11790e7	−	4.11790e7i	−0.633866	−	0.633866i
$403$	−4.64100e7	+	4.64100e7i	−0.709082	+	0.709082i
$404$			640542.i			0.00971413i
$405$		0			0
$406$	2.04545e6			0.0305640
$407$	1.10602e7	+	1.10602e7i	0.164051	+	0.164051i
$408$	7.69848e7	−	7.69848e7i	1.13351	−	1.13351i
$409$			3.34326e6i			0.0488652i	0.999701	+	0.0244326i	$0.00777792\pi$
$409$			3.34326e6i			0.0488652i	−0.999701	+	0.0244326i	$0.992222\pi$
$410$		0			0
$411$	6.35718e7			0.915670
$412$	−4.45431e7	−	4.45431e7i	−0.636925	−	0.636925i
$413$	−1.55115e7	+	1.55115e7i	−0.220193	+	0.220193i
$414$		−	1.80039e7i		−	0.253727i
$415$		0			0
$416$	−1.64848e8			−2.28983
$417$	−6.96111e7	−	6.96111e7i	−0.959998	−	0.959998i
$418$	−1.40852e7	+	1.40852e7i	−0.192857	+	0.192857i
$419$			1.26524e8i			1.72001i	0.510289	+	0.860003i	$0.329538\pi$
$419$			1.26524e8i			1.72001i	−0.510289	+	0.860003i	$0.670462\pi$
$420$		0			0
$421$	5.05108e7			0.676921			0.338460	−	0.940981i	$-0.390094\pi$
$421$	5.05108e7			0.676921			0.338460	+	0.940981i	$0.390094\pi$
$422$	−1.41018e8	−	1.41018e8i	−1.87645	−	1.87645i
$423$	1.10346e8	−	1.10346e8i	1.45792	−	1.45792i
$424$		−	3.26559e7i		−	0.428414i
$425$		0			0
$426$	1.55048e8			2.00556
$427$	2.47754e7	+	2.47754e7i	0.318228	+	0.318228i
$428$	8.60711e7	−	8.60711e7i	1.09781	−	1.09781i
$429$		−	7.07748e7i		−	0.896410i
$430$		0			0
$431$	2.32962e7			0.290973			0.145486	−	0.989360i	$-0.453525\pi$
$431$	2.32962e7			0.290973			0.145486	+	0.989360i	$0.453525\pi$
$432$	−1.09295e7	−	1.09295e7i	−0.135565	−	0.135565i
$433$	8.79741e7	−	8.79741e7i	1.08366	−	1.08366i	0.0874896	−	0.996165i	$-0.472116\pi$
$433$	8.79741e7	−	8.79741e7i	1.08366	−	1.08366i	0.996165	−	0.0874896i	$-0.0278845\pi$
$434$			3.08407e7i			0.377273i
$435$		0			0
$436$	−1.12675e8			−1.35946
$437$	−3.86822e6	−	3.86822e6i	−0.0463519	−	0.0463519i
$438$	−7.51431e7	+	7.51431e7i	−0.894266	+	0.894266i
$439$			8.48209e7i			1.00256i	0.865286	+	0.501279i	$0.167137\pi$
$439$			8.48209e7i			1.00256i	−0.865286	+	0.501279i	$0.832863\pi$
$440$		0			0
$441$	−9.31530e7			−1.08613
$442$	2.63570e8	+	2.63570e8i	3.05231	+	3.05231i
$443$	−4.99445e7	+	4.99445e7i	−0.574482	+	0.574482i	−0.933378	−	0.358896i	$-0.883153\pi$
$443$	−4.99445e7	+	4.99445e7i	−0.574482	+	0.574482i	0.358896	+	0.933378i	$0.383153\pi$
$444$		−	1.39348e8i		−	1.59203i
$445$		0			0
$446$	1.32654e8			1.49526
$447$	8.22982e7	+	8.22982e7i	0.921441	+	0.921441i
$448$	−4.46408e7	+	4.46408e7i	−0.496475	+	0.496475i
$449$		−	5.45501e7i		−	0.602638i	−0.953523	−	0.301319i	$-0.902573\pi$
$449$		−	5.45501e7i		−	0.602638i	0.953523	−	0.301319i	$-0.0974269\pi$
$450$		0			0
$451$	−1.61376e7			−0.175918
$452$	−6.28199e7	−	6.28199e7i	−0.680271	−	0.680271i
$453$	−1.27544e8	+	1.27544e8i	−1.37204	+	1.37204i
$454$			1.63072e8i			1.74265i
$455$		0			0
$456$	5.43507e7			0.573206
$457$	−2.62925e7	−	2.62925e7i	−0.275476	−	0.275476i	0.555824	−	0.831300i	$-0.312403\pi$
$457$	−2.62925e7	−	2.62925e7i	−0.275476	−	0.275476i	−0.831300	+	0.555824i	$0.812403\pi$
$458$	7.89998e6	−	7.89998e6i	0.0822298	−	0.0822298i
$459$			7.73840e7i			0.800227i
$460$		0			0
$461$	−7.06319e7			−0.720939			−0.360469	−	0.932771i	$-0.617383\pi$
$461$	−7.06319e7			−0.720939			−0.360469	+	0.932771i	$0.617383\pi$
$462$	−2.35159e7	−	2.35159e7i	−0.238471	−	0.238471i
$463$	4.98972e7	−	4.98972e7i	0.502728	−	0.502728i	−0.409557	−	0.912285i	$-0.634317\pi$
$463$	4.98972e7	−	4.98972e7i	0.502728	−	0.502728i	0.912285	+	0.409557i	$0.134317\pi$
$464$		−	1.62117e6i		−	0.0162283i
$465$		0			0
$466$	−3.41854e7			−0.337818
$467$	5.13083e7	+	5.13083e7i	0.503775	+	0.503775i	0.912609	−	0.408834i	$-0.134064\pi$
$467$	5.13083e7	+	5.13083e7i	0.503775	+	0.503775i	−0.408834	+	0.912609i	$0.634064\pi$
$468$	−2.55669e8	+	2.55669e8i	−2.49425	+	2.49425i
$469$		−	1.69410e7i		−	0.164218i
$470$		0			0
$471$	−1.62609e8			−1.55626
$472$	−3.64437e7	−	3.64437e7i	−0.346574	−	0.346574i
$473$	2.13008e7	−	2.13008e7i	0.201286	−	0.201286i
$474$		−	2.38784e8i		−	2.24218i
$475$		0			0
$476$	1.03411e8			0.958835
$477$	6.40737e7	+	6.40737e7i	0.590370	+	0.590370i
$478$	1.41989e8	−	1.41989e8i	1.30008	−	1.30008i
$479$		−	2.14571e8i		−	1.95238i	−0.216909	−	0.976192i	$-0.569597\pi$
$479$		−	2.14571e8i		−	1.95238i	0.216909	−	0.976192i	$-0.430403\pi$
$480$		0			0
$481$	1.46115e8			1.31299
$482$	−1.51558e8	−	1.51558e8i	−1.35344	−	1.35344i
$483$	6.45817e6	−	6.45817e6i	0.0573150	−	0.0573150i
$484$		−	1.46528e8i		−	1.29236i
$485$		0			0
$486$	2.42063e8			2.10872
$487$	1.12852e8	+	1.12852e8i	0.977060	+	0.977060i	0.999743	−	0.0226827i	$-0.00722076\pi$
$487$	1.12852e8	+	1.12852e8i	0.977060	+	0.977060i	−0.0226827	+	0.999743i	$0.507221\pi$
$488$	−5.82090e7	+	5.82090e7i	−0.500876	+	0.500876i
$489$			2.31898e8i			1.98322i
$490$		0			0
$491$	7.97769e7			0.673958			0.336979	−	0.941512i	$-0.390595\pi$
$491$	7.97769e7			0.673958			0.336979	+	0.941512i	$0.390595\pi$
$492$	1.01660e8	+	1.01660e8i	0.853597	+	0.853597i
$493$	−5.73918e6	+	5.73918e6i	−0.0478971	+	0.0478971i
$494$			1.86079e8i			1.54353i
$495$		0			0
$496$	2.44435e7			0.200318
$497$	3.18933e7	+	3.18933e7i	0.259795	+	0.259795i
$498$	2.80739e8	−	2.80739e8i	2.27308	−	2.27308i
$499$			4.67133e7i			0.375958i	0.982173	+	0.187979i	$0.0601937\pi$
$499$			4.67133e7i			0.375958i	−0.982173	+	0.187979i	$0.939806\pi$
$500$		0			0
$501$	−2.10598e8			−1.67471
$502$	1.90745e6	+	1.90745e6i	0.0150780	+	0.0150780i
$503$	−1.20462e8	+	1.20462e8i	−0.946553	+	0.946553i	−0.998642	−	0.0520893i	$-0.983412\pi$
$503$	−1.20462e8	+	1.20462e8i	−0.946553	+	0.946553i	0.0520893	+	0.998642i	$0.483412\pi$
$504$			5.20349e7i			0.406446i
$505$		0			0
$506$	−7.86441e6			−0.0607036
$507$	−3.26401e8	−	3.26401e8i	−2.50454	−	2.50454i
$508$	1.81137e8	−	1.81137e8i	1.38171	−	1.38171i
$509$			1.04726e8i			0.794148i	0.917787	+	0.397074i	$0.129974\pi$
$509$			1.04726e8i			0.794148i	−0.917787	+	0.397074i	$0.870026\pi$
$510$		0			0
$511$	−3.09138e7			−0.231681
$512$	6.72168e7	+	6.72168e7i	0.500804	+	0.500804i
$513$	−2.73163e7	+	2.73163e7i	−0.202334	+	0.202334i
$514$			9.63928e7i			0.709832i
$515$		0			0
$516$	−2.68370e8			−1.95337
$517$	−4.82009e7	−	4.82009e7i	−0.348805	−	0.348805i
$518$	4.85488e7	−	4.85488e7i	0.349292	−	0.349292i
$519$		−	5.94086e7i		−	0.424959i
$520$		0			0
$521$	1.80765e8			1.27821			0.639103	−	0.769121i	$-0.279306\pi$
$521$	1.80765e8			1.27821			0.639103	+	0.769121i	$0.279306\pi$
$522$	−9.42922e6	−	9.42922e6i	−0.0662925	−	0.0662925i
$523$	−6.88840e7	+	6.88840e7i	−0.481519	+	0.481519i	−0.905616	−	0.424098i	$-0.860591\pi$
$523$	−6.88840e7	+	6.88840e7i	−0.481519	+	0.481519i	0.424098	+	0.905616i	$0.360591\pi$
$524$			2.18220e8i			1.51671i
$525$		0			0
$526$	−3.78822e8			−2.60302
$527$	−8.65338e7	−	8.65338e7i	−0.591227	−	0.591227i
$528$	−1.86381e7	+	1.86381e7i	−0.126619	+	0.126619i
$529$			1.45876e8i			0.985410i
$530$		0			0
$531$	1.43011e8			0.955184
$532$	3.65036e7	+	3.65036e7i	0.242438	+	0.242438i
$533$	−1.06596e8	+	1.06596e8i	−0.703982	+	0.703982i
$534$		−	5.80733e8i		−	3.81376i
$535$		0			0
$536$	3.98023e7			0.258472
$537$	1.36356e8	+	1.36356e8i	0.880543	+	0.880543i
$538$	−1.48978e8	+	1.48978e8i	−0.956699	+	0.956699i
$539$			4.06908e7i			0.259854i
$540$		0			0
$541$	1.61258e7			0.101843			0.0509214	−	0.998703i	$-0.483784\pi$
$541$	1.61258e7			0.101843			0.0509214	+	0.998703i	$0.483784\pi$
$542$	3.54202e7	+	3.54202e7i	0.222460	+	0.222460i
$543$	1.58787e8	−	1.58787e8i	0.991780	−	0.991780i
$544$		−	3.07367e8i		−	1.90924i
$545$		0			0
$546$	−3.10666e8			−1.90861
$547$	−2.03578e8	−	2.03578e8i	−1.24385	−	1.24385i	−0.958389	−	0.285466i	$-0.907852\pi$
$547$	−2.03578e8	−	2.03578e8i	−1.24385	−	1.24385i	−0.285466	−	0.958389i	$-0.592148\pi$
$548$	−1.00314e8	+	1.00314e8i	−0.609566	+	0.609566i
$549$		−	2.28422e8i		−	1.38045i
$550$		0			0
$551$	−4.05182e6			−0.0242212
$552$	1.51732e7	+	1.51732e7i	0.0902112	+	0.0902112i
$553$	4.91178e7	−	4.91178e7i	0.290445	−	0.290445i
$554$			1.70781e8i			1.00441i
$555$		0			0
$556$	2.19688e8			1.27815
$557$	4.42173e7	+	4.42173e7i	0.255874	+	0.255874i	0.823374	−	0.567500i	$-0.192089\pi$
$557$	4.42173e7	+	4.42173e7i	0.255874	+	0.255874i	−0.567500	+	0.823374i	$0.692089\pi$
$558$	1.42171e8	−	1.42171e8i	0.818294	−	0.818294i
$559$		−	2.81403e8i		−	1.61099i
$560$		0			0
$561$	1.31963e8			0.747419
$562$	−8.30449e7	−	8.30449e7i	−0.467847	−	0.467847i
$563$	−4.33443e7	+	4.33443e7i	−0.242888	+	0.242888i	−0.818044	−	0.575156i	$-0.804941\pi$
$563$	−4.33443e7	+	4.33443e7i	−0.242888	+	0.242888i	0.575156	+	0.818044i	$0.304941\pi$
$564$			6.07285e8i			3.38497i
$565$		0			0
$566$	−2.18851e8			−1.20698
$567$	3.03389e7	+	3.03389e7i	0.166438	+	0.166438i
$568$	−7.49321e7	+	7.49321e7i	−0.408905	+	0.408905i
$569$			2.33604e7i			0.126807i	0.997988	+	0.0634036i	$0.0201955\pi$
$569$			2.33604e7i			0.126807i	−0.997988	+	0.0634036i	$0.979804\pi$
$570$		0			0
$571$	−7.55506e7			−0.405817			−0.202908	−	0.979198i	$-0.565039\pi$
$571$	−7.55506e7			−0.405817			−0.202908	+	0.979198i	$0.565039\pi$
$572$	1.11680e8	+	1.11680e8i	0.596745	+	0.596745i
$573$	−3.48805e7	+	3.48805e7i	−0.185404	+	0.185404i
$574$			7.08363e7i			0.374559i
$575$		0			0
$576$	4.11575e8			2.15368
$577$	5.38335e7	+	5.38335e7i	0.280237	+	0.280237i	0.833203	−	0.552967i	$-0.186504\pi$
$577$	5.38335e7	+	5.38335e7i	0.280237	+	0.280237i	−0.552967	+	0.833203i	$0.686504\pi$
$578$	−2.78088e8	+	2.78088e8i	−1.44012	+	1.44012i
$579$			3.84258e8i			1.97965i
$580$		0			0
$581$	1.15496e8			0.588895
$582$	4.34536e8	+	4.34536e8i	2.20423	+	2.20423i
$583$	2.79884e7	−	2.79884e7i	0.141245	−	0.141245i
$584$		−	7.26309e7i		−	0.364656i
$585$		0			0
$586$	5.58902e8			2.77743
$587$	−6.94772e7	−	6.94772e7i	−0.343501	−	0.343501i	0.514181	−	0.857682i	$-0.328096\pi$
$587$	−6.94772e7	−	6.94772e7i	−0.343501	−	0.343501i	−0.857682	+	0.514181i	$0.828096\pi$
$588$	2.56333e8	−	2.56333e8i	1.26087	−	1.26087i
$589$		−	6.10922e7i		−	0.298979i
$590$		0			0
$591$	2.52677e8			1.22406
$592$	−3.84785e7	−	3.84785e7i	−0.185461	−	0.185461i
$593$	2.55874e8	−	2.55874e8i	1.22705	−	1.22705i	0.261977	−	0.965074i	$-0.415625\pi$
$593$	2.55874e8	−	2.55874e8i	1.22705	−	1.22705i	0.965074	−	0.261977i	$-0.0843745\pi$
$594$			5.55362e7i			0.264982i
$595$		0			0
$596$	−2.59728e8			−1.22682
$597$	1.72644e8	+	1.72644e8i	0.811387	+	0.811387i
$598$	−5.19480e7	+	5.19480e7i	−0.242921	+	0.242921i
$599$		−	4.45082e7i		−	0.207090i	−0.994625	−	0.103545i	$-0.966981\pi$
$599$		−	4.45082e7i		−	0.207090i	0.994625	−	0.103545i	$-0.0330186\pi$
$600$		0			0
$601$	−8.17830e7			−0.376738			−0.188369	−	0.982098i	$-0.560320\pi$
$601$	−8.17830e7			−0.376738			−0.188369	+	0.982098i	$0.560320\pi$
$602$	−9.35001e7	−	9.35001e7i	−0.428571	−	0.428571i
$603$	−7.80956e7	+	7.80956e7i	−0.356184	+	0.356184i
$604$		−	4.02522e8i		−	1.82675i
$605$		0			0
$606$	3.58799e6			0.0161225
$607$	−7.06661e7	−	7.06661e7i	−0.315970	−	0.315970i	0.531247	−	0.847217i	$-0.321724\pi$
$607$	−7.06661e7	−	7.06661e7i	−0.315970	−	0.315970i	−0.847217	+	0.531247i	$0.821724\pi$
$608$	1.08499e8	−	1.08499e8i	0.482744	−	0.482744i
$609$		−	6.76469e6i		−	0.0299499i
$610$		0			0
$611$	−6.36777e8			−2.79167
$612$	−4.76707e8	−	4.76707e8i	−2.07968	−	2.07968i
$613$	−2.07342e8	+	2.07342e8i	−0.900132	+	0.900132i	−0.995447	−	0.0953156i	$-0.969614\pi$
$613$	−2.07342e8	+	2.07342e8i	−0.900132	+	0.900132i	0.0953156	+	0.995447i	$0.469614\pi$
$614$		−	3.88766e8i		−	1.67951i
$615$		0			0
$616$	2.27297e7			0.0972415
$617$	−2.64675e7	−	2.64675e7i	−0.112683	−	0.112683i	0.648517	−	0.761200i	$-0.275389\pi$
$617$	−2.64675e7	−	2.64675e7i	−0.112683	−	0.112683i	−0.761200	+	0.648517i	$0.775389\pi$
$618$	−2.49507e8	+	2.49507e8i	−1.05711	+	1.05711i
$619$		−	1.82882e8i		−	0.771081i	−0.922691	−	0.385541i	$-0.874015\pi$
$619$		−	1.82882e8i		−	0.771081i	0.922691	−	0.385541i	$-0.125985\pi$
$620$		0			0
$621$	−1.52519e7			−0.0636868
$622$	6.81532e7	+	6.81532e7i	0.283214	+	0.283214i
$623$	1.19457e8	−	1.19457e8i	0.494022	−	0.494022i
$624$			2.46226e8i			1.01340i
$625$		0			0
$626$	3.01185e8			1.22775
$627$	4.65825e7	+	4.65825e7i	0.188982	+	0.188982i
$628$	2.56593e8	−	2.56593e8i	1.03601	−	1.03601i
$629$			2.72439e8i			1.09476i
$630$		0			0
$631$	−2.33033e8			−0.927535			−0.463767	−	0.885957i	$-0.653503\pi$
$631$	−2.33033e8			−0.927535			−0.463767	+	0.885957i	$0.653503\pi$
$632$	1.15400e8	+	1.15400e8i	0.457147	+	0.457147i
$633$	−4.66373e8	+	4.66373e8i	−1.83875	+	1.83875i
$634$			1.45462e8i			0.570797i
$635$		0			0
$636$	−3.52628e8			−1.37071
$637$	2.68781e8	+	2.68781e8i	1.03987	+	1.03987i
$638$	−4.11884e6	+	4.11884e6i	−0.0158603	+	0.0158603i
$639$		−	2.94047e8i		−	1.12697i
$640$		0			0
$641$	−5.32618e7			−0.202228			−0.101114	−	0.994875i	$-0.532241\pi$
$641$	−5.32618e7			−0.202228			−0.101114	+	0.994875i	$0.532241\pi$
$642$	−4.82126e8	−	4.82126e8i	−1.82203	−	1.82203i
$643$	−1.85020e6	+	1.85020e6i	−0.00695963	+	0.00695963i	−0.710578	−	0.703618i	$-0.751566\pi$
$643$	−1.85020e6	+	1.85020e6i	−0.00695963	+	0.00695963i	0.703618	+	0.710578i	$0.251566\pi$
$644$			2.03816e7i			0.0763098i
$645$		0			0
$646$	−3.46953e8			−1.28698
$647$	1.21876e8	+	1.21876e8i	0.449994	+	0.449994i	0.895352	−	0.445359i	$-0.146924\pi$
$647$	1.21876e8	+	1.21876e8i	0.449994	+	0.449994i	−0.445359	+	0.895352i	$0.646924\pi$
$648$	−7.12802e7	+	7.12802e7i	−0.261965	+	0.261965i
$649$		−	6.24698e7i		−	0.228526i
$650$		0			0
$651$	1.01996e8			0.369693
$652$	−3.65928e8	−	3.65928e8i	−1.32024	−	1.32024i
$653$	3.46654e8	−	3.46654e8i	1.24497	−	1.24497i	0.287049	−	0.957916i	$-0.407326\pi$
$653$	3.46654e8	−	3.46654e8i	1.24497	−	1.24497i	0.957916	−	0.287049i	$-0.0926744\pi$
$654$			6.31146e8i			2.25630i
$655$		0			0
$656$	5.61429e7			0.198877
$657$	1.42508e8	+	1.42508e8i	0.502509	+	0.502509i
$658$	−2.11578e8	+	2.11578e8i	−0.742665	+	0.742665i
$659$			4.27915e8i			1.49521i	0.664145	+	0.747604i	$0.268796\pi$
$659$			4.27915e8i			1.49521i	−0.664145	+	0.747604i	$0.731204\pi$
$660$		0			0
$661$	−8.54029e7			−0.295712			−0.147856	−	0.989009i	$-0.547237\pi$
$661$	−8.54029e7			−0.295712			−0.147856	+	0.989009i	$0.547237\pi$
$662$	5.75899e6	+	5.75899e6i	0.0198505	+	0.0198505i
$663$	8.71676e8	−	8.71676e8i	2.99099	−	2.99099i
$664$			2.71353e8i			0.926895i
$665$		0			0
$666$	−4.47605e8			−1.51521
$667$	−1.13116e6	−	1.13116e6i	−0.00381193	−	0.00381193i
$668$	3.32317e8	−	3.32317e8i	1.11487	−	1.11487i
$669$		−	4.38712e8i		−	1.46521i
$670$		0			0
$671$	−9.97786e7			−0.330271
$672$	1.81145e8	+	1.81145e8i	0.596922	+	0.596922i
$673$	2.58551e7	−	2.58551e7i	0.0848204	−	0.0848204i	−0.663424	−	0.748244i	$-0.730897\pi$
$673$	2.58551e7	−	2.58551e7i	0.0848204	−	0.0848204i	0.748244	+	0.663424i	$0.230897\pi$
$674$		−	6.43036e8i		−	2.10018i
$675$		0			0
$676$	1.03010e9			3.33457
$677$	−9.13090e7	−	9.13090e7i	−0.294271	−	0.294271i	0.544494	−	0.838765i	$-0.316722\pi$
$677$	−9.13090e7	−	9.13090e7i	−0.294271	−	0.294271i	−0.838765	+	0.544494i	$0.816722\pi$
$678$	−3.51885e8	+	3.51885e8i	−1.12905	+	1.12905i
$679$			1.78768e8i			0.571057i
$680$		0			0
$681$	5.39310e8			1.70764
$682$	−6.21027e7	−	6.21027e7i	−0.195775	−	0.195775i
$683$	−1.98546e8	+	1.98546e8i	−0.623158	+	0.623158i	−0.946338	−	0.323180i	$-0.895248\pi$
$683$	−1.98546e8	+	1.98546e8i	−0.623158	+	0.623158i	0.323180	+	0.946338i	$0.395248\pi$
$684$		−	3.36552e8i		−	1.05168i
$685$		0			0
$686$	3.99691e8			1.23809
$687$	−2.61267e7	−	2.61267e7i	−0.0805777	−	0.0805777i
$688$	−7.41057e7	+	7.41057e7i	−0.227555	+	0.227555i
$689$		−	3.69753e8i		−	1.13046i
$690$		0			0
$691$	−6.62261e7			−0.200722			−0.100361	−	0.994951i	$-0.532000\pi$
$691$	−6.62261e7			−0.200722			−0.100361	+	0.994951i	$0.532000\pi$
$692$	9.37448e7	+	9.37448e7i	0.282897	+	0.282897i
$693$	−4.45977e7	+	4.45977e7i	−0.134002	+	0.134002i
$694$			7.34592e8i			2.19770i
$695$		0			0
$696$	1.58934e7			0.0471399
$697$	−1.98755e8	−	1.98755e8i	−0.586974	−	0.586974i
$698$	−3.83628e8	+	3.83628e8i	−1.12809	+	1.12809i
$699$			1.13058e8i			0.331031i
$700$		0			0
$701$	5.74414e8			1.66752			0.833759	−	0.552128i	$-0.186184\pi$
$701$	5.74414e8			1.66752			0.833759	+	0.552128i	$0.186184\pi$
$702$	3.66842e8	+	3.66842e8i	1.06039	+	1.06039i
$703$	−9.61700e7	+	9.61700e7i	−0.276805	+	0.276805i
$704$		−	1.79783e8i		−	0.515264i
$705$		0			0
$706$	−5.20732e8			−1.47979
$707$	738049.	+	738049.i	0.00208846	+	0.00208846i
$708$	−3.93530e8	+	3.93530e8i	−1.10886	+	1.10886i
$709$			1.65207e8i			0.463542i	0.972770	+	0.231771i	$0.0744521\pi$
$709$			1.65207e8i			0.463542i	−0.972770	+	0.231771i	$0.925548\pi$
$710$		0			0
$711$	−4.52851e8			−1.25993
$712$	2.80659e8	+	2.80659e8i	0.777569	+	0.777569i
$713$	1.70553e7	−	1.70553e7i	0.0470533	−	0.0470533i
$714$		−	5.79253e8i		−	1.59138i
$715$		0			0
$716$	−4.30330e8			−1.17236
$717$	−4.69584e8	−	4.69584e8i	−1.27396	−	1.27396i
$718$	4.60923e8	−	4.60923e8i	1.24525	−	1.24525i
$719$			1.80021e7i			0.0484324i	0.999707	+	0.0242162i	$0.00770901\pi$
$719$			1.80021e7i			0.0484324i	−0.999707	+	0.0242162i	$0.992291\pi$
$720$		0			0
$721$	−1.02647e8			−0.273868
$722$	2.93364e8	+	2.93364e8i	0.779463	+	0.779463i
$723$	−5.01233e8	+	5.01233e8i	−1.32625	+	1.32625i
$724$			5.01122e8i			1.32047i
$725$		0			0
$726$	−8.20774e8			−2.14493
$727$	4.52060e8	+	4.52060e8i	1.17650	+	1.17650i	0.980629	+	0.195873i	$0.0627541\pi$
$727$	4.52060e8	+	4.52060e8i	1.17650	+	1.17650i	0.195873	+	0.980629i	$0.437246\pi$
$728$	1.50140e8	−	1.50140e8i	0.389137	−	0.389137i
$729$		−	5.92483e8i		−	1.52930i
$730$		0			0
$731$	5.24690e8			1.34323
$732$	6.28558e8	+	6.28558e8i	1.60255	+	1.60255i
$733$	−1.41562e8	+	1.41562e8i	−0.359446	+	0.359446i	−0.863609	−	0.504163i	$-0.831801\pi$
$733$	−1.41562e8	+	1.41562e8i	−0.359446	+	0.359446i	0.504163	+	0.863609i	$0.331801\pi$
$734$		−	3.27224e8i		−	0.827478i
$735$		0			0
$736$	6.05801e7			0.151949
$737$	3.41134e7	+	3.41134e7i	0.0852164	+	0.0852164i
$738$	3.26545e8	−	3.26545e8i	0.812407	−	0.812407i
$739$			4.98809e8i			1.23595i	0.786198	+	0.617975i	$0.212047\pi$
$739$			4.98809e8i			1.23595i	−0.786198	+	0.617975i	$0.787953\pi$
$740$		0			0
$741$	6.15397e8			1.51252
$742$	−1.22855e8	−	1.22855e8i	−0.300734	−	0.300734i
$743$	5.72035e7	−	5.72035e7i	0.139462	−	0.139462i	−0.633929	−	0.773391i	$-0.718559\pi$
$743$	5.72035e7	−	5.72035e7i	0.139462	−	0.139462i	0.773391	+	0.633929i	$0.218559\pi$
$744$			2.39636e8i			0.581880i
$745$		0			0
$746$	7.25958e8			1.74862
$747$	−5.32419e8	−	5.32419e8i	−1.27730	−	1.27730i
$748$	−2.08234e8	+	2.08234e8i	−0.497561	+	0.497561i
$749$		−	1.98346e8i		−	0.472040i
$750$		0			0
$751$	−5.14078e8			−1.21369			−0.606847	−	0.794818i	$-0.707566\pi$
$751$	−5.14078e8			−1.21369			−0.606847	+	0.794818i	$0.707566\pi$
$752$	1.67691e8	+	1.67691e8i	0.394327	+	0.394327i
$753$	6.30831e6	−	6.30831e6i	0.0147750	−	0.0147750i
$754$			5.44136e7i			0.126939i
$755$		0			0
$756$	1.43929e8			0.333106
$757$	1.29126e8	+	1.29126e8i	0.297665	+	0.297665i	0.840099	−	0.542434i	$-0.182497\pi$
$757$	1.29126e8	+	1.29126e8i	0.297665	+	0.297665i	−0.542434	+	0.840099i	$0.682497\pi$
$758$	5.68793e8	−	5.68793e8i	1.30601	−	1.30601i
$759$			2.60091e7i			0.0594840i
$760$		0			0
$761$	−5.96655e8			−1.35385			−0.676923	−	0.736054i	$-0.736687\pi$
$761$	−5.96655e8			−1.35385			−0.676923	+	0.736054i	$0.736687\pi$
$762$	−1.01464e9	−	1.01464e9i	−2.29322	−	2.29322i
$763$	−1.29826e8	+	1.29826e8i	−0.292274	+	0.292274i
$764$		−	1.10081e8i		−	0.246849i
$765$		0			0
$766$	9.20272e7			0.204753
$767$	−4.12641e8	−	4.12641e8i	−0.914506	−	0.914506i
$768$	−1.68537e8	+	1.68537e8i	−0.372058	+	0.372058i
$769$		−	4.27962e7i		−	0.0941079i	−0.998892	−	0.0470539i	$-0.985017\pi$
$769$		−	4.27962e7i		−	0.0941079i	0.998892	−	0.0470539i	$-0.0149833\pi$
$770$		0			0
$771$	3.18789e8			0.695570
$772$	−6.06347e8	−	6.06347e8i	−1.31786	−	1.31786i
$773$	3.80772e8	−	3.80772e8i	0.824377	−	0.824377i	−0.162355	−	0.986732i	$-0.551909\pi$
$773$	3.80772e8	−	3.80772e8i	0.824377	−	0.824377i	0.986732	+	0.162355i	$0.0519090\pi$
$774$			8.62043e8i			1.85911i
$775$		0			0
$776$	−4.20008e8			−0.898819
$777$	−1.60560e8	−	1.60560e8i	−0.342275	−	0.342275i
$778$	9.46773e8	−	9.46773e8i	2.01051	−	2.01051i
$779$		−	1.40319e8i		−	0.296828i
$780$		0			0
$781$	−1.28444e8			−0.269626
$782$	−9.68597e7	−	9.68597e7i	−0.202546	−	0.202546i
$783$	−7.98790e6	+	7.98790e6i	−0.0166398	+	0.0166398i
$784$		−	1.41563e8i		−	0.293767i
$785$		0			0
$786$	1.22236e9			2.51728
$787$	4.94781e8	+	4.94781e8i	1.01505	+	1.01505i	0.999885	+	0.0151691i	$0.00482865\pi$
$787$	4.94781e8	+	4.94781e8i	1.01505	+	1.01505i	0.0151691	+	0.999885i	$0.495171\pi$
$788$	−3.98716e8	+	3.98716e8i	−0.814864	+	0.814864i
$789$			1.25284e9i			2.55072i
$790$		0			0
$791$	−1.44765e8			−0.292506
$792$	−1.04781e8	−	1.04781e8i	−0.210914	−	0.210914i
$793$	−6.59083e8	+	6.59083e8i	−1.32166	+	1.32166i
$794$		−	5.18760e8i		−	1.03635i
$795$		0			0
$796$	−5.44853e8			−1.08029
$797$	1.18588e8	+	1.18588e8i	0.234244	+	0.234244i	0.814461	−	0.580218i	$-0.197033\pi$
$797$	1.18588e8	+	1.18588e8i	0.234244	+	0.234244i	−0.580218	+	0.814461i	$0.697033\pi$
$798$	2.04474e8	−	2.04474e8i	0.402374	−	0.402374i
$799$		−	1.18730e9i		−	2.32767i
$800$		0			0
$801$	−1.10135e9			−2.14304
$802$	7.65959e8	+	7.65959e8i	1.48485	+	1.48485i
$803$	6.22499e7	−	6.22499e7i	0.120224	−	0.120224i
$804$		−	4.29797e8i		−	0.826980i
$805$		0			0
$806$	−8.20434e8			−1.56689
$807$	4.92698e8	+	4.92698e8i	0.937477	+	0.937477i
$808$	−1.73402e6	+	1.73402e6i	−0.00328715	+	0.00328715i
$809$			2.52466e8i			0.476823i	0.971164	+	0.238411i	$0.0766266\pi$
$809$			2.52466e8i			0.476823i	−0.971164	+	0.238411i	$0.923373\pi$
$810$		0			0
$811$	7.07237e8			1.32587			0.662937	−	0.748675i	$-0.269310\pi$
$811$	7.07237e8			1.32587			0.662937	+	0.748675i	$0.269310\pi$
$812$	1.06745e7	+	1.06745e7i	0.0199378	+	0.0199378i
$813$	1.17141e8	−	1.17141e8i	0.217991	−	0.217991i
$814$			1.95521e8i			0.362511i
$815$		0			0
$816$	−4.59100e8			−0.844962
$817$	1.85214e8	+	1.85214e8i	0.339631	+	0.339631i
$818$	−2.95510e7	+	2.95510e7i	−0.0539898	+	0.0539898i
$819$			5.89176e8i			1.07249i
$820$		0			0
$821$	−4.75910e8			−0.859994			−0.429997	−	0.902830i	$-0.641485\pi$
$821$	−4.75910e8			−0.859994			−0.429997	+	0.902830i	$0.641485\pi$
$822$	5.61909e8	+	5.61909e8i	1.01170	+	1.01170i
$823$	−1.64668e8	+	1.64668e8i	−0.295399	+	0.295399i	−0.839209	−	0.543810i	$-0.816981\pi$
$823$	−1.64668e8	+	1.64668e8i	−0.295399	+	0.295399i	0.543810	+	0.839209i	$0.316981\pi$
$824$		−	2.41166e8i		−	0.431056i
$825$		0			0
$826$	−2.74212e8			−0.486570
$827$	−6.30299e8	−	6.30299e8i	−1.11437	−	1.11437i	−0.992552	−	0.121819i	$-0.961127\pi$
$827$	−6.30299e8	−	6.30299e8i	−1.11437	−	1.11437i	−0.121819	−	0.992552i	$-0.538873\pi$
$828$	9.39560e7	−	9.39560e7i	0.165514	−	0.165514i
$829$			3.96747e8i			0.696386i	0.937423	+	0.348193i	$0.113205\pi$
$829$			3.96747e8i			0.696386i	−0.937423	+	0.348193i	$0.886795\pi$
$830$		0			0
$831$	5.64807e8			0.984230
$832$	−1.18755e9	−	1.18755e9i	−2.06196	−	2.06196i
$833$	−5.01156e8	+	5.01156e8i	−0.867037	+	0.867037i
$834$		−	1.23058e9i		−	2.12135i
$835$		0			0
$836$	−1.47011e8			−0.251613
$837$	−1.20439e8	−	1.20439e8i	−0.205396	−	0.205396i
$838$	−1.11834e9	+	1.11834e9i	−1.90039	+	1.90039i
$839$			7.25077e8i			1.22772i	0.789416	+	0.613858i	$0.210383\pi$
$839$			7.25077e8i			1.22772i	−0.789416	+	0.613858i	$0.789617\pi$
$840$		0			0
$841$	5.93638e8			0.998008
$842$	4.46463e8	+	4.46463e8i	0.747910	+	0.747910i
$843$	−2.74645e8	+	2.74645e8i	−0.458447	+	0.458447i
$844$		−	1.47184e9i		−	2.44813i
$845$		0			0
$846$	1.95069e9			3.22164
$847$	−1.68833e8	−	1.68833e8i	−0.277848	−	0.277848i
$848$	−9.73719e7	+	9.73719e7i	−0.159678	+	0.159678i
$849$			7.23780e8i			1.18272i
$850$		0			0
$851$	−5.36960e7			−0.0871272
$852$	8.09139e8	+	8.09139e8i	1.30829	+	1.30829i
$853$	6.00614e8	−	6.00614e8i	0.967717	−	0.967717i	−0.0317782	−	0.999495i	$-0.510117\pi$
$853$	6.00614e8	−	6.00614e8i	0.967717	−	0.967717i	0.999495	+	0.0317782i	$0.0101170\pi$
$854$			4.37979e8i			0.703201i
$855$		0			0
$856$	4.66007e8			0.742970
$857$	2.16143e8	+	2.16143e8i	0.343398	+	0.343398i	0.857643	−	0.514245i	$-0.171928\pi$
$857$	2.16143e8	+	2.16143e8i	0.343398	+	0.343398i	−0.514245	+	0.857643i	$0.671928\pi$
$858$	6.25576e8	−	6.25576e8i	0.990418	−	0.990418i
$859$			1.64496e8i			0.259523i	0.991545	+	0.129761i	$0.0414211\pi$
$859$			1.64496e8i			0.259523i	−0.991545	+	0.129761i	$0.958579\pi$
$860$		0			0
$861$	2.34269e8			0.367034
$862$	2.05914e8	+	2.05914e8i	0.321488	+	0.321488i
$863$	2.22225e8	−	2.22225e8i	0.345749	−	0.345749i	−0.512774	−	0.858523i	$-0.671382\pi$
$863$	2.22225e8	−	2.22225e8i	0.345749	−	0.345749i	0.858523	+	0.512774i	$0.171382\pi$
$864$		−	4.27799e8i		−	0.663283i
$865$		0			0
$866$	1.55520e9			2.39460
$867$	9.19691e8	+	9.19691e8i	1.41119	+	1.41119i
$868$	−1.60947e8	+	1.60947e8i	−0.246107	+	0.246107i
$869$			1.97813e8i			0.301436i
$870$		0			0
$871$	4.50669e8			0.682030
$872$	−3.05022e8	−	3.05022e8i	−0.460026	−	0.460026i
$873$	8.24093e8	−	8.24093e8i	1.23861	−	1.23861i
$874$		−	6.83822e7i		−	0.102426i
$875$		0			0
$876$	−7.84290e8			−1.16671
$877$	−6.14318e8	−	6.14318e8i	−0.910740	−	0.910740i	0.0855907	−	0.996330i	$-0.472722\pi$
$877$	−6.14318e8	−	6.14318e8i	−0.910740	−	0.910740i	−0.996330	+	0.0855907i	$0.972722\pi$
$878$	−7.49729e8	+	7.49729e8i	−1.10770	+	1.10770i
$879$		−	1.84839e9i		−	2.72162i
$880$		0			0
$881$	−1.10446e9			−1.61519			−0.807594	−	0.589739i	$-0.799231\pi$
$881$	−1.10446e9			−1.61519			−0.807594	+	0.589739i	$0.799231\pi$
$882$	−8.23377e8	−	8.23377e8i	−1.20003	−	1.20003i
$883$	4.38785e8	−	4.38785e8i	0.637337	−	0.637337i	−0.312561	−	0.949898i	$-0.601187\pi$
$883$	4.38785e8	−	4.38785e8i	0.637337	−	0.637337i	0.949898	+	0.312561i	$0.101187\pi$
$884$			2.75096e9i			3.98223i
$885$		0			0
$886$	−8.82916e8			−1.26946
$887$	2.51891e8	+	2.51891e8i	0.360946	+	0.360946i	0.864161	−	0.503215i	$-0.167850\pi$
$887$	2.51891e8	+	2.51891e8i	0.360946	+	0.360946i	−0.503215	+	0.864161i	$0.667850\pi$
$888$	3.77230e8	−	3.77230e8i	0.538725	−	0.538725i
$889$		−	4.17422e8i		−	0.594114i
$890$		0			0
$891$	−1.22185e8			−0.172736
$892$	6.92274e8	+	6.92274e8i	0.975401	+	0.975401i
$893$	4.19114e8	−	4.19114e8i	0.588542	−	0.588542i
$894$			1.45486e9i			2.03615i
$895$		0			0
$896$	−3.92564e8			−0.545741
$897$	1.71802e8	+	1.71802e8i	0.238040	+	0.238040i
$898$	4.82167e8	−	4.82167e8i	0.665837	−	0.665837i
$899$		−	1.78648e7i		−	0.0245877i
$900$		0			0
$901$	6.89422e8			0.942564
$902$	−1.42640e8	−	1.42640e8i	−0.194367	−	0.194367i
$903$	−3.09223e8	+	3.09223e8i	−0.419960	+	0.419960i
$904$		−	3.40121e8i		−	0.460392i
$905$		0			0
$906$	−2.25472e9			−3.03186
$907$	−6.82031e8	−	6.82031e8i	−0.914075	−	0.914075i	0.0825146	−	0.996590i	$-0.473705\pi$
$907$	−6.82031e8	−	6.82031e8i	−0.914075	−	0.914075i	−0.996590	+	0.0825146i	$0.973705\pi$
$908$	−8.51013e8	+	8.51013e8i	−1.13679	+	1.13679i
$909$		−	6.80459e6i		−	0.00905963i
$910$		0			0
$911$	1.10544e9			1.46212			0.731058	−	0.682316i	$-0.239027\pi$
$911$	1.10544e9			1.46212			0.731058	+	0.682316i	$0.239027\pi$
$912$	−1.62061e8	−	1.62061e8i	−0.213645	−	0.213645i
$913$	−2.32569e8	+	2.32569e8i	−0.305591	+	0.305591i
$914$		−	4.64797e8i		−	0.608731i
$915$		0			0
$916$	8.24543e7			0.107282
$917$	2.51439e8	+	2.51439e8i	0.326080	+	0.326080i
$918$	−6.83995e8	+	6.83995e8i	−0.884148	+	0.884148i
$919$		−	4.59502e8i		−	0.592027i	−0.955184	−	0.296013i	$-0.904343\pi$
$919$		−	4.59502e8i		−	0.592027i	0.955184	−	0.296013i	$-0.0956573\pi$
$920$		0			0
$921$	−1.28572e9			−1.64577
$922$	−6.24314e8	−	6.24314e8i	−0.796545	−	0.796545i
$923$	−8.48434e8	+	8.48434e8i	−1.07898	+	1.07898i
$924$		−	2.45442e8i		−	0.311124i
$925$		0			0
$926$	8.82079e8			1.11090
$927$	4.73188e8	+	4.73188e8i	0.594012	+	0.594012i
$928$	3.17277e7	−	3.17277e7i	0.0397004	−	0.0397004i
$929$		−	1.27492e9i		−	1.59014i	−0.606520	−	0.795068i	$-0.707435\pi$
$929$		−	1.27492e9i		−	1.59014i	0.606520	−	0.795068i	$-0.292565\pi$
$930$		0			0
$931$	−3.53812e8			−0.438454
$932$	−1.78401e8	−	1.78401e8i	−0.220369	−	0.220369i
$933$	2.25395e8	−	2.25395e8i	0.277524	−	0.277524i
$934$			9.07025e8i			1.11321i
$935$		0			0
$936$	−1.38425e9			−1.68805
$937$	−4.23988e8	−	4.23988e8i	−0.515389	−	0.515389i	0.400784	−	0.916173i	$-0.368738\pi$
$937$	−4.23988e8	−	4.23988e8i	−0.515389	−	0.515389i	−0.916173	+	0.400784i	$0.868738\pi$
$938$	1.49741e8	−	1.49741e8i	0.181440	−	0.181440i
$939$		−	9.96076e8i		−	1.20308i
$940$		0			0
$941$	−1.02319e9			−1.22797			−0.613983	−	0.789320i	$-0.710434\pi$
$941$	−1.02319e9			−1.22797			−0.613983	+	0.789320i	$0.710434\pi$
$942$	−1.43730e9	−	1.43730e9i	−1.71947	−	1.71947i
$943$	3.91733e7	−	3.91733e7i	0.0467148	−	0.0467148i
$944$			2.17333e8i			0.258350i
$945$		0			0
$946$	3.76555e8			0.444790
$947$	−7.59174e8	−	7.59174e8i	−0.893905	−	0.893905i	0.100983	−	0.994888i	$-0.467801\pi$
$947$	−7.59174e8	−	7.59174e8i	−0.893905	−	0.893905i	−0.994888	+	0.100983i	$0.967801\pi$
$948$	1.24613e9	−	1.24613e9i	1.46264	−	1.46264i
$949$		−	8.22378e8i		−	0.962217i
$950$		0			0
$951$	4.81070e8			0.559329
$952$	2.79944e8	+	2.79944e8i	0.324459	+	0.324459i
$953$	2.24088e8	−	2.24088e8i	0.258904	−	0.258904i	−0.565704	−	0.824608i	$-0.691396\pi$
$953$	2.24088e8	−	2.24088e8i	0.258904	−	0.258904i	0.824608	+	0.565704i	$0.191396\pi$
$954$			1.13269e9i			1.30457i
$955$		0			0
$956$	1.48198e9			1.69616
$957$	1.36218e7	+	1.36218e7i	0.0155417	+	0.0155417i
$958$	1.89659e9	−	1.89659e9i	2.15713	−	2.15713i
$959$			2.31169e8i			0.262104i
$960$		0			0
$961$	−6.18144e8			−0.696497
$962$	1.29151e9	+	1.29151e9i	1.45068	+	1.45068i
$963$	−9.14347e8	+	9.14347e8i	−1.02384	+	1.02384i
$964$		−	1.58186e9i		−	1.76578i
$965$		0			0
$966$	1.14167e8			0.126651
$967$	5.99603e8	+	5.99603e8i	0.663108	+	0.663108i	0.956111	−	0.293003i	$-0.0946546\pi$
$967$	5.99603e8	+	5.99603e8i	0.663108	+	0.663108i	−0.293003	+	0.956111i	$0.594655\pi$
$968$	3.96667e8	−	3.96667e8i	0.437320	−	0.437320i
$969$			1.14744e9i			1.26113i
$970$		0			0
$971$	4.81757e8			0.526223			0.263112	−	0.964765i	$-0.415251\pi$
$971$	4.81757e8			0.526223			0.263112	+	0.964765i	$0.415251\pi$
$972$	1.26324e9	+	1.26324e9i	1.37558	+	1.37558i
$973$	2.53130e8	−	2.53130e8i	0.274793	−	0.274793i
$974$			1.99499e9i			2.15905i
$975$		0			0
$976$	3.47130e8			0.373373
$977$	−9.34567e8	−	9.34567e8i	−1.00214	−	1.00214i	−0.999998	−	0.00213845i	$-0.999319\pi$
$977$	−9.34567e8	−	9.34567e8i	−1.00214	−	1.00214i	−0.00213845	−	0.999998i	$-0.500681\pi$
$978$	−2.04974e9	+	2.04974e9i	−2.19121	+	2.19121i
$979$			4.81090e8i			0.512718i
$980$		0			0
$981$	1.19696e9			1.26787
$982$	7.05146e8	+	7.05146e8i	0.744637	+	0.744637i
$983$	7.35916e8	−	7.35916e8i	0.774761	−	0.774761i	−0.204174	−	0.978935i	$-0.565451\pi$
$983$	7.35916e8	−	7.35916e8i	0.774761	−	0.774761i	0.978935	+	0.204174i	$0.0654508\pi$
$984$			5.50407e8i			0.577695i
$985$		0			0
$986$	−1.01457e8			−0.105840
$987$	6.99729e8	+	6.99729e8i	0.727744	+	0.727744i
$988$	−9.71077e8	+	9.71077e8i	−1.00689	+	1.00689i
$989$			1.03413e8i			0.106902i
$990$		0			0
$991$	1.07755e9			1.10718			0.553590	−	0.832790i	$-0.313258\pi$
$991$	1.07755e9			1.10718			0.553590	+	0.832790i	$0.313258\pi$
$992$	4.78382e8	+	4.78382e8i	0.490049	+	0.490049i
$993$	1.90461e7	−	1.90461e7i	0.0194517	−	0.0194517i
$994$			5.63808e8i			0.574079i
$995$		0			0
$996$	2.93015e9			2.96560
$997$	4.85603e7	+	4.85603e7i	0.0489999	+	0.0489999i	0.731182	−	0.682182i	$-0.238969\pi$
$997$	4.85603e7	+	4.85603e7i	0.0489999	+	0.0489999i	−0.682182	+	0.731182i	$0.738969\pi$
$998$	−4.12898e8	+	4.12898e8i	−0.415385	+	0.415385i
$999$			3.79186e8i			0.380326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.7.c.d.7.4	yes	8
3.2	odd	2		225.7.g.f.82.1		8
5.2	odd	4	inner	25.7.c.d.18.1	yes	8
5.3	odd	4	inner	25.7.c.d.18.4	yes	8
5.4	even	2	inner	25.7.c.d.7.1	✓	8
15.2	even	4		225.7.g.f.118.4		8
15.8	even	4		225.7.g.f.118.1		8
15.14	odd	2		225.7.g.f.82.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.7.c.d.7.1	✓	8	5.4	even	2	inner
25.7.c.d.7.4	yes	8	1.1	even	1	trivial
25.7.c.d.18.1	yes	8	5.2	odd	4	inner
25.7.c.d.18.4	yes	8	5.3	odd	4	inner
225.7.g.f.82.1		8	3.2	odd	2
225.7.g.f.82.4		8	15.14	odd	2
225.7.g.f.118.1		8	15.8	even	4
225.7.g.f.118.4		8	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(8.83897 + 8.83897i) q^{2} +(29.2322 - 29.2322i) q^{3} +92.2549i q^{4} +516.765 q^{6} +(106.298 + 106.298i) q^{7} +(-249.744 + 249.744i) q^{8} -980.039i q^{9} +O(q^{10})\)	\(q+(8.83897 + 8.83897i) q^{2} +(29.2322 - 29.2322i) q^{3} +92.2549i q^{4} +516.765 q^{6} +(106.298 + 106.298i) q^{7} +(-249.744 + 249.744i) q^{8} -980.039i q^{9} -428.097 q^{11} +(2696.81 + 2696.81i) q^{12} +(-2827.78 + 2827.78i) q^{13} +1879.14i q^{14} +1489.35 q^{16} +(-5272.53 - 5272.53i) q^{17} +(8662.54 - 8662.54i) q^{18} -3722.37i q^{19} +6214.66 q^{21} +(-3783.94 - 3783.94i) q^{22} +(1039.18 - 1039.18i) q^{23} +14601.1i q^{24} -49989.3 q^{26} +(-7338.41 - 7338.41i) q^{27} +(-9806.54 + 9806.54i) q^{28} -1088.51i q^{29} +16412.2 q^{31} +(29148.0 + 29148.0i) q^{32} +(-12514.2 + 12514.2i) q^{33} -93207.5i q^{34} +90413.3 q^{36} +(-25835.7 - 25835.7i) q^{37} +(32901.9 - 32901.9i) q^{38} +165324. i q^{39} +37696.2 q^{41} +(54931.2 + 54931.2i) q^{42} +(-49757.0 + 49757.0i) q^{43} -39494.0i q^{44} +18370.6 q^{46} +(112593. + 112593. i) q^{47} +(43537.0 - 43537.0i) q^{48} -95050.3i q^{49} -308255. q^{51} +(-260876. - 260876. i) q^{52} +(-65378.7 + 65378.7i) q^{53} -129728. i q^{54} -53094.7 q^{56} +(-108813. - 108813. i) q^{57} +(9621.27 - 9621.27i) q^{58} +145924. i q^{59} +233075. q^{61} +(145067. + 145067. i) q^{62} +(104176. - 104176. i) q^{63} +419957. i q^{64} -221225. q^{66} +(-79686.2 - 79686.2i) q^{67} +(486417. - 486417. i) q^{68} -60755.1i q^{69} +300036. q^{71} +(244759. + 244759. i) q^{72} +(-145411. + 145411. i) q^{73} -456722. i q^{74} +343407. q^{76} +(-45506.0 - 45506.0i) q^{77} +(-1.46129e6 + 1.46129e6i) q^{78} -462075. i q^{79} +285413. q^{81} +(333196. + 333196. i) q^{82} +(543263. - 543263. i) q^{83} +573333. i q^{84} -879601. q^{86} +(-31819.4 - 31819.4i) q^{87} +(106915. - 106915. i) q^{88} -1.12379e6i q^{89} -601176. q^{91} +(95869.7 + 95869.7i) q^{92} +(479764. - 479764. i) q^{93} +1.99042e6i q^{94} +1.70412e6 q^{96} +(840877. + 840877. i) q^{97} +(840147. - 840147. i) q^{98} +419552. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2436 q^{6}+O(q^{10}) \) 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

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