LMFDB - Embedded newform 950.2.f.c.493.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(493,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("950.493");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.f (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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 24x^{14} + 212x^{12} + 880x^{10} + 1858x^{8} + 1960x^{6} + 892x^{4} + 96x^{2} + 1 $ x^16 + 24x^14 + 212x^12 + 880x^10 + 1858x^8 + 1960x^6 + 892x^4 + 96*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			493.4
Root			$3.07801i$ of defining polynomial
Character	$\chi$	$=$	950.493
Dual form			950.2.f.c.607.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(2.20701 - 2.20701i) q^{3} +1.00000i q^{4} -3.12119 q^{6} +(-1.65823 + 1.65823i) q^{7} +(0.707107 - 0.707107i) q^{8} -6.74181i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(2.20701 - 2.20701i) q^{3} +1.00000i q^{4} -3.12119 q^{6} +(-1.65823 + 1.65823i) q^{7} +(0.707107 - 0.707107i) q^{8} -6.74181i q^{9} -0.804733 q^{11} +(2.20701 + 2.20701i) q^{12} +(3.05219 - 3.05219i) q^{13} +2.34509 q^{14} -1.00000 q^{16} +(4.37090 - 4.37090i) q^{17} +(-4.76718 + 4.76718i) q^{18} +(3.48315 + 2.62062i) q^{19} +7.31946i q^{21} +(0.569032 + 0.569032i) q^{22} +(-6.20477 - 6.20477i) q^{23} -3.12119i q^{24} -4.31645 q^{26} +(-8.25822 - 8.25822i) q^{27} +(-1.65823 - 1.65823i) q^{28} -5.64487 q^{29} -3.13000i q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.77606 + 1.77606i) q^{33} -6.18139 q^{34} +6.74181 q^{36} +(-0.524538 - 0.524538i) q^{37} +(-0.609901 - 4.31602i) q^{38} -13.4725i q^{39} +1.45541i q^{41} +(5.17564 - 5.17564i) q^{42} +(-1.90794 - 1.90794i) q^{43} -0.804733i q^{44} +8.77487i q^{46} +(-0.499434 + 0.499434i) q^{47} +(-2.20701 + 2.20701i) q^{48} +1.50057i q^{49} -19.2933i q^{51} +(3.05219 + 3.05219i) q^{52} +(-3.40535 + 3.40535i) q^{53} +11.6789i q^{54} +2.34509i q^{56} +(13.4711 - 1.90361i) q^{57} +(3.99153 + 3.99153i) q^{58} +2.77684 q^{59} +6.17945 q^{61} +(-2.21324 + 2.21324i) q^{62} +(11.1794 + 11.1794i) q^{63} -1.00000i q^{64} +2.51172 q^{66} +(-0.345265 - 0.345265i) q^{67} +(4.37090 + 4.37090i) q^{68} -27.3880 q^{69} +6.68211i q^{71} +(-4.76718 - 4.76718i) q^{72} +(-1.05445 - 1.05445i) q^{73} +0.741809i q^{74} +(-2.62062 + 3.48315i) q^{76} +(1.33443 - 1.33443i) q^{77} +(-9.52647 + 9.52647i) q^{78} +7.16924 q^{79} -16.2266 q^{81} +(1.02913 - 1.02913i) q^{82} +(4.12119 + 4.12119i) q^{83} -7.31946 q^{84} +2.69824i q^{86} +(-12.4583 + 12.4583i) q^{87} +(-0.569032 + 0.569032i) q^{88} +16.7356 q^{89} +10.1225i q^{91} +(6.20477 - 6.20477i) q^{92} +(-6.90794 - 6.90794i) q^{93} +0.706307 q^{94} +3.12119 q^{96} +(8.25033 + 8.25033i) q^{97} +(1.06106 - 1.06106i) q^{98} +5.42535i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} - 16 q^{16} + 32 q^{17} + 8 q^{23} - 32 q^{26} - 8 q^{28} + 32 q^{36} - 8 q^{38} + 32 q^{42} - 24 q^{43} - 32 q^{47} + 48 q^{57} - 64 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{66} + 32 q^{68} - 16 q^{73} - 16 q^{76} - 72 q^{77} + 16 q^{81} - 40 q^{82} + 16 q^{83} + 8 q^{87} - 8 q^{92} - 104 q^{93}+O(q^{100}) $ 16 * q - 8 * q^7 - 16 * q^16 + 32 * q^17 + 8 * q^23 - 32 * q^26 - 8 * q^28 + 32 * q^36 - 8 * q^38 + 32 * q^42 - 24 * q^43 - 32 * q^47 + 48 * q^57 - 64 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^66 + 32 * q^68 - 16 * q^73 - 16 * q^76 - 72 * q^77 + 16 * q^81 - 40 * q^82 + 16 * q^83 + 8 * q^87 - 8 * q^92 - 104 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	2.20701	−	2.20701i	1.27422	−	1.27422i	0.330367	−	0.943853i	$-0.392828\pi$
$3$	2.20701	−	2.20701i	1.27422	−	1.27422i	0.943853	−	0.330367i	$-0.107172\pi$
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	−3.12119			−1.27422
$7$	−1.65823	+	1.65823i	−0.626751	+	0.626751i	−0.947249	−	0.320498i	$-0.896150\pi$
$7$	−1.65823	+	1.65823i	−0.626751	+	0.626751i	0.320498	+	0.947249i	$0.396150\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		−	6.74181i		−	2.24727i
$10$		0			0
$11$	−0.804733			−0.242636			−0.121318	−	0.992614i	$-0.538712\pi$
$11$	−0.804733			−0.242636			−0.121318	+	0.992614i	$0.538712\pi$
$12$	2.20701	+	2.20701i	0.637110	+	0.637110i
$13$	3.05219	−	3.05219i	0.846526	−	0.846526i	−0.143172	−	0.989698i	$-0.545730\pi$
$13$	3.05219	−	3.05219i	0.846526	−	0.846526i	0.989698	+	0.143172i	$0.0457301\pi$
$14$	2.34509			0.626751
$15$		0			0
$16$	−1.00000			−0.250000
$17$	4.37090	−	4.37090i	1.06010	−	1.06010i	0.0620254	−	0.998075i	$-0.480244\pi$
$17$	4.37090	−	4.37090i	1.06010	−	1.06010i	0.998075	−	0.0620254i	$-0.0197560\pi$
$18$	−4.76718	+	4.76718i	−1.12363	+	1.12363i
$19$	3.48315	+	2.62062i	0.799090	+	0.601212i
$19$	3.48315	+	2.62062i	0.799090	+	0.601212i
$20$		0			0
$21$			7.31946i			1.59724i
$22$	0.569032	+	0.569032i	0.121318	+	0.121318i
$23$	−6.20477	−	6.20477i	−1.29378	−	1.29378i	−0.932428	−	0.361356i	$-0.882314\pi$
$23$	−6.20477	−	6.20477i	−1.29378	−	1.29378i	−0.361356	−	0.932428i	$-0.617686\pi$
$24$		−	3.12119i		−	0.637110i
$25$		0			0
$26$	−4.31645			−0.846526
$27$	−8.25822	−	8.25822i	−1.58929	−	1.58929i
$28$	−1.65823	−	1.65823i	−0.313375	−	0.313375i
$29$	−5.64487			−1.04823			−0.524113	−	0.851649i	$-0.675603\pi$
$29$	−5.64487			−1.04823			−0.524113	+	0.851649i	$0.675603\pi$
$30$		0			0
$31$		−	3.13000i		−	0.562164i	−0.959684	−	0.281082i	$-0.909307\pi$
$31$		−	3.13000i		−	0.562164i	0.959684	−	0.281082i	$-0.0906933\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−1.77606	+	1.77606i	−0.309172	+	0.309172i
$34$	−6.18139			−1.06010
$35$		0			0
$36$	6.74181			1.12363
$37$	−0.524538	−	0.524538i	−0.0862335	−	0.0862335i	0.662674	−	0.748908i	$-0.269421\pi$
$37$	−0.524538	−	0.524538i	−0.0862335	−	0.0862335i	−0.748908	+	0.662674i	$0.769421\pi$
$38$	−0.609901	−	4.31602i	−0.0989390	−	0.700151i
$39$		−	13.4725i		−	2.15732i
$40$		0			0
$41$			1.45541i			0.227297i	0.993521	+	0.113649i	$0.0362538\pi$
$41$			1.45541i			0.227297i	−0.993521	+	0.113649i	$0.963746\pi$
$42$	5.17564	−	5.17564i	0.798618	−	0.798618i
$43$	−1.90794	−	1.90794i	−0.290959	−	0.290959i	0.546500	−	0.837459i	$-0.315960\pi$
$43$	−1.90794	−	1.90794i	−0.290959	−	0.290959i	−0.837459	+	0.546500i	$0.815960\pi$
$44$		−	0.804733i		−	0.121318i
$45$		0			0
$46$			8.77487i			1.29378i
$47$	−0.499434	+	0.499434i	−0.0728500	+	0.0728500i	−0.742593	−	0.669743i	$-0.766404\pi$
$47$	−0.499434	+	0.499434i	−0.0728500	+	0.0728500i	0.669743	+	0.742593i	$0.266404\pi$
$48$	−2.20701	+	2.20701i	−0.318555	+	0.318555i
$49$			1.50057i			0.214367i
$50$		0			0
$51$		−	19.2933i		−	2.70160i
$52$	3.05219	+	3.05219i	0.423263	+	0.423263i
$53$	−3.40535	+	3.40535i	−0.467760	+	0.467760i	−0.901188	−	0.433428i	$-0.857304\pi$
$53$	−3.40535	+	3.40535i	−0.467760	+	0.467760i	0.433428	+	0.901188i	$0.357304\pi$
$54$			11.6789i			1.58929i
$55$		0			0
$56$			2.34509i			0.313375i
$57$	13.4711	−	1.90361i	1.78429	−	0.252140i
$58$	3.99153	+	3.99153i	0.524113	+	0.524113i
$59$	2.77684			0.361514			0.180757	−	0.983528i	$-0.442145\pi$
$59$	2.77684			0.361514			0.180757	+	0.983528i	$0.442145\pi$
$60$		0			0
$61$	6.17945			0.791197			0.395599	−	0.918423i	$-0.370537\pi$
$61$	6.17945			0.791197			0.395599	+	0.918423i	$0.370537\pi$
$62$	−2.21324	+	2.21324i	−0.281082	+	0.281082i
$63$	11.1794	+	11.1794i	1.40848	+	1.40848i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	2.51172			0.309172
$67$	−0.345265	−	0.345265i	−0.0421808	−	0.0421808i	0.685702	−	0.727883i	$-0.259495\pi$
$67$	−0.345265	−	0.345265i	−0.0421808	−	0.0421808i	−0.727883	+	0.685702i	$0.759495\pi$
$68$	4.37090	+	4.37090i	0.530050	+	0.530050i
$69$	−27.3880			−3.29713
$70$		0			0
$71$			6.68211i			0.793020i	0.918030	+	0.396510i	$0.129779\pi$
$71$			6.68211i			0.793020i	−0.918030	+	0.396510i	$0.870221\pi$
$72$	−4.76718	−	4.76718i	−0.561817	−	0.561817i
$73$	−1.05445	−	1.05445i	−0.123414	−	0.123414i	0.642702	−	0.766116i	$-0.277813\pi$
$73$	−1.05445	−	1.05445i	−0.123414	−	0.123414i	−0.766116	+	0.642702i	$0.777813\pi$
$74$			0.741809i			0.0862335i
$75$		0			0
$76$	−2.62062	+	3.48315i	−0.300606	+	0.399545i
$77$	1.33443	−	1.33443i	0.152072	−	0.152072i
$78$	−9.52647	+	9.52647i	−1.07866	+	1.07866i
$79$	7.16924			0.806603			0.403301	−	0.915067i	$-0.367863\pi$
$79$	7.16924			0.806603			0.403301	+	0.915067i	$0.367863\pi$
$80$		0			0
$81$	−16.2266			−1.80295
$82$	1.02913	−	1.02913i	0.113649	−	0.113649i
$83$	4.12119	+	4.12119i	0.452359	+	0.452359i	0.896137	−	0.443778i	$-0.146362\pi$
$83$	4.12119	+	4.12119i	0.452359	+	0.452359i	−0.443778	+	0.896137i	$0.646362\pi$
$84$	−7.31946			−0.798618
$85$		0			0
$86$			2.69824i			0.290959i
$87$	−12.4583	+	12.4583i	−1.33567	+	1.33567i
$88$	−0.569032	+	0.569032i	−0.0606590	+	0.0606590i
$89$	16.7356			1.77397			0.886986	−	0.461797i	$-0.152795\pi$
$89$	16.7356			1.77397			0.886986	+	0.461797i	$0.152795\pi$
$90$		0			0
$91$			10.1225i			1.06112i
$92$	6.20477	−	6.20477i	0.646892	−	0.646892i
$93$	−6.90794	−	6.90794i	−0.716320	−	0.716320i
$94$	0.706307			0.0728500
$95$		0			0
$96$	3.12119			0.318555
$97$	8.25033	+	8.25033i	0.837694	+	0.837694i	0.988555	−	0.150861i	$-0.0482046\pi$
$97$	8.25033	+	8.25033i	0.837694	+	0.837694i	−0.150861	+	0.988555i	$0.548205\pi$
$98$	1.06106	−	1.06106i	0.107183	−	0.107183i
$99$			5.42535i			0.545269i
$100$		0			0
$101$	−1.75296			−0.174426			−0.0872132	−	0.996190i	$-0.527796\pi$
$101$	−1.75296			−0.174426			−0.0872132	+	0.996190i	$0.527796\pi$
$102$	−13.6424	+	13.6424i	−1.35080	+	1.35080i
$103$	−5.55918	+	5.55918i	−0.547762	+	0.547762i	−0.925793	−	0.378031i	$-0.876601\pi$
$103$	−5.55918	+	5.55918i	−0.547762	+	0.547762i	0.378031	+	0.925793i	$0.376601\pi$
$104$		−	4.31645i		−	0.423263i
$105$		0			0
$106$	4.81589			0.467760
$107$	−2.01985	−	2.01985i	−0.195266	−	0.195266i	0.602701	−	0.797967i	$-0.294091\pi$
$107$	−2.01985	−	2.01985i	−0.195266	−	0.195266i	−0.797967	+	0.602701i	$0.794091\pi$
$108$	8.25822	−	8.25822i	0.794647	−	0.794647i
$109$	13.3175			1.27558			0.637792	−	0.770209i	$-0.279848\pi$
$109$	13.3175			1.27558			0.637792	+	0.770209i	$0.279848\pi$
$110$		0			0
$111$	−2.31532			−0.219761
$112$	1.65823	−	1.65823i	0.156688	−	0.156688i
$113$	10.8883	−	10.8883i	1.02429	−	1.02429i	0.0245874	−	0.999698i	$-0.492173\pi$
$113$	10.8883	−	10.8883i	1.02429	−	1.02429i	0.999698	−	0.0245874i	$-0.00782719\pi$
$114$	−10.8716	−	8.17945i	−1.01822	−	0.766076i
$115$		0			0
$116$		−	5.64487i		−	0.524113i
$117$	−20.5773	−	20.5773i	−1.90237	−	1.90237i
$118$	−1.96353	−	1.96353i	−0.180757	−	0.180757i
$119$			14.4959i			1.32884i
$120$		0			0
$121$	−10.3524			−0.941128
$122$	−4.36953	−	4.36953i	−0.395599	−	0.395599i
$123$	3.21211	+	3.21211i	0.289626	+	0.289626i
$124$	3.13000			0.281082
$125$		0			0
$126$		−	15.8101i		−	1.40848i
$127$	10.4120	+	10.4120i	0.923920	+	0.923920i	0.997304	−	0.0733839i	$-0.0233798\pi$
$127$	10.4120	+	10.4120i	0.923920	+	0.923920i	−0.0733839	+	0.997304i	$0.523380\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−8.42171			−0.741491
$130$		0			0
$131$	−15.4836			−1.35281			−0.676405	−	0.736530i	$-0.736463\pi$
$131$	−15.4836			−1.35281			−0.676405	+	0.736530i	$0.736463\pi$
$132$	−1.77606	−	1.77606i	−0.154586	−	0.154586i
$133$	−10.1214	+	1.43027i	−0.877640	+	0.124020i
$134$			0.488279i			0.0421808i
$135$		0			0
$136$		−	6.18139i		−	0.530050i
$137$	3.37204	−	3.37204i	0.288092	−	0.288092i	−0.548233	−	0.836326i	$-0.684699\pi$
$137$	3.37204	−	3.37204i	0.288092	−	0.288092i	0.836326	+	0.548233i	$0.184699\pi$
$138$	19.3662	+	19.3662i	1.64856	+	1.64856i
$139$		−	2.05826i		−	0.174580i	−0.996183	−	0.0872898i	$-0.972179\pi$
$139$		−	2.05826i		−	0.174580i	0.996183	−	0.0872898i	$-0.0278206\pi$
$140$		0			0
$141$			2.20452i			0.185654i
$142$	4.72496	−	4.72496i	0.396510	−	0.396510i
$143$	−2.45620	+	2.45620i	−0.205398	+	0.205398i
$144$			6.74181i			0.561817i
$145$		0			0
$146$			1.49122i			0.123414i
$147$	3.31177	+	3.31177i	0.273150	+	0.273150i
$148$	0.524538	−	0.524538i	0.0431167	−	0.0431167i
$149$		−	19.5419i		−	1.60093i	−0.599377	−	0.800467i	$-0.704585\pi$
$149$		−	19.5419i		−	1.60093i	0.599377	−	0.800467i	$-0.295415\pi$
$150$		0			0
$151$		−	0.641287i		−	0.0521872i	−0.999660	−	0.0260936i	$-0.991693\pi$
$151$		−	0.641287i		−	0.0521872i	0.999660	−	0.0260936i	$-0.00830680\pi$
$152$	4.31602	−	0.609901i	0.350075	−	0.0494695i
$153$	−29.4678	−	29.4678i	−2.38233	−	2.38233i
$154$	−1.88717			−0.152072
$155$		0			0
$156$	13.4725			1.07866
$157$	−12.6689	+	12.6689i	−1.01109	+	1.01109i	−0.0111472	+	0.999938i	$0.503548\pi$
$157$	−12.6689	+	12.6689i	−1.01109	+	1.01109i	−0.999938	+	0.0111472i	$0.996452\pi$
$158$	−5.06942	−	5.06942i	−0.403301	−	0.403301i
$159$			15.0313i			1.19206i
$160$		0			0
$161$	20.5778			1.62176
$162$	11.4739	+	11.4739i	0.901475	+	0.901475i
$163$	3.47143	+	3.47143i	0.271904	+	0.271904i	0.829866	−	0.557962i	$-0.188417\pi$
$163$	3.47143	+	3.47143i	0.271904	+	0.271904i	−0.557962	+	0.829866i	$0.688417\pi$
$164$	−1.45541			−0.113649
$165$		0			0
$166$		−	5.82824i		−	0.452359i
$167$	−13.1032	−	13.1032i	−1.01396	−	1.01396i	−0.999901	−	0.0140549i	$-0.995526\pi$
$167$	−13.1032	−	13.1032i	−1.01396	−	1.01396i	−0.0140549	−	0.999901i	$-0.504474\pi$
$168$	5.17564	+	5.17564i	0.399309	+	0.399309i
$169$		−	5.63178i		−	0.433214i
$170$		0			0
$171$	17.6677	−	23.4827i	1.35108	−	1.79577i
$172$	1.90794	−	1.90794i	0.145479	−	0.145479i
$173$	7.50662	−	7.50662i	0.570718	−	0.570718i	−0.361611	−	0.932329i	$-0.617773\pi$
$173$	7.50662	−	7.50662i	0.570718	−	0.570718i	0.932329	+	0.361611i	$0.117773\pi$
$174$	17.6187			1.33567
$175$		0			0
$176$	0.804733			0.0606590
$177$	6.12853	−	6.12853i	0.460649	−	0.460649i
$178$	−11.8339	−	11.8339i	−0.886986	−	0.886986i
$179$	19.4273			1.45206			0.726031	−	0.687662i	$-0.241363\pi$
$179$	19.4273			1.45206			0.726031	+	0.687662i	$0.241363\pi$
$180$		0			0
$181$			4.58541i			0.340831i	0.985372	+	0.170415i	$0.0545110\pi$
$181$			4.58541i			0.340831i	−0.985372	+	0.170415i	$0.945489\pi$
$182$	7.15766	−	7.15766i	0.530561	−	0.530561i
$183$	13.6381	−	13.6381i	1.00816	−	1.00816i
$184$	−8.77487			−0.646892
$185$		0			0
$186$			9.76931i			0.716320i
$187$	−3.51741	+	3.51741i	−0.257218	+	0.257218i
$188$	−0.499434	−	0.499434i	−0.0364250	−	0.0364250i
$189$	27.3880			1.99218
$190$		0			0
$191$	4.86413			0.351956			0.175978	−	0.984394i	$-0.443691\pi$
$191$	4.86413			0.351956			0.175978	+	0.984394i	$0.443691\pi$
$192$	−2.20701	−	2.20701i	−0.159277	−	0.159277i
$193$	10.3313	−	10.3313i	0.743660	−	0.743660i	−0.229620	−	0.973280i	$-0.573748\pi$
$193$	10.3313	−	10.3313i	0.743660	−	0.743660i	0.973280	+	0.229620i	$0.0737485\pi$
$194$		−	11.6677i		−	0.837694i
$195$		0			0
$196$	−1.50057			−0.107183
$197$	−8.32327	+	8.32327i	−0.593009	+	0.593009i	−0.938443	−	0.345434i	$-0.887732\pi$
$197$	−8.32327	+	8.32327i	−0.593009	+	0.593009i	0.345434	+	0.938443i	$0.387732\pi$
$198$	3.83630	−	3.83630i	0.272634	−	0.272634i
$199$			23.1042i			1.63782i	0.573925	+	0.818908i	$0.305420\pi$
$199$			23.1042i			1.63782i	−0.573925	+	0.818908i	$0.694580\pi$
$200$		0			0
$201$	−1.52401			−0.107495
$202$	1.23953	+	1.23953i	0.0872132	+	0.0872132i
$203$	9.36048	−	9.36048i	0.656977	−	0.656977i
$204$	19.2933			1.35080
$205$		0			0
$206$	7.86186			0.547762
$207$	−41.8314	+	41.8314i	−2.90748	+	2.90748i
$208$	−3.05219	+	3.05219i	−0.211632	+	0.211632i
$209$	−2.80301	−	2.10890i	−0.193888	−	0.145876i
$210$		0			0
$211$			15.3492i			1.05668i	0.849033	+	0.528340i	$0.177185\pi$
$211$			15.3492i			1.05668i	−0.849033	+	0.528340i	$0.822815\pi$
$212$	−3.40535	−	3.40535i	−0.233880	−	0.233880i
$213$	14.7475	+	14.7475i	1.01048	+	1.01048i
$214$			2.85650i			0.195266i
$215$		0			0
$216$	−11.6789			−0.794647
$217$	5.19025	+	5.19025i	0.352337	+	0.352337i
$218$	−9.41688	−	9.41688i	−0.637792	−	0.637792i
$219$	−4.65437			−0.314513
$220$		0			0
$221$		−	26.6817i		−	1.79481i
$222$	1.63718	+	1.63718i	0.109880	+	0.109880i
$223$	−18.5974	+	18.5974i	−1.24537	+	1.24537i	−0.287629	+	0.957742i	$0.592867\pi$
$223$	−18.5974	+	18.5974i	−1.24537	+	1.24537i	−0.957742	+	0.287629i	$0.907133\pi$
$224$	−2.34509			−0.156688
$225$		0			0
$226$	−15.3984			−1.02429
$227$	5.51878	+	5.51878i	0.366294	+	0.366294i	0.866124	−	0.499830i	$-0.166604\pi$
$227$	5.51878	+	5.51878i	0.366294	+	0.366294i	−0.499830	+	0.866124i	$0.666604\pi$
$228$	1.90361	+	13.4711i	0.126070	+	0.892146i
$229$			9.94379i			0.657104i	0.944486	+	0.328552i	$0.106561\pi$
$229$			9.94379i			0.657104i	−0.944486	+	0.328552i	$0.893439\pi$
$230$		0			0
$231$		−	5.89021i		−	0.387547i
$232$	−3.99153	+	3.99153i	−0.262057	+	0.262057i
$233$	5.11116	+	5.11116i	0.334843	+	0.334843i	0.854422	−	0.519579i	$-0.173911\pi$
$233$	5.11116	+	5.11116i	0.334843	+	0.334843i	−0.519579	+	0.854422i	$0.673911\pi$
$234$			29.1007i			1.90237i
$235$		0			0
$236$			2.77684i			0.180757i
$237$	15.8226	−	15.8226i	1.02779	−	1.02779i
$238$	10.2502	−	10.2502i	0.664419	−	0.664419i
$239$			9.30530i			0.601910i	0.953638	+	0.300955i	$0.0973053\pi$
$239$			9.30530i			0.601910i	−0.953638	+	0.300955i	$0.902695\pi$
$240$		0			0
$241$			8.31390i			0.535545i	0.963482	+	0.267773i	$0.0862876\pi$
$241$			8.31390i			0.535545i	−0.963482	+	0.267773i	$0.913712\pi$
$242$	7.32026	+	7.32026i	0.470564	+	0.470564i
$243$	−11.0376	+	11.0376i	−0.708060	+	0.708060i
$244$			6.17945i			0.395599i
$245$		0			0
$246$		−	4.54261i		−	0.289626i
$247$	18.6299	−	2.63261i	1.18539	−	0.167509i
$248$	−2.21324	−	2.21324i	−0.140541	−	0.140541i
$249$	18.1910			1.15281
$250$		0			0
$251$	10.7710			0.679862			0.339931	−	0.940450i	$-0.389596\pi$
$251$	10.7710			0.679862			0.339931	+	0.940450i	$0.389596\pi$
$252$	−11.1794	+	11.1794i	−0.704239	+	0.704239i
$253$	4.99318	+	4.99318i	0.313919	+	0.313919i
$254$		−	14.7249i		−	0.923920i
$255$		0			0
$256$	1.00000			0.0625000
$257$	19.8607	+	19.8607i	1.23888	+	1.23888i	0.960460	+	0.278417i	$0.0898097\pi$
$257$	19.8607	+	19.8607i	1.23888	+	1.23888i	0.278417	+	0.960460i	$0.410190\pi$
$258$	5.95505	+	5.95505i	0.370745	+	0.370745i
$259$	1.73961			0.108094
$260$		0			0
$261$			38.0566i			2.35565i
$262$	10.9486	+	10.9486i	0.676405	+	0.676405i
$263$	−13.1964	−	13.1964i	−0.813725	−	0.813725i	0.171465	−	0.985190i	$-0.445150\pi$
$263$	−13.1964	−	13.1964i	−0.813725	−	0.813725i	−0.985190	+	0.171465i	$0.945150\pi$
$264$			2.51172i			0.154586i
$265$		0			0
$266$	8.16829	+	6.14559i	0.500830	+	0.376810i
$267$	36.9357	−	36.9357i	2.26043	−	2.26043i
$268$	0.345265	−	0.345265i	0.0210904	−	0.0210904i
$269$	−18.1260			−1.10516			−0.552581	−	0.833459i	$-0.686357\pi$
$269$	−18.1260			−1.10516			−0.552581	+	0.833459i	$0.686357\pi$
$270$		0			0
$271$	−7.62288			−0.463057			−0.231529	−	0.972828i	$-0.574373\pi$
$271$	−7.62288			−0.463057			−0.231529	+	0.972828i	$0.574373\pi$
$272$	−4.37090	+	4.37090i	−0.265025	+	0.265025i
$273$	22.3404	+	22.3404i	1.35210	+	1.35210i
$274$	−4.76878			−0.288092
$275$		0			0
$276$		−	27.3880i		−	1.64856i
$277$	1.94710	−	1.94710i	0.116990	−	0.116990i	−0.646188	−	0.763178i	$-0.723638\pi$
$277$	1.94710	−	1.94710i	0.116990	−	0.116990i	0.763178	+	0.646188i	$0.223638\pi$
$278$	−1.45541	+	1.45541i	−0.0872898	+	0.0872898i
$279$	−21.1018			−1.26333
$280$		0			0
$281$		−	5.77885i		−	0.344737i	−0.985033	−	0.172369i	$-0.944858\pi$
$281$		−	5.77885i		−	0.344737i	0.985033	−	0.172369i	$-0.0551420\pi$
$282$	1.55883	−	1.55883i	0.0928269	−	0.0928269i
$283$	21.2948	+	21.2948i	1.26585	+	1.26585i	0.948214	+	0.317634i	$0.102888\pi$
$283$	21.2948	+	21.2948i	1.26585	+	1.26585i	0.317634	+	0.948214i	$0.397112\pi$
$284$	−6.68211			−0.396510
$285$		0			0
$286$	3.47359			0.205398
$287$	−2.41340	−	2.41340i	−0.142459	−	0.142459i
$288$	4.76718	−	4.76718i	0.280909	−	0.280909i
$289$		−	21.2096i		−	1.24762i
$290$		0			0
$291$	36.4172			2.13481
$292$	1.05445	−	1.05445i	0.0617070	−	0.0617070i
$293$	5.94185	−	5.94185i	0.347126	−	0.347126i	−0.511912	−	0.859038i	$-0.671062\pi$
$293$	5.94185	−	5.94185i	0.347126	−	0.347126i	0.859038	+	0.511912i	$0.171062\pi$
$294$		−	4.68355i		−	0.273150i
$295$		0			0
$296$	−0.741809			−0.0431167
$297$	6.64566	+	6.64566i	0.385620	+	0.385620i
$298$	−13.8182	+	13.8182i	−0.800467	+	0.800467i
$299$	−37.8763			−2.19044
$300$		0			0
$301$	6.32761			0.364717
$302$	−0.453459	+	0.453459i	−0.0260936	+	0.0260936i
$303$	−3.86881	+	3.86881i	−0.222258	+	0.222258i
$304$	−3.48315	−	2.62062i	−0.199772	−	0.150303i
$305$		0			0
$306$			41.6738i			2.38233i
$307$	−2.67442	−	2.67442i	−0.152637	−	0.152637i	0.626658	−	0.779295i	$-0.284422\pi$
$307$	−2.67442	−	2.67442i	−0.152637	−	0.152637i	−0.779295	+	0.626658i	$0.784422\pi$
$308$	1.33443	+	1.33443i	0.0760362	+	0.0760362i
$309$			24.5383i			1.39594i
$310$		0			0
$311$	18.8112			1.06669			0.533343	−	0.845899i	$-0.320935\pi$
$311$	18.8112			1.06669			0.533343	+	0.845899i	$0.320935\pi$
$312$	−9.52647	−	9.52647i	−0.539330	−	0.539330i
$313$	−14.6481	−	14.6481i	−0.827959	−	0.827959i	0.159275	−	0.987234i	$-0.449084\pi$
$313$	−14.6481	−	14.6481i	−0.827959	−	0.827959i	−0.987234	+	0.159275i	$0.949084\pi$
$314$	17.9165			1.01109
$315$		0			0
$316$			7.16924i			0.403301i
$317$	0.943658	+	0.943658i	0.0530011	+	0.0530011i	0.733111	−	0.680109i	$-0.238068\pi$
$317$	0.943658	+	0.943658i	0.0530011	+	0.0530011i	−0.680109	+	0.733111i	$0.738068\pi$
$318$	10.6287	−	10.6287i	0.596029	−	0.596029i
$319$	4.54261			0.254337
$320$		0			0
$321$	−8.91567			−0.497624
$322$	−14.5507	−	14.5507i	−0.810880	−	0.810880i
$323$	26.6790	−	3.77004i	1.48446	−	0.209770i
$324$		−	16.2266i		−	0.901475i
$325$		0			0
$326$		−	4.90935i		−	0.271904i
$327$	29.3918	−	29.3918i	1.62537	−	1.62537i
$328$	1.02913	+	1.02913i	0.0568243	+	0.0568243i
$329$		−	1.65635i		−	0.0913176i
$330$		0			0
$331$		−	14.9698i		−	0.822817i	−0.911451	−	0.411409i	$-0.865037\pi$
$331$		−	14.9698i		−	0.822817i	0.911451	−	0.411409i	$-0.134963\pi$
$332$	−4.12119	+	4.12119i	−0.226180	+	0.226180i
$333$	−3.53633	+	3.53633i	−0.193790	+	0.193790i
$334$			18.5307i			1.01396i
$335$		0			0
$336$		−	7.31946i		−	0.399309i
$337$	−18.4481	−	18.4481i	−1.00493	−	1.00493i	−0.999988	−	0.00494423i	$-0.998426\pi$
$337$	−18.4481	−	18.4481i	−1.00493	−	1.00493i	−0.00494423	−	0.999988i	$-0.501574\pi$
$338$	−3.98227	+	3.98227i	−0.216607	+	0.216607i
$339$		−	48.0612i		−	2.61033i
$340$		0			0
$341$			2.51881i			0.136401i
$342$	−29.0978	+	4.11183i	−1.57343	+	0.222342i
$343$	−14.0959	−	14.0959i	−0.761105	−	0.761105i
$344$	−2.69824			−0.145479
$345$		0			0
$346$	−10.6160			−0.570718
$347$	−13.3578	+	13.3578i	−0.717083	+	0.717083i	−0.968007	−	0.250924i	$-0.919266\pi$
$347$	−13.3578	+	13.3578i	−0.717083	+	0.717083i	0.250924	+	0.968007i	$0.419266\pi$
$348$	−12.4583	−	12.4583i	−0.667835	−	0.667835i
$349$			7.74830i			0.414757i	0.978261	+	0.207379i	$0.0664932\pi$
$349$			7.74830i			0.414757i	−0.978261	+	0.207379i	$0.933507\pi$
$350$		0			0
$351$	−50.4114			−2.69076
$352$	−0.569032	−	0.569032i	−0.0303295	−	0.0303295i
$353$	24.2462	+	24.2462i	1.29049	+	1.29049i	0.934481	+	0.356014i	$0.115864\pi$
$353$	24.2462	+	24.2462i	1.29049	+	1.29049i	0.356014	+	0.934481i	$0.384136\pi$
$354$	−8.66705			−0.460649
$355$		0			0
$356$			16.7356i			0.886986i
$357$	31.9926	+	31.9926i	1.69323	+	1.69323i
$358$	−13.7371	−	13.7371i	−0.726031	−	0.726031i
$359$		−	0.430016i		−	0.0226954i	−0.999936	−	0.0113477i	$-0.996388\pi$
$359$		−	0.430016i		−	0.0226954i	0.999936	−	0.0113477i	$-0.00361216\pi$
$360$		0			0
$361$	5.26469	+	18.2560i	0.277089	+	0.960844i
$362$	3.24237	−	3.24237i	0.170415	−	0.170415i
$363$	−22.8479	+	22.8479i	−1.19920	+	1.19920i
$364$	−10.1225			−0.530561
$365$		0			0
$366$	−19.2872			−1.00816
$367$	7.94174	−	7.94174i	0.414555	−	0.414555i	−0.468767	−	0.883322i	$-0.655302\pi$
$367$	7.94174	−	7.94174i	0.414555	−	0.414555i	0.883322	+	0.468767i	$0.155302\pi$
$368$	6.20477	+	6.20477i	0.323446	+	0.323446i
$369$	9.81211			0.510798
$370$		0			0
$371$		−	11.2937i		−	0.586339i
$372$	6.90794	−	6.90794i	0.358160	−	0.358160i
$373$	5.72661	−	5.72661i	0.296513	−	0.296513i	−0.543134	−	0.839646i	$-0.682762\pi$
$373$	5.72661	−	5.72661i	0.296513	−	0.296513i	0.839646	+	0.543134i	$0.182762\pi$
$374$	4.97437			0.257218
$375$		0			0
$376$			0.706307i			0.0364250i
$377$	−17.2292	+	17.2292i	−0.887351	+	0.887351i
$378$	−19.3662	−	19.3662i	−0.996092	−	0.996092i
$379$	1.74355			0.0895599			0.0447800	−	0.998997i	$-0.485741\pi$
$379$	1.74355			0.0895599			0.0447800	+	0.998997i	$0.485741\pi$
$380$		0			0
$381$	45.9590			2.35455
$382$	−3.43946	−	3.43946i	−0.175978	−	0.175978i
$383$	−14.9492	+	14.9492i	−0.763867	+	0.763867i	−0.977019	−	0.213152i	$-0.931627\pi$
$383$	−14.9492	+	14.9492i	−0.763867	+	0.763867i	0.213152	+	0.977019i	$0.431627\pi$
$384$			3.12119i			0.159277i
$385$		0			0
$386$	−14.6106			−0.743660
$387$	−12.8630	+	12.8630i	−0.653863	+	0.653863i
$388$	−8.25033	+	8.25033i	−0.418847	+	0.418847i
$389$		−	9.21427i		−	0.467182i	−0.972335	−	0.233591i	$-0.924952\pi$
$389$		−	9.21427i		−	0.467182i	0.972335	−	0.233591i	$-0.0750477\pi$
$390$		0			0
$391$	−54.2409			−2.74308
$392$	1.06106	+	1.06106i	0.0535916	+	0.0535916i
$393$	−34.1725	+	34.1725i	−1.72378	+	1.72378i
$394$	11.7709			0.593009
$395$		0			0
$396$	−5.42535			−0.272634
$397$	9.28722	−	9.28722i	0.466112	−	0.466112i	−0.434540	−	0.900652i	$-0.643089\pi$
$397$	9.28722	−	9.28722i	0.466112	−	0.466112i	0.900652	+	0.434540i	$0.143089\pi$
$398$	16.3372	−	16.3372i	0.818908	−	0.818908i
$399$	−19.1815	+	25.4948i	−0.960277	+	1.27634i
$400$		0			0
$401$		−	38.6944i		−	1.93231i	−0.257971	−	0.966153i	$-0.583054\pi$
$401$		−	38.6944i		−	1.93231i	0.257971	−	0.966153i	$-0.416946\pi$
$402$	1.07764	+	1.07764i	0.0537476	+	0.0537476i
$403$	−9.55336	−	9.55336i	−0.475887	−	0.475887i
$404$		−	1.75296i		−	0.0872132i
$405$		0			0
$406$	−13.2377			−0.656977
$407$	0.422113	+	0.422113i	0.0209234	+	0.0209234i
$408$	−13.6424	−	13.6424i	−0.675400	−	0.675400i
$409$	−14.6817			−0.725964			−0.362982	−	0.931796i	$-0.618241\pi$
$409$	−14.6817			−0.725964			−0.362982	+	0.931796i	$0.618241\pi$
$410$		0			0
$411$		−	14.8842i		−	0.734186i
$412$	−5.55918	−	5.55918i	−0.273881	−	0.273881i
$413$	−4.60464	+	4.60464i	−0.226579	+	0.226579i
$414$	59.1585			2.90748
$415$		0			0
$416$	4.31645			0.211632
$417$	−4.54261	−	4.54261i	−0.222453	−	0.222453i
$418$	0.490807	+	3.47324i	0.0240062	+	0.169882i
$419$			1.27584i			0.0623290i	0.999514	+	0.0311645i	$0.00992157\pi$
$419$			1.27584i			0.0623290i	−0.999514	+	0.0311645i	$0.990078\pi$
$420$		0			0
$421$			6.74319i			0.328643i	0.986407	+	0.164321i	$0.0525434\pi$
$421$			6.74319i			0.328643i	−0.986407	+	0.164321i	$0.947457\pi$
$422$	10.8535	−	10.8535i	0.528340	−	0.528340i
$423$	3.36709	+	3.36709i	0.163714	+	0.163714i
$424$			4.81589i			0.233880i
$425$		0			0
$426$		−	20.8561i		−	1.01048i
$427$	−10.2469	+	10.2469i	−0.495884	+	0.495884i
$428$	2.01985	−	2.01985i	0.0976332	−	0.0976332i
$429$			10.8417i			0.523444i
$430$		0			0
$431$			11.0055i			0.530118i	0.964232	+	0.265059i	$0.0853915\pi$
$431$			11.0055i			0.530118i	−0.964232	+	0.265059i	$0.914608\pi$
$432$	8.25822	+	8.25822i	0.397324	+	0.397324i
$433$	3.70282	−	3.70282i	0.177946	−	0.177946i	−0.612514	−	0.790460i	$-0.709842\pi$
$433$	3.70282	−	3.70282i	0.177946	−	0.177946i	0.790460	+	0.612514i	$0.209842\pi$
$434$		−	7.34012i		−	0.352337i
$435$		0			0
$436$			13.3175i			0.637792i
$437$	−5.35180	−	37.8725i	−0.256011	−	1.81169i
$438$	3.29114	+	3.29114i	0.157257	+	0.157257i
$439$	32.4807			1.55022			0.775110	−	0.631826i	$-0.217694\pi$
$439$	32.4807			1.55022			0.775110	+	0.631826i	$0.217694\pi$
$440$		0			0
$441$	10.1165			0.481739
$442$	−18.8668	+	18.8668i	−0.897403	+	0.897403i
$443$	−9.15145	−	9.15145i	−0.434798	−	0.434798i	0.455459	−	0.890257i	$-0.349475\pi$
$443$	−9.15145	−	9.15145i	−0.434798	−	0.434798i	−0.890257	+	0.455459i	$0.849475\pi$
$444$		−	2.31532i		−	0.109880i
$445$		0			0
$446$	26.3006			1.24537
$447$	−43.1292	−	43.1292i	−2.03994	−	2.03994i
$448$	1.65823	+	1.65823i	0.0783439	+	0.0783439i
$449$	−0.503369			−0.0237554			−0.0118777	−	0.999929i	$-0.503781\pi$
$449$	−0.503369			−0.0237554			−0.0118777	+	0.999929i	$0.503781\pi$
$450$		0			0
$451$		−	1.17122i		−	0.0551505i
$452$	10.8883	+	10.8883i	0.512143	+	0.512143i
$453$	−1.41533	−	1.41533i	−0.0664980	−	0.0664980i
$454$		−	7.80473i		−	0.366294i
$455$		0			0
$456$	8.17945	−	10.8716i	0.383038	−	0.509108i
$457$	−8.26087	+	8.26087i	−0.386427	+	0.386427i	−0.873411	−	0.486984i	$-0.838097\pi$
$457$	−8.26087	+	8.26087i	−0.386427	+	0.386427i	0.486984	+	0.873411i	$0.338097\pi$
$458$	7.03132	−	7.03132i	0.328552	−	0.328552i
$459$	−72.1918			−3.36962
$460$		0			0
$461$	18.1189			0.843882			0.421941	−	0.906623i	$-0.361349\pi$
$461$	18.1189			0.843882			0.421941	+	0.906623i	$0.361349\pi$
$462$	−4.16500	+	4.16500i	−0.193774	+	0.193774i
$463$	−20.7494	−	20.7494i	−0.964308	−	0.964308i	0.0350766	−	0.999385i	$-0.488832\pi$
$463$	−20.7494	−	20.7494i	−0.964308	−	0.964308i	−0.999385	+	0.0350766i	$0.988832\pi$
$464$	5.64487			0.262057
$465$		0			0
$466$		−	7.22827i		−	0.334843i
$467$	−18.0874	+	18.0874i	−0.836985	+	0.836985i	−0.988461	−	0.151476i	$-0.951597\pi$
$467$	−18.0874	+	18.0874i	−0.836985	+	0.836985i	0.151476	+	0.988461i	$0.451597\pi$
$468$	20.5773	−	20.5773i	0.951186	−	0.951186i
$469$	1.14506			0.0528738
$470$		0			0
$471$			55.9207i			2.57669i
$472$	1.96353	−	1.96353i	0.0903786	−	0.0903786i
$473$	1.53539	+	1.53539i	0.0705971	+	0.0705971i
$474$	−22.3765			−1.02779
$475$		0			0
$476$	−14.4959			−0.664419
$477$	22.9582	+	22.9582i	1.05118	+	1.05118i
$478$	6.57984	−	6.57984i	0.300955	−	0.300955i
$479$		−	1.97995i		−	0.0904662i	−0.998976	−	0.0452331i	$-0.985597\pi$
$479$		−	1.97995i		−	0.0904662i	0.998976	−	0.0452331i	$-0.0144031\pi$
$480$		0			0
$481$	−3.20198			−0.145998
$482$	5.87881	−	5.87881i	0.267773	−	0.267773i
$483$	45.4155	−	45.4155i	2.06648	−	2.06648i
$484$		−	10.3524i		−	0.470564i
$485$		0			0
$486$	15.6095			0.708060
$487$	1.84597	+	1.84597i	0.0836489	+	0.0836489i	0.747693	−	0.664044i	$-0.231161\pi$
$487$	1.84597	+	1.84597i	0.0836489	+	0.0836489i	−0.664044	+	0.747693i	$0.731161\pi$
$488$	4.36953	−	4.36953i	0.197799	−	0.197799i
$489$	15.3230			0.692930
$490$		0			0
$491$	−5.60811			−0.253091			−0.126545	−	0.991961i	$-0.540389\pi$
$491$	−5.60811			−0.253091			−0.126545	+	0.991961i	$0.540389\pi$
$492$	−3.21211	+	3.21211i	−0.144813	+	0.144813i
$493$	−24.6732	+	24.6732i	−1.11122	+	1.11122i
$494$	−15.0349	−	11.3118i	−0.676450	−	0.508942i
$495$		0			0
$496$			3.13000i			0.140541i
$497$	−11.0805	−	11.0805i	−0.497026	−	0.497026i
$498$	−12.8630	−	12.8630i	−0.576405	−	0.576405i
$499$		−	18.8853i		−	0.845422i	−0.906264	−	0.422711i	$-0.861078\pi$
$499$		−	18.8853i		−	0.845422i	0.906264	−	0.422711i	$-0.138922\pi$
$500$		0			0
$501$	−57.8379			−2.58400
$502$	−7.61628	−	7.61628i	−0.339931	−	0.339931i
$503$	26.9767	+	26.9767i	1.20283	+	1.20283i	0.973301	+	0.229532i	$0.0737196\pi$
$503$	26.9767	+	26.9767i	1.20283	+	1.20283i	0.229532	+	0.973301i	$0.426280\pi$
$504$	15.8101			0.704239
$505$		0			0
$506$		−	7.06142i		−	0.313919i
$507$	−12.4294	−	12.4294i	−0.552009	−	0.552009i
$508$	−10.4120	+	10.4120i	−0.461960	+	0.461960i
$509$	30.3840			1.34675			0.673374	−	0.739302i	$-0.264844\pi$
$509$	30.3840			1.34675			0.673374	+	0.739302i	$0.264844\pi$
$510$		0			0
$511$	3.49704			0.154700
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−7.12296	−	50.4063i	−0.314486	−	2.22549i
$514$		−	28.0873i		−	1.23888i
$515$		0			0
$516$		−	8.42171i		−	0.370745i
$517$	0.401911	−	0.401911i	0.0176760	−	0.0176760i
$518$	−1.23009	−	1.23009i	−0.0540469	−	0.0540469i
$519$		−	33.1344i		−	1.45444i
$520$		0			0
$521$		−	41.3468i		−	1.81143i	−0.423882	−	0.905717i	$-0.639333\pi$
$521$		−	41.3468i		−	1.81143i	0.423882	−	0.905717i	$-0.360667\pi$
$522$	26.9101	−	26.9101i	1.17782	−	1.17782i
$523$	10.9169	−	10.9169i	0.477361	−	0.477361i	−0.426926	−	0.904287i	$-0.640403\pi$
$523$	10.9169	−	10.9169i	0.477361	−	0.477361i	0.904287	+	0.426926i	$0.140403\pi$
$524$		−	15.4836i		−	0.676405i
$525$		0			0
$526$			18.6625i			0.813725i
$527$	−13.6809	−	13.6809i	−0.595950	−	0.595950i
$528$	1.77606	−	1.77606i	0.0772929	−	0.0772929i
$529$			53.9983i			2.34775i
$530$		0			0
$531$		−	18.7210i		−	0.812420i
$532$	−1.43027	−	10.1214i	−0.0620101	−	0.438820i
$533$	4.44220	+	4.44220i	0.192413	+	0.192413i
$534$	−52.2350			−2.26043
$535$		0			0
$536$	−0.488279			−0.0210904
$537$	42.8762	−	42.8762i	1.85024	−	1.85024i
$538$	12.8170	+	12.8170i	0.552581	+	0.552581i
$539$		−	1.20755i		−	0.0520130i
$540$		0			0
$541$	41.7436			1.79470			0.897350	−	0.441320i	$-0.145490\pi$
$541$	41.7436			1.79470			0.897350	+	0.441320i	$0.145490\pi$
$542$	5.39019	+	5.39019i	0.231529	+	0.231529i
$543$	10.1201	+	10.1201i	0.434293	+	0.434293i
$544$	6.18139			0.265025
$545$		0			0
$546$		−	31.5941i		−	1.35210i
$547$	−16.6189	−	16.6189i	−0.710571	−	0.710571i	0.256083	−	0.966655i	$-0.417568\pi$
$547$	−16.6189	−	16.6189i	−0.710571	−	0.710571i	−0.966655	+	0.256083i	$0.917568\pi$
$548$	3.37204	+	3.37204i	0.144046	+	0.144046i
$549$		−	41.6607i		−	1.77803i
$550$		0			0
$551$	−19.6619	−	14.7931i	−0.837627	−	0.630206i
$552$	−19.3662	+	19.3662i	−0.824282	+	0.824282i
$553$	−11.8882	+	11.8882i	−0.505539	+	0.505539i
$554$	−2.75362			−0.116990
$555$		0			0
$556$	2.05826			0.0872898
$557$	−14.9213	+	14.9213i	−0.632234	+	0.632234i	−0.948628	−	0.316394i	$-0.897528\pi$
$557$	−14.9213	+	14.9213i	−0.632234	+	0.632234i	0.316394	+	0.948628i	$0.397528\pi$
$558$	14.9213	+	14.9213i	0.631667	+	0.631667i
$559$	−11.6468			−0.492609
$560$		0			0
$561$			15.5259i			0.655506i
$562$	−4.08626	+	4.08626i	−0.172369	+	0.172369i
$563$	−24.7032	+	24.7032i	−1.04112	+	1.04112i	−0.0419980	+	0.999118i	$0.513372\pi$
$563$	−24.7032	+	24.7032i	−1.04112	+	1.04112i	−0.999118	+	0.0419980i	$0.986628\pi$
$564$	−2.20452			−0.0928269
$565$		0			0
$566$		−	30.1155i		−	1.26585i
$567$	26.9073	−	26.9073i	1.13000	−	1.13000i
$568$	4.72496	+	4.72496i	0.198255	+	0.198255i
$569$	−19.1003			−0.800725			−0.400362	−	0.916357i	$-0.631116\pi$
$569$	−19.1003			−0.800725			−0.400362	+	0.916357i	$0.631116\pi$
$570$		0			0
$571$	−33.3161			−1.39424			−0.697118	−	0.716957i	$-0.745535\pi$
$571$	−33.3161			−1.39424			−0.697118	+	0.716957i	$0.745535\pi$
$572$	−2.45620	−	2.45620i	−0.102699	−	0.102699i
$573$	10.7352	−	10.7352i	0.448469	−	0.448469i
$574$			3.41307i			0.142459i
$575$		0			0
$576$	−6.74181			−0.280909
$577$	−15.5550	+	15.5550i	−0.647564	+	0.647564i	−0.952404	−	0.304840i	$-0.901397\pi$
$577$	−15.5550	+	15.5550i	−0.647564	+	0.647564i	0.304840	+	0.952404i	$0.401397\pi$
$578$	−14.9975	+	14.9975i	−0.623812	+	0.623812i
$579$		−	45.6024i		−	1.89517i
$580$		0			0
$581$	−13.6677			−0.567033
$582$	−25.7508	−	25.7508i	−1.06741	−	1.06741i
$583$	2.74039	−	2.74039i	0.113496	−	0.113496i
$584$	−1.49122			−0.0617070
$585$		0			0
$586$	−8.40304			−0.347126
$587$	12.0651	−	12.0651i	0.497979	−	0.497979i	−0.412829	−	0.910808i	$-0.635459\pi$
$587$	12.0651	−	12.0651i	0.497979	−	0.497979i	0.910808	+	0.412829i	$0.135459\pi$
$588$	−3.31177	+	3.31177i	−0.136575	+	0.136575i
$589$	8.20254	−	10.9023i	0.337980	−	0.449220i
$590$		0			0
$591$			36.7391i			1.51125i
$592$	0.524538	+	0.524538i	0.0215584	+	0.0215584i
$593$	−11.1513	−	11.1513i	−0.457931	−	0.457931i	0.440045	−	0.897976i	$-0.354963\pi$
$593$	−11.1513	−	11.1513i	−0.457931	−	0.457931i	−0.897976	+	0.440045i	$0.854963\pi$
$594$		−	9.39838i		−	0.385620i
$595$		0			0
$596$	19.5419			0.800467
$597$	50.9913	+	50.9913i	2.08694	+	2.08694i
$598$	26.7826	+	26.7826i	1.09522	+	1.09522i
$599$	−9.96626			−0.407210			−0.203605	−	0.979053i	$-0.565266\pi$
$599$	−9.96626			−0.407210			−0.203605	+	0.979053i	$0.565266\pi$
$600$		0			0
$601$			13.6021i			0.554840i	0.960749	+	0.277420i	$0.0894794\pi$
$601$			13.6021i			0.554840i	−0.960749	+	0.277420i	$0.910521\pi$
$602$	−4.47430	−	4.47430i	−0.182359	−	0.182359i
$603$	−2.32771	+	2.32771i	−0.0947917	+	0.0947917i
$604$	0.641287			0.0260936
$605$		0			0
$606$	5.47133			0.222258
$607$	11.0390	+	11.0390i	0.448060	+	0.448060i	0.894709	−	0.446649i	$-0.147383\pi$
$607$	11.0390	+	11.0390i	0.448060	+	0.448060i	−0.446649	+	0.894709i	$0.647383\pi$
$608$	0.609901	+	4.31602i	0.0247347	+	0.175038i
$609$		−	41.3174i		−	1.67426i
$610$		0			0
$611$			3.04874i			0.123339i
$612$	29.4678	−	29.4678i	1.19117	−	1.19117i
$613$	−11.0338	−	11.0338i	−0.445651	−	0.445651i	0.448255	−	0.893906i	$-0.352046\pi$
$613$	−11.0338	−	11.0338i	−0.445651	−	0.445651i	−0.893906	+	0.448255i	$0.852046\pi$
$614$			3.78220i			0.152637i
$615$		0			0
$616$		−	1.88717i		−	0.0760362i
$617$	−4.29188	+	4.29188i	−0.172785	+	0.172785i	−0.788202	−	0.615417i	$-0.788988\pi$
$617$	−4.29188	+	4.29188i	−0.172785	+	0.172785i	0.615417	+	0.788202i	$0.288988\pi$
$618$	17.3512	−	17.3512i	0.697969	−	0.697969i
$619$			34.2230i			1.37554i	0.725929	+	0.687770i	$0.241410\pi$
$619$			34.2230i			1.37554i	−0.725929	+	0.687770i	$0.758590\pi$
$620$		0			0
$621$			102.481i			4.11241i
$622$	−13.3015	−	13.3015i	−0.533343	−	0.533343i
$623$	−27.7514	+	27.7514i	−1.11184	+	1.11184i
$624$			13.4725i			0.539330i
$625$		0			0
$626$			20.7155i			0.827959i
$627$	−10.8406	+	1.53190i	−0.432933	+	0.0611782i
$628$	−12.6689	−	12.6689i	−0.505543	−	0.505543i
$629$	−4.58541			−0.182832
$630$		0			0
$631$	−14.1221			−0.562192			−0.281096	−	0.959680i	$-0.590698\pi$
$631$	−14.1221			−0.562192			−0.281096	+	0.959680i	$0.590698\pi$
$632$	5.06942	−	5.06942i	0.201651	−	0.201651i
$633$	33.8758	+	33.8758i	1.34644	+	1.34644i
$634$		−	1.33453i		−	0.0530011i
$635$		0			0
$636$	−15.0313			−0.596029
$637$	4.58002	+	4.58002i	0.181467	+	0.181467i
$638$	−3.21211	−	3.21211i	−0.127169	−	0.127169i
$639$	45.0495			1.78213
$640$		0			0
$641$			18.1482i			0.716812i	0.933566	+	0.358406i	$0.116680\pi$
$641$			18.1482i			0.716812i	−0.933566	+	0.358406i	$0.883320\pi$
$642$	6.30433	+	6.30433i	0.248812	+	0.248812i
$643$	7.69230	+	7.69230i	0.303355	+	0.303355i	0.842325	−	0.538970i	$-0.181186\pi$
$643$	7.69230	+	7.69230i	0.303355	+	0.303355i	−0.538970	+	0.842325i	$0.681186\pi$
$644$			20.5778i			0.810880i
$645$		0			0
$646$	−21.5307	−	16.1991i	−0.847115	−	0.637345i
$647$	−18.0736	+	18.0736i	−0.710545	+	0.710545i	−0.966649	−	0.256104i	$-0.917561\pi$
$647$	−18.0736	+	18.0736i	−0.710545	+	0.710545i	0.256104	+	0.966649i	$0.417561\pi$
$648$	−11.4739	+	11.4739i	−0.450738	+	0.450738i
$649$	−2.23462			−0.0877164
$650$		0			0
$651$	22.9099			0.897909
$652$	−3.47143	+	3.47143i	−0.135952	+	0.135952i
$653$	−14.3290	−	14.3290i	−0.560736	−	0.560736i	0.368781	−	0.929516i	$-0.379775\pi$
$653$	−14.3290	−	14.3290i	−0.560736	−	0.560736i	−0.929516	+	0.368781i	$0.879775\pi$
$654$	−41.5663			−1.62537
$655$		0			0
$656$		−	1.45541i		−	0.0568243i
$657$	−7.10890	+	7.10890i	−0.277345	+	0.277345i
$658$	−1.17122	+	1.17122i	−0.0456588	+	0.0456588i
$659$	−15.0999			−0.588208			−0.294104	−	0.955773i	$-0.595021\pi$
$659$	−15.0999			−0.588208			−0.294104	+	0.955773i	$0.595021\pi$
$660$		0			0
$661$			37.7035i			1.46650i	0.679962	+	0.733248i	$0.261996\pi$
$661$			37.7035i			1.46650i	−0.679962	+	0.733248i	$0.738004\pi$
$662$	−10.5853	+	10.5853i	−0.411409	+	0.411409i
$663$	−58.8868	−	58.8868i	−2.28698	−	2.28698i
$664$	5.82824			0.226180
$665$		0			0
$666$	5.00113			0.193790
$667$	35.0251	+	35.0251i	1.35618	+	1.35618i
$668$	13.1032	−	13.1032i	0.506978	−	0.506978i
$669$			82.0892i			3.17375i
$670$		0			0
$671$	−4.97281			−0.191973
$672$	−5.17564	+	5.17564i	−0.199655	+	0.199655i
$673$	20.8241	−	20.8241i	0.802710	−	0.802710i	−0.180808	−	0.983518i	$-0.557871\pi$
$673$	20.8241	−	20.8241i	0.802710	−	0.802710i	0.983518	+	0.180808i	$0.0578714\pi$
$674$			26.0896i			1.00493i
$675$		0			0
$676$	5.63178			0.216607
$677$	−22.3987	−	22.3987i	−0.860850	−	0.860850i	0.130587	−	0.991437i	$-0.458314\pi$
$677$	−22.3987	−	22.3987i	−0.860850	−	0.860850i	−0.991437	+	0.130587i	$0.958314\pi$
$678$	−33.9844	+	33.9844i	−1.30516	+	1.30516i
$679$	−27.3618			−1.05005
$680$		0			0
$681$	24.3600			0.933478
$682$	1.78107	−	1.78107i	0.0682007	−	0.0682007i
$683$	−3.33340	+	3.33340i	−0.127549	+	0.127549i	−0.767999	−	0.640451i	$-0.778748\pi$
$683$	−3.33340	+	3.33340i	−0.127549	+	0.127549i	0.640451	+	0.767999i	$0.278748\pi$
$684$	23.4827	+	17.6677i	0.897885	+	0.675542i
$685$		0			0
$686$			19.9346i			0.761105i
$687$	21.9461	+	21.9461i	0.837295	+	0.837295i
$688$	1.90794	+	1.90794i	0.0727397	+	0.0727397i
$689$			20.7876i			0.791943i
$690$		0			0
$691$	−0.218008			−0.00829342			−0.00414671	−	0.999991i	$-0.501320\pi$
$691$	−0.218008			−0.00829342			−0.00414671	+	0.999991i	$0.501320\pi$
$692$	7.50662	+	7.50662i	0.285359	+	0.285359i
$693$	−8.99647	−	8.99647i	−0.341748	−	0.341748i
$694$	18.8907			0.717083
$695$		0			0
$696$			17.6187i			0.667835i
$697$	6.36146	+	6.36146i	0.240958	+	0.240958i
$698$	5.47888	−	5.47888i	0.207379	−	0.207379i
$699$	22.5608			0.853328
$700$		0			0
$701$	−4.66660			−0.176255			−0.0881275	−	0.996109i	$-0.528088\pi$
$701$	−4.66660			−0.176255			−0.0881275	+	0.996109i	$0.528088\pi$
$702$	35.6462	+	35.6462i	1.34538	+	1.34538i
$703$	−0.452430	−	3.20166i	−0.0170637	−	0.120753i
$704$			0.804733i			0.0303295i
$705$		0			0
$706$		−	34.2893i		−	1.29049i
$707$	2.90681	−	2.90681i	0.109322	−	0.109322i
$708$	6.12853	+	6.12853i	0.230324	+	0.230324i
$709$		−	0.424223i		−	0.0159320i	−0.999968	−	0.00796602i	$-0.997464\pi$
$709$		−	0.424223i		−	0.0159320i	0.999968	−	0.00796602i	$-0.00253569\pi$
$710$		0			0
$711$		−	48.3336i		−	1.81265i
$712$	11.8339	−	11.8339i	0.443493	−	0.443493i
$713$	−19.4209	+	19.4209i	−0.727319	+	0.727319i
$714$		−	45.2444i		−	1.69323i
$715$		0			0
$716$			19.4273i			0.726031i
$717$	20.5369	+	20.5369i	0.766965	+	0.766965i
$718$	−0.304067	+	0.304067i	−0.0113477	+	0.0113477i
$719$			9.56441i			0.356692i	0.983968	+	0.178346i	$0.0570747\pi$
$719$			9.56441i			0.356692i	−0.983968	+	0.178346i	$0.942925\pi$
$720$		0			0
$721$		−	18.4368i		−	0.686621i
$722$	9.18628	−	16.6317i	0.341878	−	0.618967i
$723$	18.3489	+	18.3489i	0.682402	+	0.682402i
$724$	−4.58541			−0.170415
$725$		0			0
$726$	32.3118			1.19920
$727$	−2.48083	+	2.48083i	−0.0920089	+	0.0920089i	−0.751613	−	0.659604i	$-0.770724\pi$
$727$	−2.48083	+	2.48083i	−0.0920089	+	0.0920089i	0.659604	+	0.751613i	$0.270724\pi$
$728$	7.15766	+	7.15766i	0.265281	+	0.265281i
$729$			0.0403915i			0.00149598i
$730$		0			0
$731$	−16.6789			−0.616891
$732$	13.6381	+	13.6381i	0.504080	+	0.504080i
$733$	16.0819	+	16.0819i	0.594000	+	0.594000i	0.938709	−	0.344710i	$-0.112023\pi$
$733$	16.0819	+	16.0819i	0.594000	+	0.594000i	−0.344710	+	0.938709i	$0.612023\pi$
$734$	−11.2313			−0.414555
$735$		0			0
$736$		−	8.77487i		−	0.323446i
$737$	0.277846	+	0.277846i	0.0102346	+	0.0102346i
$738$	−6.93821	−	6.93821i	−0.255399	−	0.255399i
$739$			35.9583i			1.32275i	0.750056	+	0.661374i	$0.230027\pi$
$739$			35.9583i			1.32275i	−0.750056	+	0.661374i	$0.769973\pi$
$740$		0			0
$741$	35.3062	−	46.9266i	1.29701	−	1.72389i
$742$	−7.98584	+	7.98584i	−0.293169	+	0.293169i
$743$	−24.1408	+	24.1408i	−0.885639	+	0.885639i	−0.994101	−	0.108462i	$-0.965407\pi$
$743$	−24.1408	+	24.1408i	−0.885639	+	0.885639i	0.108462	+	0.994101i	$0.465407\pi$
$744$	−9.76931			−0.358160
$745$		0			0
$746$	−8.09865			−0.296513
$747$	27.7843	−	27.7843i	1.01657	−	1.01657i
$748$	−3.51741	−	3.51741i	−0.128609	−	0.128609i
$749$	6.69874			0.244767
$750$		0			0
$751$		−	1.42885i		−	0.0521395i	−0.999660	−	0.0260697i	$-0.991701\pi$
$751$		−	1.42885i		−	0.0521395i	0.999660	−	0.0260697i	$-0.00829920\pi$
$752$	0.499434	−	0.499434i	0.0182125	−	0.0182125i
$753$	23.7718	−	23.7718i	0.866294	−	0.866294i
$754$	24.3658			0.887351
$755$		0			0
$756$			27.3880i			0.996092i
$757$	17.6271	−	17.6271i	0.640668	−	0.640668i	−0.310051	−	0.950720i	$-0.600346\pi$
$757$	17.6271	−	17.6271i	0.640668	−	0.640668i	0.950720	+	0.310051i	$0.100346\pi$
$758$	−1.23287	−	1.23287i	−0.0447800	−	0.0447800i
$759$	22.0400			0.800002
$760$		0			0
$761$	−33.0942			−1.19966			−0.599832	−	0.800126i	$-0.704766\pi$
$761$	−33.0942			−1.19966			−0.599832	+	0.800126i	$0.704766\pi$
$762$	−32.4980	−	32.4980i	−1.17728	−	1.17728i
$763$	−22.0834	+	22.0834i	−0.799473	+	0.799473i
$764$			4.86413i			0.175978i
$765$		0			0
$766$	21.1413			0.763867
$767$	8.47547	−	8.47547i	0.306031	−	0.306031i
$768$	2.20701	−	2.20701i	0.0796387	−	0.0796387i
$769$			2.61399i			0.0942629i	0.998889	+	0.0471314i	$0.0150080\pi$
$769$			2.61399i			0.0942629i	−0.998889	+	0.0471314i	$0.984992\pi$
$770$		0			0
$771$	87.6657			3.15720
$772$	10.3313	+	10.3313i	0.371830	+	0.371830i
$773$	14.4070	−	14.4070i	0.518182	−	0.518182i	−0.398839	−	0.917021i	$-0.630587\pi$
$773$	14.4070	−	14.4070i	0.518182	−	0.518182i	0.917021	+	0.398839i	$0.130587\pi$
$774$	18.1910			0.653863
$775$		0			0
$776$	11.6677			0.418847
$777$	3.83933	−	3.83933i	0.137735	−	0.137735i
$778$	−6.51547	+	6.51547i	−0.233591	+	0.233591i
$779$	−3.81408	+	5.06942i	−0.136654	+	0.181631i
$780$		0			0
$781$		−	5.37731i		−	0.192415i
$782$	38.3541	+	38.3541i	1.37154	+	1.37154i
$783$	46.6166	+	46.6166i	1.66594	+	1.66594i
$784$		−	1.50057i		−	0.0535916i
$785$		0			0
$786$	48.3273			1.72378
$787$	−28.5405	−	28.5405i	−1.01736	−	1.01736i	−0.999847	−	0.0175140i	$-0.994425\pi$
$787$	−28.5405	−	28.5405i	−1.01736	−	1.01736i	−0.0175140	−	0.999847i	$-0.505575\pi$
$788$	−8.32327	−	8.32327i	−0.296504	−	0.296504i
$789$	−58.2492			−2.07373
$790$		0			0
$791$			36.1105i			1.28394i
$792$	3.83630	+	3.83630i	0.136317	+	0.136317i
$793$	18.8609	−	18.8609i	0.669769	−	0.669769i
$794$	−13.1341			−0.466112
$795$		0			0
$796$	−23.1042			−0.818908
$797$	19.4519	+	19.4519i	0.689021	+	0.689021i	0.962016	−	0.272995i	$-0.0880141\pi$
$797$	19.4519	+	19.4519i	0.689021	+	0.689021i	−0.272995	+	0.962016i	$0.588014\pi$
$798$	31.5909	−	4.46414i	1.11831	−	0.158029i
$799$			4.36596i			0.154457i
$800$		0			0
$801$		−	112.828i		−	3.98659i
$802$	−27.3611	+	27.3611i	−0.966153	+	0.966153i
$803$	0.848550	+	0.848550i	0.0299447	+	0.0299447i
$804$		−	1.52401i		−	0.0537476i
$805$		0			0
$806$			13.5105i			0.475887i
$807$	−40.0043	+	40.0043i	−1.40822	+	1.40822i
$808$	−1.23953	+	1.23953i	−0.0436066	+	0.0436066i
$809$		−	1.15579i		−	0.0406353i	−0.999794	−	0.0203176i	$-0.993532\pi$
$809$		−	1.15579i		−	0.0406353i	0.999794	−	0.0203176i	$-0.00646775\pi$
$810$		0			0
$811$		−	39.4268i		−	1.38446i	−0.721675	−	0.692232i	$-0.756628\pi$
$811$		−	39.4268i		−	1.38446i	0.721675	−	0.692232i	$-0.243372\pi$
$812$	9.36048	+	9.36048i	0.328488	+	0.328488i
$813$	−16.8238	+	16.8238i	−0.590036	+	0.590036i
$814$		−	0.596958i		−	0.0209234i
$815$		0			0
$816$			19.2933i			0.675400i
$817$	−1.64566	−	11.6457i	−0.0575743	−	0.407430i
$818$	10.3815	+	10.3815i	0.362982	+	0.362982i
$819$	68.2437			2.38463
$820$		0			0
$821$	12.3926			0.432504			0.216252	−	0.976338i	$-0.430617\pi$
$821$	12.3926			0.432504			0.216252	+	0.976338i	$0.430617\pi$
$822$	−10.5248	+	10.5248i	−0.367093	+	0.367093i
$823$	−15.3766	−	15.3766i	−0.535994	−	0.535994i	0.386356	−	0.922350i	$-0.373734\pi$
$823$	−15.3766	−	15.3766i	−0.535994	−	0.535994i	−0.922350	+	0.386356i	$0.873734\pi$
$824$			7.86186i			0.273881i
$825$		0			0
$826$	6.51194			0.226579
$827$	−26.9516	−	26.9516i	−0.937197	−	0.937197i	0.0609437	−	0.998141i	$-0.480589\pi$
$827$	−26.9516	−	26.9516i	−0.937197	−	0.937197i	−0.998141	+	0.0609437i	$0.980589\pi$
$828$	−41.8314	−	41.8314i	−1.45374	−	1.45374i
$829$	12.4871			0.433696			0.216848	−	0.976205i	$-0.430422\pi$
$829$	12.4871			0.433696			0.216848	+	0.976205i	$0.430422\pi$
$830$		0			0
$831$		−	8.59455i		−	0.298142i
$832$	−3.05219	−	3.05219i	−0.105816	−	0.105816i
$833$	6.55883	+	6.55883i	0.227250	+	0.227250i
$834$			6.42422i			0.222453i
$835$		0			0
$836$	2.10890	−	2.80301i	0.0729378	−	0.0969440i
$837$	−25.8482	+	25.8482i	−0.893445	+	0.893445i
$838$	0.902156	−	0.902156i	0.0311645	−	0.0311645i
$839$	6.90128			0.238259			0.119129	−	0.992879i	$-0.461990\pi$
$839$	6.90128			0.238259			0.119129	+	0.992879i	$0.461990\pi$
$840$		0			0
$841$	2.86456			0.0987778
$842$	4.76815	−	4.76815i	0.164321	−	0.164321i
$843$	−12.7540	−	12.7540i	−0.439271	−	0.439271i
$844$	−15.3492			−0.528340
$845$		0			0
$846$		−	4.76179i		−	0.163714i
$847$	17.1666	−	17.1666i	0.589853	−	0.589853i
$848$	3.40535	−	3.40535i	0.116940	−	0.116940i
$849$	93.9960			3.22593
$850$		0			0
$851$			6.50927i			0.223135i
$852$	−14.7475	+	14.7475i	−0.505241	+	0.505241i
$853$	19.4959	+	19.4959i	0.667527	+	0.667527i	0.957143	−	0.289616i	$-0.0935276\pi$
$853$	19.4959	+	19.4959i	0.667527	+	0.667527i	−0.289616	+	0.957143i	$0.593528\pi$
$854$	14.4913			0.495884
$855$		0			0
$856$	−2.85650			−0.0976332
$857$	−31.0425	−	31.0425i	−1.06039	−	1.06039i	−0.998055	−	0.0623378i	$-0.980144\pi$
$857$	−31.0425	−	31.0425i	−1.06039	−	1.06039i	−0.0623378	−	0.998055i	$-0.519856\pi$
$858$	7.66626	−	7.66626i	0.261722	−	0.261722i
$859$		−	33.3721i		−	1.13864i	−0.822115	−	0.569321i	$-0.807206\pi$
$859$		−	33.3721i		−	1.13864i	0.822115	−	0.569321i	$-0.192794\pi$
$860$		0			0
$861$	−10.6528			−0.363047
$862$	7.78210	−	7.78210i	0.265059	−	0.265059i
$863$	−10.3810	+	10.3810i	−0.353373	+	0.353373i	−0.861363	−	0.507990i	$-0.830389\pi$
$863$	−10.3810	+	10.3810i	−0.353373	+	0.353373i	0.507990	+	0.861363i	$0.330389\pi$
$864$		−	11.6789i		−	0.397324i
$865$		0			0
$866$	−5.23658			−0.177946
$867$	−46.8099	−	46.8099i	−1.58975	−	1.58975i
$868$	−5.19025	+	5.19025i	−0.176168	+	0.176168i
$869$	−5.76932			−0.195711
$870$		0			0
$871$	−2.10763			−0.0714144
$872$	9.41688	−	9.41688i	0.318896	−	0.318896i
$873$	55.6221	−	55.6221i	1.88252	−	1.88252i
$874$	−22.9956	+	30.5642i	−0.777838	+	1.03385i
$875$		0			0
$876$		−	4.65437i		−	0.157257i
$877$	1.64017	+	1.64017i	0.0553847	+	0.0553847i	0.734257	−	0.678872i	$-0.237531\pi$
$877$	1.64017	+	1.64017i	0.0553847	+	0.0553847i	−0.678872	+	0.734257i	$0.737531\pi$
$878$	−22.9673	−	22.9673i	−0.775110	−	0.775110i
$879$		−	26.2275i		−	0.884631i
$880$		0			0
$881$	−44.0880			−1.48536			−0.742681	−	0.669645i	$-0.766446\pi$
$881$	−44.0880			−1.48536			−0.742681	+	0.669645i	$0.766446\pi$
$882$	−7.15346	−	7.15346i	−0.240870	−	0.240870i
$883$	−15.3555	−	15.3555i	−0.516754	−	0.516754i	0.399834	−	0.916588i	$-0.369068\pi$
$883$	−15.3555	−	15.3555i	−0.516754	−	0.516754i	−0.916588	+	0.399834i	$0.869068\pi$
$884$	26.6817			0.897403
$885$		0			0
$886$			12.9421i			0.434798i
$887$	20.5729	+	20.5729i	0.690769	+	0.690769i	0.962401	−	0.271632i	$-0.0875633\pi$
$887$	20.5729	+	20.5729i	0.690769	+	0.690769i	−0.271632	+	0.962401i	$0.587563\pi$
$888$	−1.63718	+	1.63718i	−0.0549402	+	0.0549402i
$889$	−34.5311			−1.15814
$890$		0			0
$891$	13.0580			0.437461
$892$	−18.5974	−	18.5974i	−0.622686	−	0.622686i
$893$	−3.04843	+	0.430777i	−0.102012	+	0.0144154i
$894$			60.9939i			2.03994i
$895$		0			0
$896$		−	2.34509i		−	0.0783439i
$897$	−83.5935	+	83.5935i	−2.79111	+	2.79111i
$898$	0.355936	+	0.355936i	0.0118777	+	0.0118777i
$899$			17.6684i			0.589275i
$900$		0			0
$901$			29.7689i			0.991746i
$902$	−0.828176	+	0.828176i	−0.0275752	+	0.0275752i
$903$	13.9651	−	13.9651i	0.464730	−	0.464730i
$904$		−	15.3984i		−	0.512143i
$905$		0			0
$906$			2.00158i			0.0664980i
$907$	34.7376	+	34.7376i	1.15344	+	1.15344i	0.985858	+	0.167584i	$0.0535966\pi$
$907$	34.7376	+	34.7376i	1.15344	+	1.15344i	0.167584	+	0.985858i	$0.446403\pi$
$908$	−5.51878	+	5.51878i	−0.183147	+	0.183147i
$909$			11.8182i			0.391983i
$910$		0			0
$911$			30.8489i			1.02207i	0.859560	+	0.511035i	$0.170738\pi$
$911$			30.8489i			1.02207i	−0.859560	+	0.511035i	$0.829262\pi$
$912$	−13.4711	+	1.90361i	−0.446073	+	0.0630350i
$913$	−3.31645	−	3.31645i	−0.109759	−	0.109759i
$914$	11.6826			0.386427
$915$		0			0
$916$	−9.94379			−0.328552
$917$	25.6754	−	25.6754i	0.847875	−	0.847875i
$918$	51.0473	+	51.0473i	1.68481	+	1.68481i
$919$		−	31.7256i		−	1.04653i	−0.852170	−	0.523265i	$-0.824714\pi$
$919$		−	31.7256i		−	1.04653i	0.852170	−	0.523265i	$-0.175286\pi$
$920$		0			0
$921$	−11.8050			−0.388986
$922$	−12.8120	−	12.8120i	−0.421941	−	0.421941i
$923$	20.3951	+	20.3951i	0.671313	+	0.671313i
$924$	5.89021			0.193774
$925$		0			0
$926$			29.3441i			0.964308i
$927$	37.4789	+	37.4789i	1.23097	+	1.23097i
$928$	−3.99153	−	3.99153i	−0.131028	−	0.131028i
$929$		−	5.78107i		−	0.189671i	−0.995493	−	0.0948354i	$-0.969768\pi$
$929$		−	5.78107i		−	0.189671i	0.995493	−	0.0948354i	$-0.0302325\pi$
$930$		0			0
$931$	−3.93241	+	5.22670i	−0.128880	+	0.171298i
$932$	−5.11116	+	5.11116i	−0.167422	+	0.167422i
$933$	41.5166	−	41.5166i	1.35919	−	1.35919i
$934$	25.5794			0.836985
$935$		0			0
$936$	−29.1007			−0.951186
$937$	−12.5571	+	12.5571i	−0.410222	+	0.410222i	−0.881816	−	0.471594i	$-0.843679\pi$
$937$	−12.5571	+	12.5571i	−0.410222	+	0.410222i	0.471594	+	0.881816i	$0.343679\pi$
$938$	−0.809677	−	0.809677i	−0.0264369	−	0.0264369i
$939$	−64.6571			−2.11000
$940$		0			0
$941$		−	26.4197i		−	0.861258i	−0.902529	−	0.430629i	$-0.858292\pi$
$941$		−	26.4197i		−	0.861258i	0.902529	−	0.430629i	$-0.141708\pi$
$942$	39.5419	−	39.5419i	1.28834	−	1.28834i
$943$	9.03049	−	9.03049i	0.294073	−	0.294073i
$944$	−2.77684			−0.0903786
$945$		0			0
$946$		−	2.17136i		−	0.0705971i
$947$	−0.351274	+	0.351274i	−0.0114149	+	0.0114149i	−0.712791	−	0.701376i	$-0.752569\pi$
$947$	−0.351274	+	0.351274i	−0.0114149	+	0.0114149i	0.701376	+	0.712791i	$0.252569\pi$
$948$	15.8226	+	15.8226i	0.513894	+	0.513894i
$949$	−6.43677			−0.208946
$950$		0			0
$951$	4.16533			0.135070
$952$	10.2502	+	10.2502i	0.332209	+	0.332209i
$953$	37.8897	−	37.8897i	1.22737	−	1.22737i	0.262411	−	0.964956i	$-0.415482\pi$
$953$	37.8897	−	37.8897i	1.22737	−	1.22737i	0.964956	−	0.262411i	$-0.0845176\pi$
$954$		−	32.4678i		−	1.05118i
$955$		0			0
$956$	−9.30530			−0.300955
$957$	10.0256	−	10.0256i	0.324082	−	0.324082i
$958$	−1.40004	+	1.40004i	−0.0452331	+	0.0452331i
$959$			11.1832i			0.361124i
$960$		0			0
$961$	21.2031			0.683971
$962$	2.26414	+	2.26414i	0.0729989	+	0.0729989i
$963$	−13.6175	+	13.6175i	−0.438816	+	0.438816i
$964$	−8.31390			−0.267773
$965$		0			0
$966$	−64.2273			−2.06648
$967$	−29.9302	+	29.9302i	−0.962489	+	0.962489i	−0.999321	−	0.0368326i	$-0.988273\pi$
$967$	−29.9302	+	29.9302i	−0.962489	+	0.962489i	0.0368326	+	0.999321i	$0.488273\pi$
$968$	−7.32026	+	7.32026i	−0.235282	+	0.235282i
$969$	50.5604	−	67.2014i	1.62423	−	2.15882i
$970$		0			0
$971$			20.7610i			0.666252i	0.942882	+	0.333126i	$0.108103\pi$
$971$			20.7610i			0.666252i	−0.942882	+	0.333126i	$0.891897\pi$
$972$	−11.0376	−	11.0376i	−0.354030	−	0.354030i
$973$	3.41307	+	3.41307i	0.109418	+	0.109418i
$974$		−	2.61060i		−	0.0836489i
$975$		0			0
$976$	−6.17945			−0.197799
$977$	−3.40331	−	3.40331i	−0.108882	−	0.108882i	0.650567	−	0.759449i	$-0.274531\pi$
$977$	−3.40331	−	3.40331i	−0.108882	−	0.108882i	−0.759449	+	0.650567i	$0.774531\pi$
$978$	−10.8350	−	10.8350i	−0.346465	−	0.346465i
$979$	−13.4677			−0.430429
$980$		0			0
$981$		−	89.7839i		−	2.86658i
$982$	3.96554	+	3.96554i	0.126545	+	0.126545i
$983$	29.7757	−	29.7757i	0.949699	−	0.949699i	−0.0490954	−	0.998794i	$-0.515634\pi$
$983$	29.7757	−	29.7757i	0.949699	−	0.949699i	0.998794	+	0.0490954i	$0.0156339\pi$
$984$	4.54261			0.144813
$985$		0			0
$986$	34.8932			1.11122
$987$	−3.65559	−	3.65559i	−0.116359	−	0.116359i
$988$	2.63261	+	18.6299i	0.0837544	+	0.592696i
$989$			23.6767i			0.752875i
$990$		0			0
$991$		−	45.0530i		−	1.43116i	−0.698532	−	0.715578i	$-0.746163\pi$
$991$		−	45.0530i		−	1.43116i	0.698532	−	0.715578i	$-0.253837\pi$
$992$	2.21324	−	2.21324i	0.0702705	−	0.0702705i
$993$	−33.0386	−	33.0386i	−1.04845	−	1.04845i
$994$			15.6701i			0.497026i
$995$		0			0
$996$			18.1910i			0.576405i
$997$	0.131537	−	0.131537i	0.00416581	−	0.00416581i	−0.705021	−	0.709187i	$-0.749062\pi$
$997$	0.131537	−	0.131537i	0.00416581	−	0.00416581i	0.709187	+	0.705021i	$0.249062\pi$
$998$	−13.3539	+	13.3539i	−0.422711	+	0.422711i
$999$			8.66350i			0.274101i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.f.c.493.4		16
5.2	odd	4	inner	950.2.f.c.607.5		16
5.3	odd	4		190.2.f.b.37.4	✓	16
5.4	even	2		190.2.f.b.113.5	yes	16
15.8	even	4		1710.2.p.b.37.8		16
15.14	odd	2		1710.2.p.b.1063.4		16
19.18	odd	2	inner	950.2.f.c.493.5		16
95.18	even	4		190.2.f.b.37.5	yes	16
95.37	even	4	inner	950.2.f.c.607.4		16
95.94	odd	2		190.2.f.b.113.4	yes	16
285.113	odd	4		1710.2.p.b.37.4		16
285.284	even	2		1710.2.p.b.1063.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.f.b.37.4	✓	16	5.3	odd	4
190.2.f.b.37.5	yes	16	95.18	even	4
190.2.f.b.113.4	yes	16	95.94	odd	2
190.2.f.b.113.5	yes	16	5.4	even	2
950.2.f.c.493.4		16	1.1	even	1	trivial
950.2.f.c.493.5		16	19.18	odd	2	inner
950.2.f.c.607.4		16	95.37	even	4	inner
950.2.f.c.607.5		16	5.2	odd	4	inner
1710.2.p.b.37.4		16	285.113	odd	4
1710.2.p.b.37.8		16	15.8	even	4
1710.2.p.b.1063.4		16	15.14	odd	2
1710.2.p.b.1063.8		16	285.284	even	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(2.20701 - 2.20701i) q^{3} +1.00000i q^{4} -3.12119 q^{6} +(-1.65823 + 1.65823i) q^{7} +(0.707107 - 0.707107i) q^{8} -6.74181i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(2.20701 - 2.20701i) q^{3} +1.00000i q^{4} -3.12119 q^{6} +(-1.65823 + 1.65823i) q^{7} +(0.707107 - 0.707107i) q^{8} -6.74181i q^{9} -0.804733 q^{11} +(2.20701 + 2.20701i) q^{12} +(3.05219 - 3.05219i) q^{13} +2.34509 q^{14} -1.00000 q^{16} +(4.37090 - 4.37090i) q^{17} +(-4.76718 + 4.76718i) q^{18} +(3.48315 + 2.62062i) q^{19} +7.31946i q^{21} +(0.569032 + 0.569032i) q^{22} +(-6.20477 - 6.20477i) q^{23} -3.12119i q^{24} -4.31645 q^{26} +(-8.25822 - 8.25822i) q^{27} +(-1.65823 - 1.65823i) q^{28} -5.64487 q^{29} -3.13000i q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.77606 + 1.77606i) q^{33} -6.18139 q^{34} +6.74181 q^{36} +(-0.524538 - 0.524538i) q^{37} +(-0.609901 - 4.31602i) q^{38} -13.4725i q^{39} +1.45541i q^{41} +(5.17564 - 5.17564i) q^{42} +(-1.90794 - 1.90794i) q^{43} -0.804733i q^{44} +8.77487i q^{46} +(-0.499434 + 0.499434i) q^{47} +(-2.20701 + 2.20701i) q^{48} +1.50057i q^{49} -19.2933i q^{51} +(3.05219 + 3.05219i) q^{52} +(-3.40535 + 3.40535i) q^{53} +11.6789i q^{54} +2.34509i q^{56} +(13.4711 - 1.90361i) q^{57} +(3.99153 + 3.99153i) q^{58} +2.77684 q^{59} +6.17945 q^{61} +(-2.21324 + 2.21324i) q^{62} +(11.1794 + 11.1794i) q^{63} -1.00000i q^{64} +2.51172 q^{66} +(-0.345265 - 0.345265i) q^{67} +(4.37090 + 4.37090i) q^{68} -27.3880 q^{69} +6.68211i q^{71} +(-4.76718 - 4.76718i) q^{72} +(-1.05445 - 1.05445i) q^{73} +0.741809i q^{74} +(-2.62062 + 3.48315i) q^{76} +(1.33443 - 1.33443i) q^{77} +(-9.52647 + 9.52647i) q^{78} +7.16924 q^{79} -16.2266 q^{81} +(1.02913 - 1.02913i) q^{82} +(4.12119 + 4.12119i) q^{83} -7.31946 q^{84} +2.69824i q^{86} +(-12.4583 + 12.4583i) q^{87} +(-0.569032 + 0.569032i) q^{88} +16.7356 q^{89} +10.1225i q^{91} +(6.20477 - 6.20477i) q^{92} +(-6.90794 - 6.90794i) q^{93} +0.706307 q^{94} +3.12119 q^{96} +(8.25033 + 8.25033i) q^{97} +(1.06106 - 1.06106i) q^{98} +5.42535i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} - 16 q^{16} + 32 q^{17} + 8 q^{23} - 32 q^{26} - 8 q^{28} + 32 q^{36} - 8 q^{38} + 32 q^{42} - 24 q^{43} - 32 q^{47} + 48 q^{57} - 64 q^{61} + 8 q^{62} + 16 q^{63} + 16 q^{66} + 32 q^{68} - 16 q^{73} - 16 q^{76} - 72 q^{77} + 16 q^{81} - 40 q^{82} + 16 q^{83} + 8 q^{87} - 8 q^{92} - 104 q^{93}+O(q^{100}) \) 16 * q - 8 * q^7 - 16 * q^16 + 32 * q^17 + 8 * q^23 - 32 * q^26 - 8 * q^28 + 32 * q^36 - 8 * q^38 + 32 * q^42 - 24 * q^43 - 32 * q^47 + 48 * q^57 - 64 * q^61 + 8 * q^62 + 16 * q^63 + 16 * q^66 + 32 * q^68 - 16 * q^73 - 16 * q^76 - 72 * q^77 + 16 * q^81 - 40 * q^82 + 16 * q^83 + 8 * q^87 - 8 * q^92 - 104 * q^93

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