LMFDB - Embedded newform 825.2.bx.h.499.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(49,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 4]))

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

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

chi := DirichletCharacter("825.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.bx (of order $10$, degree $4$, not 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{14} + 15x^{12} - 59x^{10} + 104x^{8} - 59x^{6} + 15x^{4} - x^{2} + 1 $ x^16 - x^14 + 15x^12 - 59x^10 + 104x^8 - 59x^6 + 15*x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			499.3
Root			$-1.23158 + 1.69513i$ of defining polynomial
Character	$\chi$	$=$	825.499
Dual form			825.2.bx.h.124.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.817172 - 1.12474i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.0207616 + 0.0638975i) q^{4} +(1.12474 - 0.817172i) q^{6} +(1.21506 - 0.394797i) q^{7} +(2.73326 + 0.888090i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.817172 - 1.12474i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.0207616 + 0.0638975i) q^{4} +(1.12474 - 0.817172i) q^{6} +(1.21506 - 0.394797i) q^{7} +(2.73326 + 0.888090i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-1.20381 + 3.09044i) q^{11} +0.0671858i q^{12} +(-0.833694 + 1.14748i) q^{13} +(0.548870 - 1.68925i) q^{14} +(3.12371 - 2.26951i) q^{16} +(2.93893 + 4.04508i) q^{17} +(1.32221 - 0.429613i) q^{18} +(-0.0488697 + 0.150406i) q^{19} +1.27759 q^{21} +(2.49222 + 3.87940i) q^{22} -5.00829i q^{23} +(2.32505 + 1.68925i) q^{24} +(0.609348 + 1.87538i) q^{26} +(0.587785 + 0.809017i) q^{27} +(0.0504531 + 0.0694428i) q^{28} +(-1.93913 - 5.96802i) q^{29} +(-2.46735 - 1.79264i) q^{31} +0.379898i q^{32} +(-2.09989 + 2.56719i) q^{33} +6.95128 q^{34} +(-0.0207616 + 0.0638975i) q^{36} +(-4.46988 + 1.45235i) q^{37} +(0.129232 + 0.177873i) q^{38} +(-1.14748 + 0.833694i) q^{39} +(2.34419 - 7.21469i) q^{41} +(1.04401 - 1.43696i) q^{42} +5.41324i q^{43} +(-0.222465 - 0.0127583i) q^{44} +(-5.63303 - 4.09264i) q^{46} +(7.82920 + 2.54386i) q^{47} +(3.67214 - 1.19315i) q^{48} +(-4.34261 + 3.15509i) q^{49} +(1.54508 + 4.75528i) q^{51} +(-0.0906300 - 0.0294475i) q^{52} +(5.50548 - 7.57764i) q^{53} +1.39026 q^{54} +3.67169 q^{56} +(-0.0929558 + 0.127943i) q^{57} +(-8.29708 - 2.69588i) q^{58} +(-2.50256 - 7.70209i) q^{59} +(11.5623 - 8.40047i) q^{61} +(-4.03250 + 1.31024i) q^{62} +(1.21506 + 0.394797i) q^{63} +(6.67470 + 4.84945i) q^{64} +(1.17144 + 4.45967i) q^{66} +7.38362i q^{67} +(-0.197454 + 0.271772i) q^{68} +(1.54765 - 4.76317i) q^{69} +(5.48204 - 3.98294i) q^{71} +(1.68925 + 2.32505i) q^{72} +(-8.23717 + 2.67642i) q^{73} +(-2.01914 + 6.21429i) q^{74} -0.0106252 q^{76} +(-0.242610 + 4.23034i) q^{77} +1.97189i q^{78} +(-2.05953 - 1.49634i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-6.19905 - 8.53225i) q^{82} +(-5.94964 - 8.18897i) q^{83} +(0.0265248 + 0.0816349i) q^{84} +(6.08850 + 4.42355i) q^{86} -6.27515i q^{87} +(-6.03493 + 7.37788i) q^{88} -11.0447 q^{89} +(-0.559967 + 1.72340i) q^{91} +(0.320017 - 0.103980i) q^{92} +(-1.79264 - 2.46735i) q^{93} +(9.25900 - 6.72705i) q^{94} +(-0.117395 + 0.361304i) q^{96} +(-3.76886 + 5.18739i) q^{97} +7.46257i q^{98} +(-2.79042 + 1.79264i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 + 4 * q^9	$ 16 q + 4 q^{4} + 4 q^{9} - 6 q^{11} + 20 q^{14} - 40 q^{16} - 12 q^{19} - 8 q^{21} + 40 q^{24} - 16 q^{26} + 6 q^{31} - 100 q^{34} - 4 q^{36} - 12 q^{39} - 50 q^{41} - 14 q^{44} - 12 q^{46} - 42 q^{49} - 20 q^{51} - 20 q^{54} + 40 q^{56} - 70 q^{59} + 42 q^{61} + 154 q^{64} + 50 q^{66} + 10 q^{69} + 50 q^{71} + 58 q^{74} - 28 q^{76} - 60 q^{79} - 4 q^{81} + 68 q^{84} - 68 q^{86} - 64 q^{89} + 74 q^{91} + 78 q^{94} + 20 q^{96} + 6 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 + 4 * q^9 - 6 * q^11 + 20 * q^14 - 40 * q^16 - 12 * q^19 - 8 * q^21 + 40 * q^24 - 16 * q^26 + 6 * q^31 - 100 * q^34 - 4 * q^36 - 12 * q^39 - 50 * q^41 - 14 * q^44 - 12 * q^46 - 42 * q^49 - 20 * q^51 - 20 * q^54 + 40 * q^56 - 70 * q^59 + 42 * q^61 + 154 * q^64 + 50 * q^66 + 10 * q^69 + 50 * q^71 + 58 * q^74 - 28 * q^76 - 60 * q^79 - 4 * q^81 + 68 * q^84 - 68 * q^86 - 64 * q^89 + 74 * q^91 + 78 * q^94 + 20 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$-1$

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 $

$2$	0.817172	−	1.12474i	0.577828	−	0.795312i	−0.415627	−	0.909535i	$-0.636438\pi$
$2$	0.817172	−	1.12474i	0.577828	−	0.795312i	0.993455	+	0.114223i	$0.0364378\pi$
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	0.0207616	+	0.0638975i	0.0103808	+	0.0319487i
$5$		0			0
$5$		0			0
$6$	1.12474	−	0.817172i	0.459174	−	0.333609i
$7$	1.21506	−	0.394797i	0.459250	−	0.149219i	−0.0702498	−	0.997529i	$-0.522380\pi$
$7$	1.21506	−	0.394797i	0.459250	−	0.149219i	0.529500	+	0.848310i	$0.322380\pi$
$8$	2.73326	+	0.888090i	0.966353	+	0.313987i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$		0			0
$11$	−1.20381	+	3.09044i	−0.362964	+	0.931803i
$11$	−1.20381	+	3.09044i	−0.362964	+	0.931803i
$12$			0.0671858i			0.0193949i
$13$	−0.833694	+	1.14748i	−0.231225	+	0.318254i	−0.908826	−	0.417176i	$-0.863020\pi$
$13$	−0.833694	+	1.14748i	−0.231225	+	0.318254i	0.677601	+	0.735430i	$0.263020\pi$
$14$	0.548870	−	1.68925i	0.146692	−	0.451470i
$15$		0			0
$16$	3.12371	−	2.26951i	0.780927	−	0.567377i
$17$	2.93893	+	4.04508i	0.712794	+	0.981077i	0.999733	+	0.0231281i	$0.00736256\pi$
$17$	2.93893	+	4.04508i	0.712794	+	0.981077i	−0.286938	+	0.957949i	$0.592637\pi$
$18$	1.32221	−	0.429613i	0.311649	−	0.101261i
$19$	−0.0488697	+	0.150406i	−0.0112115	+	0.0345054i	−0.956506	−	0.291713i	$-0.905775\pi$
$19$	−0.0488697	+	0.150406i	−0.0112115	+	0.0345054i	0.945294	+	0.326219i	$0.105775\pi$
$20$		0			0
$21$	1.27759			0.278793
$22$	2.49222	+	3.87940i	0.531344	+	0.827092i
$23$		−	5.00829i		−	1.04430i	−0.852853	−	0.522150i	$-0.825130\pi$
$23$		−	5.00829i		−	1.04430i	0.852853	−	0.522150i	$-0.174870\pi$
$24$	2.32505	+	1.68925i	0.474599	+	0.344816i
$25$		0			0
$26$	0.609348	+	1.87538i	0.119503	+	0.367792i
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	0.0504531	+	0.0694428i	0.00953474	+	0.0131234i
$29$	−1.93913	−	5.96802i	−0.360087	−	1.10823i	−0.953001	−	0.302967i	$-0.902023\pi$
$29$	−1.93913	−	5.96802i	−0.360087	−	1.10823i	0.592914	−	0.805266i	$-0.297977\pi$
$30$		0			0
$31$	−2.46735	−	1.79264i	−0.443149	−	0.321967i	0.343736	−	0.939066i	$-0.388308\pi$
$31$	−2.46735	−	1.79264i	−0.443149	−	0.321967i	−0.786885	+	0.617100i	$0.788308\pi$
$32$			0.379898i			0.0671570i
$33$	−2.09989	+	2.56719i	−0.365545	+	0.446890i
$34$	6.95128			1.19214
$35$		0			0
$36$	−0.0207616	+	0.0638975i	−0.00346026	+	0.0106496i
$37$	−4.46988	+	1.45235i	−0.734844	+	0.238765i	−0.652447	−	0.757834i	$-0.726258\pi$
$37$	−4.46988	+	1.45235i	−0.734844	+	0.238765i	−0.0823971	+	0.996600i	$0.526258\pi$
$38$	0.129232	+	0.177873i	0.0209643	+	0.0288548i
$39$	−1.14748	+	0.833694i	−0.183744	+	0.133498i
$40$		0			0
$41$	2.34419	−	7.21469i	0.366101	−	1.12674i	−0.583187	−	0.812338i	$-0.698194\pi$
$41$	2.34419	−	7.21469i	0.366101	−	1.12674i	0.949288	−	0.314407i	$-0.101806\pi$
$42$	1.04401	−	1.43696i	0.161095	−	0.221728i
$43$			5.41324i			0.825512i	0.910842	+	0.412756i	$0.135434\pi$
$43$			5.41324i			0.825512i	−0.910842	+	0.412756i	$0.864566\pi$
$44$	−0.222465	−	0.0127583i	−0.0335378	−	0.00192339i
$45$		0			0
$46$	−5.63303	−	4.09264i	−0.830545	−	0.603426i
$47$	7.82920	+	2.54386i	1.14201	+	0.371060i	0.818127	−	0.575038i	$-0.195013\pi$
$47$	7.82920	+	2.54386i	1.14201	+	0.371060i	0.323880	+	0.946098i	$0.395013\pi$
$48$	3.67214	−	1.19315i	0.530027	−	0.172216i
$49$	−4.34261	+	3.15509i	−0.620373	+	0.450727i
$50$		0			0
$51$	1.54508	+	4.75528i	0.216355	+	0.665873i
$52$	−0.0906300	−	0.0294475i	−0.0125681	−	0.00408363i
$53$	5.50548	−	7.57764i	0.756236	−	1.04087i	−0.241282	−	0.970455i	$-0.577568\pi$
$53$	5.50548	−	7.57764i	0.756236	−	1.04087i	0.997518	−	0.0704143i	$-0.0224321\pi$
$54$	1.39026			0.189190
$55$		0			0
$56$	3.67169			0.490651
$57$	−0.0929558	+	0.127943i	−0.0123123	+	0.0169464i
$58$	−8.29708	−	2.69588i	−1.08946	−	0.353987i
$59$	−2.50256	−	7.70209i	−0.325806	−	1.00273i	−0.971076	−	0.238772i	$-0.923255\pi$
$59$	−2.50256	−	7.70209i	−0.325806	−	1.00273i	0.645270	−	0.763955i	$-0.276745\pi$
$60$		0			0
$61$	11.5623	−	8.40047i	1.48039	−	1.07557i	0.502965	−	0.864307i	$-0.332242\pi$
$61$	11.5623	−	8.40047i	1.48039	−	1.07557i	0.977429	−	0.211263i	$-0.0677576\pi$
$62$	−4.03250	+	1.31024i	−0.512128	+	0.166401i
$63$	1.21506	+	0.394797i	0.153083	+	0.0497398i
$64$	6.67470	+	4.84945i	0.834338	+	0.606182i
$65$		0			0
$66$	1.17144	+	4.45967i	0.144195	+	0.548948i
$67$			7.38362i			0.902053i	0.892511	+	0.451026i	$0.148942\pi$
$67$			7.38362i			0.902053i	−0.892511	+	0.451026i	$0.851058\pi$
$68$	−0.197454	+	0.271772i	−0.0239448	+	0.0329572i
$69$	1.54765	−	4.76317i	0.186315	−	0.573418i
$70$		0			0
$71$	5.48204	−	3.98294i	0.650599	−	0.472688i	−0.212876	−	0.977079i	$-0.568283\pi$
$71$	5.48204	−	3.98294i	0.650599	−	0.472688i	0.863475	+	0.504391i	$0.168283\pi$
$72$	1.68925	+	2.32505i	0.199080	+	0.274010i
$73$	−8.23717	+	2.67642i	−0.964087	+	0.313251i	−0.748427	−	0.663217i	$-0.769190\pi$
$73$	−8.23717	+	2.67642i	−0.964087	+	0.313251i	−0.215661	+	0.976468i	$0.569190\pi$
$74$	−2.01914	+	6.21429i	−0.234721	+	0.722396i
$75$		0			0
$76$	−0.0106252			−0.00121879
$77$	−0.242610	+	4.23034i	−0.0276480	+	0.482092i
$78$			1.97189i			0.223273i
$79$	−2.05953	−	1.49634i	−0.231716	−	0.168351i	0.465869	−	0.884854i	$-0.345742\pi$
$79$	−2.05953	−	1.49634i	−0.231716	−	0.168351i	−0.697585	+	0.716502i	$0.745742\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−6.19905	−	8.53225i	−0.684570	−	0.942230i
$83$	−5.94964	−	8.18897i	−0.653057	−	0.898856i	0.346170	−	0.938172i	$-0.387482\pi$
$83$	−5.94964	−	8.18897i	−0.653057	−	0.898856i	−0.999227	+	0.0393157i	$0.987482\pi$
$84$	0.0265248	+	0.0816349i	0.00289409	+	0.00890709i
$85$		0			0
$86$	6.08850	+	4.42355i	0.656539	+	0.477004i
$87$		−	6.27515i		−	0.672766i
$88$	−6.03493	+	7.37788i	−0.643325	+	0.786485i
$89$	−11.0447			−1.17073			−0.585367	−	0.810768i	$-0.699050\pi$
$89$	−11.0447			−1.17073			−0.585367	+	0.810768i	$0.699050\pi$
$90$		0			0
$91$	−0.559967	+	1.72340i	−0.0587005	+	0.180661i
$92$	0.320017	−	0.103980i	0.0333641	−	0.0108407i
$93$	−1.79264	−	2.46735i	−0.185888	−	0.255852i
$94$	9.25900	−	6.72705i	0.954993	−	0.693843i
$95$		0			0
$96$	−0.117395	+	0.361304i	−0.0119816	+	0.0368754i
$97$	−3.76886	+	5.18739i	−0.382669	+	0.526699i	−0.956289	−	0.292422i	$-0.905539\pi$
$97$	−3.76886	+	5.18739i	−0.382669	+	0.526699i	0.573620	+	0.819122i	$0.305539\pi$
$98$			7.46257i			0.753833i
$99$	−2.79042	+	1.79264i	−0.280448	+	0.180167i
$100$		0			0
$101$	−7.09624	−	5.15572i	−0.706102	−	0.513013i	0.175812	−	0.984424i	$-0.443745\pi$
$101$	−7.09624	−	5.15572i	−0.706102	−	0.513013i	−0.881914	+	0.471411i	$0.843745\pi$
$102$	6.61106	+	2.14807i	0.654593	+	0.212690i
$103$	−11.0005	+	3.57429i	−1.08391	+	0.352185i	−0.795892	−	0.605439i	$-0.792998\pi$
$103$	−11.0005	+	3.57429i	−1.08391	+	0.352185i	−0.288022	+	0.957624i	$0.592998\pi$
$104$	−3.29777	+	2.39597i	−0.323373	+	0.234944i
$105$		0			0
$106$	−4.02396	−	12.3845i	−0.390842	−	1.20289i
$107$	−14.5955	−	4.74238i	−1.41100	−	0.458463i	−0.498272	−	0.867021i	$-0.666032\pi$
$107$	−14.5955	−	4.74238i	−1.41100	−	0.458463i	−0.912733	+	0.408557i	$0.866032\pi$
$108$	−0.0394908	+	0.0543544i	−0.00380001	+	0.00523026i
$109$	−14.4004			−1.37931			−0.689656	−	0.724137i	$-0.742238\pi$
$109$	−14.4004			−1.37931			−0.689656	+	0.724137i	$0.742238\pi$
$110$		0			0
$111$	−4.69991			−0.446096
$112$	2.89950	−	3.99082i	0.273977	−	0.377097i
$113$	18.4168	+	5.98397i	1.73250	+	0.562924i	0.993808	−	0.111115i	$-0.0354422\pi$
$113$	18.4168	+	5.98397i	1.73250	+	0.562924i	0.738695	+	0.674039i	$0.235442\pi$
$114$	0.0679415	+	0.209102i	0.00636330	+	0.0195842i
$115$		0			0
$116$	0.341082	−	0.247811i	0.0316687	−	0.0230086i
$117$	−1.34895	+	0.438299i	−0.124710	+	0.0405207i
$118$	−10.7079	−	3.47920i	−0.985741	−	0.320287i
$119$	5.16796	+	3.75475i	0.473747	+	0.344197i
$120$		0			0
$121$	−8.10166	−	7.44064i	−0.736515	−	0.676422i
$122$		−	19.8692i		−	1.79887i
$123$	4.45892	−	6.13718i	0.402047	−	0.553371i
$124$	0.0633189	−	0.194875i	0.00568620	−	0.0175003i
$125$		0			0
$126$	1.43696	−	1.04401i	0.128015	−	0.0930080i
$127$	−3.54091	−	4.87364i	−0.314205	−	0.432466i	0.622482	−	0.782634i	$-0.286124\pi$
$127$	−3.54091	−	4.87364i	−0.314205	−	0.432466i	−0.936687	+	0.350168i	$0.886124\pi$
$128$	10.1862	−	3.30968i	0.900337	−	0.292537i
$129$	−1.67278	+	5.14830i	−0.147280	+	0.453282i
$130$		0			0
$131$	−18.7278			−1.63626			−0.818130	−	0.575034i	$-0.804989\pi$
$131$	−18.7278			−1.63626			−0.818130	+	0.575034i	$0.804989\pi$
$132$	−0.207634	−	0.0808792i	−0.0180722	−	0.00703963i
$133$			0.202046i			0.0175196i
$134$	8.30467	+	6.03369i	0.717414	+	0.521232i
$135$		0			0
$136$	4.44045	+	13.6663i	0.380765	+	1.17188i
$137$	1.78521	+	2.45714i	0.152521	+	0.209927i	0.878440	−	0.477853i	$-0.158585\pi$
$137$	1.78521	+	2.45714i	0.152521	+	0.209927i	−0.725918	+	0.687781i	$0.758585\pi$
$138$	−4.09264	−	5.63303i	−0.348388	−	0.479516i
$139$	0.683520	+	2.10366i	0.0579754	+	0.178430i	0.975851	−	0.218439i	$-0.0700966\pi$
$139$	0.683520	+	2.10366i	0.0579754	+	0.178430i	−0.917875	+	0.396869i	$0.870097\pi$
$140$		0			0
$141$	6.65992	+	4.83871i	0.560866	+	0.407493i
$142$		−	9.42063i		−	0.790562i
$143$	−2.54261	−	3.95784i	−0.212624	−	0.330971i
$144$	3.86111			0.321760
$145$		0			0
$146$	−3.72091	+	11.4518i	−0.307945	+	0.947756i
$147$	−5.10504	+	1.65873i	−0.421057	+	0.136810i
$148$	−0.185603	−	0.255461i	−0.0152565	−	0.0209988i
$149$	1.19833	−	0.870637i	0.0981710	−	0.0713254i	−0.537617	−	0.843189i	$-0.680675\pi$
$149$	1.19833	−	0.870637i	0.0981710	−	0.0713254i	0.635788	+	0.771864i	$0.280675\pi$
$150$		0			0
$151$	−2.79165	+	8.59180i	−0.227181	+	0.699191i	0.770882	+	0.636978i	$0.219816\pi$
$151$	−2.79165	+	8.59180i	−0.227181	+	0.699191i	−0.998063	+	0.0622129i	$0.980184\pi$
$152$	−0.267147	+	0.367697i	−0.0216685	+	0.0298242i
$153$			5.00000i			0.404226i
$154$	4.55978	+	3.72979i	0.367438	+	0.300555i
$155$		0			0
$156$	−0.0770945	−	0.0560124i	−0.00617250	−	0.00448458i
$157$	16.7744	+	5.45034i	1.33874	+	0.434985i	0.888891	−	0.458118i	$-0.151476\pi$
$157$	16.7744	+	5.45034i	1.33874	+	0.434985i	0.449853	+	0.893102i	$0.351476\pi$
$158$	−3.36599	+	1.09368i	−0.267784	+	0.0870082i
$159$	7.57764	−	5.50548i	0.600946	−	0.436613i
$160$		0			0
$161$	−1.97726	−	6.08538i	−0.155830	−	0.479595i
$162$	1.32221	+	0.429613i	0.103883	+	0.0337536i
$163$	13.8153	−	19.0152i	1.08210	−	1.48938i	0.224910	−	0.974379i	$-0.427791\pi$
$163$	13.8153	−	19.0152i	1.08210	−	1.48938i	0.857189	−	0.515002i	$-0.172209\pi$
$164$	0.509669			0.0397985
$165$		0			0
$166$	−14.0724			−1.09223
$167$	−0.354276	+	0.487619i	−0.0274147	+	0.0377331i	−0.822504	−	0.568759i	$-0.807424\pi$
$167$	−0.354276	+	0.487619i	−0.0274147	+	0.0377331i	0.795090	+	0.606492i	$0.207424\pi$
$168$	3.49199	+	1.13462i	0.269413	+	0.0875375i
$169$	3.39555	+	10.4504i	0.261196	+	0.803880i
$170$		0			0
$171$	−0.127943	+	0.0929558i	−0.00978402	+	0.00710851i
$172$	−0.345893	+	0.112387i	−0.0263741	+	0.00856945i
$173$	9.19091	+	2.98631i	0.698772	+	0.227045i	0.636795	−	0.771033i	$-0.280260\pi$
$173$	9.19091	+	2.98631i	0.698772	+	0.227045i	0.0619764	+	0.998078i	$0.480260\pi$
$174$	−7.05792	−	5.12788i	−0.535059	−	0.388743i
$175$		0			0
$176$	3.25341	+	12.3857i	0.245235	+	0.933607i
$177$		−	8.09846i		−	0.608718i
$178$	−9.02542	+	12.4224i	−0.676484	+	0.931100i
$179$	0.369495	−	1.13719i	0.0276174	−	0.0849975i	−0.936298	−	0.351207i	$-0.885771\pi$
$179$	0.369495	−	1.13719i	0.0276174	−	0.0849975i	0.963915	+	0.266210i	$0.0857713\pi$
$180$		0			0
$181$	−12.5997	+	9.15421i	−0.936527	+	0.680427i	−0.947582	−	0.319512i	$-0.896481\pi$
$181$	−12.5997	+	9.15421i	−0.936527	+	0.680427i	0.0110551	+	0.999939i	$0.496481\pi$
$182$	1.48079	+	2.03813i	0.109763	+	0.151076i
$183$	13.5922	−	4.41639i	1.00477	−	0.326469i
$184$	4.44781	−	13.6890i	0.327897	−	1.00916i
$185$		0			0
$186$	−4.24002			−0.310894
$187$	−16.0390	+	4.21305i	−1.17289	+	0.308089i
$188$			0.553081i			0.0403376i
$189$	1.03359	+	0.750949i	0.0751828	+	0.0546235i
$190$		0			0
$191$	5.68641	+	17.5010i	0.411454	+	1.26633i	0.915384	+	0.402581i	$0.131887\pi$
$191$	5.68641	+	17.5010i	0.411454	+	1.26633i	−0.503930	+	0.863744i	$0.668113\pi$
$192$	4.84945	+	6.67470i	0.349979	+	0.481705i
$193$	−0.921640	−	1.26853i	−0.0663411	−	0.0913107i	0.774557	−	0.632504i	$-0.217973\pi$
$193$	−0.921640	−	1.26853i	−0.0663411	−	0.0913107i	−0.840898	+	0.541193i	$0.817973\pi$
$194$	2.75466	+	8.47798i	0.197773	+	0.608683i
$195$		0			0
$196$	−0.291762	−	0.211977i	−0.0208401	−	0.0151412i
$197$		−	7.97000i		−	0.567839i	−0.958848	−	0.283920i	$-0.908365\pi$
$197$		−	7.97000i		−	0.567839i	0.958848	−	0.283920i	$-0.0916349\pi$
$198$	−0.264005	+	4.60340i	−0.0187620	+	0.327149i
$199$	−3.53141			−0.250335			−0.125167	−	0.992136i	$-0.539947\pi$
$199$	−3.53141			−0.250335			−0.125167	+	0.992136i	$0.539947\pi$
$200$		0			0
$201$	−2.28166	+	7.02224i	−0.160936	+	0.495311i
$202$	−11.5977	+	3.76832i	−0.816011	+	0.265138i
$203$	−4.71232	−	6.48595i	−0.330740	−	0.455224i
$204$	−0.271772	+	0.197454i	−0.0190279	+	0.0138246i
$205$		0			0
$206$	−4.96918	+	15.2936i	−0.346219	+	1.06555i
$207$	2.94380	−	4.05179i	0.204608	−	0.281619i
$208$			5.47647i			0.379725i
$209$	−0.405990	−	0.332090i	−0.0280829	−	0.0229711i
$210$		0			0
$211$	−16.3867	−	11.9056i	−1.12810	−	0.819616i	−0.142686	−	0.989768i	$-0.545574\pi$
$211$	−16.3867	−	11.9056i	−1.12810	−	0.819616i	−0.985418	+	0.170152i	$0.945574\pi$
$212$	0.598495	+	0.194463i	0.0411048	+	0.0133558i
$213$	6.44453	−	2.09395i	0.441572	−	0.143475i
$214$	−17.2610	+	12.5409i	−1.17994	+	0.857276i
$215$		0			0
$216$	0.888090	+	2.73326i	0.0604269	+	0.185975i
$217$	−3.70571	−	1.20406i	−0.251560	−	0.0817368i
$218$	−11.7676	+	16.1968i	−0.797005	+	1.09698i
$219$	−8.66107			−0.585261
$220$		0			0
$221$	−7.09183			−0.477048
$222$	−3.84064	+	5.28619i	−0.257767	+	0.354786i
$223$	21.4463	+	6.96833i	1.43615	+	0.466634i	0.920695	−	0.390282i	$-0.127623\pi$
$223$	21.4463	+	6.96833i	1.43615	+	0.466634i	0.515456	+	0.856916i	$0.327623\pi$
$224$	0.149983	+	0.461599i	0.0100211	+	0.0308419i
$225$		0			0
$226$	21.7801	−	15.8242i	1.44879	−	1.05261i
$227$	17.8857	−	5.81143i	1.18712	−	0.385718i	0.352112	−	0.935958i	$-0.385464\pi$
$227$	17.8857	−	5.81143i	1.18712	−	0.385718i	0.835007	+	0.550240i	$0.185464\pi$
$228$	−0.0101051	−	0.00328335i	−0.000669228	−	0.000217445i
$229$	−19.2805	−	14.0081i	−1.27409	−	0.925681i	−0.274732	−	0.961521i	$-0.588589\pi$
$229$	−19.2805	−	14.0081i	−1.27409	−	0.925681i	−0.999358	+	0.0358402i	$0.988589\pi$
$230$		0			0
$231$	−1.53798	+	3.94832i	−0.101192	+	0.259780i
$232$		−	18.0343i		−	1.18401i
$233$	−5.93183	+	8.16446i	−0.388607	+	0.534871i	−0.957839	−	0.287305i	$-0.907241\pi$
$233$	−5.93183	+	8.16446i	−0.388607	+	0.534871i	0.569232	+	0.822177i	$0.307241\pi$
$234$	−0.609348	+	1.87538i	−0.0398343	+	0.122597i
$235$		0			0
$236$	0.440187	−	0.319815i	0.0286538	−	0.0208182i
$237$	−1.49634	−	2.05953i	−0.0971977	−	0.133781i
$238$	8.44624	−	2.74435i	0.547488	−	0.177890i
$239$	−0.0516759	+	0.159042i	−0.00334264	+	0.0102876i	−0.952714	−	0.303869i	$-0.901722\pi$
$239$	−0.0516759	+	0.159042i	−0.00334264	+	0.0102876i	0.949371	+	0.314156i	$0.101722\pi$
$240$		0			0
$241$	0.965256			0.0621776			0.0310888	−	0.999517i	$-0.490103\pi$
$241$	0.965256			0.0621776			0.0310888	+	0.999517i	$0.490103\pi$
$242$	−14.9892	+	3.03199i	−0.963545	+	0.194904i
$243$			1.00000i			0.0641500i
$244$	0.776819	+	0.564392i	0.0497307	+	0.0361315i
$245$		0			0
$246$	−3.25903	−	10.0303i	−0.207788	−	0.639506i
$247$	−0.131845	−	0.181469i	−0.00838911	−	0.0115466i
$248$	−5.15189	−	7.09097i	−0.327145	−	0.450277i
$249$	−3.12791	−	9.62671i	−0.198223	−	0.610068i
$250$		0			0
$251$	19.0201	+	13.8189i	1.20054	+	0.872244i	0.994338	−	0.106265i	$-0.0338893\pi$
$251$	19.0201	+	13.8189i	1.20054	+	0.872244i	0.206203	+	0.978509i	$0.433889\pi$
$252$			0.0858360i			0.00540716i
$253$	15.4778	+	6.02905i	0.973083	+	0.379043i
$254$	−8.37512			−0.525502
$255$		0			0
$256$	−0.497709	+	1.53179i	−0.0311068	+	0.0957369i
$257$	−6.26055	+	2.03418i	−0.390522	+	0.126888i	−0.497695	−	0.867352i	$-0.665820\pi$
$257$	−6.26055	+	2.03418i	−0.390522	+	0.126888i	0.107173	+	0.994240i	$0.465820\pi$
$258$	4.42355	+	6.08850i	0.275398	+	0.379053i
$259$	−4.85780	+	3.52940i	−0.301849	+	0.219306i
$260$		0			0
$261$	1.93913	−	5.96802i	0.120029	−	0.369411i
$262$	−15.3039	+	21.0640i	−0.945477	+	1.30134i
$263$			12.4538i			0.767936i	0.923346	+	0.383968i	$0.125443\pi$
$263$			12.4538i			0.767936i	−0.923346	+	0.383968i	$0.874557\pi$
$264$	−8.01945	+	5.15189i	−0.493563	+	0.317077i
$265$		0			0
$266$	0.227249	+	0.165106i	0.0139335	+	0.0101233i
$267$	−10.5041	−	3.41300i	−0.642842	−	0.208872i
$268$	−0.471795	+	0.153295i	−0.0288195	+	0.00936401i
$269$	16.8057	−	12.2100i	1.02466	−	0.744459i	0.0574266	−	0.998350i	$-0.481710\pi$
$269$	16.8057	−	12.2100i	1.02466	−	0.744459i	0.967233	+	0.253891i	$0.0817105\pi$
$270$		0			0
$271$	4.44683	+	13.6859i	0.270126	+	0.831362i	0.990468	+	0.137743i	$0.0439848\pi$
$271$	4.44683	+	13.6859i	0.270126	+	0.831362i	−0.720342	+	0.693619i	$0.756015\pi$
$272$	18.3607	+	5.96575i	1.11328	+	0.361727i
$273$	−1.06512	+	1.46601i	−0.0644640	+	0.0887271i
$274$	4.22247			0.255089
$275$		0			0
$276$	0.336486			0.0202541
$277$	10.2787	−	14.1474i	0.617589	−	0.850038i	−0.379586	−	0.925156i	$-0.623934\pi$
$277$	10.2787	−	14.1474i	0.617589	−	0.850038i	0.997175	+	0.0751187i	$0.0239336\pi$
$278$	2.92462	+	0.950268i	0.175407	+	0.0569933i
$279$	−0.942444	−	2.90055i	−0.0564227	−	0.173651i
$280$		0			0
$281$	15.2791	−	11.1009i	0.911474	−	0.662224i	−0.0299134	−	0.999552i	$-0.509523\pi$
$281$	15.2791	−	11.1009i	0.911474	−	0.662224i	0.941387	+	0.337328i	$0.109523\pi$
$282$	10.8846	−	3.53662i	0.648169	−	0.210603i
$283$	−12.9166	−	4.19686i	−0.767813	−	0.249478i	−0.101185	−	0.994868i	$-0.532263\pi$
$283$	−12.9166	−	4.19686i	−0.767813	−	0.249478i	−0.666629	+	0.745390i	$0.732263\pi$
$284$	0.368316	+	0.267597i	0.0218555	+	0.0158790i
$285$		0			0
$286$	−6.52930	−	0.374455i	−0.386085	−	0.0221420i
$287$		−	9.69177i		−	0.572087i
$288$	−0.223298	+	0.307344i	−0.0131580	+	0.0181104i
$289$	−2.47214	+	7.60845i	−0.145420	+	0.447556i
$290$		0			0
$291$	−5.18739	+	3.76886i	−0.304090	+	0.220934i
$292$	−0.342033	−	0.470768i	−0.0200159	−	0.0275496i
$293$	−18.9282	+	6.15016i	−1.10580	+	0.359296i	−0.804332	−	0.594180i	$-0.797477\pi$
$293$	−18.9282	+	6.15016i	−1.10580	+	0.359296i	−0.301468	+	0.953476i	$0.597477\pi$
$294$	−2.30606	+	7.09732i	−0.134492	+	0.413924i
$295$		0			0
$296$	−13.5072			−0.785088
$297$	−3.20780	+	0.842610i	−0.186136	+	0.0488932i
$298$		−	2.05927i		−	0.119290i
$299$	5.74692	+	4.17538i	0.332353	+	0.241469i
$300$		0			0
$301$	2.13713	+	6.57742i	0.123182	+	0.379116i
$302$	7.38230	+	10.1609i	0.424804	+	0.584692i
$303$	−5.15572	−	7.09624i	−0.296188	−	0.407668i
$304$	0.188692	+	0.580733i	0.0108222	+	0.0333073i
$305$		0			0
$306$	5.62371	+	4.08586i	0.321486	+	0.233573i
$307$			14.9354i			0.852410i	0.904627	+	0.426205i	$0.140150\pi$
$307$			14.9354i			0.852410i	−0.904627	+	0.426205i	$0.859850\pi$
$308$	−0.275345	+	0.0723262i	−0.0156892	+	0.00412117i
$309$	−11.5666			−0.658003
$310$		0			0
$311$	−1.54416	+	4.75243i	−0.0875611	+	0.269485i	−0.985244	−	0.171157i	$-0.945249\pi$
$311$	−1.54416	+	4.75243i	−0.0875611	+	0.269485i	0.897683	+	0.440643i	$0.145249\pi$
$312$	−3.87676	+	1.25964i	−0.219478	+	0.0713128i
$313$	−5.52311	−	7.60191i	−0.312185	−	0.429685i	0.623876	−	0.781523i	$-0.285557\pi$
$313$	−5.52311	−	7.60191i	−0.312185	−	0.429685i	−0.936061	+	0.351838i	$0.885557\pi$
$314$	19.8378	−	14.4130i	1.11951	−	0.813374i
$315$		0			0
$316$	0.0528532	−	0.162665i	0.00297322	−	0.00915064i
$317$	−1.26523	+	1.74144i	−0.0710623	+	0.0978088i	−0.843069	−	0.537806i	$-0.819253\pi$
$317$	−1.26523	+	1.74144i	−0.0710623	+	0.0978088i	0.772006	+	0.635615i	$0.219253\pi$
$318$		−	13.0218i		−	0.730227i
$319$	20.7782	+	1.19163i	1.16335	+	0.0667183i
$320$		0			0
$321$	−12.4157	−	9.02054i	−0.692978	−	0.503478i
$322$	−8.46024	−	2.74890i	−0.471471	−	0.153190i
$323$	−0.752028	+	0.244349i	−0.0418440	+	0.0135959i
$324$	−0.0543544	+	0.0394908i	−0.00301969	+	0.00219393i
$325$		0			0
$326$	−10.0976	−	31.0773i	−0.559256	−	1.72121i
$327$	−13.6956	−	4.44998i	−0.757370	−	0.246084i
$328$	12.8146	−	17.6378i	0.707567	−	0.973882i
$329$	10.5173			0.579836
$330$		0			0
$331$	−19.5116			−1.07245			−0.536227	−	0.844074i	$-0.680151\pi$
$331$	−19.5116			−1.07245			−0.536227	+	0.844074i	$0.680151\pi$
$332$	0.399731	−	0.550182i	0.0219381	−	0.0301952i
$333$	−4.46988	−	1.45235i	−0.244948	−	0.0795885i
$334$	0.258941	+	0.796938i	0.0141686	+	0.0436065i
$335$		0			0
$336$	3.99082	−	2.89950i	0.217717	−	0.158181i
$337$	30.0579	−	9.76639i	1.63736	−	0.532009i	0.661410	−	0.750024i	$-0.269958\pi$
$337$	30.0579	−	9.76639i	1.63736	−	0.532009i	0.975945	+	0.218015i	$0.0699583\pi$
$338$	14.5288	+	4.72069i	0.790262	+	0.256772i
$339$	15.6662	+	11.3822i	0.850873	+	0.618195i
$340$		0			0
$341$	8.51027	−	5.46721i	0.460857	−	0.296066i
$342$			0.219863i			0.0118888i
$343$	−9.28756	+	12.7832i	−0.501481	+	0.690230i
$344$	−4.80744	+	14.7958i	−0.259200	+	0.797736i
$345$		0			0
$346$	10.8694	−	7.89707i	0.584341	−	0.424549i
$347$	5.51527	+	7.59111i	0.296075	+	0.407512i	0.930976	−	0.365082i	$-0.118959\pi$
$347$	5.51527	+	7.59111i	0.296075	+	0.407512i	−0.634900	+	0.772594i	$0.718959\pi$
$348$	0.400966	−	0.130282i	0.0214940	−	0.00698384i
$349$	7.66768	−	23.5987i	0.410441	−	1.26321i	−0.505824	−	0.862637i	$-0.668812\pi$
$349$	7.66768	−	23.5987i	0.410441	−	1.26321i	0.916265	−	0.400572i	$-0.131188\pi$
$350$		0			0
$351$	−1.41837			−0.0757067
$352$	−1.17405	−	0.457326i	−0.0625771	−	0.0243756i
$353$		−	19.4788i		−	1.03675i	−0.855153	−	0.518375i	$-0.826537\pi$
$353$		−	19.4788i		−	1.03675i	0.855153	−	0.518375i	$-0.173463\pi$
$354$	−9.10867	−	6.61784i	−0.484121	−	0.351734i
$355$		0			0
$356$	−0.229305	−	0.705728i	−0.0121531	−	0.0374035i
$357$	3.75475	+	5.16796i	0.198722	+	0.273518i
$358$	−0.977103	−	1.34487i	−0.0516415	−	0.0710784i
$359$	−9.19946	−	28.3130i	−0.485529	−	1.49430i	−0.831213	−	0.555954i	$-0.812353\pi$
$359$	−9.19946	−	28.3130i	−0.485529	−	1.49430i	0.345684	−	0.938351i	$-0.387647\pi$
$360$		0			0
$361$	15.3511	+	11.1532i	0.807952	+	0.587012i
$362$			21.6520i			1.13800i
$363$	−5.40586	−	9.58002i	−0.283734	−	0.502820i
$364$	−0.121747			−0.00638126
$365$		0			0
$366$	6.13991	−	18.8967i	0.320938	−	0.987747i
$367$	−6.12097	+	1.98882i	−0.319512	+	0.103816i	−0.464382	−	0.885635i	$-0.653724\pi$
$367$	−6.12097	+	1.98882i	−0.319512	+	0.103816i	0.144870	+	0.989451i	$0.453724\pi$
$368$	−11.3663	−	15.6444i	−0.592512	−	0.815523i
$369$	6.13718	−	4.45892i	0.319489	−	0.232122i
$370$		0			0
$371$	3.69786	−	11.3809i	0.191983	−	0.590864i
$372$	0.120440	−	0.165771i	0.00624451	−	0.00859482i
$373$		−	20.8924i		−	1.08177i	−0.841098	−	0.540883i	$-0.818090\pi$
$373$		−	20.8924i		−	1.08177i	0.841098	−	0.540883i	$-0.181910\pi$
$374$	−8.36806	+	21.4825i	−0.432702	+	1.11084i
$375$		0			0
$376$	19.1401	+	13.9061i	0.987074	+	0.717151i
$377$	8.46483	+	2.75039i	0.435961	+	0.141652i
$378$	1.68925	−	0.548870i	0.0868855	−	0.0282308i
$379$	−11.4873	+	8.34603i	−0.590064	+	0.428707i	−0.842338	−	0.538949i	$-0.818822\pi$
$379$	−11.4873	+	8.34603i	−0.590064	+	0.428707i	0.252274	+	0.967656i	$0.418822\pi$
$380$		0			0
$381$	−1.86157	−	5.72931i	−0.0953709	−	0.293521i
$382$	24.3308	+	7.90557i	1.24487	+	0.404484i
$383$	−15.5635	+	21.4214i	−0.795260	+	1.09458i	0.198173	+	0.980167i	$0.436499\pi$
$383$	−15.5635	+	21.4214i	−0.795260	+	1.09458i	−0.993433	+	0.114415i	$0.963501\pi$
$384$	10.7104			0.546561
$385$		0			0
$386$	−2.17990			−0.110954
$387$	−3.18182	+	4.37940i	−0.161741	+	0.222618i
$388$	−0.409708	−	0.133122i	−0.0207998	−	0.00675826i
$389$	11.2780	+	34.7102i	0.571819	+	1.75988i	0.646766	+	0.762689i	$0.276121\pi$
$389$	11.2780	+	34.7102i	0.571819	+	1.75988i	−0.0749470	+	0.997188i	$0.523879\pi$
$390$		0			0
$391$	20.2590	−	14.7190i	1.02454	−	0.744372i
$392$	−14.6715	+	4.76705i	−0.741022	+	0.240773i
$393$	−17.8112	−	5.78722i	−0.898458	−	0.291927i
$394$	−8.96419	−	6.51287i	−0.451610	−	0.328114i
$395$		0			0
$396$	−0.172478	−	0.141083i	−0.00866737	−	0.00708969i
$397$			8.03969i			0.403500i	0.979437	+	0.201750i	$0.0646629\pi$
$397$			8.03969i			0.403500i	−0.979437	+	0.201750i	$0.935337\pi$
$398$	−2.88577	+	3.97192i	−0.144651	+	0.199094i
$399$	−0.0624355	+	0.192157i	−0.00312569	+	0.00961988i
$400$		0			0
$401$	22.7255	−	16.5110i	1.13486	−	0.824521i	0.148461	−	0.988918i	$-0.452568\pi$
$401$	22.7255	−	16.5110i	1.13486	−	0.824521i	0.986394	+	0.164397i	$0.0525679\pi$
$402$	6.03369	+	8.30467i	0.300933	+	0.414199i
$403$	4.11403	−	1.33673i	0.204935	−	0.0665873i
$404$	0.182109	−	0.560473i	0.00906024	−	0.0278846i
$405$		0			0
$406$	−11.1458			−0.553156
$407$	0.892497	−	15.5623i	0.0442394	−	0.771393i
$408$			14.3696i			0.711401i
$409$	−4.83752	−	3.51466i	−0.239200	−	0.173789i	0.461727	−	0.887022i	$-0.347230\pi$
$409$	−4.83752	−	3.51466i	−0.239200	−	0.173789i	−0.700927	+	0.713233i	$0.747230\pi$
$410$		0			0
$411$	0.938543	+	2.88854i	0.0462949	+	0.142481i
$412$	−0.456776	−	0.628698i	−0.0225037	−	0.0309737i
$413$	−6.08153	−	8.37051i	−0.299253	−	0.411886i
$414$	−2.15163	−	6.62203i	−0.105747	−	0.325455i
$415$		0			0
$416$	−0.435925	−	0.316718i	−0.0213730	−	0.0155284i
$417$			2.21192i			0.108318i
$418$	−0.705278	+	0.185259i	−0.0344963	+	0.00906131i
$419$	15.4707			0.755795			0.377897	−	0.925847i	$-0.376647\pi$
$419$	15.4707			0.755795			0.377897	+	0.925847i	$0.376647\pi$
$420$		0			0
$421$	10.6841	−	32.8824i	0.520713	−	1.60259i	−0.251927	−	0.967746i	$-0.581064\pi$
$421$	10.6841	−	32.8824i	0.520713	−	1.60259i	0.772640	−	0.634844i	$-0.218936\pi$
$422$	−26.7815	+	8.70182i	−1.30370	+	0.423598i
$423$	4.83871	+	6.65992i	0.235266	+	0.323816i
$424$	21.7775	−	15.8223i	1.05761	−	0.768399i
$425$		0			0
$426$	2.91113	−	8.95955i	0.141045	−	0.434092i
$427$	10.7324	−	14.7718i	0.519375	−	0.714859i
$428$		−	1.03108i		−	0.0498390i
$429$	−1.19513	−	4.54984i	−0.0577013	−	0.219668i
$430$		0			0
$431$	−2.71871	−	1.97526i	−0.130956	−	0.0951450i	0.520379	−	0.853935i	$-0.325791\pi$
$431$	−2.71871	−	1.97526i	−0.130956	−	0.0951450i	−0.651335	+	0.758790i	$0.725791\pi$
$432$	3.67214	+	1.19315i	0.176676	+	0.0574055i
$433$	−3.49779	+	1.13650i	−0.168093	+	0.0546167i	−0.391855	−	0.920027i	$-0.628166\pi$
$433$	−3.49779	+	1.13650i	−0.168093	+	0.0546167i	0.223761	+	0.974644i	$0.428166\pi$
$434$	−4.38246	+	3.18404i	−0.210365	+	0.152839i
$435$		0			0
$436$	−0.298975	−	0.920152i	−0.0143183	−	0.0440673i
$437$	0.753275	+	0.244754i	0.0360340	+	0.0117082i
$438$	−7.07759	+	9.74146i	−0.338180	+	0.465465i
$439$	1.55432			0.0741835			0.0370917	−	0.999312i	$-0.488191\pi$
$439$	1.55432			0.0741835			0.0370917	+	0.999312i	$0.488191\pi$
$440$		0			0
$441$	−5.36776			−0.255608
$442$	−5.79524	+	7.97647i	−0.275652	+	0.379402i
$443$	20.1680	+	6.55298i	0.958211	+	0.311342i	0.746047	−	0.665893i	$-0.231949\pi$
$443$	20.1680	+	6.55298i	0.958211	+	0.311342i	0.212163	+	0.977234i	$0.431949\pi$
$444$	−0.0975775	−	0.300313i	−0.00463082	−	0.0142522i
$445$		0			0
$446$	25.3629	−	18.4272i	1.20097	−	0.872555i
$447$	1.40872	−	0.457721i	0.0666302	−	0.0216495i
$448$	10.0247	+	3.25723i	0.473624	+	0.153890i
$449$	12.2247	+	8.88179i	0.576921	+	0.419157i	0.837613	−	0.546265i	$-0.183951\pi$
$449$	12.2247	+	8.88179i	0.576921	+	0.419157i	−0.260692	+	0.965422i	$0.583951\pi$
$450$		0			0
$451$	19.4746	+	15.9297i	0.917023	+	0.750102i
$452$			1.30102i			0.0611949i
$453$	−5.31002	+	7.30862i	−0.249487	+	0.343389i
$454$	8.07938	−	24.8658i	0.379184	−	1.16701i
$455$		0			0
$456$	−0.367697	+	0.267147i	−0.0172190	+	0.0125103i
$457$	24.2780	+	33.4158i	1.13568	+	1.56312i	0.776810	+	0.629735i	$0.216837\pi$
$457$	24.2780	+	33.4158i	1.13568	+	1.56312i	0.358866	+	0.933389i	$0.383163\pi$
$458$	−31.5110	+	10.2385i	−1.47241	+	0.478415i
$459$	−1.54508	+	4.75528i	−0.0721184	+	0.221958i
$460$		0			0
$461$	−16.3158			−0.759901			−0.379951	−	0.925007i	$-0.624059\pi$
$461$	−16.3158			−0.759901			−0.379951	+	0.925007i	$0.624059\pi$
$462$	3.18404	+	4.95629i	0.148135	+	0.230588i
$463$			8.47904i			0.394054i	0.980398	+	0.197027i	$0.0631287\pi$
$463$			8.47904i			0.394054i	−0.980398	+	0.197027i	$0.936871\pi$
$464$	−19.6017	−	14.2415i	−0.909987	−	0.661144i
$465$		0			0
$466$	4.33558	+	13.3435i	0.200842	+	0.618128i
$467$	−21.4935	−	29.5833i	−0.994601	−	1.36895i	−0.928580	−	0.371133i	$-0.878969\pi$
$467$	−21.4935	−	29.5833i	−0.994601	−	1.36895i	−0.0660214	−	0.997818i	$-0.521031\pi$
$468$	−0.0560124	−	0.0770945i	−0.00258917	−	0.00356369i
$469$	2.91503	+	8.97155i	0.134604	+	0.414268i
$470$		0			0
$471$	14.2692	+	10.3672i	0.657489	+	0.477694i
$472$		−	23.2743i		−	1.07129i
$473$	−16.7293	−	6.51654i	−0.769214	−	0.299631i
$474$	−3.53921			−0.162561
$475$		0			0
$476$	−0.132624	+	0.408174i	−0.00607881	+	0.0187086i
$477$	8.90805	−	2.89440i	0.407872	−	0.132526i
$478$	0.136653	+	0.188087i	0.00625037	+	0.00860289i
$479$	−31.5123	+	22.8950i	−1.43983	+	1.04610i	−0.451756	+	0.892142i	$0.649202\pi$
$479$	−31.5123	+	22.8950i	−1.43983	+	1.04610i	−0.988077	+	0.153958i	$0.950798\pi$
$480$		0			0
$481$	2.05997	−	6.33993i	0.0939264	−	0.289076i
$482$	0.788781	−	1.08566i	0.0359280	−	0.0494506i
$483$		−	6.39855i		−	0.291144i
$484$	0.307235	−	0.672155i	0.0139652	−	0.0305525i
$485$		0			0
$486$	1.12474	+	0.817172i	0.0510193	+	0.0370677i
$487$	−7.86723	−	2.55622i	−0.356498	−	0.115833i	0.125292	−	0.992120i	$-0.460013\pi$
$487$	−7.86723	−	2.55622i	−0.356498	−	0.115833i	−0.481790	+	0.876287i	$0.660013\pi$
$488$	39.0630	−	12.6923i	1.76830	−	0.574555i
$489$	19.0152	−	13.8153i	0.859895	−	0.624750i
$490$		0			0
$491$	−3.74905	−	11.5384i	−0.169192	−	0.520720i	0.830128	−	0.557572i	$-0.188267\pi$
$491$	−3.74905	−	11.5384i	−0.169192	−	0.520720i	−0.999321	+	0.0368519i	$0.988267\pi$
$492$	0.484724	+	0.157496i	0.0218531	+	0.00710049i
$493$	18.4422	−	25.3835i	0.830594	−	1.14322i
$494$	−0.311846			−0.0140306
$495$		0			0
$496$	−11.7757			−0.528744
$497$	5.08857	−	7.00381i	0.228253	−	0.314164i
$498$	−13.3836	−	4.34860i	−0.599734	−	0.194865i
$499$	8.76312	+	26.9701i	0.392291	+	1.20735i	0.931051	+	0.364889i	$0.118893\pi$
$499$	8.76312	+	26.9701i	0.392291	+	1.20735i	−0.538760	+	0.842459i	$0.681107\pi$
$500$		0			0
$501$	−0.487619	+	0.354276i	−0.0217852	+	0.0158279i
$502$	31.0855	−	10.1003i	1.38741	−	0.450798i
$503$	−14.5321	−	4.72177i	−0.647955	−	0.210533i	−0.0334427	−	0.999441i	$-0.510647\pi$
$503$	−14.5321	−	4.72177i	−0.647955	−	0.210533i	−0.614512	+	0.788907i	$0.710647\pi$
$504$	2.97046	+	2.15817i	0.132315	+	0.0961324i
$505$		0			0
$506$	19.4292	−	12.4818i	0.863733	−	0.554883i
$507$			10.9882i			0.488005i
$508$	0.237899	−	0.327439i	0.0105550	−	0.0145278i
$509$	6.81363	−	20.9702i	0.302009	−	0.929488i	−0.678768	−	0.734353i	$-0.737486\pi$
$509$	6.81363	−	20.9702i	0.302009	−	0.929488i	0.980776	−	0.195134i	$-0.0625143\pi$
$510$		0			0
$511$	−8.95202	+	6.50402i	−0.396014	+	0.287721i
$512$	13.9069	+	19.1413i	0.614605	+	0.845932i
$513$	−0.150406	+	0.0488697i	−0.00664057	+	0.00215765i
$514$	−2.82803	+	8.70377i	−0.124739	+	0.383907i
$515$		0			0
$516$	−0.363693			−0.0160107
$517$	−17.2866	+	21.1334i	−0.760262	+	0.929444i
$518$			8.34789i			0.366785i
$519$	7.81825	+	5.68029i	0.343183	+	0.249337i
$520$		0			0
$521$	−7.39725	−	22.7664i	−0.324079	−	0.997413i	−0.971855	−	0.235582i	$-0.924300\pi$
$521$	−7.39725	−	22.7664i	−0.324079	−	0.997413i	0.647775	−	0.761831i	$-0.275700\pi$
$522$	−5.12788	−	7.05792i	−0.224441	−	0.308917i
$523$	14.8957	+	20.5022i	0.651344	+	0.896498i	0.999156	−	0.0410660i	$-0.0130754\pi$
$523$	14.8957	+	20.5022i	0.651344	+	0.896498i	−0.347812	+	0.937564i	$0.613075\pi$
$524$	−0.388819	−	1.19666i	−0.0169856	−	0.0522764i
$525$		0			0
$526$	14.0073	+	10.1769i	0.610749	+	0.443735i
$527$		−	15.2491i		−	0.664260i
$528$	−0.733212	+	12.7849i	−0.0319089	+	0.556390i
$529$	−2.08298			−0.0905642
$530$		0			0
$531$	2.50256	−	7.70209i	0.108602	−	0.334242i
$532$	−0.0129102	+	0.00419478i	−0.000559729	+	0.000181867i
$533$	6.32438	+	8.70476i	0.273939	+	0.377045i
$534$	−12.4224	+	9.02542i	−0.537571	+	0.390568i
$535$		0			0
$536$	−6.55732	+	20.1814i	−0.283233	+	0.871702i
$537$	0.702822	−	0.967351i	0.0303290	−	0.0417443i
$538$		−	28.8797i		−	1.24509i
$539$	−4.52293	−	17.2187i	−0.194816	−	0.741663i
$540$		0			0
$541$	28.3669	+	20.6097i	1.21959	+	0.886082i	0.996066	−	0.0886168i	$-0.0282447\pi$
$541$	28.3669	+	20.6097i	1.21959	+	0.886082i	0.223522	+	0.974699i	$0.428245\pi$
$542$	19.0270	+	6.18224i	0.817279	+	0.265550i
$543$	−14.8118	+	4.81265i	−0.635636	+	0.206531i
$544$	−1.53672	+	1.11649i	−0.0658862	+	0.0478692i
$545$		0			0
$546$	0.778498	+	2.39597i	0.0333166	+	0.102538i
$547$	1.05364	+	0.342349i	0.0450505	+	0.0146378i	0.331456	−	0.943471i	$-0.392460\pi$
$547$	1.05364	+	0.342349i	0.0450505	+	0.0146378i	−0.286405	+	0.958109i	$0.592460\pi$
$548$	−0.119941	+	0.165085i	−0.00512363	+	0.00705207i
$549$	14.2917			0.609956
$550$		0			0
$551$	0.992388			0.0422771
$552$	8.46024	−	11.6445i	0.360092	−	0.495624i
$553$	−3.09321	−	1.00505i	−0.131537	−	0.0427389i
$554$	−7.51273	−	23.1218i	−0.319185	−	0.982352i
$555$		0			0
$556$	−0.120228	+	0.0873504i	−0.00509878	+	0.00370448i
$557$	−5.15461	+	1.67483i	−0.218408	+	0.0709650i	−0.416177	−	0.909284i	$-0.636630\pi$
$557$	−5.15461	+	1.67483i	−0.218408	+	0.0709650i	0.197769	+	0.980249i	$0.436630\pi$
$558$	−4.03250	−	1.31024i	−0.170709	−	0.0554669i
$559$	−6.21159	−	4.51299i	−0.262722	−	0.190879i
$560$		0			0
$561$	−16.5559	−	0.949482i	−0.698991	−	0.0400872i
$562$		−	26.2564i		−	1.10756i
$563$	19.2469	−	26.4911i	0.811161	−	1.11647i	−0.179982	−	0.983670i	$-0.557604\pi$
$563$	19.2469	−	26.4911i	0.811161	−	1.11647i	0.991143	−	0.132798i	$-0.0423962\pi$
$564$	−0.170911	+	0.526011i	−0.00719667	+	0.0221491i
$565$		0			0
$566$	−15.2755	+	11.0983i	−0.642077	+	0.466496i
$567$	0.750949	+	1.03359i	0.0315369	+	0.0434068i
$568$	18.5211	−	6.01786i	0.777126	−	0.252504i
$569$	1.08692	−	3.34521i	0.0455662	−	0.140238i	−0.925685	−	0.378295i	$-0.876510\pi$
$569$	1.08692	−	3.34521i	0.0455662	−	0.140238i	0.971251	+	0.238057i	$0.0765104\pi$
$570$		0			0
$571$	−36.0252			−1.50761			−0.753804	−	0.657099i	$-0.771783\pi$
$571$	−36.0252			−1.50761			−0.753804	+	0.657099i	$0.771783\pi$
$572$	0.200107	−	0.244637i	0.00836691	−	0.0102288i
$573$			18.4016i			0.768738i
$574$	−10.9007	−	7.91984i	−0.454988	−	0.330568i
$575$		0			0
$576$	2.54951	+	7.84658i	0.106230	+	0.326941i
$577$	9.14009	+	12.5803i	0.380507	+	0.523723i	0.955719	−	0.294281i	$-0.0950803\pi$
$577$	9.14009	+	12.5803i	0.380507	+	0.523723i	−0.575212	+	0.818005i	$0.695080\pi$
$578$	6.53738	+	8.99793i	0.271919	+	0.374265i
$579$	−0.484535	−	1.49124i	−0.0201366	−	0.0619740i
$580$		0			0
$581$	−10.4622	−	7.60120i	−0.434043	−	0.315351i
$582$			8.91428i			0.369509i
$583$	16.7907	+	26.1364i	0.695399	+	1.08246i
$584$	−24.8912			−1.03001
$585$		0			0
$586$	−8.55030	+	26.3151i	−0.353210	+	1.08707i
$587$	−23.0730	+	7.49687i	−0.952324	+	0.309429i	−0.743660	−	0.668558i	$-0.766912\pi$
$587$	−23.0730	+	7.49687i	−0.952324	+	0.309429i	−0.208665	+	0.977987i	$0.566912\pi$
$588$	−0.211977	−	0.291762i	−0.00874180	−	0.0120320i
$589$	0.390201	−	0.283498i	0.0160780	−	0.0116813i
$590$		0			0
$591$	2.46287	−	7.57992i	0.101309	−	0.311796i
$592$	−10.6665	+	14.6812i	−0.438390	+	0.603392i
$593$			27.4019i			1.12526i	0.826709	+	0.562630i	$0.190210\pi$
$593$			27.4019i			1.12526i	−0.826709	+	0.562630i	$0.809790\pi$
$594$	−1.67361	+	4.29651i	−0.0686691	+	0.176288i
$595$		0			0
$596$	0.0805107	+	0.0584945i	0.00329785	+	0.00239603i
$597$	−3.35857	−	1.09127i	−0.137457	−	0.0446625i
$598$	9.39245	−	3.05179i	0.384086	−	0.124797i
$599$	8.63810	−	6.27594i	0.352943	−	0.256428i	−0.397160	−	0.917750i	$-0.630004\pi$
$599$	8.63810	−	6.27594i	0.352943	−	0.256428i	0.750103	+	0.661321i	$0.230004\pi$
$600$		0			0
$601$	3.41967	+	10.5247i	0.139491	+	0.429310i	0.996262	−	0.0863885i	$-0.0275326\pi$
$601$	3.41967	+	10.5247i	0.139491	+	0.429310i	−0.856770	+	0.515698i	$0.827533\pi$
$602$	9.14430	+	2.97116i	0.372694	+	0.121096i
$603$	−4.33998	+	5.97348i	−0.176738	+	0.243259i
$604$	−0.606953			−0.0246966
$605$		0			0
$606$	−12.1945			−0.495370
$607$	0.302426	−	0.416254i	0.0122751	−	0.0168952i	−0.802835	−	0.596201i	$-0.796676\pi$
$607$	0.302426	−	0.416254i	0.0122751	−	0.0168952i	0.815110	+	0.579306i	$0.196676\pi$
$608$	−0.0571387	−	0.0185655i	−0.00231728	−	0.000752930i
$609$	−2.47741	−	7.62469i	−0.100390	−	0.308968i
$610$		0			0
$611$	−9.44619	+	6.86306i	−0.382152	+	0.277650i
$612$	−0.319487	+	0.103808i	−0.0129145	+	0.00419618i
$613$	18.1630	+	5.90150i	0.733595	+	0.238360i	0.651908	−	0.758298i	$-0.273969\pi$
$613$	18.1630	+	5.90150i	0.733595	+	0.238360i	0.0816877	+	0.996658i	$0.473969\pi$
$614$	16.7985	+	12.2048i	0.677932	+	0.492546i
$615$		0			0
$616$	−4.42004	+	11.3472i	−0.178088	+	0.457190i
$617$			4.70745i			0.189515i	0.995500	+	0.0947573i	$0.0302075\pi$
$617$			4.70745i			0.189515i	−0.995500	+	0.0947573i	$0.969792\pi$
$618$	−9.45194	+	13.0095i	−0.380213	+	0.523318i
$619$	−11.5477	+	35.5402i	−0.464141	+	1.42848i	0.395919	+	0.918286i	$0.370426\pi$
$619$	−11.5477	+	35.5402i	−0.464141	+	1.42848i	−0.860060	+	0.510194i	$0.829574\pi$
$620$		0			0
$621$	4.05179	−	2.94380i	0.162593	−	0.118131i
$622$	4.08341	+	5.62033i	0.163730	+	0.225355i
$623$	−13.4200	+	4.36041i	−0.537660	+	0.174696i
$624$	−1.69232	+	5.20843i	−0.0677471	+	0.208504i
$625$		0			0
$626$	−13.0635			−0.522123
$627$	−0.283498	−	0.441294i	−0.0113218	−	0.0176236i
$628$			1.18500i			0.0472867i
$629$	−19.0115	−	13.8127i	−0.758040	−	0.550748i
$630$		0			0
$631$	10.9908	+	33.8262i	0.437536	+	1.34660i	0.890465	+	0.455052i	$0.150379\pi$
$631$	10.9908	+	33.8262i	0.437536	+	1.34660i	−0.452928	+	0.891547i	$0.649621\pi$
$632$	−4.30036	−	5.91893i	−0.171059	−	0.235443i
$633$	−11.9056	−	16.3867i	−0.473205	−	0.651311i
$634$	0.924756	+	2.84611i	0.0367268	+	0.113033i
$635$		0			0
$636$	0.509110	+	0.369890i	0.0201875	+	0.0146671i
$637$		−	7.61344i		−	0.301656i
$638$	18.3196	−	22.3963i	0.725281	−	0.886678i
$639$	6.77618			0.268062
$640$		0			0
$641$	3.77305	−	11.6123i	0.149027	−	0.458657i	−0.848480	−	0.529227i	$-0.822482\pi$
$641$	3.77305	−	11.6123i	0.149027	−	0.458657i	0.997507	+	0.0705705i	$0.0224820\pi$
$642$	−20.2916	+	6.59313i	−0.800844	+	0.260210i
$643$	12.3197	+	16.9567i	0.485843	+	0.668705i	0.979615	−	0.200886i	$-0.0643822\pi$
$643$	12.3197	+	16.9567i	0.485843	+	0.668705i	−0.493772	+	0.869591i	$0.664382\pi$
$644$	0.347790	−	0.252684i	0.0137048	−	0.00995714i
$645$		0			0
$646$	−0.339707	+	1.04551i	−0.0133656	+	0.0411351i
$647$	−8.74424	+	12.0354i	−0.343772	+	0.473161i	−0.945538	−	0.325511i	$-0.894464\pi$
$647$	−8.74424	+	12.0354i	−0.343772	+	0.473161i	0.601767	+	0.798672i	$0.294464\pi$
$648$			2.87392i			0.112898i
$649$	26.8155	+	1.53787i	1.05260	+	0.0603666i
$650$		0			0
$651$	−3.15227	−	2.29026i	−0.123547	−	0.0897622i
$652$	1.50185	+	0.487980i	0.0588169	+	0.0191108i
$653$	11.5370	−	3.74861i	0.451479	−	0.146694i	−0.0744465	−	0.997225i	$-0.523719\pi$
$653$	11.5370	−	3.74861i	0.451479	−	0.146694i	0.525926	+	0.850531i	$0.323719\pi$
$654$	−16.1968	+	11.7676i	−0.633344	+	0.460151i
$655$		0			0
$656$	−9.05120	−	27.8567i	−0.353390	−	1.08762i
$657$	−8.23717	−	2.67642i	−0.321362	−	0.104417i
$658$	8.59443	−	11.8292i	0.335046	−	0.461151i
$659$	−7.49994			−0.292156			−0.146078	−	0.989273i	$-0.546665\pi$
$659$	−7.49994			−0.292156			−0.146078	+	0.989273i	$0.546665\pi$
$660$		0			0
$661$	9.65248			0.375438			0.187719	−	0.982223i	$-0.439891\pi$
$661$	9.65248			0.375438			0.187719	+	0.982223i	$0.439891\pi$
$662$	−15.9443	+	21.9455i	−0.619694	+	0.852936i
$663$	−6.74473	−	2.19149i	−0.261943	−	0.0851106i
$664$	−8.98936	−	27.6664i	−0.348855	−	1.07366i
$665$		0			0
$666$	−5.28619	+	3.84064i	−0.204836	+	0.148822i
$667$	−29.8896	+	9.71171i	−1.15733	+	0.376039i
$668$	−0.0385130	−	0.0125136i	−0.00149011	−	0.000484167i
$669$	18.2433	+	13.2546i	0.705328	+	0.512451i
$670$		0			0
$671$	12.0424	+	45.8451i	0.464890	+	1.76983i
$672$			0.485354i			0.0187229i
$673$	14.3711	−	19.7801i	0.553966	−	0.762469i	−0.436578	−	0.899667i	$-0.643810\pi$
$673$	14.3711	−	19.7801i	0.553966	−	0.762469i	0.990544	+	0.137198i	$0.0438096\pi$
$674$	13.5778	−	41.7881i	0.522997	−	1.60962i
$675$		0			0
$676$	−0.597260	+	0.433935i	−0.0229715	+	0.0166898i
$677$	27.4728	+	37.8130i	1.05586	+	1.45327i	0.883613	+	0.468219i	$0.155104\pi$
$677$	27.4728	+	37.8130i	1.05586	+	1.45327i	0.172251	+	0.985053i	$0.444896\pi$
$678$	25.6040	−	8.31925i	0.983317	−	0.319499i
$679$	−2.53143	+	7.79093i	−0.0971472	+	0.298988i
$680$		0			0
$681$	18.8062			0.720654
$682$	0.805166	−	14.0395i	0.0308314	−	0.537600i
$683$		−	28.1941i		−	1.07882i	−0.842045	−	0.539408i	$-0.818648\pi$
$683$		−	28.1941i		−	1.07882i	0.842045	−	0.539408i	$-0.181352\pi$
$684$	−0.00859593	−	0.00624531i	−0.000328674	−	0.000238795i
$685$		0			0
$686$	6.78829	+	20.8922i	0.259178	+	0.797668i
$687$	−14.0081	−	19.2805i	−0.534442	−	0.735596i
$688$	12.2854	+	16.9094i	0.468376	+	0.644664i
$689$	4.10532	+	12.6349i	0.156400	+	0.481350i
$690$		0			0
$691$	−9.38225	−	6.81661i	−0.356918	−	0.259316i	0.394848	−	0.918747i	$-0.370797\pi$
$691$	−9.38225	−	6.81661i	−0.356918	−	0.259316i	−0.751765	+	0.659431i	$0.770797\pi$
$692$			0.649276i			0.0246818i
$693$	−2.68281	+	3.27981i	−0.101911	+	0.124590i
$694$	13.0450			0.495180
$695$		0			0
$696$	5.57289	−	17.1516i	0.211240	−	0.650130i
$697$	36.0734	−	11.7210i	1.36638	−	0.443963i
$698$	−20.2766	−	27.9083i	−0.767481	−	1.05635i
$699$	−8.16446	+	5.93183i	−0.308808	+	0.224362i
$700$		0			0
$701$	−11.3415	+	34.9056i	−0.428363	+	1.31837i	0.471373	+	0.881934i	$0.343759\pi$
$701$	−11.3415	+	34.9056i	−0.428363	+	1.31837i	−0.899737	+	0.436433i	$0.856241\pi$
$702$	−1.15905	+	1.59529i	−0.0437455	+	0.0602105i
$703$		−	0.743272i		−	0.0280330i
$704$	−23.0221	+	14.7899i	−0.867676	+	0.557417i
$705$		0			0
$706$	−21.9086	−	15.9175i	−0.824540	−	0.599064i
$707$	−10.6578	−	3.46294i	−0.400829	−	0.130237i
$708$	0.517471	−	0.168137i	0.0194478	−	0.00631896i
$709$	29.5214	−	21.4486i	1.10870	−	0.805518i	0.126242	−	0.991999i	$-0.459708\pi$
$709$	29.5214	−	21.4486i	1.10870	−	0.805518i	0.982458	+	0.186482i	$0.0597085\pi$
$710$		0			0
$711$	−0.786672	−	2.42113i	−0.0295025	−	0.0907994i
$712$	−30.1880	−	9.80868i	−1.13134	−	0.367596i
$713$	−8.97804	+	12.3572i	−0.336230	+	0.462781i
$714$	8.88090			0.332359
$715$		0			0
$716$	0.0803349			0.00300225
$717$	−0.0982934	+	0.135289i	−0.00367084	+	0.00505247i
$718$	−39.3624	−	12.7896i	−1.46899	−	0.477304i
$719$	2.88278	+	8.87229i	0.107510	+	0.330881i	0.990311	−	0.138865i	$-0.0443455\pi$
$719$	2.88278	+	8.87229i	0.107510	+	0.330881i	−0.882802	+	0.469746i	$0.844346\pi$
$720$		0			0
$721$	−11.9552	+	8.68596i	−0.445235	+	0.323482i
$722$	25.0890	−	8.15190i	0.933715	−	0.303382i
$723$	0.918013	+	0.298281i	0.0341413	+	0.0110932i
$724$	−0.846520	−	0.615033i	−0.0314607	−	0.0228575i
$725$		0			0
$726$	−15.1926	−	1.74834i	−0.563849	−	0.0648869i
$727$			8.46883i			0.314091i	0.987591	+	0.157046i	$0.0501970\pi$
$727$			8.46883i			0.314091i	−0.987591	+	0.157046i	$0.949803\pi$
$728$	−3.06107	+	4.21320i	−0.113451	+	0.156152i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$		0			0
$731$	−21.8970	+	15.9091i	−0.809891	+	0.588420i
$732$	0.564392	+	0.776819i	0.0208605	+	0.0287121i
$733$	−27.6253	+	8.97601i	−1.02036	+	0.331537i	−0.770974	−	0.636866i	$-0.780230\pi$
$733$	−27.6253	+	8.97601i	−1.02036	+	0.331537i	−0.249391	+	0.968403i	$0.580230\pi$
$734$	−2.76498	+	8.50972i	−0.102057	+	0.314100i
$735$		0			0
$736$	1.90264			0.0701322
$737$	−22.8187	−	8.88851i	−0.840536	−	0.327412i
$738$		−	10.5464i		−	0.388220i
$739$	−11.1281	−	8.08505i	−0.409354	−	0.297413i	0.363986	−	0.931404i	$-0.381416\pi$
$739$	−11.1281	−	8.08505i	−0.409354	−	0.297413i	−0.773340	+	0.633991i	$0.781416\pi$
$740$		0			0
$741$	−0.0693151	−	0.213330i	−0.00254636	−	0.00783688i
$742$	−9.77872	−	13.4593i	−0.358988	−	0.494105i
$743$	20.5217	+	28.2456i	0.752867	+	1.03623i	0.997774	+	0.0666857i	$0.0212425\pi$
$743$	20.5217	+	28.2456i	0.752867	+	1.03623i	−0.244907	+	0.969547i	$0.578758\pi$
$744$	−2.70851	−	8.33593i	−0.0992988	−	0.305610i
$745$		0			0
$746$	−23.4985	−	17.0727i	−0.860343	−	0.625075i
$747$		−	10.1221i		−	0.370349i
$748$	−0.602198	−	0.937384i	−0.0220185	−	0.0342741i
$749$	−19.6068			−0.716416
$750$		0			0
$751$	6.82903	−	21.0176i	0.249195	−	0.766943i	−0.745723	−	0.666256i	$-0.767896\pi$
$751$	6.82903	−	21.0176i	0.249195	−	0.766943i	0.994918	−	0.100687i	$-0.0321042\pi$
$752$	30.2294	−	9.82214i	1.10235	−	0.358177i
$753$	13.8189	+	19.0201i	0.503590	+	0.693133i
$754$	10.0107	−	7.27320i	0.364568	−	0.264874i
$755$		0			0
$756$	−0.0265248	+	0.0816349i	−0.000964697	+	0.00296903i
$757$	26.4680	−	36.4300i	0.961994	−	1.32407i	0.0160057	−	0.999872i	$-0.494905\pi$
$757$	26.4680	−	36.4300i	0.961994	−	1.32407i	0.945989	−	0.324200i	$-0.105095\pi$
$758$			19.7404i			0.717004i
$759$	12.8572	+	10.5169i	0.466687	+	0.381739i
$760$		0			0
$761$	−27.1831	−	19.7496i	−0.985385	−	0.715924i	−0.0264794	−	0.999649i	$-0.508430\pi$
$761$	−27.1831	−	19.7496i	−0.985385	−	0.715924i	−0.958906	+	0.283725i	$0.908430\pi$
$762$	−7.96521	−	2.58805i	−0.288549	−	0.0937553i
$763$	−17.4974	+	5.68525i	−0.633449	+	0.205820i
$764$	−1.00021	+	0.726694i	−0.0361863	+	0.0262909i
$765$		0			0
$766$	11.3754	+	35.0099i	0.411011	+	1.26496i
$767$	10.9244	+	3.54955i	0.394457	+	0.128167i
$768$	−0.946698	+	1.30302i	−0.0341610	+	0.0470186i
$769$	−24.6086			−0.887408			−0.443704	−	0.896173i	$-0.646336\pi$
$769$	−24.6086			−0.887408			−0.443704	+	0.896173i	$0.646336\pi$
$770$		0			0
$771$	−6.58273			−0.237071
$772$	0.0619211	−	0.0852271i	0.00222859	−	0.00306739i
$773$	−22.5225	−	7.31802i	−0.810080	−	0.263211i	−0.125448	−	0.992100i	$-0.540037\pi$
$773$	−22.5225	−	7.31802i	−0.810080	−	0.263211i	−0.684632	+	0.728889i	$0.740037\pi$
$774$	2.32560	+	7.15746i	0.0835919	+	0.257269i
$775$		0			0
$776$	−14.9081	+	10.8314i	−0.535171	+	0.388824i
$777$	−5.71068	+	1.85551i	−0.204870	+	0.0665662i
$778$	48.2561	+	15.6794i	1.73006	+	0.562132i
$779$	0.970569	+	0.705160i	0.0347742	+	0.0252650i
$780$		0			0
$781$	5.70968	+	21.7367i	0.204308	+	0.777799i
$782$		−	34.8141i		−	1.24495i
$783$	3.68844	−	5.07670i	0.131814	−	0.181426i
$784$	−6.40454	+	19.7112i	−0.228734	+	0.703970i
$785$		0			0
$786$	−21.0640	+	15.3039i	−0.751327	+	0.545871i
$787$	−10.8276	−	14.9029i	−0.385963	−	0.531232i	0.571189	−	0.820819i	$-0.306482\pi$
$787$	−10.8276	−	14.9029i	−0.385963	−	0.531232i	−0.957152	+	0.289586i	$0.906482\pi$
$788$	0.509263	−	0.165470i	0.0181418	−	0.00589461i
$789$	−3.84845	+	11.8443i	−0.137008	+	0.421668i
$790$		0			0
$791$	24.7399			0.879651
$792$	−9.21897	+	2.42159i	−0.327582	+	0.0860476i
$793$			20.2709i			0.719840i
$794$	9.04257	+	6.56981i	0.320909	+	0.233154i
$795$		0			0
$796$	−0.0733175	−	0.225648i	−0.00259867	−	0.00799788i
$797$	−3.82451	−	5.26399i	−0.135471	−	0.186460i	0.735892	−	0.677099i	$-0.236763\pi$
$797$	−3.82451	−	5.26399i	−0.135471	−	0.186460i	−0.871363	+	0.490639i	$0.836763\pi$
$798$	0.165106	+	0.227249i	0.00584470	+	0.00804453i
$799$	12.7193	+	39.1460i	0.449977	+	1.38489i
$800$		0			0
$801$	−8.93534	−	6.49191i	−0.315715	−	0.229380i
$802$		−	39.0526i		−	1.37900i
$803$	1.64471	−	28.6784i	0.0580404	−	1.01204i
$804$	−0.496074			−0.0174952
$805$		0			0
$806$	1.85840	−	5.71956i	0.0654593	−	0.201463i
$807$	19.7562	−	6.41919i	0.695453	−	0.225966i
$808$	−14.8171	−	20.3940i	−0.521264	−	0.717459i
$809$	9.58727	−	6.96556i	0.337071	−	0.244896i	−0.406354	−	0.913716i	$-0.633200\pi$
$809$	9.58727	−	6.96556i	0.337071	−	0.244896i	0.743425	+	0.668819i	$0.233200\pi$
$810$		0			0
$811$	2.32193	−	7.14616i	0.0815339	−	0.250936i	−0.901977	−	0.431784i	$-0.857884\pi$
$811$	2.32193	−	7.14616i	0.0815339	−	0.250936i	0.983511	+	0.180848i	$0.0578843\pi$
$812$	0.316601	−	0.435763i	0.0111105	−	0.0152923i
$813$			14.3903i			0.504688i
$814$	−16.7742	−	13.7209i	−0.587936	−	0.480917i
$815$		0			0
$816$	15.6185	+	11.3475i	0.546758	+	0.397243i
$817$	−0.814182	−	0.264544i	−0.0284846	−	0.00925521i
$818$	−7.90618	+	2.56887i	−0.276433	+	0.0898185i
$819$	−1.46601	+	1.06512i	−0.0512266	+	0.0372183i
$820$		0			0
$821$	−11.5376	−	35.5092i	−0.402666	−	1.23928i	−0.922829	−	0.385211i	$-0.874129\pi$
$821$	−11.5376	−	35.5092i	−0.402666	−	1.23928i	0.520163	−	0.854067i	$-0.325871\pi$
$822$	4.01581	+	1.30482i	0.140067	+	0.0455107i
$823$	−25.3040	+	34.8280i	−0.882043	+	1.21403i	0.0938075	+	0.995590i	$0.470096\pi$
$823$	−25.3040	+	34.8280i	−0.882043	+	1.21403i	−0.975851	+	0.218438i	$0.929904\pi$
$824$	−33.2416			−1.15803
$825$		0			0
$826$	−14.3843			−0.500495
$827$	11.7736	−	16.2049i	0.409407	−	0.563500i	−0.553667	−	0.832738i	$-0.686772\pi$
$827$	11.7736	−	16.2049i	0.409407	−	0.563500i	0.963074	+	0.269238i	$0.0867719\pi$
$828$	0.320017	+	0.103980i	0.0111214	+	0.00361355i
$829$	14.8083	+	45.5753i	0.514314	+	1.58289i	0.784527	+	0.620094i	$0.212906\pi$
$829$	14.8083	+	45.5753i	0.514314	+	1.58289i	−0.270213	+	0.962800i	$0.587094\pi$
$830$		0			0
$831$	14.1474	−	10.2787i	0.490770	−	0.356565i
$832$	−11.1293	+	3.61613i	−0.385840	+	0.125367i
$833$	−25.5252	−	8.29365i	−0.884396	−	0.287358i
$834$	2.48783	+	1.80752i	0.0861467	+	0.0625892i
$835$		0			0
$836$	0.0127907	−	0.0328364i	0.000442376	−	0.00113567i
$837$		−	3.04981i		−	0.105417i
$838$	12.6423	−	17.4006i	0.436720	−	0.601093i
$839$	−0.686305	+	2.11223i	−0.0236939	+	0.0729222i	−0.962204	−	0.272329i	$-0.912206\pi$
$839$	−0.686305	+	2.11223i	−0.0236939	+	0.0729222i	0.938510	+	0.345251i	$0.112206\pi$
$840$		0			0
$841$	−8.39554	+	6.09971i	−0.289501	+	0.210335i
$842$	−28.2534	−	38.8875i	−0.973677	−	1.34015i
$843$	17.9616	−	5.83609i	0.618632	−	0.201006i
$844$	0.420526	−	1.29425i	0.0144751	−	0.0445498i
$845$		0			0
$846$	11.4447			0.393479
$847$	−12.7816	−	5.84231i	−0.439180	−	0.200744i
$848$		−	36.1651i		−	1.24191i
$849$	−10.9875	−	7.98291i	−0.377091	−	0.273973i
$850$		0			0
$851$	7.27381	+	22.3865i	0.249343	+	0.767398i
$852$	0.267597	+	0.368316i	0.00916772	+	0.0126183i
$853$	3.74514	+	5.15474i	0.128231	+	0.176495i	0.868305	−	0.496030i	$-0.165210\pi$
$853$	3.74514	+	5.15474i	0.128231	+	0.176495i	−0.740074	+	0.672525i	$0.765210\pi$
$854$	−7.84430	−	24.1423i	−0.268426	−	0.826131i
$855$		0			0
$856$	−35.6818	−	25.9243i	−1.21958	−	0.886075i
$857$		−	35.9060i		−	1.22653i	−0.789878	−	0.613263i	$-0.789856\pi$
$857$		−	35.9060i		−	1.22653i	0.789878	−	0.613263i	$-0.210144\pi$
$858$	−6.09402	−	2.37379i	−0.208046	−	0.0810399i
$859$	−56.4697			−1.92672			−0.963360	−	0.268212i	$-0.913567\pi$
$859$	−56.4697			−1.92672			−0.963360	+	0.268212i	$0.913567\pi$
$860$		0			0
$861$	2.99492	−	9.21742i	0.102067	−	0.314129i
$862$	−4.44332	+	1.44372i	−0.151340	+	0.0491733i
$863$	18.2649	+	25.1395i	0.621745	+	0.855759i	0.997479	−	0.0709688i	$-0.0226091\pi$
$863$	18.2649	+	25.1395i	0.621745	+	0.855759i	−0.375733	+	0.926728i	$0.622609\pi$
$864$	−0.307344	+	0.223298i	−0.0104560	+	0.00759676i
$865$		0			0
$866$	−1.58003	+	4.86283i	−0.0536915	+	0.165246i
$867$	−4.70228	+	6.47214i	−0.159698	+	0.219805i
$868$		−	0.261784i		−	0.00888552i
$869$	7.10365	−	4.56356i	0.240975	−	0.154808i
$870$		0			0
$871$	−8.47257	−	6.15568i	−0.287082	−	0.208577i
$872$	−39.3601	−	12.7889i	−1.33290	−	0.433086i
$873$	−6.09814	+	1.98141i	−0.206391	+	0.0670604i
$874$	0.890840	−	0.647233i	0.0301331	−	0.0218930i
$875$		0			0
$876$	−0.179817	−	0.553421i	−0.00607546	−	0.0186983i
$877$	−15.9991	−	5.19841i	−0.540250	−	0.175538i	0.0261655	−	0.999658i	$-0.491670\pi$
$877$	−15.9991	−	5.19841i	−0.540250	−	0.175538i	−0.566416	+	0.824120i	$0.691670\pi$
$878$	1.27014	−	1.74820i	0.0428653	−	0.0589990i
$879$	−19.9023			−0.671289
$880$		0			0
$881$	26.5633			0.894940			0.447470	−	0.894299i	$-0.352325\pi$
$881$	26.5633			0.894940			0.447470	+	0.894299i	$0.352325\pi$
$882$	−4.38639	+	6.03734i	−0.147697	+	0.203288i
$883$	−51.7129	−	16.8026i	−1.74028	−	0.565451i	−0.745409	−	0.666608i	$-0.767746\pi$
$883$	−51.7129	−	16.8026i	−1.74028	−	0.565451i	−0.994870	+	0.101157i	$0.967746\pi$
$884$	−0.147237	−	0.453150i	−0.00495213	−	0.0152411i
$885$		0			0
$886$	23.8511	−	17.3289i	0.801295	−	0.582175i
$887$	−39.2084	+	12.7396i	−1.31649	+	0.427753i	−0.881288	−	0.472580i	$-0.843323\pi$
$887$	−39.2084	+	12.7396i	−1.31649	+	0.427753i	−0.435202	+	0.900333i	$0.643323\pi$
$888$	−12.8461	−	4.17395i	−0.431086	−	0.140068i
$889$	−6.22652	−	4.52383i	−0.208831	−	0.151724i
$890$		0			0
$891$	−3.31118	−	0.189896i	−0.110929	−	0.00636177i
$892$			1.51504i			0.0507273i
$893$	−0.765222	+	1.05324i	−0.0256072	+	0.0352453i
$894$	0.636350	−	1.95848i	0.0212827	−	0.0655015i
$895$		0			0
$896$	11.0702	−	8.04293i	0.369828	−	0.268696i
$897$	4.17538	+	5.74692i	0.139412	+	0.191884i
$898$	19.9794	−	6.49171i	0.666722	−	0.216631i
$899$	−5.91398	+	18.2013i	−0.197242	+	0.607049i
$900$		0			0
$901$	46.8324			1.56021
$902$	33.8309	−	8.88654i	1.12645	−	0.295889i
$903$			6.91591i			0.230147i
$904$	45.0235	+	32.7115i	1.49746	+	1.08797i
$905$		0			0
$906$	3.88110	+	11.9448i	0.128941	+	0.396840i
$907$	24.9248	+	34.3060i	0.827614	+	1.13911i	0.988362	+	0.152117i	$0.0486092\pi$
$907$	24.9248	+	34.3060i	0.827614	+	1.13911i	−0.160748	+	0.986995i	$0.551391\pi$
$908$	0.742671	+	1.02220i	0.0246464	+	0.0339229i
$909$	−2.71052	−	8.34213i	−0.0899023	−	0.276691i
$910$		0			0
$911$	6.48184	+	4.70933i	0.214753	+	0.156027i	0.689962	−	0.723846i	$-0.257627\pi$
$911$	6.48184	+	4.70933i	0.214753	+	0.156027i	−0.475209	+	0.879873i	$0.657627\pi$
$912$			0.610619i			0.0202196i
$913$	32.4698	−	8.52900i	1.07459	−	0.282269i
$914$	57.4234			1.89940
$915$		0			0
$916$	0.494789	−	1.52280i	0.0163483	−	0.0503149i
$917$	−22.7555	+	7.39370i	−0.751452	+	0.244162i
$918$	4.08586	+	5.62371i	0.134854	+	0.185610i
$919$	33.3587	−	24.2365i	1.10040	−	0.799489i	0.119277	−	0.992861i	$-0.461942\pi$
$919$	33.3587	−	24.2365i	1.10040	−	0.799489i	0.981125	+	0.193372i	$0.0619424\pi$
$920$		0			0
$921$	−4.61530	+	14.2044i	−0.152079	+	0.468052i
$922$	−13.3328	+	18.3510i	−0.439092	+	0.604359i
$923$			9.61110i			0.316353i
$924$	−0.284219	−	0.0162999i	−0.00935011	−	0.000536229i
$925$		0			0
$926$	9.53672	+	6.92884i	0.313396	+	0.227696i
$927$	−11.0005	−	3.57429i	−0.361305	−	0.117395i
$928$	2.26724	−	0.736670i	0.0744257	−	0.0241824i
$929$	−12.2921	+	8.93073i	−0.403291	+	0.293008i	−0.770880	−	0.636980i	$-0.780183\pi$
$929$	−12.2921	+	8.93073i	−0.403291	+	0.293008i	0.367589	+	0.929988i	$0.380183\pi$
$930$		0			0
$931$	−0.262321	−	0.807341i	−0.00859723	−	0.0264595i
$932$	−0.644842	−	0.209522i	−0.0211225	−	0.00686312i
$933$	−2.93716	+	4.04266i	−0.0961583	+	0.132351i
$934$	−50.8375			−1.66345
$935$		0			0
$936$	−4.07627			−0.133237
$937$	−15.0011	+	20.6472i	−0.490064	+	0.674515i	−0.980400	−	0.197019i	$-0.936874\pi$
$937$	−15.0011	+	20.6472i	−0.490064	+	0.674515i	0.490336	+	0.871533i	$0.336874\pi$
$938$	12.4728	+	4.05265i	0.407250	+	0.132324i
$939$	−2.90367	−	8.93658i	−0.0947577	−	0.291634i
$940$		0			0
$941$	−26.1857	+	19.0250i	−0.853629	+	0.620198i	−0.926144	−	0.377170i	$-0.876897\pi$
$941$	−26.1857	+	19.0250i	−0.853629	+	0.620198i	0.0725154	+	0.997367i	$0.476897\pi$
$942$	23.3208	−	7.57737i	0.759831	−	0.246884i
$943$	−36.1332	−	11.7404i	−1.17666	−	0.382320i
$944$	−25.2972	−	18.3795i	−0.823354	−	0.598202i
$945$		0			0
$946$	−21.0001	+	13.4910i	−0.682774	+	0.438631i
$947$			40.1516i			1.30475i	0.757896	+	0.652375i	$0.226227\pi$
$947$			40.1516i			1.30475i	−0.757896	+	0.652375i	$0.773773\pi$
$948$	0.100533	−	0.138371i	0.00326515	−	0.00449410i
$949$	3.79614	−	11.6833i	0.123228	−	0.379256i
$950$		0			0
$951$	−1.74144	+	1.26523i	−0.0564699	+	0.0410278i
$952$	10.7908	+	14.8523i	0.349733	+	0.481366i
$953$	−33.9064	+	11.0168i	−1.09833	+	0.356871i	−0.801461	−	0.598046i	$-0.795944\pi$
$953$	−33.9064	+	11.0168i	−1.09833	+	0.356871i	−0.296873	+	0.954917i	$0.595944\pi$
$954$	4.02396	−	12.3845i	0.130281	−	0.400962i
$955$		0			0
$956$	−0.0112353			−0.000363374
$957$	19.3930	+	7.55411i	0.626886	+	0.244190i
$958$			54.1524i			1.74958i
$959$	3.13922	+	2.28077i	0.101371	+	0.0736501i
$960$		0			0
$961$	−6.70525	−	20.6366i	−0.216298	−	0.665698i
$962$	−5.44743	−	7.49774i	−0.175632	−	0.241737i
$963$	−9.02054	−	12.4157i	−0.290683	−	0.400091i
$964$	0.0200402	+	0.0616775i	0.000645452	+	0.00198650i
$965$		0			0
$966$	−7.19671	−	5.22872i	−0.231550	−	0.168231i
$967$			20.0622i			0.645156i	0.946543	+	0.322578i	$0.104549\pi$
$967$			20.0622i			0.645156i	−0.946543	+	0.322578i	$0.895451\pi$
$968$	−15.5360	−	27.5322i	−0.499346	−	0.884918i
$969$	−0.790729			−0.0254019
$970$		0			0
$971$	−12.8646	+	39.5931i	−0.412844	+	1.27060i	0.501321	+	0.865261i	$0.332848\pi$
$971$	−12.8646	+	39.5931i	−0.412844	+	1.27060i	−0.914165	+	0.405342i	$0.867152\pi$
$972$	−0.0638975	+	0.0207616i	−0.00204951	+	0.000665927i
$973$	1.66104	+	2.28622i	0.0532504	+	0.0732929i
$974$	−9.30396	+	6.75972i	−0.298118	+	0.216596i
$975$		0			0
$976$	17.0522	−	52.4812i	0.545827	−	1.67988i
$977$	−11.2104	+	15.4297i	−0.358651	+	0.493641i	−0.949772	−	0.312942i	$-0.898685\pi$
$977$	−11.2104	+	15.4297i	−0.358651	+	0.493641i	0.591121	+	0.806583i	$0.298685\pi$
$978$		−	32.6766i		−	1.04488i
$979$	13.2958	−	34.1330i	0.424934	−	1.09089i
$980$		0			0
$981$	−11.6502	−	8.46436i	−0.371962	−	0.270246i
$982$	−16.0413	−	5.21214i	−0.511899	−	0.166326i
$983$	−25.2566	+	8.20635i	−0.805559	+	0.261742i	−0.682716	−	0.730684i	$-0.739201\pi$
$983$	−25.2566	+	8.20635i	−0.805559	+	0.261742i	−0.122843	+	0.992426i	$0.539201\pi$
$984$	17.6378	−	12.8146i	0.562271	−	0.408514i
$985$		0			0
$986$	−13.4794	−	41.4854i	−0.429272	−	1.32116i
$987$	10.0025	+	3.25002i	0.318384	+	0.103449i
$988$	0.00885813	−	0.0121922i	0.000281815	−	0.000387884i
$989$	27.1111			0.862082
$990$		0			0
$991$	−24.2494			−0.770307			−0.385153	−	0.922853i	$-0.625851\pi$
$991$	−24.2494			−0.770307			−0.385153	+	0.922853i	$0.625851\pi$
$992$	0.681018	−	0.937341i	0.0216223	−	0.0297606i
$993$	−18.5566	−	6.02941i	−0.588877	−	0.191338i
$994$	−3.71924	−	11.4466i	−0.117967	−	0.363065i
$995$		0			0
$996$	0.550182	−	0.399731i	0.0174332	−	0.0126660i
$997$	15.2755	−	4.96330i	0.483779	−	0.157189i	−0.0569657	−	0.998376i	$-0.518143\pi$
$997$	15.2755	−	4.96330i	0.483779	−	0.157189i	0.540745	+	0.841187i	$0.318143\pi$
$998$	37.4954	+	12.1830i	1.18690	+	0.385646i
$999$	−3.80231	−	2.76254i	−0.120300	−	0.0874029i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.bx.h.499.3		16
5.2	odd	4		165.2.m.a.136.2	yes	8
5.3	odd	4		825.2.n.k.301.1		8
5.4	even	2	inner	825.2.bx.h.499.2		16
11.3	even	5	inner	825.2.bx.h.124.2		16
15.2	even	4		495.2.n.d.136.1		8
55.3	odd	20		825.2.n.k.751.1		8
55.14	even	10	inner	825.2.bx.h.124.3		16
55.17	even	20		1815.2.a.o.1.4		4
55.27	odd	20		1815.2.a.x.1.1		4
55.28	even	20		9075.2.a.dj.1.1		4
55.38	odd	20		9075.2.a.cl.1.4		4
55.47	odd	20		165.2.m.a.91.2	✓	8
165.17	odd	20		5445.2.a.bv.1.1		4
165.47	even	20		495.2.n.d.91.1		8
165.137	even	20		5445.2.a.be.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.a.91.2	✓	8	55.47	odd	20
165.2.m.a.136.2	yes	8	5.2	odd	4
495.2.n.d.91.1		8	165.47	even	20
495.2.n.d.136.1		8	15.2	even	4
825.2.n.k.301.1		8	5.3	odd	4
825.2.n.k.751.1		8	55.3	odd	20
825.2.bx.h.124.2		16	11.3	even	5	inner
825.2.bx.h.124.3		16	55.14	even	10	inner
825.2.bx.h.499.2		16	5.4	even	2	inner
825.2.bx.h.499.3		16	1.1	even	1	trivial
1815.2.a.o.1.4		4	55.17	even	20
1815.2.a.x.1.1		4	55.27	odd	20
5445.2.a.be.1.4		4	165.137	even	20
5445.2.a.bv.1.1		4	165.17	odd	20
9075.2.a.cl.1.4		4	55.38	odd	20
9075.2.a.dj.1.1		4	55.28	even	20

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.bx (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.817172 - 1.12474i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.0207616 + 0.0638975i) q^{4} +(1.12474 - 0.817172i) q^{6} +(1.21506 - 0.394797i) q^{7} +(2.73326 + 0.888090i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.817172 - 1.12474i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.0207616 + 0.0638975i) q^{4} +(1.12474 - 0.817172i) q^{6} +(1.21506 - 0.394797i) q^{7} +(2.73326 + 0.888090i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-1.20381 + 3.09044i) q^{11} +0.0671858i q^{12} +(-0.833694 + 1.14748i) q^{13} +(0.548870 - 1.68925i) q^{14} +(3.12371 - 2.26951i) q^{16} +(2.93893 + 4.04508i) q^{17} +(1.32221 - 0.429613i) q^{18} +(-0.0488697 + 0.150406i) q^{19} +1.27759 q^{21} +(2.49222 + 3.87940i) q^{22} -5.00829i q^{23} +(2.32505 + 1.68925i) q^{24} +(0.609348 + 1.87538i) q^{26} +(0.587785 + 0.809017i) q^{27} +(0.0504531 + 0.0694428i) q^{28} +(-1.93913 - 5.96802i) q^{29} +(-2.46735 - 1.79264i) q^{31} +0.379898i q^{32} +(-2.09989 + 2.56719i) q^{33} +6.95128 q^{34} +(-0.0207616 + 0.0638975i) q^{36} +(-4.46988 + 1.45235i) q^{37} +(0.129232 + 0.177873i) q^{38} +(-1.14748 + 0.833694i) q^{39} +(2.34419 - 7.21469i) q^{41} +(1.04401 - 1.43696i) q^{42} +5.41324i q^{43} +(-0.222465 - 0.0127583i) q^{44} +(-5.63303 - 4.09264i) q^{46} +(7.82920 + 2.54386i) q^{47} +(3.67214 - 1.19315i) q^{48} +(-4.34261 + 3.15509i) q^{49} +(1.54508 + 4.75528i) q^{51} +(-0.0906300 - 0.0294475i) q^{52} +(5.50548 - 7.57764i) q^{53} +1.39026 q^{54} +3.67169 q^{56} +(-0.0929558 + 0.127943i) q^{57} +(-8.29708 - 2.69588i) q^{58} +(-2.50256 - 7.70209i) q^{59} +(11.5623 - 8.40047i) q^{61} +(-4.03250 + 1.31024i) q^{62} +(1.21506 + 0.394797i) q^{63} +(6.67470 + 4.84945i) q^{64} +(1.17144 + 4.45967i) q^{66} +7.38362i q^{67} +(-0.197454 + 0.271772i) q^{68} +(1.54765 - 4.76317i) q^{69} +(5.48204 - 3.98294i) q^{71} +(1.68925 + 2.32505i) q^{72} +(-8.23717 + 2.67642i) q^{73} +(-2.01914 + 6.21429i) q^{74} -0.0106252 q^{76} +(-0.242610 + 4.23034i) q^{77} +1.97189i q^{78} +(-2.05953 - 1.49634i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-6.19905 - 8.53225i) q^{82} +(-5.94964 - 8.18897i) q^{83} +(0.0265248 + 0.0816349i) q^{84} +(6.08850 + 4.42355i) q^{86} -6.27515i q^{87} +(-6.03493 + 7.37788i) q^{88} -11.0447 q^{89} +(-0.559967 + 1.72340i) q^{91} +(0.320017 - 0.103980i) q^{92} +(-1.79264 - 2.46735i) q^{93} +(9.25900 - 6.72705i) q^{94} +(-0.117395 + 0.361304i) q^{96} +(-3.76886 + 5.18739i) q^{97} +7.46257i q^{98} +(-2.79042 + 1.79264i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 + 4 * q^9	\( 16 q + 4 q^{4} + 4 q^{9} - 6 q^{11} + 20 q^{14} - 40 q^{16} - 12 q^{19} - 8 q^{21} + 40 q^{24} - 16 q^{26} + 6 q^{31} - 100 q^{34} - 4 q^{36} - 12 q^{39} - 50 q^{41} - 14 q^{44} - 12 q^{46} - 42 q^{49} - 20 q^{51} - 20 q^{54} + 40 q^{56} - 70 q^{59} + 42 q^{61} + 154 q^{64} + 50 q^{66} + 10 q^{69} + 50 q^{71} + 58 q^{74} - 28 q^{76} - 60 q^{79} - 4 q^{81} + 68 q^{84} - 68 q^{86} - 64 q^{89} + 74 q^{91} + 78 q^{94} + 20 q^{96} + 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 + 4 * q^9 - 6 * q^11 + 20 * q^14 - 40 * q^16 - 12 * q^19 - 8 * q^21 + 40 * q^24 - 16 * q^26 + 6 * q^31 - 100 * q^34 - 4 * q^36 - 12 * q^39 - 50 * q^41 - 14 * q^44 - 12 * q^46 - 42 * q^49 - 20 * q^51 - 20 * q^54 + 40 * q^56 - 70 * q^59 + 42 * q^61 + 154 * q^64 + 50 * q^66 + 10 * q^69 + 50 * q^71 + 58 * q^74 - 28 * q^76 - 60 * q^79 - 4 * q^81 + 68 * q^84 - 68 * q^86 - 64 * q^89 + 74 * q^91 + 78 * q^94 + 20 * q^96 + 6 * q^99

Introduction

L-functions

Modular forms

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Database

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