LMFDB - Embedded newform 308.2.j.c.225.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,2,Mod(113,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("308.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	308.j (of order $5$, degree $4$, 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:	$2.45939238226$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{11} + 11x^{10} - 18x^{9} + 48x^{8} - 22x^{7} + 80x^{6} + 68x^{5} + 26x^{4} - 24x^{3} + 9x^{2} + 1 $ x^12 - 4x^11 + 11x^10 - 18x^9 + 48x^8 - 22x^7 + 80x^6 + 68x^5 + 26x^4 - 24x^3 + 9x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			225.1
Root			$-0.607074 + 1.86838i$ of defining polynomial
Character	$\chi$	$=$	308.225
Dual form			308.2.j.c.141.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17753 - 0.855526i) q^{3} +(0.0324904 - 0.0999953i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(-0.272398 - 0.838356i) q^{9} +O(q^{10})$	\(q+(-1.17753 - 0.855526i) q^{3} +(0.0324904 - 0.0999953i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(-0.272398 - 0.838356i) q^{9} +(0.648271 - 3.25265i) q^{11} +(-1.20429 - 3.70642i) q^{13} +(-0.123807 + 0.0899510i) q^{15} +(-0.283358 + 0.872086i) q^{17} +(-4.89471 - 3.55622i) q^{19} +1.45551 q^{21} -8.31334 q^{23} +(4.03614 + 2.93243i) q^{25} +(-1.74581 + 5.37304i) q^{27} +(5.36281 - 3.89631i) q^{29} +(-2.83253 - 8.71764i) q^{31} +(-3.54609 + 3.27548i) q^{33} +(0.0324904 + 0.0999953i) q^{35} +(1.94300 - 1.41167i) q^{37} +(-1.75285 + 5.39472i) q^{39} +(3.10660 + 2.25707i) q^{41} +12.2277 q^{43} -0.0926819 q^{45} +(4.26001 + 3.09508i) q^{47} +(0.309017 - 0.951057i) q^{49} +(1.07975 - 0.784488i) q^{51} +(0.631250 + 1.94279i) q^{53} +(-0.304187 - 0.170504i) q^{55} +(2.72124 + 8.37510i) q^{57} +(-10.4030 + 7.55822i) q^{59} +(-1.05960 + 3.26111i) q^{61} +(0.713148 + 0.518132i) q^{63} -0.409753 q^{65} +12.1194 q^{67} +(9.78920 + 7.11227i) q^{69} +(-1.49819 + 4.61095i) q^{71} +(1.16581 - 0.847008i) q^{73} +(-2.24391 - 6.90604i) q^{75} +(1.38740 + 3.01249i) q^{77} +(-1.30702 - 4.02259i) q^{79} +(4.51307 - 3.27894i) q^{81} +(0.330694 - 1.01777i) q^{83} +(0.0779981 + 0.0566689i) q^{85} -9.64826 q^{87} -7.06635 q^{89} +(3.15287 + 2.29070i) q^{91} +(-4.12277 + 12.6886i) q^{93} +(-0.514636 + 0.373905i) q^{95} +(-1.26557 - 3.89501i) q^{97} +(-2.90347 + 0.342535i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + q^{5} - 3 q^{7} + q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 + q^5 - 3 * q^7 + q^9	$ 12 q + 6 q^{3} + q^{5} - 3 q^{7} + q^{9} + 2 q^{11} - 7 q^{13} - 4 q^{15} + 3 q^{17} - 23 q^{19} - 4 q^{21} - 38 q^{23} + 2 q^{25} - 18 q^{27} + 29 q^{29} + 9 q^{31} - 4 q^{33} + q^{35} + 3 q^{37} + 25 q^{39} - 18 q^{41} + 34 q^{43} + 14 q^{45} + 9 q^{47} - 3 q^{49} + 35 q^{51} + 13 q^{53} + 16 q^{55} + 9 q^{57} - 17 q^{59} - 19 q^{61} - 9 q^{63} + 8 q^{65} - 20 q^{67} - 14 q^{69} + 15 q^{71} + 9 q^{73} - 47 q^{75} - 8 q^{77} - 14 q^{79} - 49 q^{81} + 41 q^{83} - 66 q^{85} + 40 q^{87} + 34 q^{89} + 13 q^{91} - 40 q^{93} + 42 q^{95} - 10 q^{97} - 24 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 + q^5 - 3 * q^7 + q^9 + 2 * q^11 - 7 * q^13 - 4 * q^15 + 3 * q^17 - 23 * q^19 - 4 * q^21 - 38 * q^23 + 2 * q^25 - 18 * q^27 + 29 * q^29 + 9 * q^31 - 4 * q^33 + q^35 + 3 * q^37 + 25 * q^39 - 18 * q^41 + 34 * q^43 + 14 * q^45 + 9 * q^47 - 3 * q^49 + 35 * q^51 + 13 * q^53 + 16 * q^55 + 9 * q^57 - 17 * q^59 - 19 * q^61 - 9 * q^63 + 8 * q^65 - 20 * q^67 - 14 * q^69 + 15 * q^71 + 9 * q^73 - 47 * q^75 - 8 * q^77 - 14 * q^79 - 49 * q^81 + 41 * q^83 - 66 * q^85 + 40 * q^87 + 34 * q^89 + 13 * q^91 - 40 * q^93 + 42 * q^95 - 10 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$

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			0
$2$		0			0
$3$	−1.17753	−	0.855526i	−0.679847	−	0.493938i	0.193460	−	0.981108i	$-0.438029\pi$
$3$	−1.17753	−	0.855526i	−0.679847	−	0.493938i	−0.873307	+	0.487170i	$0.838029\pi$
$4$		0			0
$5$	0.0324904	−	0.0999953i	0.0145302	−	0.0447192i	−0.943529	−	0.331291i	$-0.892516\pi$
$5$	0.0324904	−	0.0999953i	0.0145302	−	0.0447192i	0.958059	+	0.286572i	$0.0925158\pi$
$6$		0			0
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$8$		0			0
$9$	−0.272398	−	0.838356i	−0.0907994	−	0.279452i
$10$		0			0
$11$	0.648271	−	3.25265i	0.195461	−	0.980711i
$11$	0.648271	−	3.25265i	0.195461	−	0.980711i
$12$		0			0
$13$	−1.20429	−	3.70642i	−0.334010	−	1.02798i	−0.967208	−	0.253987i	$-0.918258\pi$
$13$	−1.20429	−	3.70642i	−0.334010	−	1.02798i	0.633198	−	0.773990i	$-0.281742\pi$
$14$		0			0
$15$	−0.123807	+	0.0899510i	−0.0319668	+	0.0232253i
$16$		0			0
$17$	−0.283358	+	0.872086i	−0.0687244	+	0.211512i	−0.979520	−	0.201345i	$-0.935469\pi$
$17$	−0.283358	+	0.872086i	−0.0687244	+	0.211512i	0.910796	+	0.412857i	$0.135469\pi$
$18$		0			0
$19$	−4.89471	−	3.55622i	−1.12292	−	0.815852i	−0.138274	−	0.990394i	$-0.544156\pi$
$19$	−4.89471	−	3.55622i	−1.12292	−	0.815852i	−0.984650	+	0.174542i	$0.944156\pi$
$20$		0			0
$21$	1.45551			0.317618
$22$		0			0
$23$	−8.31334			−1.73345			−0.866725	−	0.498786i	$-0.833780\pi$
$23$	−8.31334			−1.73345			−0.866725	+	0.498786i	$0.833780\pi$
$24$		0			0
$25$	4.03614	+	2.93243i	0.807228	+	0.586486i
$26$		0			0
$27$	−1.74581	+	5.37304i	−0.335981	+	1.03404i
$28$		0			0
$29$	5.36281	−	3.89631i	0.995849	−	0.723526i	0.0346545	−	0.999399i	$-0.488967\pi$
$29$	5.36281	−	3.89631i	0.995849	−	0.723526i	0.961194	+	0.275873i	$0.0889669\pi$
$30$		0			0
$31$	−2.83253	−	8.71764i	−0.508738	−	1.56573i	−0.794395	−	0.607402i	$-0.792212\pi$
$31$	−2.83253	−	8.71764i	−0.508738	−	1.56573i	0.285657	−	0.958332i	$-0.407788\pi$
$32$		0			0
$33$	−3.54609	+	3.27548i	−0.617294	+	0.570188i
$34$		0			0
$35$	0.0324904	+	0.0999953i	0.00549188	+	0.0169023i
$36$		0			0
$37$	1.94300	−	1.41167i	0.319428	−	0.232078i	−0.416504	−	0.909134i	$-0.636745\pi$
$37$	1.94300	−	1.41167i	0.319428	−	0.232078i	0.735931	+	0.677056i	$0.236745\pi$
$38$		0			0
$39$	−1.75285	+	5.39472i	−0.280681	+	0.863847i
$40$		0			0
$41$	3.10660	+	2.25707i	0.485169	+	0.352496i	0.803323	−	0.595543i	$-0.203063\pi$
$41$	3.10660	+	2.25707i	0.485169	+	0.352496i	−0.318154	+	0.948039i	$0.603063\pi$
$42$		0			0
$43$	12.2277			1.86471			0.932354	−	0.361547i	$-0.117751\pi$
$43$	12.2277			1.86471			0.932354	+	0.361547i	$0.117751\pi$
$44$		0			0
$45$	−0.0926819			−0.0138162
$46$		0			0
$47$	4.26001	+	3.09508i	0.621387	+	0.451464i	0.853406	−	0.521247i	$-0.174533\pi$
$47$	4.26001	+	3.09508i	0.621387	+	0.451464i	−0.232019	+	0.972711i	$0.574533\pi$
$48$		0			0
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$		0			0
$51$	1.07975	−	0.784488i	0.151196	−	0.109850i
$52$		0			0
$53$	0.631250	+	1.94279i	0.0867089	+	0.266863i	0.985004	−	0.172529i	$-0.0551940\pi$
$53$	0.631250	+	1.94279i	0.0867089	+	0.266863i	−0.898295	+	0.439392i	$0.855194\pi$
$54$		0			0
$55$	−0.304187	−	0.170504i	−0.0410166	−	0.0229908i
$56$		0			0
$57$	2.72124	+	8.37510i	0.360436	+	1.10931i
$58$		0			0
$59$	−10.4030	+	7.55822i	−1.35435	+	0.983996i	−0.355573	+	0.934649i	$0.615714\pi$
$59$	−10.4030	+	7.55822i	−1.35435	+	0.983996i	−0.998782	+	0.0493474i	$0.984286\pi$
$60$		0			0
$61$	−1.05960	+	3.26111i	−0.135668	+	0.417543i	−0.995693	−	0.0927084i	$-0.970448\pi$
$61$	−1.05960	+	3.26111i	−0.135668	+	0.417543i	0.860025	+	0.510251i	$0.170448\pi$
$62$		0			0
$63$	0.713148	+	0.518132i	0.0898482	+	0.0652785i
$64$		0			0
$65$	−0.409753			−0.0508236
$66$		0			0
$67$	12.1194			1.48062			0.740310	−	0.672266i	$-0.234679\pi$
$67$	12.1194			1.48062			0.740310	+	0.672266i	$0.234679\pi$
$68$		0			0
$69$	9.78920	+	7.11227i	1.17848	+	0.856217i
$70$		0			0
$71$	−1.49819	+	4.61095i	−0.177802	+	0.547219i	−0.999750	−	0.0223436i	$-0.992887\pi$
$71$	−1.49819	+	4.61095i	−0.177802	+	0.547219i	0.821948	+	0.569562i	$0.192887\pi$
$72$		0			0
$73$	1.16581	−	0.847008i	0.136447	−	0.0991348i	−0.517468	−	0.855703i	$-0.673125\pi$
$73$	1.16581	−	0.847008i	0.136447	−	0.0991348i	0.653915	+	0.756568i	$0.273125\pi$
$74$		0			0
$75$	−2.24391	−	6.90604i	−0.259104	−	0.797441i
$76$		0			0
$77$	1.38740	+	3.01249i	0.158109	+	0.343306i
$78$		0			0
$79$	−1.30702	−	4.02259i	−0.147051	−	0.452577i	0.850218	−	0.526431i	$-0.176470\pi$
$79$	−1.30702	−	4.02259i	−0.147051	−	0.452577i	−0.997269	+	0.0738539i	$0.976470\pi$
$80$		0			0
$81$	4.51307	−	3.27894i	0.501452	−	0.364326i
$82$		0			0
$83$	0.330694	−	1.01777i	0.0362984	−	0.111715i	−0.931266	−	0.364341i	$-0.881294\pi$
$83$	0.330694	−	1.01777i	0.0362984	−	0.111715i	0.967564	+	0.252626i	$0.0812942\pi$
$84$		0			0
$85$	0.0779981	+	0.0566689i	0.00846008	+	0.00614661i
$86$		0			0
$87$	−9.64826			−1.03440
$88$		0			0
$89$	−7.06635			−0.749032			−0.374516	−	0.927220i	$-0.622191\pi$
$89$	−7.06635			−0.749032			−0.374516	+	0.927220i	$0.622191\pi$
$90$		0			0
$91$	3.15287	+	2.29070i	0.330511	+	0.240130i
$92$		0			0
$93$	−4.12277	+	12.6886i	−0.427511	+	1.31574i
$94$		0			0
$95$	−0.514636	+	0.373905i	−0.0528005	+	0.0383618i
$96$		0			0
$97$	−1.26557	−	3.89501i	−0.128499	−	0.395479i	0.866023	−	0.500003i	$-0.166668\pi$
$97$	−1.26557	−	3.89501i	−0.128499	−	0.395479i	−0.994522	+	0.104525i	$0.966668\pi$
$98$		0			0
$99$	−2.90347	+	0.342535i	−0.291809	+	0.0344261i
$100$		0			0
$101$	−3.93478	−	12.1100i	−0.391525	−	1.20499i	−0.931635	−	0.363396i	$-0.881617\pi$
$101$	−3.93478	−	12.1100i	−0.391525	−	1.20499i	0.540109	−	0.841595i	$-0.318383\pi$
$102$		0			0
$103$	3.90370	−	2.83620i	0.384643	−	0.279459i	−0.378614	−	0.925555i	$-0.623599\pi$
$103$	3.90370	−	2.83620i	0.384643	−	0.279459i	0.763257	+	0.646095i	$0.223599\pi$
$104$		0			0
$105$	0.0472900	−	0.145544i	0.00461504	−	0.0142036i
$106$		0			0
$107$	−3.12240	−	2.26855i	−0.301854	−	0.219309i	0.426540	−	0.904469i	$-0.359732\pi$
$107$	−3.12240	−	2.26855i	−0.301854	−	0.219309i	−0.728393	+	0.685159i	$0.759732\pi$
$108$		0			0
$109$	8.24788			0.790004			0.395002	−	0.918680i	$-0.370744\pi$
$109$	8.24788			0.790004			0.395002	+	0.918680i	$0.370744\pi$
$110$		0			0
$111$	−3.49567			−0.331794
$112$		0			0
$113$	4.94040	+	3.58941i	0.464754	+	0.337663i	0.795393	−	0.606094i	$-0.207264\pi$
$113$	4.94040	+	3.58941i	0.464754	+	0.337663i	−0.330640	+	0.943757i	$0.607264\pi$
$114$		0			0
$115$	−0.270104	+	0.831294i	−0.0251873	+	0.0775186i
$116$		0			0
$117$	−2.77925	+	2.01925i	−0.256942	+	0.186679i
$118$		0			0
$119$	−0.283358	−	0.872086i	−0.0259754	−	0.0799440i
$120$		0			0
$121$	−10.1595	−	4.21720i	−0.923590	−	0.383382i
$122$		0			0
$123$	−1.72713	−	5.31555i	−0.155730	−	0.479287i
$124$		0			0
$125$	0.849670	−	0.617321i	0.0759968	−	0.0552149i
$126$		0			0
$127$	−1.10061	+	3.38731i	−0.0976629	+	0.300576i	−0.987939	−	0.154847i	$-0.950512\pi$
$127$	−1.10061	+	3.38731i	−0.0976629	+	0.300576i	0.890276	+	0.455422i	$0.150512\pi$
$128$		0			0
$129$	−14.3985	−	10.4611i	−1.26772	−	0.921050i
$130$		0			0
$131$	18.5868			1.62394			0.811970	−	0.583699i	$-0.198395\pi$
$131$	18.5868			1.62394			0.811970	+	0.583699i	$0.198395\pi$
$132$		0			0
$133$	6.05020			0.524619
$134$		0			0
$135$	0.480557	+	0.349145i	0.0413597	+	0.0300496i
$136$		0			0
$137$	−6.83359	+	21.0316i	−0.583833	+	1.79685i	0.0200727	+	0.999799i	$0.493610\pi$
$137$	−6.83359	+	21.0316i	−0.583833	+	1.79685i	−0.603906	+	0.797056i	$0.706390\pi$
$138$		0			0
$139$	16.7245	−	12.1510i	1.41855	−	1.03064i	0.426542	−	0.904468i	$-0.359732\pi$
$139$	16.7245	−	12.1510i	1.41855	−	1.03064i	0.992009	−	0.126170i	$-0.0402684\pi$
$140$		0			0
$141$	−2.36837	−	7.28910i	−0.199453	−	0.613853i
$142$		0			0
$143$	−12.8364	+	1.51437i	−1.07343	+	0.126638i
$144$		0			0
$145$	−0.215372	−	0.662848i	−0.0178857	−	0.0550465i
$146$		0			0
$147$	−1.17753	+	0.855526i	−0.0971210	+	0.0705626i
$148$		0			0
$149$	3.73788	−	11.5040i	0.306219	−	0.942446i	−0.673000	−	0.739643i	$-0.734995\pi$
$149$	3.73788	−	11.5040i	0.306219	−	0.942446i	0.979219	−	0.202804i	$-0.0650054\pi$
$150$		0			0
$151$	−14.4462	−	10.4958i	−1.17562	−	0.854136i	−0.183946	−	0.982936i	$-0.558887\pi$
$151$	−14.4462	−	10.4958i	−1.17562	−	0.854136i	−0.991671	+	0.128801i	$0.958887\pi$
$152$		0			0
$153$	0.808305			0.0653476
$154$		0			0
$155$	−0.963753			−0.0774105
$156$		0			0
$157$	0.926333	+	0.673021i	0.0739295	+	0.0537129i	0.624136	−	0.781316i	$-0.285451\pi$
$157$	0.926333	+	0.673021i	0.0739295	+	0.0537129i	−0.550207	+	0.835029i	$0.685451\pi$
$158$		0			0
$159$	0.918789	−	2.82774i	0.0728647	−	0.224255i
$160$		0			0
$161$	6.72563	−	4.88646i	0.530054	−	0.385107i
$162$		0			0
$163$	−2.84637	−	8.76024i	−0.222945	−	0.686155i	−0.998494	−	0.0548668i	$-0.982527\pi$
$163$	−2.84637	−	8.76024i	−0.222945	−	0.686155i	0.775548	−	0.631288i	$-0.217473\pi$
$164$		0			0
$165$	0.212319	+	0.461014i	0.0165290	+	0.0358899i
$166$		0			0
$167$	5.46281	+	16.8128i	0.422725	+	1.30101i	0.905156	+	0.425080i	$0.139754\pi$
$167$	5.46281	+	16.8128i	0.422725	+	1.30101i	−0.482430	+	0.875934i	$0.660246\pi$
$168$		0			0
$169$	−1.77003	+	1.28601i	−0.136156	+	0.0989235i
$170$		0			0
$171$	−1.64806	+	5.07222i	−0.126031	+	0.387882i
$172$		0			0
$173$	−14.8968	−	10.8232i	−1.13259	−	0.822872i	−0.146517	−	0.989208i	$-0.546806\pi$
$173$	−14.8968	−	10.8232i	−1.13259	−	0.822872i	−0.986069	+	0.166337i	$0.946806\pi$
$174$		0			0
$175$	−4.98895			−0.377129
$176$		0			0
$177$	18.7161			1.40679
$178$		0			0
$179$	6.36956	+	4.62775i	0.476083	+	0.345895i	0.799807	−	0.600257i	$-0.204935\pi$
$179$	6.36956	+	4.62775i	0.476083	+	0.345895i	−0.323724	+	0.946151i	$0.604935\pi$
$180$		0			0
$181$	4.75363	−	14.6302i	0.353335	−	1.08745i	−0.603634	−	0.797262i	$-0.706281\pi$
$181$	4.75363	−	14.6302i	0.353335	−	1.08745i	0.956969	−	0.290191i	$-0.0937189\pi$
$182$		0			0
$183$	4.03768	−	2.93354i	0.298474	−	0.216854i
$184$		0			0
$185$	−0.0780317	−	0.240157i	−0.00573701	−	0.0176567i
$186$		0			0
$187$	2.65290	+	1.48701i	0.193999	+	0.108741i
$188$		0			0
$189$	−1.74581	−	5.37304i	−0.126989	−	0.390831i
$190$		0			0
$191$	−6.25765	+	4.54645i	−0.452787	+	0.328969i	−0.790695	−	0.612210i	$-0.790281\pi$
$191$	−6.25765	+	4.54645i	−0.452787	+	0.328969i	0.337908	+	0.941179i	$0.390281\pi$
$192$		0			0
$193$	3.65232	−	11.2407i	0.262900	−	0.809122i	−0.729270	−	0.684226i	$-0.760140\pi$
$193$	3.65232	−	11.2407i	0.262900	−	0.809122i	0.992170	−	0.124896i	$-0.0398598\pi$
$194$		0			0
$195$	0.482496	+	0.350554i	0.0345522	+	0.0251037i
$196$		0			0
$197$	−19.8737			−1.41594			−0.707972	−	0.706240i	$-0.750390\pi$
$197$	−19.8737			−1.41594			−0.707972	+	0.706240i	$0.750390\pi$
$198$		0			0
$199$	−9.16741			−0.649860			−0.324930	−	0.945738i	$-0.605341\pi$
$199$	−9.16741			−0.649860			−0.324930	+	0.945738i	$0.605341\pi$
$200$		0			0
$201$	−14.2709	−	10.3684i	−1.00659	−	0.731334i
$202$		0			0
$203$	−2.04841	+	6.30436i	−0.143770	+	0.442479i
$204$		0			0
$205$	0.326631	−	0.237312i	0.0228129	−	0.0165746i
$206$		0			0
$207$	2.26454	+	6.96954i	0.157396	+	0.484416i
$208$		0			0
$209$	−14.7402	+	13.6154i	−1.01960	+	0.941797i
$210$		0			0
$211$	−2.52678	−	7.77662i	−0.173950	−	0.535364i	0.825634	−	0.564207i	$-0.190818\pi$
$211$	−2.52678	−	7.77662i	−0.173950	−	0.535364i	−0.999584	+	0.0288424i	$0.990818\pi$
$212$		0			0
$213$	5.70894	−	4.14779i	0.391170	−	0.284202i
$214$		0			0
$215$	0.397283	−	1.22271i	0.0270945	−	0.0833883i
$216$		0			0
$217$	7.41567	+	5.38780i	0.503408	+	0.365747i
$218$		0			0
$219$	−2.09741			−0.141730
$220$		0			0
$221$	3.57357			0.240384
$222$		0			0
$223$	−3.20511	−	2.32865i	−0.214630	−	0.155938i	0.475276	−	0.879837i	$-0.342348\pi$
$223$	−3.20511	−	2.32865i	−0.214630	−	0.155938i	−0.689906	+	0.723899i	$0.742348\pi$
$224$		0			0
$225$	1.35898	−	4.18251i	0.0905987	−	0.278834i
$226$		0			0
$227$	10.0820	−	7.32497i	0.669163	−	0.486175i	−0.200582	−	0.979677i	$-0.564283\pi$
$227$	10.0820	−	7.32497i	0.669163	−	0.486175i	0.869745	+	0.493502i	$0.164283\pi$
$228$		0			0
$229$	7.96266	+	24.5066i	0.526188	+	1.61944i	0.761955	+	0.647630i	$0.224240\pi$
$229$	7.96266	+	24.5066i	0.526188	+	1.61944i	−0.235768	+	0.971809i	$0.575760\pi$
$230$		0			0
$231$	0.943563	−	4.73426i	0.0620819	−	0.311491i
$232$		0			0
$233$	−4.10021	−	12.6191i	−0.268614	−	0.826708i	−0.990839	−	0.135050i	$-0.956881\pi$
$233$	−4.10021	−	12.6191i	−0.268614	−	0.826708i	0.722225	−	0.691658i	$-0.243119\pi$
$234$		0			0
$235$	0.447903	−	0.325421i	0.0292180	−	0.0212281i
$236$		0			0
$237$	−1.90238	+	5.85491i	−0.123573	+	0.380317i
$238$		0			0
$239$	6.82334	+	4.95745i	0.441365	+	0.320670i	0.786177	−	0.618001i	$-0.212057\pi$
$239$	6.82334	+	4.95745i	0.441365	+	0.320670i	−0.344812	+	0.938672i	$0.612057\pi$
$240$		0			0
$241$	−3.46659			−0.223303			−0.111651	−	0.993747i	$-0.535614\pi$
$241$	−3.46659			−0.223303			−0.111651	+	0.993747i	$0.535614\pi$
$242$		0			0
$243$	8.82916			0.566391
$244$		0			0
$245$	−0.0850610	−	0.0618005i	−0.00543435	−	0.00394829i
$246$		0			0
$247$	−7.28619	+	22.4246i	−0.463609	+	1.42684i
$248$		0			0
$249$	−1.26013	+	0.915540i	−0.0798576	+	0.0580200i
$250$		0			0
$251$	−2.56765	−	7.90242i	−0.162069	−	0.498796i	0.836740	−	0.547601i	$-0.184459\pi$
$251$	−2.56765	−	7.90242i	−0.162069	−	0.498796i	−0.998808	+	0.0488046i	$0.984459\pi$
$252$		0			0
$253$	−5.38930	+	27.0404i	−0.338822	+	1.70002i
$254$		0			0
$255$	−0.0433634	−	0.133459i	−0.00271552	−	0.00835751i
$256$		0			0
$257$	3.22913	−	2.34610i	0.201427	−	0.146346i	−0.482499	−	0.875896i	$-0.660271\pi$
$257$	3.22913	−	2.34610i	0.201427	−	0.146346i	0.683927	+	0.729551i	$0.260271\pi$
$258$		0			0
$259$	−0.742161	+	2.28414i	−0.0461156	+	0.141929i
$260$		0			0
$261$	−4.72731	−	3.43459i	−0.292613	−	0.212596i
$262$		0			0
$263$	5.37057			0.331163			0.165582	−	0.986196i	$-0.447050\pi$
$263$	5.37057			0.331163			0.165582	+	0.986196i	$0.447050\pi$
$264$		0			0
$265$	0.214779			0.0131938
$266$		0			0
$267$	8.32084	+	6.04544i	0.509227	+	0.369975i
$268$		0			0
$269$	−5.54944	+	17.0794i	−0.338355	+	1.04135i	0.626691	+	0.779268i	$0.284409\pi$
$269$	−5.54944	+	17.0794i	−0.338355	+	1.04135i	−0.965046	+	0.262082i	$0.915591\pi$
$270$		0			0
$271$	13.8740	−	10.0800i	0.842785	−	0.612319i	−0.0803625	−	0.996766i	$-0.525608\pi$
$271$	13.8740	−	10.0800i	0.842785	−	0.612319i	0.923147	+	0.384447i	$0.125608\pi$
$272$		0			0
$273$	−1.75285	−	5.39472i	−0.106087	−	0.326504i
$274$		0			0
$275$	12.1547	−	11.2272i	0.732955	−	0.677023i
$276$		0			0
$277$	−3.69611	−	11.3755i	−0.222078	−	0.683486i	−0.998575	−	0.0533648i	$-0.983005\pi$
$277$	−3.69611	−	11.3755i	−0.222078	−	0.683486i	0.776497	−	0.630121i	$-0.216995\pi$
$278$		0			0
$279$	−6.53691	+	4.74934i	−0.391354	+	0.284336i
$280$		0			0
$281$	5.39578	−	16.6065i	0.321885	−	0.990660i	−0.650942	−	0.759127i	$-0.725626\pi$
$281$	5.39578	−	16.6065i	0.321885	−	0.990660i	0.972827	−	0.231533i	$-0.0743741\pi$
$282$		0			0
$283$	20.5595	+	14.9374i	1.22214	+	0.887935i	0.996276	−	0.0862243i	$-0.0274802\pi$
$283$	20.5595	+	14.9374i	1.22214	+	0.887935i	0.225862	+	0.974159i	$0.427480\pi$
$284$		0			0
$285$	0.925885			0.0548447
$286$		0			0
$287$	−3.83997			−0.226666
$288$		0			0
$289$	13.0730	+	9.49812i	0.769003	+	0.558713i
$290$		0			0
$291$	−1.84204	+	5.66922i	−0.107982	+	0.332336i
$292$		0			0
$293$	7.40319	−	5.37873i	0.432499	−	0.314229i	−0.350148	−	0.936694i	$-0.613869\pi$
$293$	7.40319	−	5.37873i	0.432499	−	0.314229i	0.782647	+	0.622465i	$0.213869\pi$
$294$		0			0
$295$	0.417788	+	1.28582i	0.0243246	+	0.0748633i
$296$		0			0
$297$	16.3449	+	9.16169i	0.948426	+	0.531615i
$298$		0			0
$299$	10.0117	+	30.8127i	0.578990	+	1.78195i
$300$		0			0
$301$	−9.89242	+	7.18727i	−0.570190	+	0.414267i
$302$		0			0
$303$	−5.72710	+	17.6262i	−0.329013	+	1.01260i
$304$		0			0
$305$	0.291669	+	0.211910i	0.0167009	+	0.0121339i
$306$		0			0
$307$	6.56076			0.374443			0.187221	−	0.982318i	$-0.440052\pi$
$307$	6.56076			0.374443			0.187221	+	0.982318i	$0.440052\pi$
$308$		0			0
$309$	−7.02316			−0.399534
$310$		0			0
$311$	16.0457	+	11.6579i	0.909870	+	0.661059i	0.940982	−	0.338457i	$-0.109905\pi$
$311$	16.0457	+	11.6579i	0.909870	+	0.661059i	−0.0311121	+	0.999516i	$0.509905\pi$
$312$		0			0
$313$	−1.96332	+	6.04247i	−0.110973	+	0.341540i	−0.991086	−	0.133224i	$-0.957467\pi$
$313$	−1.96332	+	6.04247i	−0.110973	+	0.341540i	0.880113	+	0.474765i	$0.157467\pi$
$314$		0			0
$315$	0.0749813	−	0.0544771i	0.00422472	−	0.00306944i
$316$		0			0
$317$	5.22697	+	16.0869i	0.293576	+	0.903533i	0.983696	+	0.179838i	$0.0575575\pi$
$317$	5.22697	+	16.0869i	0.293576	+	0.903533i	−0.690121	+	0.723694i	$0.742442\pi$
$318$		0			0
$319$	−9.19678	−	19.9692i	−0.514921	−	1.11806i
$320$		0			0
$321$	1.73591	+	5.34258i	0.0968890	+	0.298194i
$322$		0			0
$323$	4.48828	−	3.26093i	0.249735	−	0.181443i
$324$		0			0
$325$	6.00814	−	18.4911i	0.333271	−	1.02570i
$326$		0			0
$327$	−9.71213	−	7.05627i	−0.537082	−	0.390213i
$328$		0			0
$329$	−5.26567			−0.290306
$330$		0			0
$331$	24.4054			1.34144			0.670721	−	0.741710i	$-0.265985\pi$
$331$	24.4054			1.34144			0.670721	+	0.741710i	$0.265985\pi$
$332$		0			0
$333$	−1.71276	−	1.24439i	−0.0938585	−	0.0681922i
$334$		0			0
$335$	0.393764	−	1.21188i	0.0215136	−	0.0662122i
$336$		0			0
$337$	−0.680304	+	0.494270i	−0.0370585	+	0.0269246i	−0.606160	−	0.795342i	$-0.707291\pi$
$337$	−0.680304	+	0.494270i	−0.0370585	+	0.0269246i	0.569102	+	0.822267i	$0.307291\pi$
$338$		0			0
$339$	−2.74664	−	8.45327i	−0.149177	−	0.459119i
$340$		0			0
$341$	−30.1917	+	3.56185i	−1.63497	+	0.192885i
$342$		0			0
$343$	0.309017	+	0.951057i	0.0166853	+	0.0513522i
$344$		0			0
$345$	1.02925	−	0.747793i	0.0554129	−	0.0402598i
$346$		0			0
$347$	−6.60583	+	20.3306i	−0.354619	+	1.09141i	0.601611	+	0.798790i	$0.294526\pi$
$347$	−6.60583	+	20.3306i	−0.354619	+	1.09141i	−0.956230	+	0.292617i	$0.905474\pi$
$348$		0			0
$349$	−16.5258	−	12.0067i	−0.884608	−	0.642705i	0.0498588	−	0.998756i	$-0.484123\pi$
$349$	−16.5258	−	12.0067i	−0.884608	−	0.642705i	−0.934466	+	0.356051i	$0.884123\pi$
$350$		0			0
$351$	22.0172			1.17519
$352$		0			0
$353$	26.1056			1.38946			0.694730	−	0.719271i	$-0.255524\pi$
$353$	26.1056			1.38946			0.694730	+	0.719271i	$0.255524\pi$
$354$		0			0
$355$	0.412396	+	0.299623i	0.0218877	+	0.0159023i
$356$		0			0
$357$	−0.412430	+	1.26933i	−0.0218281	+	0.0671799i
$358$		0			0
$359$	−13.4560	+	9.77638i	−0.710182	+	0.515977i	−0.883232	−	0.468936i	$-0.844638\pi$
$359$	−13.4560	+	9.77638i	−0.710182	+	0.515977i	0.173050	+	0.984913i	$0.444638\pi$
$360$		0			0
$361$	5.44021	+	16.7432i	0.286327	+	0.881223i
$362$		0			0
$363$	8.35518	+	13.6576i	0.438533	+	0.716837i
$364$		0			0
$365$	−0.0468192	−	0.144095i	−0.00245063	−	0.00754227i
$366$		0			0
$367$	−1.21757	+	0.884615i	−0.0635566	+	0.0461766i	−0.619110	−	0.785304i	$-0.712506\pi$
$367$	−1.21757	+	0.884615i	−0.0635566	+	0.0461766i	0.555553	+	0.831481i	$0.312506\pi$
$368$		0			0
$369$	1.04600	−	3.21926i	0.0544526	−	0.167588i
$370$		0			0
$371$	−1.65263	−	1.20071i	−0.0858005	−	0.0623377i
$372$		0			0
$373$	−13.0946			−0.678010			−0.339005	−	0.940785i	$-0.610090\pi$
$373$	−13.0946			−0.678010			−0.339005	+	0.940785i	$0.610090\pi$
$374$		0			0
$375$	−1.52865			−0.0789390
$376$		0			0
$377$	−20.8997	−	15.1846i	−1.07639	−	0.782044i
$378$		0			0
$379$	5.48527	−	16.8819i	0.281759	−	0.867167i	−0.705592	−	0.708619i	$-0.749319\pi$
$379$	5.48527	−	16.8819i	0.281759	−	0.867167i	0.987351	−	0.158548i	$-0.0506813\pi$
$380$		0			0
$381$	4.19393	−	3.04707i	0.214862	−	0.156106i
$382$		0			0
$383$	−1.75764	−	5.40945i	−0.0898110	−	0.276410i	0.896056	−	0.443942i	$-0.146420\pi$
$383$	−1.75764	−	5.40945i	−0.0898110	−	0.276410i	−0.985867	+	0.167532i	$0.946420\pi$
$384$		0			0
$385$	0.346312	−	0.0408560i	0.0176497	−	0.00208221i
$386$		0			0
$387$	−3.33081	−	10.2512i	−0.169314	−	0.521096i
$388$		0			0
$389$	18.2685	−	13.2728i	0.926249	−	0.672959i	−0.0188226	−	0.999823i	$-0.505992\pi$
$389$	18.2685	−	13.2728i	0.926249	−	0.672959i	0.945072	+	0.326864i	$0.105992\pi$
$390$		0			0
$391$	2.35565	−	7.24995i	0.119130	−	0.366646i
$392$		0			0
$393$	−21.8866	−	15.9015i	−1.10403	−	0.802125i
$394$		0			0
$395$	−0.444706			−0.0223756
$396$		0			0
$397$	−35.1870			−1.76599			−0.882993	−	0.469386i	$-0.844475\pi$
$397$	−35.1870			−1.76599			−0.882993	+	0.469386i	$0.844475\pi$
$398$		0			0
$399$	−7.12429	−	5.17610i	−0.356661	−	0.259129i
$400$		0			0
$401$	9.74002	−	29.9767i	0.486393	−	1.49696i	−0.343560	−	0.939131i	$-0.611633\pi$
$401$	9.74002	−	29.9767i	0.486393	−	1.49696i	0.829953	−	0.557834i	$-0.188367\pi$
$402$		0			0
$403$	−28.9001	+	20.9971i	−1.43961	+	1.04594i
$404$		0			0
$405$	−0.181247	−	0.557820i	−0.00900621	−	0.0277183i
$406$		0			0
$407$	−3.33209	−	7.23506i	−0.165166	−	0.358629i
$408$		0			0
$409$	3.85148	+	11.8536i	0.190444	+	0.586125i	1.00000		0.000917558i	$-0.000292068\pi$
$409$	3.85148	+	11.8536i	0.190444	+	0.586125i	−0.809556	+	0.587043i	$0.800292\pi$
$410$		0			0
$411$	26.0399	−	18.9191i	1.28445	−	0.933209i
$412$		0			0
$413$	3.97359	−	12.2295i	0.195528	−	0.601772i
$414$		0			0
$415$	−0.0910280	−	0.0661357i	−0.00446839	−	0.00324647i
$416$		0			0
$417$	−30.0891			−1.47347
$418$		0			0
$419$	−17.8358			−0.871334			−0.435667	−	0.900108i	$-0.643488\pi$
$419$	−17.8358			−0.871334			−0.435667	+	0.900108i	$0.643488\pi$
$420$		0			0
$421$	−10.3518	−	7.52102i	−0.504516	−	0.366552i	0.306223	−	0.951960i	$-0.400935\pi$
$421$	−10.3518	−	7.52102i	−0.504516	−	0.366552i	−0.810739	+	0.585407i	$0.800935\pi$
$422$		0			0
$423$	1.43436	−	4.41450i	0.0697409	−	0.214640i
$424$		0			0
$425$	−3.70100	+	2.68894i	−0.179525	+	0.130433i
$426$		0			0
$427$	−1.05960	−	3.26111i	−0.0512776	−	0.157816i
$428$		0			0
$429$	16.4108	+	9.19866i	0.792323	+	0.444116i
$430$		0			0
$431$	−8.46864	−	26.0638i	−0.407920	−	1.25545i	−0.918432	−	0.395578i	$-0.870544\pi$
$431$	−8.46864	−	26.0638i	−0.407920	−	1.25545i	0.510513	−	0.859870i	$-0.329456\pi$
$432$		0			0
$433$	−19.0410	+	13.8341i	−0.915053	+	0.664825i	−0.942288	−	0.334804i	$-0.891330\pi$
$433$	−19.0410	+	13.8341i	−0.915053	+	0.664825i	0.0272348	+	0.999629i	$0.491330\pi$
$434$		0			0
$435$	−0.313476	+	0.964780i	−0.0150300	+	0.0462577i
$436$		0			0
$437$	40.6914	+	29.5640i	1.94653	+	1.41424i
$438$		0			0
$439$	36.4914			1.74164			0.870821	−	0.491601i	$-0.163588\pi$
$439$	36.4914			1.74164			0.870821	+	0.491601i	$0.163588\pi$
$440$		0			0
$441$	−0.881499			−0.0419762
$442$		0			0
$443$	−10.0738	−	7.31907i	−0.478622	−	0.347739i	0.322170	−	0.946682i	$-0.395588\pi$
$443$	−10.0738	−	7.31907i	−0.478622	−	0.347739i	−0.800792	+	0.598942i	$0.795588\pi$
$444$		0			0
$445$	−0.229589	+	0.706602i	−0.0108836	+	0.0334961i
$446$		0			0
$447$	−14.2435	+	10.3485i	−0.673692	+	0.489466i
$448$		0			0
$449$	−3.27476	−	10.0787i	−0.154545	−	0.475641i	0.843569	−	0.537020i	$-0.180450\pi$
$449$	−3.27476	−	10.0787i	−0.154545	−	0.475641i	−0.998115	+	0.0613790i	$0.980450\pi$
$450$		0			0
$451$	9.35540	−	8.64148i	0.440528	−	0.406912i
$452$		0			0
$453$	8.03144	+	24.7182i	0.377350	+	1.16136i
$454$		0			0
$455$	0.331497	−	0.240847i	0.0155408	−	0.0112911i
$456$		0			0
$457$	−5.32271	+	16.3816i	−0.248986	+	0.766300i	0.745969	+	0.665980i	$0.231987\pi$
$457$	−5.32271	+	16.3816i	−0.248986	+	0.766300i	−0.994955	+	0.100320i	$0.968013\pi$
$458$		0			0
$459$	−4.19107	−	3.04499i	−0.195622	−	0.142128i
$460$		0			0
$461$	−16.6269			−0.774394			−0.387197	−	0.921997i	$-0.626557\pi$
$461$	−16.6269			−0.774394			−0.387197	+	0.921997i	$0.626557\pi$
$462$		0			0
$463$	−25.3558			−1.17839			−0.589193	−	0.807993i	$-0.700554\pi$
$463$	−25.3558			−1.17839			−0.589193	+	0.807993i	$0.700554\pi$
$464$		0			0
$465$	1.13485	+	0.824515i	0.0526273	+	0.0382360i
$466$		0			0
$467$	10.3315	−	31.7972i	0.478086	−	1.47140i	−0.363665	−	0.931530i	$-0.618475\pi$
$467$	10.3315	−	31.7972i	0.478086	−	1.47140i	0.841750	−	0.539867i	$-0.181525\pi$
$468$		0			0
$469$	−9.80479	+	7.12360i	−0.452743	+	0.328937i
$470$		0			0
$471$	−0.514999	−	1.58500i	−0.0237299	−	0.0730331i
$472$		0			0
$473$	7.92687	−	39.7725i	0.364478	−	1.82874i
$474$		0			0
$475$	−9.32740	−	28.7068i	−0.427970	−	1.31716i
$476$		0			0
$477$	1.45680	−	1.05842i	0.0667021	−	0.0484619i
$478$		0			0
$479$	3.19586	−	9.83586i	0.146023	−	0.449412i	−0.851118	−	0.524974i	$-0.824075\pi$
$479$	3.19586	−	9.83586i	0.146023	−	0.449412i	0.997141	+	0.0755621i	$0.0240751\pi$
$480$		0			0
$481$	−7.57220	−	5.50153i	−0.345263	−	0.250848i
$482$		0			0
$483$	−12.1001			−0.550575
$484$		0			0
$485$	−0.430602			−0.0195526
$486$		0			0
$487$	−6.88305	−	5.00083i	−0.311901	−	0.226609i	0.420811	−	0.907148i	$-0.361746\pi$
$487$	−6.88305	−	5.00083i	−0.311901	−	0.226609i	−0.732712	+	0.680539i	$0.761746\pi$
$488$		0			0
$489$	−4.14292	+	12.7506i	−0.187349	+	0.576602i
$490$		0			0
$491$	−0.393026	+	0.285550i	−0.0177370	+	0.0128867i	−0.596618	−	0.802525i	$-0.703489\pi$
$491$	−0.393026	+	0.285550i	−0.0177370	+	0.0128867i	0.578881	+	0.815412i	$0.303489\pi$
$492$		0			0
$493$	1.87832	+	5.78088i	0.0845954	+	0.260358i
$494$		0			0
$495$	−0.0600830	+	0.301462i	−0.00270053	+	0.0135497i
$496$		0			0
$497$	−1.49819	−	4.61095i	−0.0672029	−	0.206829i
$498$		0			0
$499$	−12.5142	+	9.09213i	−0.560214	+	0.407020i	−0.831537	−	0.555469i	$-0.812539\pi$
$499$	−12.5142	+	9.09213i	−0.560214	+	0.407020i	0.271323	+	0.962488i	$0.412539\pi$
$500$		0			0
$501$	7.95116	−	24.4712i	0.355232	−	1.09329i
$502$		0			0
$503$	29.6452	+	21.5385i	1.32182	+	0.960356i	0.999908	+	0.0135850i	$0.00432436\pi$
$503$	29.6452	+	21.5385i	1.32182	+	0.960356i	0.321909	+	0.946771i	$0.395676\pi$
$504$		0			0
$505$	−1.33879			−0.0595752
$506$		0			0
$507$	3.18448			0.141428
$508$		0			0
$509$	9.26788	+	6.73351i	0.410792	+	0.298458i	0.773922	−	0.633281i	$-0.218292\pi$
$509$	9.26788	+	6.73351i	0.410792	+	0.298458i	−0.363131	+	0.931738i	$0.618292\pi$
$510$		0			0
$511$	−0.445298	+	1.37049i	−0.0196988	+	0.0606268i
$512$		0			0
$513$	27.6529	−	20.0910i	1.22091	−	0.887040i
$514$		0			0
$515$	−0.156774	−	0.482501i	−0.00690828	−	0.0212615i
$516$		0			0
$517$	12.8289	−	11.8499i	0.564213	−	0.521158i
$518$		0			0
$519$	8.28196	+	25.4892i	0.363538	+	1.11885i
$520$		0			0
$521$	−5.41110	+	3.93140i	−0.237065	+	0.172238i	−0.699975	−	0.714168i	$-0.746805\pi$
$521$	−5.41110	+	3.93140i	−0.237065	+	0.172238i	0.462910	+	0.886405i	$0.346805\pi$
$522$		0			0
$523$	−8.82855	+	27.1715i	−0.386045	+	1.18813i	0.549674	+	0.835380i	$0.314752\pi$
$523$	−8.82855	+	27.1715i	−0.386045	+	1.18813i	−0.935719	+	0.352746i	$0.885248\pi$
$524$		0			0
$525$	5.87463	+	4.26817i	0.256390	+	0.186278i
$526$		0			0
$527$	8.40515			0.366134
$528$		0			0
$529$	46.1116			2.00485
$530$		0			0
$531$	9.17023	+	6.66256i	0.397954	+	0.289131i
$532$		0			0
$533$	4.62443	−	14.2325i	0.200306	−	0.616479i
$534$		0			0
$535$	−0.328293	+	0.238519i	−0.0141933	+	0.0103121i
$536$		0			0
$537$	−3.54118	−	10.8986i	−0.152813	−	0.470311i
$538$		0			0
$539$	−2.89313	−	1.62167i	−0.124616	−	0.0698502i
$540$		0			0
$541$	−0.407735	−	1.25488i	−0.0175299	−	0.0539515i	0.941909	−	0.335868i	$-0.109030\pi$
$541$	−0.407735	−	1.25488i	−0.0175299	−	0.0539515i	−0.959439	+	0.281917i	$0.909030\pi$
$542$		0			0
$543$	−18.1140	+	13.1606i	−0.777348	+	0.564776i
$544$		0			0
$545$	0.267977	−	0.824749i	0.0114789	−	0.0353284i
$546$		0			0
$547$	−9.94180	−	7.22314i	−0.425081	−	0.308839i	0.354598	−	0.935019i	$-0.384618\pi$
$547$	−9.94180	−	7.22314i	−0.425081	−	0.308839i	−0.779679	+	0.626180i	$0.784618\pi$
$548$		0			0
$549$	3.02261			0.129002
$550$		0			0
$551$	−40.1055			−1.70855
$552$		0			0
$553$	3.42182	+	2.48610i	0.145511	+	0.105720i
$554$		0			0
$555$	−0.113576	+	0.349550i	−0.00482102	+	0.0148376i
$556$		0			0
$557$	−18.8829	+	13.7192i	−0.800093	+	0.581302i	−0.910941	−	0.412536i	$-0.864643\pi$
$557$	−18.8829	+	13.7192i	−0.800093	+	0.581302i	0.110848	+	0.993837i	$0.464643\pi$
$558$		0			0
$559$	−14.7257	−	45.3210i	−0.622831	−	1.91688i
$560$		0			0
$561$	−1.85169	−	4.02063i	−0.0781785	−	0.169751i
$562$		0			0
$563$	−0.0160521	−	0.0494032i	−0.000676514	−	0.00208210i	0.950718	−	0.310058i	$-0.100348\pi$
$563$	−0.0160521	−	0.0494032i	−0.000676514	−	0.00208210i	−0.951394	+	0.307976i	$0.900348\pi$
$564$		0			0
$565$	0.519440	−	0.377395i	0.0218530	−	0.0158771i
$566$		0			0
$567$	−1.72384	+	5.30543i	−0.0723944	+	0.222807i
$568$		0			0
$569$	29.6167	+	21.5178i	1.24160	+	0.902073i	0.997704	−	0.0677290i	$-0.0215753\pi$
$569$	29.6167	+	21.5178i	1.24160	+	0.902073i	0.243893	+	0.969802i	$0.421575\pi$
$570$		0			0
$571$	−28.4510			−1.19064			−0.595318	−	0.803490i	$-0.702974\pi$
$571$	−28.4510			−1.19064			−0.595318	+	0.803490i	$0.702974\pi$
$572$		0			0
$573$	11.2582			0.470317
$574$		0			0
$575$	−33.5538	−	24.3783i	−1.39929	−	1.01664i
$576$		0			0
$577$	2.45288	−	7.54920i	0.102115	−	0.314277i	−0.886928	−	0.461908i	$-0.847165\pi$
$577$	2.45288	−	7.54920i	0.102115	−	0.314277i	0.989042	+	0.147631i	$0.0471649\pi$
$578$		0			0
$579$	−13.9174	+	10.1116i	−0.578388	+	0.420223i
$580$		0			0
$581$	0.330694	+	1.01777i	0.0137195	+	0.0422243i
$582$		0			0
$583$	6.72844	−	0.793783i	0.278663	−	0.0328751i
$584$		0			0
$585$	0.111616	+	0.343518i	0.00461475	+	0.0142027i
$586$		0			0
$587$	2.11504	−	1.53667i	0.0872971	−	0.0634251i	−0.543281	−	0.839551i	$-0.682818\pi$
$587$	2.11504	−	1.53667i	0.0872971	−	0.0634251i	0.630578	+	0.776126i	$0.282818\pi$
$588$		0			0
$589$	−17.1374	+	52.7434i	−0.706133	+	2.17326i
$590$		0			0
$591$	23.4019	+	17.0025i	0.962626	+	0.699389i
$592$		0			0
$593$	40.6475			1.66919			0.834596	−	0.550862i	$-0.185701\pi$
$593$	40.6475			1.66919			0.834596	+	0.550862i	$0.185701\pi$
$594$		0			0
$595$	−0.0964109			−0.00395246
$596$		0			0
$597$	10.7949	+	7.84295i	0.441806	+	0.320991i
$598$		0			0
$599$	−13.9502	+	42.9342i	−0.569988	+	1.75424i	0.0826565	+	0.996578i	$0.473660\pi$
$599$	−13.9502	+	42.9342i	−0.569988	+	1.75424i	−0.652644	+	0.757664i	$0.726340\pi$
$600$		0			0
$601$	−7.98164	+	5.79900i	−0.325578	+	0.236546i	−0.738552	−	0.674197i	$-0.764490\pi$
$601$	−7.98164	+	5.79900i	−0.325578	+	0.236546i	0.412974	+	0.910743i	$0.364490\pi$
$602$		0			0
$603$	−3.30130	−	10.1604i	−0.134439	−	0.413762i
$604$		0			0
$605$	−0.751786	+	0.878882i	−0.0305645	+	0.0357316i
$606$		0			0
$607$	7.58694	+	23.3502i	0.307944	+	0.947755i	0.978562	+	0.205952i	$0.0660291\pi$
$607$	7.58694	+	23.3502i	0.307944	+	0.947755i	−0.670618	+	0.741803i	$0.733971\pi$
$608$		0			0
$609$	7.80561	−	5.67110i	0.316299	−	0.229805i
$610$		0			0
$611$	6.34139	−	19.5168i	0.256545	−	0.789565i
$612$		0			0
$613$	−5.39914	−	3.92271i	−0.218069	−	0.158437i	0.473388	−	0.880854i	$-0.343031\pi$
$613$	−5.39914	−	3.92271i	−0.218069	−	0.158437i	−0.691457	+	0.722417i	$0.743031\pi$
$614$		0			0
$615$	−0.587644			−0.0236961
$616$		0			0
$617$	−23.0664			−0.928620			−0.464310	−	0.885673i	$-0.653698\pi$
$617$	−23.0664			−0.928620			−0.464310	+	0.885673i	$0.653698\pi$
$618$		0			0
$619$	8.11784	+	5.89796i	0.326284	+	0.237059i	0.738852	−	0.673868i	$-0.235368\pi$
$619$	8.11784	+	5.89796i	0.326284	+	0.237059i	−0.412568	+	0.910927i	$0.635368\pi$
$620$		0			0
$621$	14.5135	−	44.6679i	0.582406	−	1.79246i
$622$		0			0
$623$	5.71680	−	4.15350i	0.229039	−	0.166406i
$624$		0			0
$625$	7.67422	+	23.6188i	0.306969	+	0.944753i
$626$		0			0
$627$	29.0054	−	3.42189i	1.15836	−	0.136657i
$628$		0			0
$629$	0.680536	+	2.09448i	0.0271348	+	0.0835122i
$630$		0			0
$631$	−14.4567	+	10.5034i	−0.575511	+	0.418133i	−0.837103	−	0.547046i	$-0.815752\pi$
$631$	−14.4567	+	10.5034i	−0.575511	+	0.418133i	0.261592	+	0.965178i	$0.415752\pi$
$632$		0			0
$633$	−3.67774	+	11.3189i	−0.146177	+	0.449887i
$634$		0			0
$635$	0.302956	+	0.220111i	0.0120225	+	0.00873482i
$636$		0			0
$637$	−3.89716			−0.154411
$638$		0			0
$639$	4.27372			0.169066
$640$		0			0
$641$	−12.5144	−	9.09224i	−0.494289	−	0.359122i	0.312542	−	0.949904i	$-0.398819\pi$
$641$	−12.5144	−	9.09224i	−0.494289	−	0.359122i	−0.806831	+	0.590782i	$0.798819\pi$
$642$		0			0
$643$	13.3822	−	41.1861i	0.527742	−	1.62422i	−0.231088	−	0.972933i	$-0.574229\pi$
$643$	13.3822	−	41.1861i	0.527742	−	1.62422i	0.758830	−	0.651289i	$-0.225771\pi$
$644$		0			0
$645$	−1.51387	+	1.09989i	−0.0596088	+	0.0433083i
$646$		0			0
$647$	1.13312	+	3.48738i	0.0445474	+	0.137103i	0.970856	−	0.239662i	$-0.0770365\pi$
$647$	1.13312	+	3.48738i	0.0445474	+	0.137103i	−0.926309	+	0.376765i	$0.877037\pi$
$648$		0			0
$649$	17.8403	+	38.7371i	0.700293	+	1.52056i
$650$		0			0
$651$	−4.12277	−	12.6886i	−0.161584	−	0.497305i
$652$		0			0
$653$	13.2390	−	9.61872i	0.518084	−	0.376410i	−0.297798	−	0.954629i	$-0.596252\pi$
$653$	13.2390	−	9.61872i	0.518084	−	0.376410i	0.815881	+	0.578219i	$0.196252\pi$
$654$		0			0
$655$	0.603894	−	1.85860i	0.0235961	−	0.0726213i
$656$		0			0
$657$	−1.02766	−	0.746637i	−0.0400928	−	0.0291291i
$658$		0			0
$659$	11.0455			0.430271			0.215135	−	0.976584i	$-0.430981\pi$
$659$	11.0455			0.430271			0.215135	+	0.976584i	$0.430981\pi$
$660$		0			0
$661$	13.4724			0.524015			0.262008	−	0.965066i	$-0.415615\pi$
$661$	13.4724			0.524015			0.262008	+	0.965066i	$0.415615\pi$
$662$		0			0
$663$	−4.20798	−	3.05728i	−0.163424	−	0.118735i
$664$		0			0
$665$	0.196573	−	0.604991i	0.00762279	−	0.0234605i
$666$		0			0
$667$	−44.5828	+	32.3913i	−1.72625	+	1.25420i
$668$		0			0
$669$	1.78189	+	5.48410i	0.0688919	+	0.212028i
$670$		0			0
$671$	9.92036	+	5.56060i	0.382971	+	0.214664i
$672$		0			0
$673$	12.2313	+	37.6441i	0.471483	+	1.45108i	0.850643	+	0.525744i	$0.176213\pi$
$673$	12.2313	+	37.6441i	0.471483	+	1.45108i	−0.379160	+	0.925331i	$0.623787\pi$
$674$		0			0
$675$	−22.8024	+	16.5669i	−0.877664	+	0.637660i
$676$		0			0
$677$	9.92059	−	30.5324i	0.381279	−	1.17346i	−0.557864	−	0.829932i	$-0.688379\pi$
$677$	9.92059	−	30.5324i	0.381279	−	1.17346i	0.939144	−	0.343525i	$-0.111621\pi$
$678$		0			0
$679$	3.31330	+	2.40725i	0.127153	+	0.0923818i
$680$		0			0
$681$	−18.1385			−0.695069
$682$		0			0
$683$	−43.5528			−1.66650			−0.833250	−	0.552896i	$-0.813523\pi$
$683$	−43.5528			−1.66650			−0.833250	+	0.552896i	$0.813523\pi$
$684$		0			0
$685$	1.88104	+	1.36665i	0.0718708	+	0.0522172i
$686$		0			0
$687$	11.5897	−	35.6695i	0.442175	−	1.36088i
$688$		0			0
$689$	6.44059	−	4.67936i	0.245367	−	0.178269i
$690$		0			0
$691$	14.5713	+	44.8458i	0.554317	+	1.70601i	0.697739	+	0.716352i	$0.254190\pi$
$691$	14.5713	+	44.8458i	0.554317	+	1.70601i	−0.143422	+	0.989662i	$0.545810\pi$
$692$		0			0
$693$	2.14762	−	1.98373i	0.0815812	−	0.0753557i
$694$		0			0
$695$	−0.671661	−	2.06716i	−0.0254776	−	0.0784118i
$696$		0			0
$697$	−2.84864	+	2.06966i	−0.107900	+	0.0783940i
$698$		0			0
$699$	−5.96788	+	18.3673i	−0.225726	+	0.694714i
$700$		0			0
$701$	17.5645	+	12.7613i	0.663400	+	0.481989i	0.867810	−	0.496897i	$-0.165527\pi$
$701$	17.5645	+	12.7613i	0.663400	+	0.481989i	−0.204409	+	0.978886i	$0.565527\pi$
$702$		0			0
$703$	−14.5307			−0.548034
$704$		0			0
$705$	−0.805825			−0.0303491
$706$		0			0
$707$	10.3014	+	7.48440i	0.387424	+	0.281480i
$708$		0			0
$709$	−4.44353	+	13.6758i	−0.166880	+	0.513605i	−0.999170	−	0.0407364i	$-0.987030\pi$
$709$	−4.44353	+	13.6758i	−0.166880	+	0.513605i	0.832290	+	0.554341i	$0.187030\pi$
$710$		0			0
$711$	−3.01633	+	2.19150i	−0.113121	+	0.0821875i
$712$		0			0
$713$	23.5478	+	72.4727i	0.881872	+	2.71412i
$714$		0			0
$715$	−0.265631	+	1.33278i	−0.00993403	+	0.0498432i
$716$		0			0
$717$	−3.79346	−	11.6751i	−0.141669	−	0.436014i
$718$		0			0
$719$	38.6060	−	28.0489i	1.43976	−	1.04605i	0.451669	−	0.892186i	$-0.350829\pi$
$719$	38.6060	−	28.0489i	1.43976	−	1.04605i	0.988092	−	0.153862i	$-0.0491711\pi$
$720$		0			0
$721$	−1.49108	+	4.58907i	−0.0555307	+	0.170906i
$722$		0			0
$723$	4.08202	+	2.96576i	0.151812	+	0.110298i
$724$		0			0
$725$	33.0707			1.22821
$726$		0			0
$727$	−21.3223			−0.790802			−0.395401	−	0.918509i	$-0.629394\pi$
$727$	−21.3223			−0.790802			−0.395401	+	0.918509i	$0.629394\pi$
$728$		0			0
$729$	−23.9358	−	17.3904i	−0.886511	−	0.644088i
$730$		0			0
$731$	−3.46482	+	10.6636i	−0.128151	+	0.394408i
$732$		0			0
$733$	−15.1817	+	11.0302i	−0.560750	+	0.407409i	−0.831733	−	0.555175i	$-0.812651\pi$
$733$	−15.1817	+	11.0302i	−0.560750	+	0.407409i	0.270983	+	0.962584i	$0.412651\pi$
$734$		0			0
$735$	0.0472900	+	0.145544i	0.00174432	+	0.00536846i
$736$		0			0
$737$	7.85665	−	39.4202i	0.289404	−	1.45206i
$738$		0			0
$739$	−6.89886	−	21.2325i	−0.253779	−	0.781051i	−0.994068	−	0.108762i	$-0.965311\pi$
$739$	−6.89886	−	21.2325i	−0.253779	−	0.781051i	0.740289	−	0.672289i	$-0.234689\pi$
$740$		0			0
$741$	27.7645	−	20.1721i	1.01995	−	0.741041i
$742$		0			0
$743$	5.76414	−	17.7402i	0.211466	−	0.650825i	−0.787920	−	0.615778i	$-0.788842\pi$
$743$	5.76414	−	17.7402i	0.211466	−	0.650825i	0.999386	−	0.0350469i	$-0.0111581\pi$
$744$		0			0
$745$	−1.02890	−	0.747541i	−0.0376961	−	0.0273878i
$746$		0			0
$747$	−0.943335			−0.0345148
$748$		0			0
$749$	3.85950			0.141023
$750$		0			0
$751$	9.71473	+	7.05816i	0.354495	+	0.257556i	0.750752	−	0.660584i	$-0.229691\pi$
$751$	9.71473	+	7.05816i	0.354495	+	0.257556i	−0.396257	+	0.918140i	$0.629691\pi$
$752$		0			0
$753$	−3.73724	+	11.5020i	−0.136192	+	0.419157i
$754$		0			0
$755$	−1.51889	+	1.10354i	−0.0552782	+	0.0401620i
$756$		0			0
$757$	7.08162	+	21.7950i	0.257386	+	0.792153i	0.993350	+	0.115132i	$0.0367292\pi$
$757$	7.08162	+	21.7950i	0.257386	+	0.792153i	−0.735964	+	0.677020i	$0.763271\pi$
$758$		0			0
$759$	29.4798	−	27.2302i	1.07005	−	0.988393i
$760$		0			0
$761$	10.4522	+	32.1687i	0.378893	+	1.16611i	0.940814	+	0.338922i	$0.110062\pi$
$761$	10.4522	+	32.1687i	0.378893	+	1.16611i	−0.561921	+	0.827191i	$0.689938\pi$
$762$		0			0
$763$	−6.67268	+	4.84798i	−0.241567	+	0.175509i
$764$		0			0
$765$	0.0262622	−	0.0808267i	0.000949511	−	0.00292229i
$766$		0			0
$767$	40.5422	+	29.4556i	1.46389	+	1.06358i
$768$		0			0
$769$	3.77778			0.136230			0.0681152	−	0.997677i	$-0.478301\pi$
$769$	3.77778			0.136230			0.0681152	+	0.997677i	$0.478301\pi$
$770$		0			0
$771$	−5.80954			−0.209225
$772$		0			0
$773$	−20.7042	−	15.0425i	−0.744680	−	0.541042i	0.149493	−	0.988763i	$-0.452236\pi$
$773$	−20.7042	−	15.0425i	−0.744680	−	0.541042i	−0.894173	+	0.447721i	$0.852236\pi$
$774$		0			0
$775$	14.1313	−	43.4918i	0.507613	−	1.56227i
$776$		0			0
$777$	2.82805	−	2.05470i	0.101456	−	0.0737120i
$778$		0			0
$779$	−7.17925	−	22.0955i	−0.257223	−	0.791652i
$780$		0			0
$781$	14.0266	+	7.86222i	0.501910	+	0.281332i
$782$		0			0
$783$	11.5726	+	35.6168i	0.413571	+	1.27284i
$784$		0			0
$785$	0.0973958	−	0.0707622i	0.00347621	−	0.00252561i
$786$		0			0
$787$	−12.4631	+	38.3574i	−0.444260	+	1.36729i	0.439033	+	0.898471i	$0.355321\pi$
$787$	−12.4631	+	38.3574i	−0.444260	+	1.36729i	−0.883293	+	0.468821i	$0.844679\pi$
$788$		0			0
$789$	−6.32400	−	4.59466i	−0.225141	−	0.163574i
$790$		0			0
$791$	−6.10667			−0.217128
$792$		0			0
$793$	13.3631			0.474539
$794$		0			0
$795$	−0.252909	−	0.183749i	−0.00896976	−	0.00651691i
$796$		0			0
$797$	4.01950	−	12.3707i	0.142378	−	0.438194i	−0.854286	−	0.519802i	$-0.826006\pi$
$797$	4.01950	−	12.3707i	0.142378	−	0.438194i	0.996665	+	0.0816080i	$0.0260056\pi$
$798$		0			0
$799$	−3.90629	+	2.83808i	−0.138195	+	0.100404i
$800$		0			0
$801$	1.92486	+	5.92412i	0.0680117	+	0.209318i
$802$		0			0
$803$	−1.99926	−	4.34105i	−0.0705525	−	0.153192i
$804$		0			0
$805$	−0.270104	−	0.831294i	−0.00951991	−	0.0292993i
$806$		0			0
$807$	21.1465	−	15.3638i	0.744392	−	0.540832i
$808$		0			0
$809$	−6.75454	+	20.7883i	−0.237477	+	0.730879i	0.759306	+	0.650733i	$0.225538\pi$
$809$	−6.75454	+	20.7883i	−0.237477	+	0.730879i	−0.996783	+	0.0801453i	$0.974462\pi$
$810$		0			0
$811$	2.78292	+	2.02191i	0.0977214	+	0.0709988i	0.635573	−	0.772041i	$-0.280764\pi$
$811$	2.78292	+	2.02191i	0.0977214	+	0.0709988i	−0.537852	+	0.843040i	$0.680764\pi$
$812$		0			0
$813$	−24.9608			−0.875412
$814$		0			0
$815$	−0.968462			−0.0339238
$816$		0			0
$817$	−59.8511	−	43.4844i	−2.09393	−	1.52133i
$818$		0			0
$819$	1.06158	−	3.26721i	0.0370946	−	0.114166i
$820$		0			0
$821$	−6.07683	+	4.41508i	−0.212083	+	0.154087i	−0.688756	−	0.724994i	$-0.741843\pi$
$821$	−6.07683	+	4.41508i	−0.212083	+	0.154087i	0.476673	+	0.879081i	$0.341843\pi$
$822$		0			0
$823$	−11.8666	−	36.5217i	−0.413645	−	1.27307i	−0.913458	−	0.406934i	$-0.866598\pi$
$823$	−11.8666	−	36.5217i	−0.413645	−	1.27307i	0.499813	−	0.866133i	$-0.333402\pi$
$824$		0			0
$825$	−23.9176	+	2.82167i	−0.832705	+	0.0982379i
$826$		0			0
$827$	3.12451	+	9.61627i	0.108650	+	0.334390i	0.990570	−	0.137009i	$-0.0437490\pi$
$827$	3.12451	+	9.61627i	0.108650	+	0.334390i	−0.881920	+	0.471400i	$0.843749\pi$
$828$		0			0
$829$	−7.38608	+	5.36630i	−0.256529	+	0.186379i	−0.708616	−	0.705595i	$-0.750680\pi$
$829$	−7.38608	+	5.36630i	−0.256529	+	0.186379i	0.452086	+	0.891974i	$0.350680\pi$
$830$		0			0
$831$	−5.37972	+	16.5571i	−0.186620	+	0.574358i
$832$		0			0
$833$	0.741841	+	0.538979i	0.0257033	+	0.0186745i
$834$		0			0
$835$	1.85869			0.0643226
$836$		0			0
$837$	51.7853			1.78996
$838$		0			0
$839$	−4.23578	−	3.07748i	−0.146235	−	0.106246i	0.512262	−	0.858829i	$-0.328808\pi$
$839$	−4.23578	−	3.07748i	−0.146235	−	0.106246i	−0.658497	+	0.752583i	$0.728808\pi$
$840$		0			0
$841$	4.61700	−	14.2097i	0.159207	−	0.489989i
$842$		0			0
$843$	−20.5610	+	14.9384i	−0.708157	+	0.514506i
$844$		0			0
$845$	0.0710852	+	0.218778i	0.00244541	+	0.00752619i
$846$		0			0
$847$	10.6980	−	2.55981i	0.367588	−	0.0879561i
$848$		0			0
$849$	−11.4302	−	35.1784i	−0.392282	−	1.20732i
$850$		0			0
$851$	−16.1528	+	11.7357i	−0.553712	+	0.402295i
$852$		0			0
$853$	14.9299	−	45.9495i	0.511190	−	1.57328i	−0.278920	−	0.960314i	$-0.589976\pi$
$853$	14.9299	−	45.9495i	0.511190	−	1.57328i	0.790109	−	0.612966i	$-0.210024\pi$
$854$		0			0
$855$	0.453651	+	0.329597i	0.0155146	+	0.0112720i
$856$		0			0
$857$	−37.9386			−1.29596			−0.647980	−	0.761658i	$-0.724386\pi$
$857$	−37.9386			−1.29596			−0.647980	+	0.761658i	$0.724386\pi$
$858$		0			0
$859$	−17.5932			−0.600271			−0.300135	−	0.953897i	$-0.597032\pi$
$859$	−17.5932			−0.600271			−0.300135	+	0.953897i	$0.597032\pi$
$860$		0			0
$861$	4.52167	+	3.28519i	0.154098	+	0.111959i
$862$		0			0
$863$	−14.5326	+	44.7269i	−0.494697	+	1.52252i	0.322732	+	0.946490i	$0.395399\pi$
$863$	−14.5326	+	44.7269i	−0.494697	+	1.52252i	−0.817429	+	0.576030i	$0.804601\pi$
$864$		0			0
$865$	−1.56627	+	1.13796i	−0.0532548	+	0.0386919i
$866$		0			0
$867$	−7.26801	−	22.3686i	−0.246835	−	0.759679i
$868$		0			0
$869$	−13.9314	+	1.64355i	−0.472590	+	0.0557536i
$870$		0			0
$871$	−14.5953	−	44.9196i	−0.494541	−	1.52204i
$872$		0			0
$873$	−2.92067	+	2.12199i	−0.0988497	+	0.0718185i
$874$		0			0
$875$	−0.324545	+	0.998847i	−0.0109716	+	0.0337672i
$876$		0			0
$877$	16.1302	+	11.7193i	0.544677	+	0.395731i	0.825819	−	0.563935i	$-0.190713\pi$
$877$	16.1302	+	11.7193i	0.544677	+	0.395731i	−0.281142	+	0.959666i	$0.590713\pi$
$878$		0			0
$879$	−13.3191			−0.449243
$880$		0			0
$881$	−30.8943			−1.04086			−0.520428	−	0.853906i	$-0.674228\pi$
$881$	−30.8943			−1.04086			−0.520428	+	0.853906i	$0.674228\pi$
$882$		0			0
$883$	29.5828	+	21.4931i	0.995540	+	0.723302i	0.961127	−	0.276106i	$-0.0890441\pi$
$883$	29.5828	+	21.4931i	0.995540	+	0.723302i	0.0344123	+	0.999408i	$0.489044\pi$
$884$		0			0
$885$	0.608094	−	1.87152i	0.0204408	−	0.0629104i
$886$		0			0
$887$	3.86898	−	2.81098i	0.129908	−	0.0943834i	−0.520934	−	0.853597i	$-0.674416\pi$
$887$	3.86898	−	2.81098i	0.129908	−	0.0943834i	0.650842	+	0.759214i	$0.274416\pi$
$888$		0			0
$889$	−1.10061	−	3.38731i	−0.0369131	−	0.113607i
$890$		0			0
$891$	−7.73955	−	16.8051i	−0.259285	−	0.562991i
$892$		0			0
$893$	−9.84476	−	30.2991i	−0.329442	−	1.01392i
$894$		0			0
$895$	0.669703	−	0.486568i	0.0223857	−	0.0162642i
$896$		0			0
$897$	14.5721	−	44.8482i	0.486547	−	1.49744i
$898$		0			0
$899$	−49.1569	−	35.7146i	−1.63948	−	1.19115i
$900$		0			0
$901$	−1.87315			−0.0624036
$902$		0			0
$903$	17.7975			0.592264
$904$		0			0
$905$	−1.30850	−	0.950682i	−0.0434960	−	0.0316017i
$906$		0			0
$907$	11.5153	−	35.4404i	0.382359	−	1.17678i	−0.556020	−	0.831169i	$-0.687672\pi$
$907$	11.5153	−	35.4404i	0.382359	−	1.17678i	0.938378	−	0.345610i	$-0.112328\pi$
$908$		0			0
$909$	−9.08067	+	6.59750i	−0.301187	+	0.218825i
$910$		0			0
$911$	10.3650	+	31.9001i	0.343407	+	1.05690i	0.962431	+	0.271526i	$0.0875281\pi$
$911$	10.3650	+	31.9001i	0.343407	+	1.05690i	−0.619025	+	0.785372i	$0.712472\pi$
$912$		0			0
$913$	−3.09608	−	1.73543i	−0.102465	−	0.0574342i
$914$		0			0
$915$	−0.162155	−	0.499061i	−0.00536067	−	0.0164984i
$916$		0			0
$917$	−15.0371	+	10.9251i	−0.496568	+	0.360778i
$918$		0			0
$919$	8.68613	−	26.7331i	0.286529	−	0.881845i	−0.699407	−	0.714723i	$-0.746553\pi$
$919$	8.68613	−	26.7331i	0.286529	−	0.881845i	0.985936	−	0.167122i	$-0.0534473\pi$
$920$		0			0
$921$	−7.72550	−	5.61290i	−0.254564	−	0.184951i
$922$		0			0
$923$	18.8944			0.621916
$924$		0			0
$925$	11.9819			0.393961
$926$		0			0
$927$	−3.44111	−	2.50011i	−0.113021	−	0.0821144i
$928$		0			0
$929$	0.686465	−	2.11272i	0.0225222	−	0.0693161i	−0.939164	−	0.343470i	$-0.888398\pi$
$929$	0.686465	−	2.11272i	0.0225222	−	0.0693161i	0.961686	+	0.274154i	$0.0883977\pi$
$930$		0			0
$931$	−4.89471	+	3.55622i	−0.160418	+	0.116550i
$932$		0			0
$933$	−8.92069	−	27.4551i	−0.292050	−	0.898838i
$934$		0			0
$935$	0.234888	−	0.216964i	0.00768166	−	0.00709547i
$936$		0			0
$937$	10.7332	+	33.0335i	0.350639	+	1.07916i	0.958495	+	0.285109i	$0.0920299\pi$
$937$	10.7332	+	33.0335i	0.350639	+	1.07916i	−0.607856	+	0.794048i	$0.707970\pi$
$938$		0			0
$939$	7.48135	−	5.43552i	0.244145	−	0.177381i
$940$		0			0
$941$	9.83539	−	30.2702i	0.320625	−	0.986781i	−0.652752	−	0.757571i	$-0.726386\pi$
$941$	9.83539	−	30.2702i	0.320625	−	0.986781i	0.973377	−	0.229210i	$-0.0736142\pi$
$942$		0			0
$943$	−25.8262	−	18.7638i	−0.841017	−	0.611034i
$944$		0			0
$945$	−0.594001			−0.0193228
$946$		0			0
$947$	0.593379			0.0192822			0.00964111	−	0.999954i	$-0.496931\pi$
$947$	0.593379			0.0192822			0.00964111	+	0.999954i	$0.496931\pi$
$948$		0			0
$949$	−4.54334	−	3.30093i	−0.147483	−	0.107153i
$950$		0			0
$951$	7.60789	−	23.4147i	0.246703	−	0.759272i
$952$		0			0
$953$	22.1287	−	16.0774i	0.716819	−	0.520799i	−0.168547	−	0.985694i	$-0.553908\pi$
$953$	22.1287	−	16.0774i	0.716819	−	0.520799i	0.885366	+	0.464894i	$0.153908\pi$
$954$		0			0
$955$	0.251309	+	0.773451i	0.00813218	+	0.0250283i
$956$		0			0
$957$	−6.25469	+	31.3824i	−0.202185	+	1.01445i
$958$		0			0
$959$	−6.83359	−	21.0316i	−0.220668	−	0.679147i
$960$		0			0
$961$	−42.8944	+	31.1646i	−1.38369	+	1.00531i
$962$		0			0
$963$	−1.05132	+	3.23563i	−0.0338783	+	0.104267i
$964$		0			0
$965$	−1.00535	−	0.730429i	−0.0323634	−	0.0235134i
$966$		0			0
$967$	11.7936			0.379255			0.189628	−	0.981856i	$-0.439272\pi$
$967$	11.7936			0.379255			0.189628	+	0.981856i	$0.439272\pi$
$968$		0			0
$969$	−8.07490			−0.259403
$970$		0			0
$971$	−4.90546	−	3.56403i	−0.157424	−	0.114375i	0.506285	−	0.862366i	$-0.331018\pi$
$971$	−4.90546	−	3.56403i	−0.157424	−	0.114375i	−0.663709	+	0.747991i	$0.731018\pi$
$972$		0			0
$973$	−6.38818	+	19.6608i	−0.204796	+	0.630296i
$974$		0			0
$975$	−22.8944	+	16.6338i	−0.733208	+	0.532707i
$976$		0			0
$977$	8.22051	+	25.3001i	0.262997	+	0.809423i	0.992148	+	0.125070i	$0.0399154\pi$
$977$	8.22051	+	25.3001i	0.262997	+	0.809423i	−0.729150	+	0.684353i	$0.760085\pi$
$978$		0			0
$979$	−4.58091	+	22.9844i	−0.146407	+	0.734584i
$980$		0			0
$981$	−2.24671	−	6.91466i	−0.0717319	−	0.220768i
$982$		0			0
$983$	37.3153	−	27.1111i	1.19017	−	0.864711i	0.196890	−	0.980426i	$-0.436916\pi$
$983$	37.3153	−	27.1111i	1.19017	−	0.864711i	0.993282	+	0.115715i	$0.0369159\pi$
$984$		0			0
$985$	−0.645706	+	1.98728i	−0.0205739	+	0.0633199i
$986$		0			0
$987$	6.20048	+	4.50491i	0.197363	+	0.143393i
$988$		0			0
$989$	−101.653			−3.23238
$990$		0			0
$991$	28.7166			0.912214			0.456107	−	0.889925i	$-0.349243\pi$
$991$	28.7166			0.912214			0.456107	+	0.889925i	$0.349243\pi$
$992$		0			0
$993$	−28.7381	−	20.8794i	−0.911975	−	0.662589i
$994$		0			0
$995$	−0.297853	+	0.916697i	−0.00944258	+	0.0290613i
$996$		0			0
$997$	−16.5530	+	12.0265i	−0.524239	+	0.380882i	−0.818198	−	0.574936i	$-0.805027\pi$
$997$	−16.5530	+	12.0265i	−0.524239	+	0.380882i	0.293960	+	0.955818i	$0.405027\pi$
$998$		0			0
$999$	4.19288	+	12.9043i	0.132657	+	0.408275i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.2.j.c.225.1	yes	12
11.3	even	5		3388.2.a.u.1.5		6
11.8	odd	10		3388.2.a.t.1.5		6
11.9	even	5	inner	308.2.j.c.141.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.j.c.141.1	✓	12	11.9	even	5	inner
308.2.j.c.225.1	yes	12	1.1	even	1	trivial
3388.2.a.t.1.5		6	11.8	odd	10
3388.2.a.u.1.5		6	11.3	even	5

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:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17753 - 0.855526i) q^{3} +(0.0324904 - 0.0999953i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(-0.272398 - 0.838356i) q^{9} +O(q^{10})\)	\(q+(-1.17753 - 0.855526i) q^{3} +(0.0324904 - 0.0999953i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(-0.272398 - 0.838356i) q^{9} +(0.648271 - 3.25265i) q^{11} +(-1.20429 - 3.70642i) q^{13} +(-0.123807 + 0.0899510i) q^{15} +(-0.283358 + 0.872086i) q^{17} +(-4.89471 - 3.55622i) q^{19} +1.45551 q^{21} -8.31334 q^{23} +(4.03614 + 2.93243i) q^{25} +(-1.74581 + 5.37304i) q^{27} +(5.36281 - 3.89631i) q^{29} +(-2.83253 - 8.71764i) q^{31} +(-3.54609 + 3.27548i) q^{33} +(0.0324904 + 0.0999953i) q^{35} +(1.94300 - 1.41167i) q^{37} +(-1.75285 + 5.39472i) q^{39} +(3.10660 + 2.25707i) q^{41} +12.2277 q^{43} -0.0926819 q^{45} +(4.26001 + 3.09508i) q^{47} +(0.309017 - 0.951057i) q^{49} +(1.07975 - 0.784488i) q^{51} +(0.631250 + 1.94279i) q^{53} +(-0.304187 - 0.170504i) q^{55} +(2.72124 + 8.37510i) q^{57} +(-10.4030 + 7.55822i) q^{59} +(-1.05960 + 3.26111i) q^{61} +(0.713148 + 0.518132i) q^{63} -0.409753 q^{65} +12.1194 q^{67} +(9.78920 + 7.11227i) q^{69} +(-1.49819 + 4.61095i) q^{71} +(1.16581 - 0.847008i) q^{73} +(-2.24391 - 6.90604i) q^{75} +(1.38740 + 3.01249i) q^{77} +(-1.30702 - 4.02259i) q^{79} +(4.51307 - 3.27894i) q^{81} +(0.330694 - 1.01777i) q^{83} +(0.0779981 + 0.0566689i) q^{85} -9.64826 q^{87} -7.06635 q^{89} +(3.15287 + 2.29070i) q^{91} +(-4.12277 + 12.6886i) q^{93} +(-0.514636 + 0.373905i) q^{95} +(-1.26557 - 3.89501i) q^{97} +(-2.90347 + 0.342535i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + q^{5} - 3 q^{7} + q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 + q^5 - 3 * q^7 + q^9	\( 12 q + 6 q^{3} + q^{5} - 3 q^{7} + q^{9} + 2 q^{11} - 7 q^{13} - 4 q^{15} + 3 q^{17} - 23 q^{19} - 4 q^{21} - 38 q^{23} + 2 q^{25} - 18 q^{27} + 29 q^{29} + 9 q^{31} - 4 q^{33} + q^{35} + 3 q^{37} + 25 q^{39} - 18 q^{41} + 34 q^{43} + 14 q^{45} + 9 q^{47} - 3 q^{49} + 35 q^{51} + 13 q^{53} + 16 q^{55} + 9 q^{57} - 17 q^{59} - 19 q^{61} - 9 q^{63} + 8 q^{65} - 20 q^{67} - 14 q^{69} + 15 q^{71} + 9 q^{73} - 47 q^{75} - 8 q^{77} - 14 q^{79} - 49 q^{81} + 41 q^{83} - 66 q^{85} + 40 q^{87} + 34 q^{89} + 13 q^{91} - 40 q^{93} + 42 q^{95} - 10 q^{97} - 24 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 + q^5 - 3 * q^7 + q^9 + 2 * q^11 - 7 * q^13 - 4 * q^15 + 3 * q^17 - 23 * q^19 - 4 * q^21 - 38 * q^23 + 2 * q^25 - 18 * q^27 + 29 * q^29 + 9 * q^31 - 4 * q^33 + q^35 + 3 * q^37 + 25 * q^39 - 18 * q^41 + 34 * q^43 + 14 * q^45 + 9 * q^47 - 3 * q^49 + 35 * q^51 + 13 * q^53 + 16 * q^55 + 9 * q^57 - 17 * q^59 - 19 * q^61 - 9 * q^63 + 8 * q^65 - 20 * q^67 - 14 * q^69 + 15 * q^71 + 9 * q^73 - 47 * q^75 - 8 * q^77 - 14 * q^79 - 49 * q^81 + 41 * q^83 - 66 * q^85 + 40 * q^87 + 34 * q^89 + 13 * q^91 - 40 * q^93 + 42 * q^95 - 10 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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