LMFDB - Embedded newform 116.2.g.b.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [116,2,Mod(25,116)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(116, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([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("116.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 116 = 2^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	116.g (of order $7$, degree $6$, 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:	$0.926264663447$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
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} - 5 x^{11} + 12 x^{10} - 16 x^{9} + 22 x^{8} + 28 x^{7} + 71 x^{6} + 154 x^{5} + 442 x^{4} + \cdots + 841 $ x^12 - 5x^11 + 12x^10 - 16x^9 + 22x^8 + 28x^7 + 71x^6 + 154x^5 + 442x^4 + 555x^3 + 1573x^2 + 1363*x + 841
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			49.1
Root			$1.30120 + 1.63166i$ of defining polynomial
Character	$\chi$	$=$	116.49
Dual form			116.2.g.b.45.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.92469 - 2.41349i) q^{3} +(-3.16565 + 1.52449i) q^{5} +(-0.677712 - 0.849824i) q^{7} +(-1.45292 + 6.36565i) q^{9} +O(q^{10})$	\(q+(-1.92469 - 2.41349i) q^{3} +(-3.16565 + 1.52449i) q^{5} +(-0.677712 - 0.849824i) q^{7} +(-1.45292 + 6.36565i) q^{9} +(-0.411526 - 1.80301i) q^{11} +(-1.46407 - 6.41449i) q^{13} +(9.77224 + 4.70606i) q^{15} +0.658856 q^{17} +(2.07266 - 2.59903i) q^{19} +(-0.746652 + 3.27130i) q^{21} +(-3.50543 - 1.68813i) q^{23} +(4.57978 - 5.74286i) q^{25} +(9.81605 - 4.72716i) q^{27} +(0.417143 + 5.36898i) q^{29} +(-2.70350 + 1.30194i) q^{31} +(-3.55949 + 4.46346i) q^{33} +(3.44095 + 1.65707i) q^{35} +(-1.35480 + 5.93579i) q^{37} +(-12.6634 + 15.8794i) q^{39} +5.19016 q^{41} +(1.06039 + 0.510658i) q^{43} +(-5.10497 - 22.3664i) q^{45} +(-1.38222 - 6.05590i) q^{47} +(1.29474 - 5.67262i) q^{49} +(-1.26809 - 1.59014i) q^{51} +(1.26659 - 0.609959i) q^{53} +(4.05143 + 5.08034i) q^{55} -10.2619 q^{57} -9.55267 q^{59} +(-5.17547 - 6.48983i) q^{61} +(6.39434 - 3.07935i) q^{63} +(14.4136 + 18.0740i) q^{65} +(2.75876 - 12.0869i) q^{67} +(2.67260 + 11.7094i) q^{69} +(-1.80831 - 7.92271i) q^{71} +(7.76268 + 3.73831i) q^{73} -22.6750 q^{75} +(-1.25335 + 1.57165i) q^{77} +(-1.24667 + 5.46204i) q^{79} +(-12.6536 - 6.09364i) q^{81} +(-2.32045 + 2.90975i) q^{83} +(-2.08570 + 1.00442i) q^{85} +(12.1551 - 11.3404i) q^{87} +(-4.02735 + 1.93947i) q^{89} +(-4.45897 + 5.59137i) q^{91} +(8.34560 + 4.01903i) q^{93} +(-2.59909 + 11.3874i) q^{95} +(4.99069 - 6.25813i) q^{97} +12.0753 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} - q^{5} - 7 q^{7} + q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 - q^5 - 7 * q^7 + q^9	$ 12 q - 3 q^{3} - q^{5} - 7 q^{7} + q^{9} + 3 q^{11} - 21 q^{13} + 29 q^{15} - 10 q^{17} + 17 q^{19} + 3 q^{21} - 19 q^{23} - 3 q^{25} + 9 q^{27} - 5 q^{29} - 27 q^{31} - 47 q^{33} + 27 q^{35} - 3 q^{37} - 37 q^{39} - 2 q^{41} - 9 q^{43} + 22 q^{45} + 19 q^{47} + 17 q^{49} + 2 q^{51} + 22 q^{53} + 49 q^{55} + 30 q^{57} + 36 q^{59} - 33 q^{61} + 9 q^{63} + 38 q^{65} - 3 q^{67} + 47 q^{69} - 35 q^{71} + 34 q^{73} - 44 q^{75} - 27 q^{77} - 19 q^{79} - 39 q^{81} - q^{83} - 34 q^{85} - 25 q^{87} - 11 q^{89} - 23 q^{91} + 7 q^{93} - 105 q^{95} + 38 q^{97} - 16 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 - q^5 - 7 * q^7 + q^9 + 3 * q^11 - 21 * q^13 + 29 * q^15 - 10 * q^17 + 17 * q^19 + 3 * q^21 - 19 * q^23 - 3 * q^25 + 9 * q^27 - 5 * q^29 - 27 * q^31 - 47 * q^33 + 27 * q^35 - 3 * q^37 - 37 * q^39 - 2 * q^41 - 9 * q^43 + 22 * q^45 + 19 * q^47 + 17 * q^49 + 2 * q^51 + 22 * q^53 + 49 * q^55 + 30 * q^57 + 36 * q^59 - 33 * q^61 + 9 * q^63 + 38 * q^65 - 3 * q^67 + 47 * q^69 - 35 * q^71 + 34 * q^73 - 44 * q^75 - 27 * q^77 - 19 * q^79 - 39 * q^81 - q^83 - 34 * q^85 - 25 * q^87 - 11 * q^89 - 23 * q^91 + 7 * q^93 - 105 * q^95 + 38 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/116\mathbb{Z}\right)^\times$.

$n$	$59$	$89$
$\chi(n)$	$1$	$e\left(\frac{6}{7}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.92469	−	2.41349i	−1.11122	−	1.39343i	−0.910365	−	0.413806i	$-0.864199\pi$
$3$	−1.92469	−	2.41349i	−1.11122	−	1.39343i	−0.200856	−	0.979621i	$-0.564372\pi$
$4$		0			0
$5$	−3.16565	+	1.52449i	−1.41572	+	0.681775i	−0.976283	−	0.216499i	$-0.930536\pi$
$5$	−3.16565	+	1.52449i	−1.41572	+	0.681775i	−0.439437	+	0.898273i	$0.644822\pi$
$6$		0			0
$7$	−0.677712	−	0.849824i	−0.256151	−	0.321203i	0.637083	−	0.770795i	$-0.280141\pi$
$7$	−0.677712	−	0.849824i	−0.256151	−	0.321203i	−0.893234	+	0.449592i	$0.851569\pi$
$8$		0			0
$9$	−1.45292	+	6.36565i	−0.484306	+	2.12188i
$10$		0			0
$11$	−0.411526	−	1.80301i	−0.124080	−	0.543629i	−0.998310	−	0.0581172i	$-0.981490\pi$
$11$	−0.411526	−	1.80301i	−0.124080	−	0.543629i	0.874230	−	0.485512i	$-0.161367\pi$
$12$		0			0
$13$	−1.46407	−	6.41449i	−0.406059	−	1.77906i	−0.602054	−	0.798455i	$-0.705651\pi$
$13$	−1.46407	−	6.41449i	−0.406059	−	1.77906i	0.195996	−	0.980605i	$-0.437206\pi$
$14$		0			0
$15$	9.77224	+	4.70606i	2.52318	+	1.21510i
$16$		0			0
$17$	0.658856			0.159796			0.0798980	−	0.996803i	$-0.474541\pi$
$17$	0.658856			0.159796			0.0798980	+	0.996803i	$0.474541\pi$
$18$		0			0
$19$	2.07266	−	2.59903i	0.475500	−	0.596258i	−0.485008	−	0.874509i	$-0.661183\pi$
$19$	2.07266	−	2.59903i	0.475500	−	0.596258i	0.960508	+	0.278252i	$0.0897549\pi$
$20$		0			0
$21$	−0.746652	+	3.27130i	−0.162933	+	0.713855i
$22$		0			0
$23$	−3.50543	−	1.68813i	−0.730934	−	0.351999i	0.0311176	−	0.999516i	$-0.490093\pi$
$23$	−3.50543	−	1.68813i	−0.730934	−	0.351999i	−0.762051	+	0.647517i	$0.775808\pi$
$24$		0			0
$25$	4.57978	−	5.74286i	0.915956	−	1.14857i
$26$		0			0
$27$	9.81605	−	4.72716i	1.88910	−	0.909742i
$28$		0			0
$29$	0.417143	+	5.36898i	0.0774615	+	0.996995i
$29$	0.417143	+	5.36898i	0.0774615	+	0.996995i
$30$		0			0
$31$	−2.70350	+	1.30194i	−0.485562	+	0.233835i	−0.660615	−	0.750724i	$-0.729705\pi$
$31$	−2.70350	+	1.30194i	−0.485562	+	0.233835i	0.175053	+	0.984559i	$0.443990\pi$
$32$		0			0
$33$	−3.55949	+	4.46346i	−0.619628	+	0.776989i
$34$		0			0
$35$	3.44095	+	1.65707i	0.581626	+	0.280096i
$36$		0			0
$37$	−1.35480	+	5.93579i	−0.222729	+	0.975838i	0.732685	+	0.680568i	$0.238267\pi$
$37$	−1.35480	+	5.93579i	−0.222729	+	0.975838i	−0.955414	+	0.295270i	$0.904590\pi$
$38$		0			0
$39$	−12.6634	+	15.8794i	−2.02777	+	2.54274i
$40$		0			0
$41$	5.19016			0.810567			0.405284	−	0.914191i	$-0.367173\pi$
$41$	5.19016			0.810567			0.405284	+	0.914191i	$0.367173\pi$
$42$		0			0
$43$	1.06039	+	0.510658i	0.161708	+	0.0778747i	0.512987	−	0.858396i	$-0.328539\pi$
$43$	1.06039	+	0.510658i	0.161708	+	0.0778747i	−0.351279	+	0.936271i	$0.614253\pi$
$44$		0			0
$45$	−5.10497	−	22.3664i	−0.761005	−	3.33418i
$46$		0			0
$47$	−1.38222	−	6.05590i	−0.201618	−	0.883344i	−0.969952	−	0.243296i	$-0.921771\pi$
$47$	−1.38222	−	6.05590i	−0.201618	−	0.883344i	0.768335	−	0.640048i	$-0.221086\pi$
$48$		0			0
$49$	1.29474	−	5.67262i	0.184963	−	0.810375i
$50$		0			0
$51$	−1.26809	−	1.59014i	−0.177569	−	0.222664i
$52$		0			0
$53$	1.26659	−	0.609959i	0.173980	−	0.0837844i	−0.344867	−	0.938652i	$-0.612076\pi$
$53$	1.26659	−	0.609959i	0.173980	−	0.0837844i	0.518847	+	0.854867i	$0.326362\pi$
$54$		0			0
$55$	4.05143	+	5.08034i	0.546295	+	0.685032i
$56$		0			0
$57$	−10.2619			−1.35923
$58$		0			0
$59$	−9.55267			−1.24365			−0.621826	−	0.783156i	$-0.713609\pi$
$59$	−9.55267			−1.24365			−0.621826	+	0.783156i	$0.713609\pi$
$60$		0			0
$61$	−5.17547	−	6.48983i	−0.662651	−	0.830938i	0.330978	−	0.943638i	$-0.392621\pi$
$61$	−5.17547	−	6.48983i	−0.662651	−	0.830938i	−0.993629	+	0.112701i	$0.964050\pi$
$62$		0			0
$63$	6.39434	−	3.07935i	0.805611	−	0.387962i
$64$		0			0
$65$	14.4136	+	18.0740i	1.78778	+	2.24181i
$66$		0			0
$67$	2.75876	−	12.0869i	0.337036	−	1.47665i	−0.468161	−	0.883643i	$-0.655083\pi$
$67$	2.75876	−	12.0869i	0.337036	−	1.47665i	0.805197	−	0.593008i	$-0.202060\pi$
$68$		0			0
$69$	2.67260	+	11.7094i	0.321744	+	1.40965i
$70$		0			0
$71$	−1.80831	−	7.92271i	−0.214606	−	0.940252i	−0.961391	−	0.275186i	$-0.911260\pi$
$71$	−1.80831	−	7.92271i	−0.214606	−	0.940252i	0.746784	−	0.665066i	$-0.231597\pi$
$72$		0			0
$73$	7.76268	+	3.73831i	0.908553	+	0.437536i	0.828971	−	0.559292i	$-0.188927\pi$
$73$	7.76268	+	3.73831i	0.908553	+	0.437536i	0.0795825	+	0.996828i	$0.474641\pi$
$74$		0			0
$75$	−22.6750			−2.61828
$76$		0			0
$77$	−1.25335	+	1.57165i	−0.142832	+	0.179106i
$78$		0			0
$79$	−1.24667	+	5.46204i	−0.140262	+	0.614527i	0.855111	+	0.518444i	$0.173489\pi$
$79$	−1.24667	+	5.46204i	−0.140262	+	0.614527i	−0.995373	+	0.0960831i	$0.969369\pi$
$80$		0			0
$81$	−12.6536	−	6.09364i	−1.40595	−	0.677071i
$82$		0			0
$83$	−2.32045	+	2.90975i	−0.254703	+	0.319387i	−0.892700	−	0.450652i	$-0.851192\pi$
$83$	−2.32045	+	2.90975i	−0.254703	+	0.319387i	0.637997	+	0.770039i	$0.279763\pi$
$84$		0			0
$85$	−2.08570	+	1.00442i	−0.226226	+	0.108945i
$86$		0			0
$87$	12.1551	−	11.3404i	1.30316	−	1.21582i
$88$		0			0
$89$	−4.02735	+	1.93947i	−0.426898	+	0.205583i	−0.634981	−	0.772528i	$-0.718992\pi$
$89$	−4.02735	+	1.93947i	−0.426898	+	0.205583i	0.208083	+	0.978111i	$0.433278\pi$
$90$		0			0
$91$	−4.45897	+	5.59137i	−0.467427	+	0.586135i
$92$		0			0
$93$	8.34560	+	4.01903i	0.865399	+	0.416754i
$94$		0			0
$95$	−2.59909	+	11.3874i	−0.266661	+	1.16832i
$96$		0			0
$97$	4.99069	−	6.25813i	0.506728	−	0.635417i	−0.461004	−	0.887398i	$-0.652511\pi$
$97$	4.99069	−	6.25813i	0.506728	−	0.635417i	0.967732	+	0.251981i	$0.0810820\pi$
$98$		0			0
$99$	12.0753			1.21361
$100$		0			0
$101$	2.09230	+	1.00760i	0.208192	+	0.100260i	0.535074	−	0.844805i	$-0.320284\pi$
$101$	2.09230	+	1.00760i	0.208192	+	0.100260i	−0.326882	+	0.945065i	$0.605998\pi$
$102$		0			0
$103$	1.71349	+	7.50727i	0.168835	+	0.739714i	0.986465	+	0.163970i	$0.0524301\pi$
$103$	1.71349	+	7.50727i	0.168835	+	0.739714i	−0.817630	+	0.575743i	$0.804713\pi$
$104$		0			0
$105$	−2.62344	−	11.4940i	−0.256021	−	1.12170i
$106$		0			0
$107$	−1.65462	+	7.24934i	−0.159958	+	0.700821i	0.829800	+	0.558061i	$0.188455\pi$
$107$	−1.65462	+	7.24934i	−0.159958	+	0.700821i	−0.989757	+	0.142759i	$0.954403\pi$
$108$		0			0
$109$	3.71648	+	4.66032i	0.355974	+	0.446378i	0.927285	−	0.374356i	$-0.122136\pi$
$109$	3.71648	+	4.66032i	0.355974	+	0.446378i	−0.571311	+	0.820734i	$0.693565\pi$
$110$		0			0
$111$	16.9335	−	8.15476i	1.60726	−	0.774015i
$112$		0			0
$113$	−11.3413	−	14.2216i	−1.06690	−	1.33785i	−0.938171	−	0.346173i	$-0.887481\pi$
$113$	−11.3413	−	14.2216i	−1.06690	−	1.33785i	−0.128731	−	0.991680i	$-0.541090\pi$
$114$		0			0
$115$	13.6705			1.27478
$116$		0			0
$117$	42.9596			3.97161
$118$		0			0
$119$	−0.446514	−	0.559911i	−0.0409319	−	0.0513270i
$120$		0			0
$121$	6.82915	−	3.28875i	0.620832	−	0.298977i
$122$		0			0
$123$	−9.98946	−	12.5264i	−0.900719	−	1.12947i
$124$		0			0
$125$	−1.83375	+	8.03417i	−0.164015	+	0.718598i
$126$		0			0
$127$	0.934500	+	4.09431i	0.0829235	+	0.363311i	0.999316	−	0.0369684i	$-0.0117701\pi$
$127$	0.934500	+	4.09431i	0.0829235	+	0.363311i	−0.916393	+	0.400280i	$0.868913\pi$
$128$		0			0
$129$	−0.808462	−	3.54210i	−0.0711811	−	0.311865i
$130$		0			0
$131$	9.92965	+	4.78187i	0.867558	+	0.417794i	0.814065	−	0.580774i	$-0.197250\pi$
$131$	9.92965	+	4.78187i	0.867558	+	0.417794i	0.0534933	+	0.998568i	$0.482964\pi$
$132$		0			0
$133$	−3.61338			−0.313320
$134$		0			0
$135$	−23.8676	+	29.9290i	−2.05420	+	2.57588i
$136$		0			0
$137$	2.07608	−	9.09590i	0.177371	−	0.777115i	−0.805466	−	0.592642i	$-0.798085\pi$
$137$	2.07608	−	9.09590i	0.177371	−	0.777115i	0.982838	−	0.184473i	$-0.0590579\pi$
$138$		0			0
$139$	−15.9167	−	7.66507i	−1.35004	−	0.650143i	−0.387644	−	0.921809i	$-0.626711\pi$
$139$	−15.9167	−	7.66507i	−1.35004	−	0.650143i	−0.962391	+	0.271667i	$0.912425\pi$
$140$		0			0
$141$	−11.9555	+	14.9917i	−1.00683	+	1.26253i
$142$		0			0
$143$	−10.9629	+	5.27946i	−0.916765	+	0.441491i
$144$		0			0
$145$	−9.50551	−	16.3604i	−0.789390	−	1.35865i
$146$		0			0
$147$	−16.1828	+	7.79321i	−1.33473	+	0.642774i
$148$		0			0
$149$	10.4619	−	13.1189i	0.857075	−	1.07474i	−0.139349	−	0.990243i	$-0.544501\pi$
$149$	10.4619	−	13.1189i	0.857075	−	1.07474i	0.996424	−	0.0844949i	$-0.0269277\pi$
$150$		0			0
$151$	−0.612042	−	0.294744i	−0.0498073	−	0.0239859i	0.408814	−	0.912618i	$-0.365942\pi$
$151$	−0.612042	−	0.294744i	−0.0498073	−	0.0239859i	−0.458622	+	0.888632i	$0.651657\pi$
$152$		0			0
$153$	−0.957264	+	4.19405i	−0.0773902	+	0.339069i
$154$		0			0
$155$	6.57352	−	8.24293i	0.527998	−	0.662088i
$156$		0			0
$157$	−1.22921			−0.0981018			−0.0490509	−	0.998796i	$-0.515620\pi$
$157$	−1.22921			−0.0981018			−0.0490509	+	0.998796i	$0.515620\pi$
$158$		0			0
$159$	−3.90993	−	1.88292i	−0.310078	−	0.149326i
$160$		0			0
$161$	0.941063	+	4.12307i	0.0741661	+	0.324943i
$162$		0			0
$163$	2.25661	+	9.88685i	0.176751	+	0.774398i	0.983117	+	0.182980i	$0.0585743\pi$
$163$	2.25661	+	9.88685i	0.176751	+	0.774398i	−0.806365	+	0.591418i	$0.798569\pi$
$164$		0			0
$165$	4.46356	−	19.5562i	0.347488	−	1.52244i
$166$		0			0
$167$	−12.3264	−	15.4569i	−0.953849	−	1.19609i	−0.980515	−	0.196445i	$-0.937060\pi$
$167$	−12.3264	−	15.4569i	−0.953849	−	1.19609i	0.0266657	−	0.999644i	$-0.491511\pi$
$168$		0			0
$169$	−27.2896	+	13.1420i	−2.09920	+	1.01092i
$170$		0			0
$171$	13.5331	+	16.9700i	1.03490	+	1.29773i
$172$		0			0
$173$	−6.04054			−0.459254			−0.229627	−	0.973279i	$-0.573751\pi$
$173$	−6.04054			−0.459254			−0.229627	+	0.973279i	$0.573751\pi$
$174$		0			0
$175$	−7.98419			−0.603548
$176$		0			0
$177$	18.3859	+	23.0552i	1.38197	+	1.73294i
$178$		0			0
$179$	12.0764	−	5.81568i	0.902631	−	0.434684i	0.0757925	−	0.997124i	$-0.475851\pi$
$179$	12.0764	−	5.81568i	0.902631	−	0.434684i	0.826839	+	0.562439i	$0.190137\pi$
$180$		0			0
$181$	1.43498	+	1.79941i	0.106661	+	0.133749i	0.832297	−	0.554330i	$-0.187026\pi$
$181$	1.43498	+	1.79941i	0.106661	+	0.133749i	−0.725636	+	0.688079i	$0.758454\pi$
$182$		0			0
$183$	−5.70194	+	24.9818i	−0.421500	+	1.84671i
$184$		0			0
$185$	−4.76024	−	20.8560i	−0.349980	−	1.53336i
$186$		0			0
$187$	−0.271137	−	1.18793i	−0.0198275	−	0.0868698i
$188$		0			0
$189$	−10.6697	−	5.13826i	−0.776107	−	0.373753i
$190$		0			0
$191$	26.8511			1.94287			0.971437	−	0.237298i	$-0.0762618\pi$
$191$	26.8511			1.94287			0.971437	+	0.237298i	$0.0762618\pi$
$192$		0			0
$193$	6.32809	−	7.93518i	0.455506	−	0.571187i	−0.500050	−	0.865997i	$-0.666685\pi$
$193$	6.32809	−	7.93518i	0.455506	−	0.571187i	0.955556	+	0.294810i	$0.0952564\pi$
$194$		0			0
$195$	15.8798	−	69.5739i	1.13718	−	4.98229i
$196$		0			0
$197$	−2.23137	−	1.07457i	−0.158979	−	0.0765600i	0.352703	−	0.935736i	$-0.385263\pi$
$197$	−2.23137	−	1.07457i	−0.158979	−	0.0765600i	−0.511681	+	0.859175i	$0.670977\pi$
$198$		0			0
$199$	5.77224	−	7.23816i	0.409183	−	0.513099i	−0.533949	−	0.845516i	$-0.679293\pi$
$199$	5.77224	−	7.23816i	0.409183	−	0.513099i	0.943132	+	0.332417i	$0.107864\pi$
$200$		0			0
$201$	−34.4814	+	16.6053i	−2.43213	+	1.17125i
$202$		0			0
$203$	4.27999	−	3.99312i	0.300396	−	0.280262i
$204$		0			0
$205$	−16.4302	+	7.91237i	−1.14754	+	0.552624i
$206$		0			0
$207$	15.8391	−	19.8617i	1.10090	−	1.38048i
$208$		0			0
$209$	−5.53904	−	2.66746i	−0.383143	−	0.184512i
$210$		0			0
$211$	−4.94301	+	21.6567i	−0.340291	+	1.49091i	0.458170	+	0.888864i	$0.348505\pi$
$211$	−4.94301	+	21.6567i	−0.340291	+	1.49091i	−0.798461	+	0.602046i	$0.794352\pi$
$212$		0			0
$213$	−15.6409	+	19.6131i	−1.07170	+	1.34387i
$214$		0			0
$215$	−4.13532			−0.282027
$216$		0			0
$217$	2.93861	+	1.41516i	0.199486	+	0.0960672i
$218$		0			0
$219$	−5.91840	−	25.9302i	−0.399929	−	1.75220i
$220$		0			0
$221$	−0.964609	−	4.22623i	−0.0648866	−	0.284287i
$222$		0			0
$223$	−6.01393	+	26.3487i	−0.402722	+	1.76444i	0.213573	+	0.976927i	$0.431490\pi$
$223$	−6.01393	+	26.3487i	−0.402722	+	1.76444i	−0.616295	+	0.787515i	$0.711367\pi$
$224$		0			0
$225$	29.9030	+	37.4972i	1.99353	+	2.49981i
$226$		0			0
$227$	−1.95644	+	0.942171i	−0.129853	+	0.0625341i	−0.497682	−	0.867359i	$-0.665815\pi$
$227$	−1.95644	+	0.942171i	−0.129853	+	0.0625341i	0.367829	+	0.929893i	$0.380101\pi$
$228$		0			0
$229$	8.78190	+	11.0122i	0.580325	+	0.727704i	0.982168	−	0.188004i	$-0.0602019\pi$
$229$	8.78190	+	11.0122i	0.580325	+	0.727704i	−0.401844	+	0.915708i	$0.631630\pi$
$230$		0			0
$231$	6.20546			0.408289
$232$		0			0
$233$	7.98101			0.522854			0.261427	−	0.965223i	$-0.415807\pi$
$233$	7.98101			0.522854			0.261427	+	0.965223i	$0.415807\pi$
$234$		0			0
$235$	13.6078	+	17.0637i	0.887676	+	1.11311i
$236$		0			0
$237$	15.5820	−	7.50390i	1.01216	−	0.487431i
$238$		0			0
$239$	−11.7831	−	14.7756i	−0.762188	−	0.955753i	0.237691	−	0.971341i	$-0.423610\pi$
$239$	−11.7831	−	14.7756i	−0.762188	−	0.955753i	−0.999879	+	0.0155876i	$0.995038\pi$
$240$		0			0
$241$	2.36797	−	10.3748i	0.152535	−	0.668297i	−0.839609	−	0.543191i	$-0.817216\pi$
$241$	2.36797	−	10.3748i	0.152535	−	0.668297i	0.992143	−	0.125106i	$-0.0399271\pi$
$242$		0			0
$243$	2.37421	+	10.4021i	0.152305	+	0.667294i
$244$		0			0
$245$	4.54920	+	19.9313i	0.290638	+	1.27337i
$246$		0			0
$247$	−19.7059	−	9.48988i	−1.25386	−	0.603827i
$248$		0			0
$249$	11.4888			0.728074
$250$		0			0
$251$	0.786881	−	0.986717i	0.0496675	−	0.0622810i	−0.756377	−	0.654136i	$-0.773033\pi$
$251$	0.786881	−	0.986717i	0.0496675	−	0.0622810i	0.806045	+	0.591855i	$0.201604\pi$
$252$		0			0
$253$	−1.60114	+	7.01506i	−0.100663	+	0.441033i
$254$		0			0
$255$	6.43850	+	3.10062i	0.403194	+	0.194168i
$256$		0			0
$257$	−3.60427	+	4.51962i	−0.224828	+	0.281926i	−0.881433	−	0.472309i	$-0.843421\pi$
$257$	−3.60427	+	4.51962i	−0.224828	+	0.281926i	0.656605	+	0.754235i	$0.271992\pi$
$258$		0			0
$259$	5.96254	−	2.87141i	0.370494	−	0.178421i
$260$		0			0
$261$	−34.7831	−	5.14531i	−2.15302	−	0.318487i
$262$		0			0
$263$	21.5800	−	10.3924i	1.33068	−	0.640822i	0.372780	−	0.927920i	$-0.378405\pi$
$263$	21.5800	−	10.3924i	1.33068	−	0.640822i	0.957901	+	0.287098i	$0.0926904\pi$
$264$		0			0
$265$	−3.07971	+	3.86183i	−0.189185	+	0.237230i
$266$		0			0
$267$	12.4323	+	5.98707i	0.760843	+	0.366403i
$268$		0			0
$269$	1.68332	−	7.37511i	0.102634	−	0.449668i	−0.897332	−	0.441357i	$-0.854497\pi$
$269$	1.68332	−	7.37511i	0.102634	−	0.449668i	0.999965	−	0.00831130i	$-0.00264560\pi$
$270$		0			0
$271$	11.8924	−	14.9126i	0.722410	−	0.905873i	−0.276062	−	0.961140i	$-0.589029\pi$
$271$	11.8924	−	14.9126i	0.722410	−	0.905873i	0.998472	+	0.0552665i	$0.0176009\pi$
$272$		0			0
$273$	22.0768			1.33615
$274$		0			0
$275$	−12.2392	−	5.89407i	−0.738049	−	0.355426i
$276$		0			0
$277$	0.922042	+	4.03973i	0.0554001	+	0.242724i	0.995045	−	0.0994282i	$-0.0317014\pi$
$277$	0.922042	+	4.03973i	0.0554001	+	0.242724i	−0.939645	+	0.342152i	$0.888844\pi$
$278$		0			0
$279$	−4.35971	−	19.1011i	−0.261009	−	1.14355i
$280$		0			0
$281$	−0.128285	+	0.562052i	−0.00765283	+	0.0335292i	−0.978610	−	0.205723i	$-0.934045\pi$
$281$	−0.128285	+	0.562052i	−0.00765283	+	0.0335292i	0.970957	+	0.239253i	$0.0769024\pi$
$282$		0			0
$283$	14.7483	+	18.4938i	0.876697	+	1.09934i	0.994336	+	0.106287i	$0.0338961\pi$
$283$	14.7483	+	18.4938i	0.876697	+	1.09934i	−0.117639	+	0.993056i	$0.537532\pi$
$284$		0			0
$285$	32.4857	−	15.6443i	1.92428	−	0.926687i
$286$		0			0
$287$	−3.51743	−	4.41072i	−0.207628	−	0.260357i
$288$		0			0
$289$	−16.5659			−0.974465
$290$		0			0
$291$	−24.7095			−1.44849
$292$		0			0
$293$	−3.17397	−	3.98003i	−0.185425	−	0.232516i	0.680427	−	0.732816i	$-0.261794\pi$
$293$	−3.17397	−	3.98003i	−0.185425	−	0.232516i	−0.865852	+	0.500300i	$0.833223\pi$
$294$		0			0
$295$	30.2404	−	14.5630i	1.76066	−	0.847890i
$296$		0			0
$297$	−12.5627	−	15.7531i	−0.728962	−	0.914089i
$298$		0			0
$299$	−5.69630	+	24.9571i	−0.329425	+	1.44331i
$300$		0			0
$301$	−0.284671	−	1.24723i	−0.0164082	−	0.0718889i
$302$		0			0
$303$	−1.59521	−	6.98907i	−0.0916424	−	0.401512i
$304$		0			0
$305$	26.2774	+	12.6545i	1.50464	+	0.724596i
$306$		0			0
$307$	−27.9505			−1.59522			−0.797609	−	0.603175i	$-0.793902\pi$
$307$	−27.9505			−1.59522			−0.797609	+	0.603175i	$0.793902\pi$
$308$		0			0
$309$	14.8208	−	18.5847i	0.843124	−	1.05724i
$310$		0			0
$311$	−3.66039	+	16.0372i	−0.207562	+	0.909386i	0.758622	+	0.651531i	$0.225873\pi$
$311$	−3.66039	+	16.0372i	−0.207562	+	0.909386i	−0.966184	+	0.257855i	$0.916984\pi$
$312$		0			0
$313$	−2.57704	−	1.24104i	−0.145663	−	0.0701475i	0.359632	−	0.933094i	$-0.382902\pi$
$313$	−2.57704	−	1.24104i	−0.145663	−	0.0701475i	−0.505295	+	0.862947i	$0.668616\pi$
$314$		0			0
$315$	−15.5478	+	19.4963i	−0.876017	+	1.09849i
$316$		0			0
$317$	−20.5844	+	9.91293i	−1.15614	+	0.556766i	−0.910871	−	0.412691i	$-0.864589\pi$
$317$	−20.5844	+	9.91293i	−1.15614	+	0.556766i	−0.245264	+	0.969456i	$0.578875\pi$
$318$		0			0
$319$	9.50869	−	2.96159i	0.532385	−	0.165817i
$320$		0			0
$321$	20.6808	−	9.95936i	1.15429	−	0.555877i
$322$		0			0
$323$	1.36558	−	1.71239i	0.0759830	−	0.0952797i
$324$		0			0
$325$	−43.5426	−	20.9690i	−2.41531	−	1.16315i
$326$		0			0
$327$	4.09454	−	17.9393i	0.226429	−	0.992048i
$328$		0			0
$329$	−4.20970	+	5.27880i	−0.232088	+	0.291030i
$330$		0			0
$331$	26.0822			1.43361			0.716803	−	0.697276i	$-0.245605\pi$
$331$	26.0822			1.43361			0.716803	+	0.697276i	$0.245605\pi$
$332$		0			0
$333$	−35.8167	−	17.2484i	−1.96274	−	0.945208i
$334$		0			0
$335$	9.69318	+	42.4686i	0.529595	+	2.32031i
$336$		0			0
$337$	7.04499	+	30.8661i	0.383765	+	1.68138i	0.685563	+	0.728013i	$0.259556\pi$
$337$	7.04499	+	30.8661i	0.383765	+	1.68138i	−0.301798	+	0.953372i	$0.597587\pi$
$338$		0			0
$339$	−12.4950	+	54.7443i	−0.678636	+	2.97330i
$340$		0			0
$341$	3.45997	+	4.33866i	0.187368	+	0.234952i
$342$		0			0
$343$	−12.5534	+	6.04542i	−0.677822	+	0.326422i
$344$		0			0
$345$	−26.3115	−	32.9936i	−1.41656	−	1.77631i
$346$		0			0
$347$	−9.10528			−0.488797			−0.244399	−	0.969675i	$-0.578591\pi$
$347$	−9.10528			−0.488797			−0.244399	+	0.969675i	$0.578591\pi$
$348$		0			0
$349$	−6.07146			−0.324998			−0.162499	−	0.986709i	$-0.551955\pi$
$349$	−6.07146			−0.324998			−0.162499	+	0.986709i	$0.551955\pi$
$350$		0			0
$351$	−44.6937	−	56.0441i	−2.38557	−	2.99141i
$352$		0			0
$353$	−0.278327	+	0.134035i	−0.0148138	+	0.00713397i	−0.441276	−	0.897371i	$-0.645474\pi$
$353$	−0.278327	+	0.134035i	−0.0148138	+	0.00713397i	0.426462	+	0.904505i	$0.359760\pi$
$354$		0			0
$355$	17.8026	+	22.3237i	0.944863	+	1.18482i
$356$		0			0
$357$	−0.491936	+	2.15531i	−0.0260360	+	0.114071i
$358$		0			0
$359$	−4.17453	−	18.2898i	−0.220323	−	0.965299i	−0.957235	−	0.289310i	$-0.906574\pi$
$359$	−4.17453	−	18.2898i	−0.220323	−	0.965299i	0.736912	−	0.675988i	$-0.236283\pi$
$360$		0			0
$361$	1.76885	+	7.74985i	0.0930976	+	0.407887i
$362$		0			0
$363$	−21.0813	−	10.1522i	−1.10648	−	0.532854i
$364$		0			0
$365$	−30.2729			−1.58456
$366$		0			0
$367$	−12.3943	+	15.5419i	−0.646976	+	0.811283i	−0.991856	−	0.127364i	$-0.959348\pi$
$367$	−12.3943	+	15.5419i	−0.646976	+	0.811283i	0.344880	+	0.938647i	$0.387920\pi$
$368$		0			0
$369$	−7.54088	+	33.0388i	−0.392563	+	1.71993i
$370$		0			0
$371$	−1.37674	−	0.663005i	−0.0714770	−	0.0344215i
$372$		0			0
$373$	8.58454	−	10.7647i	0.444491	−	0.557374i	−0.508230	−	0.861221i	$-0.669700\pi$
$373$	8.58454	−	10.7647i	0.444491	−	0.557374i	0.952721	+	0.303848i	$0.0982714\pi$
$374$		0			0
$375$	22.9198	−	11.0376i	1.18357	−	0.569978i
$376$		0			0
$377$	33.8286	−	10.5363i	1.74226	−	0.542647i
$378$		0			0
$379$	23.6083	−	11.3692i	1.21268	−	0.583994i	0.285414	−	0.958404i	$-0.407869\pi$
$379$	23.6083	−	11.3692i	1.21268	−	0.583994i	0.927263	+	0.374410i	$0.122155\pi$
$380$		0			0
$381$	8.08294	−	10.1357i	0.414102	−	0.519267i
$382$		0			0
$383$	−6.46418	−	3.11298i	−0.330304	−	0.159066i	0.261380	−	0.965236i	$-0.415822\pi$
$383$	−6.46418	−	3.11298i	−0.330304	−	0.159066i	−0.591684	+	0.806170i	$0.701537\pi$
$384$		0			0
$385$	1.57169	−	6.88601i	0.0801005	−	0.350943i
$386$		0			0
$387$	−4.79134	+	6.00814i	−0.243557	+	0.305411i
$388$		0			0
$389$	14.1936			0.719642			0.359821	−	0.933021i	$-0.382838\pi$
$389$	14.1936			0.719642			0.359821	+	0.933021i	$0.382838\pi$
$390$		0			0
$391$	−2.30958	−	1.11223i	−0.116800	−	0.0562481i
$392$		0			0
$393$	−7.57054	−	33.1687i	−0.381883	−	1.67314i
$394$		0			0
$395$	−4.38032	−	19.1914i	−0.220398	−	0.965625i
$396$		0			0
$397$	6.40334	−	28.0548i	0.321374	−	1.40803i	−0.513735	−	0.857949i	$-0.671739\pi$
$397$	6.40334	−	28.0548i	0.321374	−	1.40803i	0.835110	−	0.550084i	$-0.185404\pi$
$398$		0			0
$399$	6.95464	+	8.72084i	0.348167	+	0.436588i
$400$		0			0
$401$	−15.4286	+	7.43002i	−0.770467	+	0.371037i	−0.777455	−	0.628938i	$-0.783490\pi$
$401$	−15.4286	+	7.43002i	−0.770467	+	0.371037i	0.00698828	+	0.999976i	$0.497776\pi$
$402$		0			0
$403$	12.3094	+	15.4354i	0.613172	+	0.768894i
$404$		0			0
$405$	49.3464			2.45204
$406$		0			0
$407$	11.2599			0.558130
$408$		0			0
$409$	−1.84780	−	2.31707i	−0.0913677	−	0.114572i	0.734046	−	0.679100i	$-0.237630\pi$
$409$	−1.84780	−	2.31707i	−0.0913677	−	0.114572i	−0.825414	+	0.564528i	$0.809058\pi$
$410$		0			0
$411$	−25.9486	+	12.4962i	−1.27995	+	0.616393i
$412$		0			0
$413$	6.47395	+	8.11808i	0.318562	+	0.399465i
$414$		0			0
$415$	2.90982	−	12.7488i	0.142838	−	0.625812i
$416$		0			0
$417$	12.1352	+	53.1676i	0.594261	+	2.60363i
$418$		0			0
$419$	−1.66052	−	7.27520i	−0.0811216	−	0.355417i	0.918034	−	0.396501i	$-0.129776\pi$
$419$	−1.66052	−	7.27520i	−0.0811216	−	0.355417i	−0.999156	+	0.0410846i	$0.986919\pi$
$420$		0			0
$421$	4.21662	+	2.03062i	0.205505	+	0.0989662i	0.533806	−	0.845607i	$-0.320761\pi$
$421$	4.21662	+	2.03062i	0.205505	+	0.0989662i	−0.328300	+	0.944573i	$0.606476\pi$
$422$		0			0
$423$	40.5580			1.97200
$424$		0			0
$425$	3.01742	−	3.78372i	0.146366	−	0.183537i
$426$		0			0
$427$	−2.00774	+	8.79647i	−0.0971612	+	0.425691i
$428$		0			0
$429$	33.8422	+	16.2975i	1.63391	+	0.786852i
$430$		0			0
$431$	9.33159	−	11.7014i	0.449487	−	0.563639i	−0.504529	−	0.863395i	$-0.668334\pi$
$431$	9.33159	−	11.7014i	0.449487	−	0.563639i	0.954016	+	0.299756i	$0.0969052\pi$
$432$		0			0
$433$	25.2638	−	12.1664i	1.21410	−	0.584681i	0.286440	−	0.958098i	$-0.407528\pi$
$433$	25.2638	−	12.1664i	1.21410	−	0.584681i	0.927664	+	0.373417i	$0.121814\pi$
$434$		0			0
$435$	−21.1904	+	54.4301i	−1.01600	+	2.60972i
$436$		0			0
$437$	−11.6531	+	5.61181i	−0.557441	+	0.268449i
$438$		0			0
$439$	−12.0380	+	15.0952i	−0.574543	+	0.720454i	−0.981171	−	0.193140i	$-0.938133\pi$
$439$	−12.0380	+	15.0952i	−0.574543	+	0.720454i	0.406629	+	0.913594i	$0.366704\pi$
$440$		0			0
$441$	34.2288	+	16.4837i	1.62994	+	0.784939i
$442$		0			0
$443$	6.87527	−	30.1225i	0.326654	−	1.43116i	−0.498812	−	0.866710i	$-0.666230\pi$
$443$	6.87527	−	30.1225i	0.326654	−	1.43116i	0.825465	−	0.564453i	$-0.190913\pi$
$444$		0			0
$445$	9.79244	−	12.2793i	0.464206	−	0.582096i
$446$		0			0
$447$	−51.7982			−2.44997
$448$		0			0
$449$	−25.9693	−	12.5062i	−1.22557	−	0.590202i	−0.294711	−	0.955586i	$-0.595223\pi$
$449$	−25.9693	−	12.5062i	−1.22557	−	0.590202i	−0.930857	+	0.365384i	$0.880938\pi$
$450$		0			0
$451$	−2.13589	−	9.35794i	−0.100575	−	0.440648i
$452$		0			0
$453$	0.466632	+	2.04445i	0.0219243	+	0.0960565i
$454$		0			0
$455$	5.59150	−	24.4980i	0.262134	−	1.14848i
$456$		0			0
$457$	−22.2867	−	27.9467i	−1.04253	−	1.30729i	−0.950227	−	0.311560i	$-0.899149\pi$
$457$	−22.2867	−	27.9467i	−1.04253	−	1.30729i	−0.0923029	−	0.995731i	$-0.529423\pi$
$458$		0			0
$459$	6.46736	−	3.11452i	0.301871	−	0.145373i
$460$		0			0
$461$	8.89894	+	11.1589i	0.414465	+	0.519723i	0.944615	−	0.328181i	$-0.106436\pi$
$461$	8.89894	+	11.1589i	0.414465	+	0.519723i	−0.530150	+	0.847904i	$0.677864\pi$
$462$		0			0
$463$	−33.7695			−1.56940			−0.784701	−	0.619875i	$-0.787183\pi$
$463$	−33.7695			−1.56940			−0.784701	+	0.619875i	$0.787183\pi$
$464$		0			0
$465$	−32.5462			−1.50929
$466$		0			0
$467$	19.9471	+	25.0129i	0.923042	+	1.15746i	0.987195	+	0.159518i	$0.0509941\pi$
$467$	19.9471	+	25.0129i	0.923042	+	1.15746i	−0.0641528	+	0.997940i	$0.520434\pi$
$468$		0			0
$469$	−12.1414	+	5.84698i	−0.560637	+	0.269989i
$470$		0			0
$471$	2.36585	+	2.96669i	0.109013	+	0.136698i
$472$		0			0
$473$	0.484345	−	2.12205i	0.0222702	−	0.0975721i
$474$		0			0
$475$	−5.43355	−	23.8059i	−0.249308	−	1.09229i
$476$		0			0
$477$	2.04253	+	8.94891i	0.0935211	+	0.409743i
$478$		0			0
$479$	32.4782	+	15.6407i	1.48397	+	0.714641i	0.988108	−	0.153763i	$-0.0491392\pi$
$479$	32.4782	+	15.6407i	1.48397	+	0.714641i	0.495859	+	0.868403i	$0.334853\pi$
$480$		0			0
$481$	40.0586			1.82651
$482$		0			0
$483$	8.13971	−	10.2069i	0.370369	−	0.464429i
$484$		0			0
$485$	−6.25828	+	27.4193i	−0.284174	+	1.24505i
$486$		0			0
$487$	−23.2673	−	11.2049i	−1.05434	−	0.507743i	−0.175312	−	0.984513i	$-0.556093\pi$
$487$	−23.2673	−	11.2049i	−1.05434	−	0.507743i	−0.879028	+	0.476769i	$0.841808\pi$
$488$		0			0
$489$	19.5185	−	24.4754i	0.882657	−	1.10682i
$490$		0			0
$491$	1.85141	−	0.891590i	0.0835527	−	0.0402369i	−0.391641	−	0.920118i	$-0.628092\pi$
$491$	1.85141	−	0.891590i	0.0835527	−	0.0402369i	0.475193	+	0.879881i	$0.342378\pi$
$492$		0			0
$493$	0.274837	+	3.53739i	0.0123780	+	0.159316i
$494$		0			0
$495$	−38.2260	+	18.4087i	−1.71813	+	0.827409i
$496$		0			0
$497$	−5.50739	+	6.90605i	−0.247040	+	0.309779i
$498$		0			0
$499$	−2.90825	−	1.40054i	−0.130191	−	0.0626968i	0.367654	−	0.929963i	$-0.380161\pi$
$499$	−2.90825	−	1.40054i	−0.130191	−	0.0626968i	−0.497845	+	0.867266i	$0.665875\pi$
$500$		0			0
$501$	−13.5804	+	59.4994i	−0.606726	+	2.65824i
$502$		0			0
$503$	−9.84479	+	12.3450i	−0.438958	+	0.550435i	−0.951268	−	0.308365i	$-0.900218\pi$
$503$	−9.84479	+	12.3450i	−0.438958	+	0.550435i	0.512311	+	0.858800i	$0.328790\pi$
$504$		0			0
$505$	−8.15958			−0.363096
$506$		0			0
$507$	84.2421	+	40.5688i	3.74132	+	1.80173i
$508$		0			0
$509$	0.637926	+	2.79494i	0.0282756	+	0.123883i	0.987096	−	0.160130i	$-0.0511912\pi$
$509$	0.637926	+	2.79494i	0.0282756	+	0.123883i	−0.958820	+	0.284013i	$0.908334\pi$
$510$		0			0
$511$	−2.08396	−	9.13041i	−0.0921888	−	0.403905i
$512$		0			0
$513$	8.05927	−	35.3099i	0.355825	−	1.55897i
$514$		0			0
$515$	−16.8691	−	21.1532i	−0.743341	−	0.932120i
$516$		0			0
$517$	−10.3501	+	4.98433i	−0.455195	+	0.219210i
$518$		0			0
$519$	11.6262	+	14.5788i	0.510332	+	0.639936i
$520$		0			0
$521$	24.8422			1.08835			0.544177	−	0.838970i	$-0.316842\pi$
$521$	24.8422			1.08835			0.544177	+	0.838970i	$0.316842\pi$
$522$		0			0
$523$	−5.39629			−0.235963			−0.117982	−	0.993016i	$-0.537642\pi$
$523$	−5.39629			−0.235963			−0.117982	+	0.993016i	$0.537642\pi$
$524$		0			0
$525$	15.3671	+	19.2697i	0.670675	+	0.841000i
$526$		0			0
$527$	−1.78122	+	0.857788i	−0.0775910	+	0.0373658i
$528$		0			0
$529$	−4.90197	−	6.14688i	−0.213129	−	0.267255i
$530$		0			0
$531$	13.8792	−	60.8089i	0.602308	−	2.63888i
$532$		0			0
$533$	−7.59874	−	33.2923i	−0.329138	−	1.44205i
$534$		0			0
$535$	−5.81366	−	25.4713i	−0.251346	−	1.10122i
$536$		0			0
$537$	−37.2794	−	17.9528i	−1.60872	−	0.774720i
$538$		0			0
$539$	−10.7606			−0.463494
$540$		0			0
$541$	18.4986	−	23.1965i	0.795318	−	0.997297i	−0.204513	−	0.978864i	$-0.565561\pi$
$541$	18.4986	−	23.1965i	0.795318	−	0.997297i	0.999830	−	0.0184327i	$-0.00586764\pi$
$542$		0			0
$543$	1.58095	−	6.92660i	0.0678451	−	0.297249i
$544$		0			0
$545$	−18.8697	−	9.08716i	−0.808289	−	0.389251i
$546$		0			0
$547$	15.7762	−	19.7828i	0.674543	−	0.845850i	−0.320296	−	0.947318i	$-0.603782\pi$
$547$	15.7762	−	19.7828i	0.674543	−	0.845850i	0.994839	+	0.101467i	$0.0323538\pi$
$548$		0			0
$549$	48.8315	−	23.5160i	2.08408	−	1.00364i
$550$		0			0
$551$	14.8187	+	10.0439i	0.631299	+	0.427884i
$552$		0			0
$553$	5.48665	−	2.64223i	0.233316	−	0.112359i
$554$		0			0
$555$	−41.1737	+	51.6301i	−1.74772	+	2.19158i
$556$		0			0
$557$	−15.9825	−	7.69677i	−0.677200	−	0.326122i	0.0634772	−	0.997983i	$-0.479781\pi$
$557$	−15.9825	−	7.69677i	−0.677200	−	0.326122i	−0.740677	+	0.671861i	$0.765495\pi$
$558$		0			0
$559$	1.72313	−	7.54952i	0.0728806	−	0.319311i
$560$		0			0
$561$	−2.34519	+	2.94078i	−0.0990141	+	0.124160i
$562$		0			0
$563$	−38.5300			−1.62385			−0.811923	−	0.583764i	$-0.801579\pi$
$563$	−38.5300			−1.62385			−0.811923	+	0.583764i	$0.801579\pi$
$564$		0			0
$565$	57.5833	+	27.7307i	2.42255	+	1.16664i
$566$		0			0
$567$	3.39695	+	14.8830i	0.142659	+	0.625028i
$568$		0			0
$569$	9.30890	+	40.7850i	0.390249	+	1.70979i	0.663777	+	0.747931i	$0.268952\pi$
$569$	9.30890	+	40.7850i	0.390249	+	1.70979i	−0.273527	+	0.961864i	$0.588190\pi$
$570$		0			0
$571$	3.11838	−	13.6625i	0.130500	−	0.571758i	−0.866822	−	0.498618i	$-0.833841\pi$
$571$	3.11838	−	13.6625i	0.130500	−	0.571758i	0.997322	−	0.0731397i	$-0.0233019\pi$
$572$		0			0
$573$	−51.6800	−	64.8046i	−2.15896	−	2.70725i
$574$		0			0
$575$	−25.7488	+	12.4000i	−1.07380	+	0.517115i
$576$		0			0
$577$	−6.56773	−	8.23567i	−0.273418	−	0.342856i	0.626097	−	0.779745i	$-0.284651\pi$
$577$	−6.56773	−	8.23567i	−0.273418	−	0.342856i	−0.899515	+	0.436890i	$0.856080\pi$
$578$		0			0
$579$	−31.3311			−1.30208
$580$		0			0
$581$	4.04538			0.167830
$582$		0			0
$583$	−1.62100	−	2.03267i	−0.0671351	−	0.0841847i
$584$		0			0
$585$	−135.995	+	65.4916i	−5.62269	+	2.70775i
$586$		0			0
$587$	−7.37897	−	9.25293i	−0.304563	−	0.381909i	0.605872	−	0.795562i	$-0.292824\pi$
$587$	−7.37897	−	9.25293i	−0.304563	−	0.381909i	−0.910435	+	0.413653i	$0.864253\pi$
$588$		0			0
$589$	−2.21965	+	9.72493i	−0.0914591	+	0.400709i
$590$		0			0
$591$	1.70124	+	7.45360i	0.0699795	+	0.306600i
$592$		0			0
$593$	−0.0268289	−	0.117545i	−0.00110173	−	0.00482700i	0.974374	−	0.224934i	$-0.0722166\pi$
$593$	−0.0268289	−	0.117545i	−0.00110173	−	0.00482700i	−0.975476	+	0.220107i	$0.929359\pi$
$594$		0			0
$595$	2.26709	+	1.09177i	0.0929416	+	0.0447583i
$596$		0			0
$597$	−28.5790			−1.16966
$598$		0			0
$599$	7.03657	−	8.82358i	0.287506	−	0.360522i	−0.617014	−	0.786952i	$-0.711658\pi$
$599$	7.03657	−	8.82358i	0.287506	−	0.360522i	0.904520	+	0.426431i	$0.140229\pi$
$600$		0			0
$601$	7.81458	−	34.2379i	0.318763	−	1.39659i	−0.520961	−	0.853581i	$-0.674426\pi$
$601$	7.81458	−	34.2379i	0.318763	−	1.39659i	0.839724	−	0.543013i	$-0.182717\pi$
$602$		0			0
$603$	72.9328	+	35.1226i	2.97005	+	1.43030i
$604$		0			0
$605$	−16.6050	+	20.8220i	−0.675089	+	0.846535i
$606$		0			0
$607$	9.90776	−	4.77132i	0.402143	−	0.193662i	−0.221869	−	0.975076i	$-0.571216\pi$
$607$	9.90776	−	4.77132i	0.402143	−	0.193662i	0.624012	+	0.781414i	$0.285501\pi$
$608$		0			0
$609$	−17.8750	−	2.64416i	−0.724331	−	0.107147i
$610$		0			0
$611$	−36.8219	+	17.7325i	−1.48965	+	0.717379i
$612$		0			0
$613$	9.39569	−	11.7818i	0.379488	−	0.475863i	−0.555003	−	0.831848i	$-0.687283\pi$
$613$	9.39569	−	11.7818i	0.379488	−	0.475863i	0.934492	+	0.355985i	$0.115854\pi$
$614$		0			0
$615$	50.7195	+	24.4252i	2.04521	+	0.984920i
$616$		0			0
$617$	6.36173	−	27.8726i	0.256114	−	1.12211i	−0.669253	−	0.743034i	$-0.733386\pi$
$617$	6.36173	−	27.8726i	0.256114	−	1.12211i	0.925367	−	0.379073i	$-0.123757\pi$
$618$		0			0
$619$	11.4439	−	14.3502i	0.459969	−	0.576783i	−0.496714	−	0.867914i	$-0.665460\pi$
$619$	11.4439	−	14.3502i	0.459969	−	0.576783i	0.956683	+	0.291131i	$0.0940317\pi$
$620$		0			0
$621$	−42.3896			−1.70103
$622$		0			0
$623$	4.37758	+	2.10813i	0.175384	+	0.0844606i
$624$		0			0
$625$	1.72946	+	7.57728i	0.0691785	+	0.303091i
$626$		0			0
$627$	4.22306	+	18.5024i	0.168653	+	0.738916i
$628$		0			0
$629$	−0.892621	+	3.91083i	−0.0355911	+	0.155935i
$630$		0			0
$631$	−7.33112	−	9.19294i	−0.291847	−	0.365965i	0.614193	−	0.789156i	$-0.289482\pi$
$631$	−7.33112	−	9.19294i	−0.291847	−	0.365965i	−0.906041	+	0.423190i	$0.860910\pi$
$632$		0			0
$633$	61.7820	−	29.7526i	2.45561	−	1.18256i
$634$		0			0
$635$	−9.20005	−	11.5365i	−0.365093	−	0.457812i
$636$		0			0
$637$	−38.2826			−1.51681
$638$		0			0
$639$	53.0605			2.09904
$640$		0			0
$641$	−13.7003	−	17.1796i	−0.541128	−	0.678553i	0.433816	−	0.901001i	$-0.357167\pi$
$641$	−13.7003	−	17.1796i	−0.541128	−	0.678553i	−0.974945	+	0.222448i	$0.928595\pi$
$642$		0			0
$643$	4.28523	−	2.06366i	0.168993	−	0.0813828i	−0.347475	−	0.937689i	$-0.612961\pi$
$643$	4.28523	−	2.06366i	0.168993	−	0.0813828i	0.516468	+	0.856307i	$0.327247\pi$
$644$		0			0
$645$	7.95922	+	9.98055i	0.313394	+	0.392984i
$646$		0			0
$647$	−4.36680	+	19.1322i	−0.171677	+	0.752165i	0.813632	+	0.581381i	$0.197487\pi$
$647$	−4.36680	+	19.1322i	−0.171677	+	0.752165i	−0.985308	+	0.170784i	$0.945370\pi$
$648$		0			0
$649$	3.93117	+	17.2236i	0.154312	+	0.676085i
$650$		0			0
$651$	−2.24045	−	9.81603i	−0.0878100	−	0.384721i
$652$		0			0
$653$	24.4943	+	11.7958i	0.958535	+	0.461606i	0.846671	−	0.532117i	$-0.178603\pi$
$653$	24.4943	+	11.7958i	0.958535	+	0.461606i	0.111864	+	0.993723i	$0.464318\pi$
$654$		0			0
$655$	−38.7237			−1.51306
$656$		0			0
$657$	−35.0753	+	43.9830i	−1.36842	+	1.71594i
$658$		0			0
$659$	−10.3160	+	45.1974i	−0.401855	+	1.76064i	0.218025	+	0.975943i	$0.430038\pi$
$659$	−10.3160	+	45.1974i	−0.401855	+	1.76064i	−0.619880	+	0.784697i	$0.712819\pi$
$660$		0			0
$661$	6.61825	+	3.18718i	0.257420	+	0.123967i	0.558144	−	0.829744i	$-0.311514\pi$
$661$	6.61825	+	3.18718i	0.257420	+	0.123967i	−0.300724	+	0.953711i	$0.597228\pi$
$662$		0			0
$663$	−8.34337	+	10.4623i	−0.324030	+	0.406320i
$664$		0			0
$665$	11.4387	−	5.50857i	0.443573	−	0.213613i
$666$		0			0
$667$	7.60127	−	19.5248i	0.294322	−	0.756004i
$668$		0			0
$669$	75.1673	−	36.1987i	2.90614	−	1.39952i
$670$		0			0
$671$	−9.57142	+	12.0022i	−0.369500	+	0.463339i
$672$		0			0
$673$	31.0497	+	14.9528i	1.19688	+	0.576387i	0.922785	−	0.385316i	$-0.125908\pi$
$673$	31.0497	+	14.9528i	1.19688	+	0.576387i	0.274094	+	0.961703i	$0.411622\pi$
$674$		0			0
$675$	17.8079	−	78.0216i	0.685427	−	3.00305i
$676$		0			0
$677$	13.6693	−	17.1408i	0.525356	−	0.658775i	−0.446381	−	0.894843i	$-0.647287\pi$
$677$	13.6693	−	17.1408i	0.525356	−	0.658775i	0.971737	+	0.236068i	$0.0758588\pi$
$678$		0			0
$679$	−8.70056			−0.333897
$680$		0			0
$681$	6.03946	+	2.90845i	0.231433	+	0.111452i
$682$		0			0
$683$	6.82679	+	29.9101i	0.261220	+	1.14448i	0.919930	+	0.392082i	$0.128245\pi$
$683$	6.82679	+	29.9101i	0.261220	+	1.14448i	−0.658710	+	0.752397i	$0.728898\pi$
$684$		0			0
$685$	7.29452	+	31.9594i	0.278709	+	1.22110i
$686$		0			0
$687$	9.67524	−	42.3900i	0.369134	−	1.61728i
$688$		0			0
$689$	−5.76696	−	7.23153i	−0.219704	−	0.275500i
$690$		0			0
$691$	−5.24069	+	2.52378i	−0.199365	+	0.0960092i	−0.530902	−	0.847433i	$-0.678147\pi$
$691$	−5.24069	+	2.52378i	−0.199365	+	0.0960092i	0.331537	+	0.943442i	$0.392433\pi$
$692$		0			0
$693$	−8.18355	−	10.2619i	−0.310867	−	0.389815i
$694$		0			0
$695$	62.0719			2.35452
$696$		0			0
$697$	3.41957			0.129525
$698$		0			0
$699$	−15.3610	−	19.2621i	−0.581006	−	0.728558i
$700$		0			0
$701$	−2.16767	+	1.04389i	−0.0818717	+	0.0394273i	−0.474372	−	0.880325i	$-0.657325\pi$
$701$	−2.16767	+	1.04389i	−0.0818717	+	0.0394273i	0.392500	+	0.919752i	$0.371610\pi$
$702$		0			0
$703$	12.6192	+	15.8240i	0.475943	+	0.596814i
$704$		0			0
$705$	14.9921	−	65.6845i	0.564634	−	2.47382i
$706$		0			0
$707$	−0.561696	−	2.46095i	−0.0211248	−	0.0925536i
$708$		0			0
$709$	−3.01173	−	13.1952i	−0.113108	−	0.495558i	−0.999470	−	0.0325644i	$-0.989633\pi$
$709$	−3.01173	−	13.1952i	−0.113108	−	0.495558i	0.886362	−	0.462993i	$-0.153225\pi$
$710$		0			0
$711$	−32.9581	−	15.8718i	−1.23603	−	0.595238i
$712$		0			0
$713$	11.6748			0.437223
$714$		0			0
$715$	26.6562	−	33.4258i	0.996886	−	1.25005i
$716$		0			0
$717$	−12.9818	+	56.8769i	−0.484813	+	2.12411i
$718$		0			0
$719$	1.65460	+	0.796816i	0.0617063	+	0.0297162i	0.464482	−	0.885582i	$-0.346240\pi$
$719$	1.65460	+	0.796816i	0.0617063	+	0.0297162i	−0.402776	+	0.915299i	$0.631955\pi$
$720$		0			0
$721$	5.21861	−	6.54393i	0.194351	−	0.243709i
$722$		0			0
$723$	−29.5970	+	14.2532i	−1.10072	+	0.530080i
$724$		0			0
$725$	32.7438	+	22.1932i	1.21607	+	0.824234i
$726$		0			0
$727$	−0.917603	+	0.441894i	−0.0340320	+	0.0163890i	−0.450822	−	0.892614i	$-0.648869\pi$
$727$	−0.917603	+	0.441894i	−0.0340320	+	0.0163890i	0.416790	+	0.909003i	$0.363155\pi$
$728$		0			0
$729$	−5.73395	+	7.19015i	−0.212369	+	0.266302i
$730$		0			0
$731$	0.698646	+	0.336450i	0.0258404	+	0.0124441i
$732$		0			0
$733$	−7.87707	+	34.5117i	−0.290946	+	1.27472i	0.592265	+	0.805743i	$0.298234\pi$
$733$	−7.87707	+	34.5117i	−0.290946	+	1.27472i	−0.883211	+	0.468975i	$0.844623\pi$
$734$		0			0
$735$	39.3482	−	49.3411i	1.45138	−	1.81997i
$736$		0			0
$737$	−22.9282			−0.844570
$738$		0			0
$739$	2.75105	+	1.32484i	0.101199	+	0.0487349i	0.483798	−	0.875179i	$-0.339257\pi$
$739$	2.75105	+	1.32484i	0.101199	+	0.0487349i	−0.382599	+	0.923914i	$0.624971\pi$
$740$		0			0
$741$	15.0242	+	65.8251i	0.551926	+	2.41815i
$742$		0			0
$743$	−9.69509	−	42.4770i	−0.355679	−	1.55833i	−0.763831	−	0.645416i	$-0.776684\pi$
$743$	−9.69509	−	42.4770i	−0.355679	−	1.55833i	0.408153	−	0.912914i	$-0.366173\pi$
$744$		0			0
$745$	−13.1192	+	57.4788i	−0.480649	+	2.10586i
$746$		0			0
$747$	−15.1511	−	18.9988i	−0.554348	−	0.695130i
$748$		0			0
$749$	7.28202	−	3.50683i	0.266079	−	0.128137i
$750$		0			0
$751$	−23.2415	−	29.1440i	−0.848096	−	1.06348i	−0.997209	−	0.0746582i	$-0.976213\pi$
$751$	−23.2415	−	29.1440i	−0.848096	−	1.06348i	0.149114	−	0.988820i	$-0.452358\pi$
$752$		0			0
$753$	−3.89593			−0.141976
$754$		0			0
$755$	2.38684			0.0868662
$756$		0			0
$757$	22.5409	+	28.2654i	0.819262	+	1.02732i	0.999048	+	0.0436167i	$0.0138880\pi$
$757$	22.5409	+	28.2654i	0.819262	+	1.02732i	−0.179786	+	0.983706i	$0.557541\pi$
$758$		0			0
$759$	20.0125	−	9.63749i	0.726406	−	0.349819i
$760$		0			0
$761$	28.2947	+	35.4804i	1.02568	+	1.28616i	0.957482	+	0.288491i	$0.0931537\pi$
$761$	28.2947	+	35.4804i	1.02568	+	1.28616i	0.0681984	+	0.997672i	$0.478275\pi$
$762$		0			0
$763$	1.44175	−	6.31670i	0.0521947	−	0.228680i
$764$		0			0
$765$	−3.36344	−	14.7362i	−0.121606	−	0.532789i
$766$		0			0
$767$	13.9857	+	61.2755i	0.504995	+	2.21253i
$768$		0			0
$769$	7.01291	+	3.37724i	0.252892	+	0.121786i	0.556035	−	0.831159i	$-0.312322\pi$
$769$	7.01291	+	3.37724i	0.252892	+	0.121786i	−0.303144	+	0.952945i	$0.598036\pi$
$770$		0			0
$771$	17.8451			0.642677
$772$		0			0
$773$	−4.86134	+	6.09593i	−0.174850	+	0.219255i	−0.861532	−	0.507702i	$-0.830495\pi$
$773$	−4.86134	+	6.09593i	−0.174850	+	0.219255i	0.686682	+	0.726958i	$0.259066\pi$
$774$		0			0
$775$	−4.90458	+	21.4884i	−0.176178	+	0.771886i
$776$		0			0
$777$	−18.4062	−	8.86393i	−0.660317	−	0.317992i
$778$		0			0
$779$	10.7574	−	13.4894i	0.385425	−	0.483307i
$780$		0			0
$781$	−13.5406	+	6.52081i	−0.484520	+	0.233333i
$782$		0			0
$783$	29.4747	+	50.7303i	1.05334	+	1.81295i
$784$		0			0
$785$	3.89125	−	1.87393i	0.138885	−	0.0668833i
$786$		0			0
$787$	−21.0520	+	26.3984i	−0.750424	+	0.941003i	−0.999623	−	0.0274499i	$-0.991261\pi$
$787$	−21.0520	+	26.3984i	−0.750424	+	0.941003i	0.249199	+	0.968452i	$0.419833\pi$
$788$		0			0
$789$	−66.6168	−	32.0809i	−2.37162	−	1.14211i
$790$		0			0
$791$	−4.39968	+	19.2762i	−0.156435	+	0.685384i
$792$		0			0
$793$	−34.0517	+	42.6995i	−1.20921	+	1.51630i
$794$		0			0
$795$	15.2480			0.540790
$796$		0			0
$797$	−36.4754	−	17.5656i	−1.29202	−	0.622206i	−0.343572	−	0.939126i	$-0.611637\pi$
$797$	−36.4754	−	17.5656i	−1.29202	−	0.622206i	−0.948452	+	0.316921i	$0.897351\pi$
$798$		0			0
$799$	−0.910684	−	3.98997i	−0.0322177	−	0.141155i
$800$		0			0
$801$	−6.49457	−	28.4546i	−0.229474	−	1.00539i
$802$		0			0
$803$	3.54568	−	15.5346i	0.125124	−	0.548206i
$804$		0			0
$805$	−9.26466	−	11.6175i	−0.326536	−	0.409464i
$806$		0			0
$807$	−21.0396	+	10.1321i	−0.740629	+	0.356668i
$808$		0			0
$809$	−30.0090	−	37.6301i	−1.05506	−	1.32300i	−0.944274	−	0.329159i	$-0.893235\pi$
$809$	−30.0090	−	37.6301i	−1.05506	−	1.32300i	−0.110786	−	0.993844i	$-0.535337\pi$
$810$		0			0
$811$	26.2797			0.922806			0.461403	−	0.887191i	$-0.347346\pi$
$811$	26.2797			0.922806			0.461403	+	0.887191i	$0.347346\pi$
$812$		0			0
$813$	−58.8804			−2.06503
$814$		0			0
$815$	−22.2161	−	27.8581i	−0.778195	−	0.975825i
$816$		0			0
$817$	3.52504	−	1.69757i	0.123326	−	0.0593905i
$818$		0			0
$819$	−29.1142	−	36.5081i	−1.01733	−	1.27569i
$820$		0			0
$821$	9.85273	−	43.1676i	0.343863	−	1.50656i	−0.446981	−	0.894543i	$-0.647501\pi$
$821$	9.85273	−	43.1676i	0.343863	−	1.50656i	0.790844	−	0.612018i	$-0.209642\pi$
$822$		0			0
$823$	−2.19430	−	9.61387i	−0.0764886	−	0.335119i	0.922177	−	0.386769i	$-0.126409\pi$
$823$	−2.19430	−	9.61387i	−0.0764886	−	0.335119i	−0.998665	+	0.0516505i	$0.983552\pi$
$824$		0			0
$825$	9.33135	+	40.8833i	0.324876	+	1.42337i
$826$		0			0
$827$	−16.2539	−	7.82747i	−0.565204	−	0.272188i	0.129386	−	0.991594i	$-0.458700\pi$
$827$	−16.2539	−	7.82747i	−0.565204	−	0.272188i	−0.694589	+	0.719407i	$0.744414\pi$
$828$		0			0
$829$	11.5967			0.402770			0.201385	−	0.979512i	$-0.435456\pi$
$829$	11.5967			0.402770			0.201385	+	0.979512i	$0.435456\pi$
$830$		0			0
$831$	7.97519	−	10.0006i	0.276656	−	0.346916i
$832$		0			0
$833$	0.853047	−	3.73744i	0.0295563	−	0.129495i
$834$		0			0
$835$	62.5851	+	30.1394i	2.16585	+	1.04302i
$836$		0			0
$837$	−20.3832	+	25.5597i	−0.704546	+	0.883473i
$838$		0			0
$839$	−0.749420	+	0.360902i	−0.0258729	+	0.0124597i	−0.446775	−	0.894646i	$-0.647428\pi$
$839$	−0.749420	+	0.360902i	−0.0258729	+	0.0124597i	0.420903	+	0.907106i	$0.361713\pi$
$840$		0			0
$841$	−28.6520	+	4.47927i	−0.987999	+	0.154458i
$842$		0			0
$843$	1.60341	−	0.772164i	0.0552245	−	0.0265947i
$844$		0			0
$845$	66.3544	−	83.2057i	2.28266	−	2.86236i
$846$		0			0
$847$	−7.42305	−	3.57475i	−0.255059	−	0.122830i
$848$		0			0
$849$	16.2486	−	71.1898i	0.557650	−	2.44323i
$850$		0			0
$851$	14.7696	−	18.5204i	0.506294	−	0.634872i
$852$		0			0
$853$	3.70379			0.126815			0.0634077	−	0.997988i	$-0.479803\pi$
$853$	3.70379			0.126815			0.0634077	+	0.997988i	$0.479803\pi$
$854$		0			0
$855$	−68.7116	−	33.0898i	−2.34989	−	1.13165i
$856$		0			0
$857$	2.26556	+	9.92607i	0.0773901	+	0.339068i	0.998769	−	0.0495967i	$-0.0157936\pi$
$857$	2.26556	+	9.92607i	0.0773901	+	0.339068i	−0.921379	+	0.388665i	$0.872936\pi$
$858$		0			0
$859$	−4.88508	−	21.4029i	−0.166677	−	0.730259i	−0.987310	−	0.158804i	$-0.949236\pi$
$859$	−4.88508	−	21.4029i	−0.166677	−	0.730259i	0.820633	−	0.571455i	$-0.193621\pi$
$860$		0			0
$861$	−3.87525	+	16.9786i	−0.132068	+	0.578628i
$862$		0			0
$863$	22.1822	+	27.8156i	0.755092	+	0.946855i	0.999741	−	0.0227565i	$-0.00724423\pi$
$863$	22.1822	+	27.8156i	0.755092	+	0.946855i	−0.244649	+	0.969612i	$0.578673\pi$
$864$		0			0
$865$	19.1222	−	9.20877i	0.650174	−	0.313107i
$866$		0			0
$867$	31.8843	+	39.9816i	1.08285	+	1.35785i
$868$		0			0
$869$	10.3612			0.351479
$870$		0			0
$871$	−81.5704			−2.76391
$872$		0			0
$873$	32.5860	+	40.8616i	1.10287	+	1.38295i
$874$		0			0
$875$	8.07038	−	3.88649i	0.272829	−	0.131387i
$876$		0			0
$877$	2.05777	+	2.58037i	0.0694861	+	0.0871328i	0.815360	−	0.578955i	$-0.196539\pi$
$877$	2.05777	+	2.58037i	0.0694861	+	0.0871328i	−0.745874	+	0.666087i	$0.767968\pi$
$878$		0			0
$879$	−3.49684	+	15.3206i	−0.117945	+	0.516752i
$880$		0			0
$881$	12.1239	+	53.1184i	0.408466	+	1.78960i	0.591290	+	0.806459i	$0.298619\pi$
$881$	12.1239	+	53.1184i	0.408466	+	1.78960i	−0.182825	+	0.983146i	$0.558524\pi$
$882$		0			0
$883$	10.3680	+	45.4253i	0.348912	+	1.52868i	0.779655	+	0.626209i	$0.215394\pi$
$883$	10.3680	+	45.4253i	0.348912	+	1.52868i	−0.430743	+	0.902475i	$0.641748\pi$
$884$		0			0
$885$	−93.3509	−	44.9554i	−3.13796	−	1.51116i
$886$		0			0
$887$	41.1122			1.38041			0.690206	−	0.723613i	$-0.257520\pi$
$887$	41.1122			1.38041			0.690206	+	0.723613i	$0.257520\pi$
$888$		0			0
$889$	2.84612	−	3.56892i	0.0954558	−	0.119698i
$890$		0			0
$891$	−5.77964	+	25.3223i	−0.193625	+	0.848327i
$892$		0			0
$893$	−18.6043	−	8.95937i	−0.622570	−	0.299814i
$894$		0			0
$895$	−29.3636	+	36.8208i	−0.981516	+	1.23078i
$896$		0			0
$897$	71.1973	−	34.2868i	2.37721	−	1.14480i
$898$		0			0
$899$	−8.11782	−	13.9719i	−0.270744	−	0.465990i
$900$		0			0
$901$	0.834503	−	0.401876i	0.0278013	−	0.0133884i
$902$		0			0
$903$	−2.46226	+	3.08757i	−0.0819388	+	0.102748i
$904$		0			0
$905$	−7.28582	−	3.50866i	−0.242189	−	0.116632i
$906$		0			0
$907$	4.97208	−	21.7841i	0.165095	−	0.723330i	−0.822816	−	0.568308i	$-0.807598\pi$
$907$	4.97208	−	21.7841i	0.165095	−	0.723330i	0.987911	−	0.155021i	$-0.0495447\pi$
$908$		0			0
$909$	−9.45398	+	11.8549i	−0.313569	+	0.393203i
$910$		0			0
$911$	32.2237			1.06762			0.533810	−	0.845605i	$-0.320760\pi$
$911$	32.2237			1.06762			0.533810	+	0.845605i	$0.320760\pi$
$912$		0			0
$913$	6.20126	+	2.98637i	0.205232	+	0.0988344i
$914$		0			0
$915$	−20.0344	−	87.7762i	−0.662315	−	2.90179i
$916$		0			0
$917$	−2.66570	−	11.6792i	−0.0880291	−	0.385681i
$918$		0			0
$919$	7.53651	−	33.0196i	0.248606	−	1.08922i	−0.684329	−	0.729173i	$-0.739905\pi$
$919$	7.53651	−	33.0196i	0.248606	−	1.08922i	0.932936	−	0.360043i	$-0.117238\pi$
$920$		0			0
$921$	53.7960	+	67.4581i	1.77264	+	2.22282i
$922$		0			0
$923$	−48.1727	+	23.1987i	−1.58562	+	0.763595i
$924$		0			0
$925$	27.8837	+	34.9651i	0.916810	+	1.14964i
$926$		0			0
$927$	−50.2782			−1.65135
$928$		0			0
$929$	−42.4834			−1.39383			−0.696917	−	0.717152i	$-0.745445\pi$
$929$	−42.4834			−1.39383			−0.696917	+	0.717152i	$0.745445\pi$
$930$		0			0
$931$	−12.0598	−	15.1225i	−0.395243	−	0.495619i
$932$		0			0
$933$	45.7507	−	22.0324i	1.49781	−	0.721307i
$934$		0			0
$935$	2.66931	+	3.34721i	0.0872958	+	0.109465i
$936$		0			0
$937$	−4.08435	+	17.8947i	−0.133430	+	0.584595i	0.863364	+	0.504582i	$0.168353\pi$
$937$	−4.08435	+	17.8947i	−0.133430	+	0.584595i	−0.996794	+	0.0800130i	$0.974504\pi$
$938$		0			0
$939$	1.96478	+	8.60825i	0.0641181	+	0.280920i
$940$		0			0
$941$	−12.2586	−	53.7084i	−0.399618	−	1.75084i	−0.628904	−	0.777483i	$-0.716496\pi$
$941$	−12.2586	−	53.7084i	−0.399618	−	1.75084i	0.229285	−	0.973359i	$-0.426361\pi$
$942$		0			0
$943$	−18.1938	−	8.76166i	−0.592471	−	0.285319i
$944$		0			0
$945$	41.6097			1.35356
$946$		0			0
$947$	−30.0768	+	37.7151i	−0.977364	+	1.22558i	−0.00313982	+	0.999995i	$0.500999\pi$
$947$	−30.0768	+	37.7151i	−0.977364	+	1.22558i	−0.974224	+	0.225581i	$0.927572\pi$
$948$		0			0
$949$	12.6143	−	55.2668i	0.409477	−	1.79404i
$950$		0			0
$951$	63.5434	+	30.6009i	2.06053	+	0.992301i
$952$		0			0
$953$	19.7048	−	24.7090i	0.638300	−	0.800403i	−0.352489	−	0.935816i	$-0.614665\pi$
$953$	19.7048	−	24.7090i	0.638300	−	0.800403i	0.990789	+	0.135413i	$0.0432361\pi$
$954$		0			0
$955$	−85.0009	+	40.9343i	−2.75056	+	1.32460i
$956$		0			0
$957$	−25.4491	−	17.2489i	−0.822651	−	0.557579i
$958$		0			0
$959$	−9.13689	+	4.40010i	−0.295046	+	0.142087i
$960$		0			0
$961$	−13.7143	+	17.1972i	−0.442398	+	0.554749i
$962$		0			0
$963$	−43.7428	−	21.0654i	−1.40959	−	0.678823i
$964$		0			0
$965$	−7.93537	+	34.7671i	−0.255448	+	1.11919i
$966$		0			0
$967$	4.83947	−	6.06851i	0.155627	−	0.195150i	−0.697905	−	0.716190i	$-0.745884\pi$
$967$	4.83947	−	6.06851i	0.155627	−	0.195150i	0.853532	+	0.521040i	$0.174456\pi$
$968$		0			0
$969$	−6.76114			−0.217199
$970$		0			0
$971$	−1.17291	−	0.564846i	−0.0376406	−	0.0181268i	0.414969	−	0.909836i	$-0.363793\pi$
$971$	−1.17291	−	0.564846i	−0.0376406	−	0.0181268i	−0.452609	+	0.891709i	$0.649507\pi$
$972$		0			0
$973$	4.27296	+	18.7211i	0.136985	+	0.600170i
$974$		0			0
$975$	33.1977	+	145.448i	1.06318	+	4.65808i
$976$		0			0
$977$	−5.70479	+	24.9943i	−0.182512	+	0.799639i	0.797917	+	0.602767i	$0.205935\pi$
$977$	−5.70479	+	24.9943i	−0.182512	+	0.799639i	−0.980429	+	0.196871i	$0.936922\pi$
$978$		0			0
$979$	5.15425	+	6.46322i	0.164730	+	0.206565i
$980$		0			0
$981$	−35.0657	+	16.8867i	−1.11956	+	0.539152i
$982$		0			0
$983$	−6.69209	−	8.39161i	−0.213444	−	0.267651i	0.663571	−	0.748114i	$-0.269040\pi$
$983$	−6.69209	−	8.39161i	−0.213444	−	0.267651i	−0.877015	+	0.480463i	$0.840469\pi$
$984$		0			0
$985$	8.70190			0.277266
$986$		0			0
$987$	20.8427			0.663430
$988$		0			0
$989$	−2.85508	−	3.58016i	−0.0907863	−	0.113842i
$990$		0			0
$991$	−20.6729	+	9.95553i	−0.656695	+	0.316248i	−0.732392	−	0.680883i	$-0.761596\pi$
$991$	−20.6729	+	9.95553i	−0.656695	+	0.316248i	0.0756967	+	0.997131i	$0.475882\pi$
$992$		0			0
$993$	−50.2001	−	62.9490i	−1.59305	−	1.99763i
$994$		0			0
$995$	−7.23833	+	31.7132i	−0.229470	+	1.00538i
$996$		0			0
$997$	−9.54388	−	41.8145i	−0.302258	−	1.32428i	−0.866710	−	0.498812i	$-0.833770\pi$
$997$	−9.54388	−	41.8145i	−0.302258	−	1.32428i	0.564453	−	0.825465i	$-0.309087\pi$
$998$		0			0
$999$	14.7606	+	64.6704i	0.467004	+	2.04608i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	116.2.g.b.49.1	yes	12
3.2	odd	2		1044.2.u.c.397.2		12
4.3	odd	2		464.2.u.g.49.2		12
29.4	even	14		3364.2.a.p.1.6		6
29.10	odd	28		3364.2.c.j.1681.1		12
29.16	even	7	inner	116.2.g.b.45.1	✓	12
29.19	odd	28		3364.2.c.j.1681.12		12
29.25	even	7		3364.2.a.m.1.1		6
87.74	odd	14		1044.2.u.c.973.2		12
116.103	odd	14		464.2.u.g.161.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
116.2.g.b.45.1	✓	12	29.16	even	7	inner
116.2.g.b.49.1	yes	12	1.1	even	1	trivial
464.2.u.g.49.2		12	4.3	odd	2
464.2.u.g.161.2		12	116.103	odd	14
1044.2.u.c.397.2		12	3.2	odd	2
1044.2.u.c.973.2		12	87.74	odd	14
3364.2.a.m.1.1		6	29.25	even	7
3364.2.a.p.1.6		6	29.4	even	14
3364.2.c.j.1681.1		12	29.10	odd	28
3364.2.c.j.1681.12		12	29.19	odd	28

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:	\( N \)	\(=\)	\( 116 = 2^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	116.g (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.92469 - 2.41349i) q^{3} +(-3.16565 + 1.52449i) q^{5} +(-0.677712 - 0.849824i) q^{7} +(-1.45292 + 6.36565i) q^{9} +O(q^{10})\)	\(q+(-1.92469 - 2.41349i) q^{3} +(-3.16565 + 1.52449i) q^{5} +(-0.677712 - 0.849824i) q^{7} +(-1.45292 + 6.36565i) q^{9} +(-0.411526 - 1.80301i) q^{11} +(-1.46407 - 6.41449i) q^{13} +(9.77224 + 4.70606i) q^{15} +0.658856 q^{17} +(2.07266 - 2.59903i) q^{19} +(-0.746652 + 3.27130i) q^{21} +(-3.50543 - 1.68813i) q^{23} +(4.57978 - 5.74286i) q^{25} +(9.81605 - 4.72716i) q^{27} +(0.417143 + 5.36898i) q^{29} +(-2.70350 + 1.30194i) q^{31} +(-3.55949 + 4.46346i) q^{33} +(3.44095 + 1.65707i) q^{35} +(-1.35480 + 5.93579i) q^{37} +(-12.6634 + 15.8794i) q^{39} +5.19016 q^{41} +(1.06039 + 0.510658i) q^{43} +(-5.10497 - 22.3664i) q^{45} +(-1.38222 - 6.05590i) q^{47} +(1.29474 - 5.67262i) q^{49} +(-1.26809 - 1.59014i) q^{51} +(1.26659 - 0.609959i) q^{53} +(4.05143 + 5.08034i) q^{55} -10.2619 q^{57} -9.55267 q^{59} +(-5.17547 - 6.48983i) q^{61} +(6.39434 - 3.07935i) q^{63} +(14.4136 + 18.0740i) q^{65} +(2.75876 - 12.0869i) q^{67} +(2.67260 + 11.7094i) q^{69} +(-1.80831 - 7.92271i) q^{71} +(7.76268 + 3.73831i) q^{73} -22.6750 q^{75} +(-1.25335 + 1.57165i) q^{77} +(-1.24667 + 5.46204i) q^{79} +(-12.6536 - 6.09364i) q^{81} +(-2.32045 + 2.90975i) q^{83} +(-2.08570 + 1.00442i) q^{85} +(12.1551 - 11.3404i) q^{87} +(-4.02735 + 1.93947i) q^{89} +(-4.45897 + 5.59137i) q^{91} +(8.34560 + 4.01903i) q^{93} +(-2.59909 + 11.3874i) q^{95} +(4.99069 - 6.25813i) q^{97} +12.0753 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - q^{5} - 7 q^{7} + q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 - q^5 - 7 * q^7 + q^9	\( 12 q - 3 q^{3} - q^{5} - 7 q^{7} + q^{9} + 3 q^{11} - 21 q^{13} + 29 q^{15} - 10 q^{17} + 17 q^{19} + 3 q^{21} - 19 q^{23} - 3 q^{25} + 9 q^{27} - 5 q^{29} - 27 q^{31} - 47 q^{33} + 27 q^{35} - 3 q^{37} - 37 q^{39} - 2 q^{41} - 9 q^{43} + 22 q^{45} + 19 q^{47} + 17 q^{49} + 2 q^{51} + 22 q^{53} + 49 q^{55} + 30 q^{57} + 36 q^{59} - 33 q^{61} + 9 q^{63} + 38 q^{65} - 3 q^{67} + 47 q^{69} - 35 q^{71} + 34 q^{73} - 44 q^{75} - 27 q^{77} - 19 q^{79} - 39 q^{81} - q^{83} - 34 q^{85} - 25 q^{87} - 11 q^{89} - 23 q^{91} + 7 q^{93} - 105 q^{95} + 38 q^{97} - 16 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 - q^5 - 7 * q^7 + q^9 + 3 * q^11 - 21 * q^13 + 29 * q^15 - 10 * q^17 + 17 * q^19 + 3 * q^21 - 19 * q^23 - 3 * q^25 + 9 * q^27 - 5 * q^29 - 27 * q^31 - 47 * q^33 + 27 * q^35 - 3 * q^37 - 37 * q^39 - 2 * q^41 - 9 * q^43 + 22 * q^45 + 19 * q^47 + 17 * q^49 + 2 * q^51 + 22 * q^53 + 49 * q^55 + 30 * q^57 + 36 * q^59 - 33 * q^61 + 9 * q^63 + 38 * q^65 - 3 * q^67 + 47 * q^69 - 35 * q^71 + 34 * q^73 - 44 * q^75 - 27 * q^77 - 19 * q^79 - 39 * q^81 - q^83 - 34 * q^85 - 25 * q^87 - 11 * q^89 - 23 * q^91 + 7 * q^93 - 105 * q^95 + 38 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more