LMFDB - Embedded newform 825.2.bx.b.499.1

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + 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 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			499.1
Root			$-0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	825.499
Dual form			825.2.bx.b.124.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.951057 + 1.30902i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.190983 - 0.587785i) q^{4} +(-1.30902 + 0.951057i) q^{6} +(2.85317 - 0.927051i) q^{7} +(-2.12663 - 0.690983i) q^{8} +(0.809017 + 0.587785i) q^{9} +(2.80902 + 1.76336i) q^{11} -0.618034i q^{12} +(3.66547 - 5.04508i) q^{13} +(-1.50000 + 4.61653i) q^{14} +(3.92705 - 2.85317i) q^{16} +(-0.363271 - 0.500000i) q^{17} +(-1.53884 + 0.500000i) q^{18} +(0.263932 - 0.812299i) q^{19} +3.00000 q^{21} +(-4.97980 + 2.00000i) q^{22} -5.47214i q^{23} +(-1.80902 - 1.31433i) q^{24} +(3.11803 + 9.59632i) q^{26} +(0.587785 + 0.809017i) q^{27} +(-1.08981 - 1.50000i) q^{28} +(1.38197 + 4.25325i) q^{29} +(3.11803 + 2.26538i) q^{31} +3.38197i q^{32} +(2.12663 + 2.54508i) q^{33} +1.00000 q^{34} +(0.190983 - 0.587785i) q^{36} +(-4.02874 + 1.30902i) q^{37} +(0.812299 + 1.11803i) q^{38} +(5.04508 - 3.66547i) q^{39} +(1.83688 - 5.65334i) q^{41} +(-2.85317 + 3.92705i) q^{42} +1.76393i q^{43} +(0.500000 - 1.98787i) q^{44} +(7.16312 + 5.20431i) q^{46} +(0.587785 + 0.190983i) q^{47} +(4.61653 - 1.50000i) q^{48} +(1.61803 - 1.17557i) q^{49} +(-0.190983 - 0.587785i) q^{51} +(-3.66547 - 1.19098i) q^{52} +(-4.33901 + 5.97214i) q^{53} -1.61803 q^{54} -6.70820 q^{56} +(0.502029 - 0.690983i) q^{57} +(-6.88191 - 2.23607i) q^{58} +(1.64590 + 5.06555i) q^{59} +(-0.927051 + 0.673542i) q^{61} +(-5.93085 + 1.92705i) q^{62} +(2.85317 + 0.927051i) q^{63} +(3.42705 + 2.48990i) q^{64} +(-5.35410 + 0.363271i) q^{66} -10.5623i q^{67} +(-0.224514 + 0.309017i) q^{68} +(1.69098 - 5.20431i) q^{69} +(-11.7812 + 8.55951i) q^{71} +(-1.31433 - 1.80902i) q^{72} +(-1.17557 + 0.381966i) q^{73} +(2.11803 - 6.51864i) q^{74} -0.527864 q^{76} +(9.64932 + 2.42705i) q^{77} +10.0902i q^{78} +(0.427051 + 0.310271i) q^{79} +(0.309017 + 0.951057i) q^{81} +(5.65334 + 7.78115i) q^{82} +(7.46969 + 10.2812i) q^{83} +(-0.572949 - 1.76336i) q^{84} +(-2.30902 - 1.67760i) q^{86} +4.47214i q^{87} +(-4.75528 - 5.69098i) q^{88} -9.47214 q^{89} +(5.78115 - 17.7926i) q^{91} +(-3.21644 + 1.04508i) q^{92} +(2.26538 + 3.11803i) q^{93} +(-0.809017 + 0.587785i) q^{94} +(-1.04508 + 3.21644i) q^{96} +(-8.83702 + 12.1631i) q^{97} +3.23607i q^{98} +(1.23607 + 3.07768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{4} - 6 q^{6} + 2 q^{9} + 18 q^{11} - 12 q^{14} + 18 q^{16} + 20 q^{19} + 24 q^{21} - 10 q^{24} + 16 q^{26} + 20 q^{29} + 16 q^{31} + 8 q^{34} + 6 q^{36} + 18 q^{39} + 46 q^{41} + 4 q^{44} + 26 q^{46}+ \cdots - 8 q^{99}+O(q^{100}) $ 8 * q - 6 * q^4 - 6 * q^6 + 2 * q^9 + 18 * q^11 - 12 * q^14 + 18 * q^16 + 20 * q^19 + 24 * q^21 - 10 * q^24 + 16 * q^26 + 20 * q^29 + 16 * q^31 + 8 * q^34 + 6 * q^36 + 18 * q^39 + 46 * q^41 + 4 * q^44 + 26 * q^46 + 4 * q^49 - 6 * q^51 - 4 * q^54 + 40 * q^59 + 6 * q^61 + 14 * q^64 - 16 * q^66 + 18 * q^69 - 54 * q^71 + 8 * q^74 - 40 * q^76 - 10 * q^79 - 2 * q^81 - 18 * q^84 - 14 * q^86 - 40 * q^89 + 6 * q^91 - 2 * q^94 + 14 * q^96 - 8 * q^99

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 $

$2$	−0.951057	+	1.30902i	−0.672499	+	0.925615i	−0.999814	−	0.0193004i	$-0.993856\pi$
$2$	−0.951057	+	1.30902i	−0.672499	+	0.925615i	0.327315	+	0.944915i	$0.393856\pi$
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	−0.190983	−	0.587785i	−0.0954915	−	0.293893i
$5$		0			0
$5$		0			0
$6$	−1.30902	+	0.951057i	−0.534404	+	0.388267i
$7$	2.85317	−	0.927051i	1.07840	−	0.350392i	0.284644	−	0.958633i	$-0.408125\pi$
$7$	2.85317	−	0.927051i	1.07840	−	0.350392i	0.793752	+	0.608241i	$0.208125\pi$
$8$	−2.12663	−	0.690983i	−0.751876	−	0.244299i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$		0			0
$11$	2.80902	+	1.76336i	0.846950	+	0.531672i
$11$	2.80902	+	1.76336i	0.846950	+	0.531672i
$12$		−	0.618034i		−	0.178411i
$13$	3.66547	−	5.04508i	1.01662	−	1.39925i	0.102070	−	0.994777i	$-0.467453\pi$
$13$	3.66547	−	5.04508i	1.01662	−	1.39925i	0.914548	−	0.404478i	$-0.132547\pi$
$14$	−1.50000	+	4.61653i	−0.400892	+	1.23382i
$15$		0			0
$16$	3.92705	−	2.85317i	0.981763	−	0.713292i
$17$	−0.363271	−	0.500000i	−0.0881062	−	0.121268i	0.762688	−	0.646766i	$-0.223879\pi$
$17$	−0.363271	−	0.500000i	−0.0881062	−	0.121268i	−0.850795	+	0.525498i	$0.823879\pi$
$18$	−1.53884	+	0.500000i	−0.362708	+	0.117851i
$19$	0.263932	−	0.812299i	0.0605502	−	0.186354i	−0.916206	−	0.400707i	$-0.868764\pi$
$19$	0.263932	−	0.812299i	0.0605502	−	0.186354i	0.976756	+	0.214353i	$0.0687644\pi$
$20$		0			0
$21$	3.00000			0.654654
$22$	−4.97980	+	2.00000i	−1.06170	+	0.426401i
$23$		−	5.47214i		−	1.14102i	−0.821291	−	0.570510i	$-0.806746\pi$
$23$		−	5.47214i		−	1.14102i	0.821291	−	0.570510i	$-0.193254\pi$
$24$	−1.80902	−	1.31433i	−0.369264	−	0.268286i
$25$		0			0
$26$	3.11803	+	9.59632i	0.611497	+	1.88199i
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	−1.08981	−	1.50000i	−0.205955	−	0.283473i
$29$	1.38197	+	4.25325i	0.256625	+	0.789809i	0.993505	+	0.113787i	$0.0362980\pi$
$29$	1.38197	+	4.25325i	0.256625	+	0.789809i	−0.736881	+	0.676023i	$0.763702\pi$
$30$		0			0
$31$	3.11803	+	2.26538i	0.560015	+	0.406875i	0.831465	−	0.555578i	$-0.187503\pi$
$31$	3.11803	+	2.26538i	0.560015	+	0.406875i	−0.271449	+	0.962453i	$0.587503\pi$
$32$			3.38197i			0.597853i
$33$	2.12663	+	2.54508i	0.370198	+	0.443042i
$34$	1.00000			0.171499
$35$		0			0
$36$	0.190983	−	0.587785i	0.0318305	−	0.0979642i
$37$	−4.02874	+	1.30902i	−0.662321	+	0.215201i	−0.620839	−	0.783938i	$-0.713208\pi$
$37$	−4.02874	+	1.30902i	−0.662321	+	0.215201i	−0.0414819	+	0.999139i	$0.513208\pi$
$38$	0.812299	+	1.11803i	0.131772	+	0.181369i
$39$	5.04508	−	3.66547i	0.807860	−	0.586945i
$40$		0			0
$41$	1.83688	−	5.65334i	0.286873	−	0.882903i	−0.698958	−	0.715162i	$-0.746353\pi$
$41$	1.83688	−	5.65334i	0.286873	−	0.882903i	0.985831	−	0.167741i	$-0.0536472\pi$
$42$	−2.85317	+	3.92705i	−0.440254	+	0.605957i
$43$			1.76393i			0.268997i	0.990914	+	0.134499i	$0.0429424\pi$
$43$			1.76393i			0.268997i	−0.990914	+	0.134499i	$0.957058\pi$
$44$	0.500000	−	1.98787i	0.0753778	−	0.299683i
$45$		0			0
$46$	7.16312	+	5.20431i	1.05614	+	0.767334i
$47$	0.587785	+	0.190983i	0.0857373	+	0.0278577i	0.351572	−	0.936161i	$-0.385647\pi$
$47$	0.587785	+	0.190983i	0.0857373	+	0.0278577i	−0.265834	+	0.964019i	$0.585647\pi$
$48$	4.61653	−	1.50000i	0.666338	−	0.216506i
$49$	1.61803	−	1.17557i	0.231148	−	0.167939i
$50$		0			0
$51$	−0.190983	−	0.587785i	−0.0267430	−	0.0823064i
$52$	−3.66547	−	1.19098i	−0.508309	−	0.165160i
$53$	−4.33901	+	5.97214i	−0.596009	+	0.820336i	−0.995336	−	0.0964728i	$-0.969244\pi$
$53$	−4.33901	+	5.97214i	−0.596009	+	0.820336i	0.399327	+	0.916809i	$0.369244\pi$
$54$	−1.61803			−0.220187
$55$		0			0
$56$	−6.70820			−0.896421
$57$	0.502029	−	0.690983i	0.0664953	−	0.0915229i
$58$	−6.88191	−	2.23607i	−0.903639	−	0.293610i
$59$	1.64590	+	5.06555i	0.214278	+	0.659479i	0.999204	+	0.0398899i	$0.0127007\pi$
$59$	1.64590	+	5.06555i	0.214278	+	0.659479i	−0.784926	+	0.619589i	$0.787299\pi$
$60$		0			0
$61$	−0.927051	+	0.673542i	−0.118697	+	0.0862382i	−0.645550	−	0.763718i	$-0.723372\pi$
$61$	−0.927051	+	0.673542i	−0.118697	+	0.0862382i	0.526853	+	0.849956i	$0.323372\pi$
$62$	−5.93085	+	1.92705i	−0.753219	+	0.244736i
$63$	2.85317	+	0.927051i	0.359466	+	0.116797i
$64$	3.42705	+	2.48990i	0.428381	+	0.311237i
$65$		0			0
$66$	−5.35410	+	0.363271i	−0.659044	+	0.0447156i
$67$		−	10.5623i		−	1.29039i	−0.764017	−	0.645196i	$-0.776776\pi$
$67$		−	10.5623i		−	1.29039i	0.764017	−	0.645196i	$-0.223224\pi$
$68$	−0.224514	+	0.309017i	−0.0272263	+	0.0374738i
$69$	1.69098	−	5.20431i	0.203570	−	0.626525i
$70$		0			0
$71$	−11.7812	+	8.55951i	−1.39817	+	1.01583i	−0.403253	+	0.915089i	$0.632120\pi$
$71$	−11.7812	+	8.55951i	−1.39817	+	1.01583i	−0.994913	+	0.100738i	$0.967880\pi$
$72$	−1.31433	−	1.80902i	−0.154895	−	0.213195i
$73$	−1.17557	+	0.381966i	−0.137590	+	0.0447057i	−0.377003	−	0.926212i	$-0.623045\pi$
$73$	−1.17557	+	0.381966i	−0.137590	+	0.0447057i	0.239412	+	0.970918i	$0.423045\pi$
$74$	2.11803	−	6.51864i	0.246216	−	0.757776i
$75$		0			0
$76$	−0.527864			−0.0605502
$77$	9.64932	+	2.42705i	1.09964	+	0.276588i
$78$			10.0902i			1.14249i
$79$	0.427051	+	0.310271i	0.0480470	+	0.0349082i	0.611550	−	0.791206i	$-0.290547\pi$
$79$	0.427051	+	0.310271i	0.0480470	+	0.0349082i	−0.563503	+	0.826114i	$0.690547\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	5.65334	+	7.78115i	0.624307	+	0.859285i
$83$	7.46969	+	10.2812i	0.819906	+	1.12850i	0.989719	+	0.143027i	$0.0456835\pi$
$83$	7.46969	+	10.2812i	0.819906	+	1.12850i	−0.169813	+	0.985476i	$0.554316\pi$
$84$	−0.572949	−	1.76336i	−0.0625139	−	0.192398i
$85$		0			0
$86$	−2.30902	−	1.67760i	−0.248988	−	0.180900i
$87$			4.47214i			0.479463i
$88$	−4.75528	−	5.69098i	−0.506915	−	0.606661i
$89$	−9.47214			−1.00404			−0.502022	−	0.864855i	$-0.667410\pi$
$89$	−9.47214			−1.00404			−0.502022	+	0.864855i	$0.667410\pi$
$90$		0			0
$91$	5.78115	−	17.7926i	0.606029	−	1.86517i
$92$	−3.21644	+	1.04508i	−0.335337	+	0.108958i
$93$	2.26538	+	3.11803i	0.234909	+	0.323325i
$94$	−0.809017	+	0.587785i	−0.0834437	+	0.0606254i
$95$		0			0
$96$	−1.04508	+	3.21644i	−0.106664	+	0.328277i
$97$	−8.83702	+	12.1631i	−0.897264	+	1.23498i	0.0740689	+	0.997253i	$0.476402\pi$
$97$	−8.83702	+	12.1631i	−0.897264	+	1.23498i	−0.971333	+	0.237724i	$0.923598\pi$
$98$			3.23607i			0.326892i
$99$	1.23607	+	3.07768i	0.124230	+	0.309319i
$100$		0			0
$101$	2.42705	+	1.76336i	0.241501	+	0.175460i	0.701952	−	0.712225i	$-0.252312\pi$
$101$	2.42705	+	1.76336i	0.241501	+	0.175460i	−0.460451	+	0.887685i	$0.652312\pi$
$102$	0.951057	+	0.309017i	0.0941686	+	0.0305972i
$103$	5.70634	−	1.85410i	0.562262	−	0.182690i	−0.0140765	−	0.999901i	$-0.504481\pi$
$103$	5.70634	−	1.85410i	0.562262	−	0.182690i	0.576339	+	0.817211i	$0.304481\pi$
$104$	−11.2812	+	8.19624i	−1.10621	+	0.803707i
$105$		0			0
$106$	−3.69098	−	11.3597i	−0.358500	−	1.10335i
$107$	−0.224514	−	0.0729490i	−0.0217046	−	0.00705225i	0.298145	−	0.954521i	$-0.403632\pi$
$107$	−0.224514	−	0.0729490i	−0.0217046	−	0.00705225i	−0.319849	+	0.947468i	$0.603632\pi$
$108$	0.363271	−	0.500000i	0.0349558	−	0.0481125i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$	−4.23607			−0.402070
$112$	8.55951	−	11.7812i	0.808798	−	1.11321i
$113$	−12.0862	−	3.92705i	−1.13698	−	0.369426i	−0.320753	−	0.947163i	$-0.603936\pi$
$113$	−12.0862	−	3.92705i	−1.13698	−	0.369426i	−0.816223	+	0.577737i	$0.803936\pi$
$114$	0.427051	+	1.31433i	0.0399970	+	0.123098i
$115$		0			0
$116$	2.23607	−	1.62460i	0.207614	−	0.150840i
$117$	5.93085	−	1.92705i	0.548308	−	0.178156i
$118$	−8.19624	−	2.66312i	−0.754525	−	0.245160i
$119$	−1.50000	−	1.08981i	−0.137505	−	0.0999031i
$120$		0			0
$121$	4.78115	+	9.90659i	0.434650	+	0.900599i
$122$		−	1.85410i		−	0.167863i
$123$	3.49396	−	4.80902i	0.315039	−	0.433614i
$124$	0.736068	−	2.26538i	0.0661009	−	0.203438i
$125$		0			0
$126$	−3.92705	+	2.85317i	−0.349850	+	0.254181i
$127$	5.70634	+	7.85410i	0.506356	+	0.696939i	0.983299	−	0.181995i	$-0.0582555\pi$
$127$	5.70634	+	7.85410i	0.506356	+	0.696939i	−0.476944	+	0.878934i	$0.658255\pi$
$128$	−12.9515	+	4.20820i	−1.14476	+	0.371956i
$129$	−0.545085	+	1.67760i	−0.0479921	+	0.147704i
$130$		0			0
$131$	−13.8541			−1.21044			−0.605219	−	0.796059i	$-0.706915\pi$
$131$	−13.8541			−1.21044			−0.605219	+	0.796059i	$0.706915\pi$
$132$	1.08981	−	1.73607i	0.0948561	−	0.151105i
$133$		−	2.56231i		−	0.222180i
$134$	13.8262	+	10.0453i	1.19441	+	0.867786i
$135$		0			0
$136$	0.427051	+	1.31433i	0.0366193	+	0.112703i
$137$	−0.865300	−	1.19098i	−0.0739276	−	0.101753i	0.770452	−	0.637498i	$-0.220031\pi$
$137$	−0.865300	−	1.19098i	−0.0739276	−	0.101753i	−0.844379	+	0.535746i	$0.820031\pi$
$138$	5.20431	+	7.16312i	0.443020	+	0.609765i
$139$	−1.80902	−	5.56758i	−0.153439	−	0.472236i	0.844561	−	0.535460i	$-0.179862\pi$
$139$	−1.80902	−	5.56758i	−0.153439	−	0.472236i	−0.997999	+	0.0632239i	$0.979862\pi$
$140$		0			0
$141$	0.500000	+	0.363271i	0.0421076	+	0.0305930i
$142$		−	23.5623i		−	1.97730i
$143$	19.1926	−	7.70820i	1.60497	−	0.644592i
$144$	4.85410			0.404508
$145$		0			0
$146$	0.618034	−	1.90211i	0.0511489	−	0.157420i
$147$	1.90211	−	0.618034i	0.156884	−	0.0509746i
$148$	1.53884	+	2.11803i	0.126492	+	0.174101i
$149$	12.1353	−	8.81678i	0.994159	−	0.722299i	0.0333309	−	0.999444i	$-0.489388\pi$
$149$	12.1353	−	8.81678i	0.994159	−	0.722299i	0.960828	+	0.277146i	$0.0893885\pi$
$150$		0			0
$151$	0.618034	−	1.90211i	0.0502949	−	0.154792i	−0.922755	−	0.385388i	$-0.874068\pi$
$151$	0.618034	−	1.90211i	0.0502949	−	0.154792i	0.973050	+	0.230596i	$0.0740676\pi$
$152$	−1.12257	+	1.54508i	−0.0910524	+	0.125323i
$153$		−	0.618034i		−	0.0499651i
$154$	−12.3541	+	10.3229i	−0.995522	+	0.831840i
$155$		0			0
$156$	−3.11803	−	2.26538i	−0.249643	−	0.181376i
$157$	−9.23305	−	3.00000i	−0.736878	−	0.239426i	−0.0835524	−	0.996503i	$-0.526627\pi$
$157$	−9.23305	−	3.00000i	−0.736878	−	0.239426i	−0.653325	+	0.757077i	$0.726627\pi$
$158$	−0.812299	+	0.263932i	−0.0646231	+	0.0209973i
$159$	−5.97214	+	4.33901i	−0.473621	+	0.344106i
$160$		0			0
$161$	−5.07295	−	15.6129i	−0.399804	−	1.23047i
$162$	−1.53884	−	0.500000i	−0.120903	−	0.0392837i
$163$	−8.97578	+	12.3541i	−0.703037	+	0.967648i	0.296882	+	0.954914i	$0.404053\pi$
$163$	−8.97578	+	12.3541i	−0.703037	+	0.967648i	−0.999919	+	0.0127336i	$0.995947\pi$
$164$	−3.67376			−0.286873
$165$		0			0
$166$	−20.5623			−1.59594
$167$	11.1882	−	15.3992i	0.865766	−	1.19162i	−0.114398	−	0.993435i	$-0.536494\pi$
$167$	11.1882	−	15.3992i	0.865766	−	1.19162i	0.980164	−	0.198190i	$-0.0635062\pi$
$168$	−6.37988	−	2.07295i	−0.492219	−	0.159931i
$169$	−8.00000	−	24.6215i	−0.615385	−	1.89396i
$170$		0			0
$171$	0.690983	−	0.502029i	0.0528408	−	0.0383911i
$172$	1.03681	−	0.336881i	0.0790563	−	0.0256869i
$173$	16.7557	+	5.44427i	1.27392	+	0.413920i	0.866433	−	0.499293i	$-0.166407\pi$
$173$	16.7557	+	5.44427i	1.27392	+	0.413920i	0.407482	+	0.913213i	$0.366407\pi$
$174$	−5.85410	−	4.25325i	−0.443798	−	0.322438i
$175$		0			0
$176$	16.0623	−	1.08981i	1.21074	−	0.0821478i
$177$			5.32624i			0.400345i
$178$	9.00854	−	12.3992i	0.675218	−	0.929358i
$179$	−0.690983	+	2.12663i	−0.0516465	+	0.158952i	−0.973553	−	0.228460i	$-0.926631\pi$
$179$	−0.690983	+	2.12663i	−0.0516465	+	0.158952i	0.921907	+	0.387412i	$0.126631\pi$
$180$		0			0
$181$	6.89919	−	5.01255i	0.512813	−	0.372580i	−0.301077	−	0.953600i	$-0.597346\pi$
$181$	6.89919	−	5.01255i	0.512813	−	0.372580i	0.813889	+	0.581020i	$0.197346\pi$
$182$	17.7926	+	24.4894i	1.31887	+	1.81527i
$183$	−1.08981	+	0.354102i	−0.0805614	+	0.0261760i
$184$	−3.78115	+	11.6372i	−0.278750	+	0.857905i
$185$		0			0
$186$	−6.23607			−0.457251
$187$	−0.138757	−	2.04508i	−0.0101469	−	0.149551i
$188$		−	0.381966i		−	0.0278577i
$189$	2.42705	+	1.76336i	0.176542	+	0.128265i
$190$		0			0
$191$	0.454915	+	1.40008i	0.0329165	+	0.101307i	0.966165	−	0.257925i	$-0.0830388\pi$
$191$	0.454915	+	1.40008i	0.0329165	+	0.101307i	−0.933248	+	0.359232i	$0.883039\pi$
$192$	2.48990	+	3.42705i	0.179693	+	0.247326i
$193$	−0.918300	−	1.26393i	−0.0661007	−	0.0909798i	0.774687	−	0.632345i	$-0.217908\pi$
$193$	−0.918300	−	1.26393i	−0.0661007	−	0.0909798i	−0.840787	+	0.541365i	$0.817908\pi$
$194$	−7.51722	−	23.1356i	−0.539705	−	1.66104i
$195$		0			0
$196$	−1.00000	−	0.726543i	−0.0714286	−	0.0518959i
$197$		−	26.6180i		−	1.89646i	−0.317590	−	0.948228i	$-0.602873\pi$
$197$		−	26.6180i		−	1.89646i	0.317590	−	0.948228i	$-0.397127\pi$
$198$	−5.20431	−	1.30902i	−0.369854	−	0.0930278i
$199$	3.29180			0.233349			0.116675	−	0.993170i	$-0.462777\pi$
$199$	3.29180			0.233349			0.116675	+	0.993170i	$0.462777\pi$
$200$		0			0
$201$	3.26393	−	10.0453i	0.230220	−	0.708544i
$202$	−4.61653	+	1.50000i	−0.324818	+	0.105540i
$203$	7.88597	+	10.8541i	0.553486	+	0.761809i
$204$	−0.309017	+	0.224514i	−0.0216355	+	0.0157191i
$205$		0			0
$206$	−3.00000	+	9.23305i	−0.209020	+	0.643297i
$207$	3.21644	−	4.42705i	0.223558	−	0.307701i
$208$		−	30.2705i		−	2.09888i
$209$	2.17376	−	1.81636i	0.150362	−	0.125640i
$210$		0			0
$211$	−9.11803	−	6.62464i	−0.627711	−	0.456059i	0.227895	−	0.973686i	$-0.426816\pi$
$211$	−9.11803	−	6.62464i	−0.627711	−	0.456059i	−0.855607	+	0.517627i	$0.826816\pi$
$212$	4.33901	+	1.40983i	0.298004	+	0.0968275i
$213$	−13.8496	+	4.50000i	−0.948957	+	0.308335i
$214$	0.309017	−	0.224514i	0.0211240	−	0.0153475i
$215$		0			0
$216$	−0.690983	−	2.12663i	−0.0470154	−	0.144699i
$217$	10.9964	+	3.57295i	0.746485	+	0.242548i
$218$		0			0
$219$	−1.23607			−0.0835257
$220$		0			0
$221$	−3.85410			−0.259255
$222$	4.02874	−	5.54508i	0.270391	−	0.372162i
$223$	−12.0862	−	3.92705i	−0.809353	−	0.262975i	−0.125029	−	0.992153i	$-0.539903\pi$
$223$	−12.0862	−	3.92705i	−0.809353	−	0.262975i	−0.684324	+	0.729178i	$0.739903\pi$
$224$	3.13525	+	9.64932i	0.209483	+	0.644722i
$225$		0			0
$226$	16.6353	−	12.0862i	1.10656	−	0.803963i
$227$	10.3556	−	3.36475i	0.687327	−	0.223326i	0.0555264	−	0.998457i	$-0.482316\pi$
$227$	10.3556	−	3.36475i	0.687327	−	0.223326i	0.631800	+	0.775131i	$0.282316\pi$
$228$	−0.502029	−	0.163119i	−0.0332477	−	0.0108028i
$229$	8.09017	+	5.87785i	0.534613	+	0.388419i	0.822081	−	0.569371i	$-0.192813\pi$
$229$	8.09017	+	5.87785i	0.534613	+	0.388419i	−0.287467	+	0.957790i	$0.592813\pi$
$230$		0			0
$231$	8.42705	+	5.29007i	0.554459	+	0.348061i
$232$		−	10.0000i		−	0.656532i
$233$	5.09831	−	7.01722i	0.334001	−	0.459713i	−0.608676	−	0.793419i	$-0.708299\pi$
$233$	5.09831	−	7.01722i	0.334001	−	0.459713i	0.942677	+	0.333705i	$0.108299\pi$
$234$	−3.11803	+	9.59632i	−0.203832	+	0.627331i
$235$		0			0
$236$	2.66312	−	1.93487i	0.173354	−	0.125949i
$237$	0.310271	+	0.427051i	0.0201542	+	0.0277399i
$238$	2.85317	−	0.927051i	0.184944	−	0.0600918i
$239$	5.42705	−	16.7027i	0.351047	−	1.08041i	−0.607220	−	0.794534i	$-0.707715\pi$
$239$	5.42705	−	16.7027i	0.351047	−	1.08041i	0.958266	−	0.285877i	$-0.0922848\pi$
$240$		0			0
$241$	17.1246			1.10309			0.551547	−	0.834144i	$-0.314038\pi$
$241$	17.1246			1.10309			0.551547	+	0.834144i	$0.314038\pi$
$242$	−17.5150	−	3.16312i	−1.12591	−	0.203333i
$243$			1.00000i			0.0641500i
$244$	0.572949	+	0.416272i	0.0366793	+	0.0266491i
$245$		0			0
$246$	2.97214	+	9.14729i	0.189496	+	0.583210i
$247$	−3.13068	−	4.30902i	−0.199201	−	0.274176i
$248$	−5.06555	−	6.97214i	−0.321663	−	0.442731i
$249$	3.92705	+	12.0862i	0.248867	+	0.765933i
$250$		0			0
$251$	−13.5902	−	9.87384i	−0.857804	−	0.623231i	0.0694827	−	0.997583i	$-0.477865\pi$
$251$	−13.5902	−	9.87384i	−0.857804	−	0.623231i	−0.927287	+	0.374352i	$0.877865\pi$
$252$		−	1.85410i		−	0.116797i
$253$	9.64932	−	15.3713i	0.606648	−	0.966387i
$254$	−15.7082			−0.985620
$255$		0			0
$256$	4.19098	−	12.8985i	0.261936	−	0.806157i
$257$	−25.9888	+	8.44427i	−1.62114	+	0.526739i	−0.972210	−	0.234112i	$-0.924782\pi$
$257$	−25.9888	+	8.44427i	−1.62114	+	0.526739i	−0.648927	+	0.760851i	$0.724782\pi$
$258$	−1.67760	−	2.30902i	−0.104443	−	0.143753i
$259$	−10.2812	+	7.46969i	−0.638840	+	0.464144i
$260$		0			0
$261$	−1.38197	+	4.25325i	−0.0855415	+	0.263270i
$262$	13.1760	−	18.1353i	0.814018	−	1.12040i
$263$		−	0.673762i		−	0.0415459i	−0.999784	−	0.0207730i	$-0.993387\pi$
$263$		−	0.673762i		−	0.0415459i	0.999784	−	0.0207730i	$-0.00661272\pi$
$264$	−2.76393	−	6.88191i	−0.170108	−	0.423552i
$265$		0			0
$266$	3.35410	+	2.43690i	0.205653	+	0.149416i
$267$	−9.00854	−	2.92705i	−0.551313	−	0.179133i
$268$	−6.20837	+	2.01722i	−0.379236	+	0.123221i
$269$	19.7984	−	14.3844i	1.20713	−	0.877030i	0.212161	−	0.977235i	$-0.431950\pi$
$269$	19.7984	−	14.3844i	1.20713	−	0.877030i	0.994967	+	0.100205i	$0.0319498\pi$
$270$		0			0
$271$	1.93769	+	5.96361i	0.117707	+	0.362263i	0.992502	−	0.122229i	$-0.0390043\pi$
$271$	1.93769	+	5.96361i	0.117707	+	0.362263i	−0.874795	+	0.484493i	$0.839004\pi$
$272$	−2.85317	−	0.927051i	−0.172999	−	0.0562107i
$273$	10.9964	−	15.1353i	0.665533	−	0.916027i
$274$	2.38197			0.143900
$275$		0			0
$276$	−3.38197			−0.203570
$277$	−6.13512	+	8.44427i	−0.368624	+	0.507367i	−0.952526	−	0.304457i	$-0.901525\pi$
$277$	−6.13512	+	8.44427i	−0.368624	+	0.507367i	0.583902	+	0.811824i	$0.301525\pi$
$278$	9.00854	+	2.92705i	0.540296	+	0.175553i
$279$	1.19098	+	3.66547i	0.0713023	+	0.219446i
$280$		0			0
$281$	4.23607	−	3.07768i	0.252703	−	0.183599i	−0.454221	−	0.890889i	$-0.650082\pi$
$281$	4.23607	−	3.07768i	0.252703	−	0.183599i	0.706924	+	0.707290i	$0.250082\pi$
$282$	−0.951057	+	0.309017i	−0.0566346	+	0.0184017i
$283$	−21.0948	−	6.85410i	−1.25395	−	0.407434i	−0.394617	−	0.918846i	$-0.629123\pi$
$283$	−21.0948	−	6.85410i	−1.25395	−	0.407434i	−0.859336	+	0.511412i	$0.829123\pi$
$284$	7.28115	+	5.29007i	0.432057	+	0.313908i
$285$		0			0
$286$	−8.16312	+	32.4544i	−0.482695	+	1.91907i
$287$		−	17.8328i		−	1.05264i
$288$	−1.98787	+	2.73607i	−0.117136	+	0.161224i
$289$	5.13525	−	15.8047i	0.302074	−	0.929688i
$290$		0			0
$291$	−12.1631	+	8.83702i	−0.713015	+	0.518035i
$292$	0.449028	+	0.618034i	0.0262774	+	0.0361677i
$293$	−17.0660	+	5.54508i	−0.997007	+	0.323947i	−0.761669	−	0.647966i	$-0.775620\pi$
$293$	−17.0660	+	5.54508i	−0.997007	+	0.323947i	−0.235338	+	0.971914i	$0.575620\pi$
$294$	−1.00000	+	3.07768i	−0.0583212	+	0.179494i
$295$		0			0
$296$	9.47214			0.550557
$297$	0.224514	+	3.30902i	0.0130276	+	0.192009i
$298$			24.2705i			1.40595i
$299$	−27.6074	−	20.0579i	−1.59658	−	1.15998i
$300$		0			0
$301$	1.63525	+	5.03280i	0.0942545	+	0.290086i
$302$	1.90211	+	2.61803i	0.109454	+	0.150651i
$303$	1.76336	+	2.42705i	0.101302	+	0.139430i
$304$	−1.28115	−	3.94298i	−0.0734792	−	0.226146i
$305$		0			0
$306$	0.809017	+	0.587785i	0.0462484	+	0.0336014i
$307$			19.5623i			1.11648i	0.829680	+	0.558240i	$0.188523\pi$
$307$			19.5623i			1.11648i	−0.829680	+	0.558240i	$0.811477\pi$
$308$	−0.416272	−	6.13525i	−0.0237193	−	0.349589i
$309$	6.00000			0.341328
$310$		0			0
$311$	3.54508	−	10.9106i	0.201023	−	0.618686i	−0.798830	−	0.601557i	$-0.794547\pi$
$311$	3.54508	−	10.9106i	0.201023	−	0.618686i	0.999853	−	0.0171293i	$-0.00545269\pi$
$312$	−13.2618	+	4.30902i	−0.750801	+	0.243950i
$313$	16.3597	+	22.5172i	0.924706	+	1.27275i	0.961889	+	0.273440i	$0.0881615\pi$
$313$	16.3597	+	22.5172i	0.924706	+	1.27275i	−0.0371831	+	0.999308i	$0.511838\pi$
$314$	12.7082	−	9.23305i	0.717165	−	0.521051i
$315$		0			0
$316$	0.100813	−	0.310271i	0.00567118	−	0.0174541i
$317$	−14.9066	+	20.5172i	−0.837240	+	1.15236i	0.149292	+	0.988793i	$0.452301\pi$
$317$	−14.9066	+	20.5172i	−0.837240	+	1.15236i	−0.986532	+	0.163569i	$0.947699\pi$
$318$		−	11.9443i		−	0.669802i
$319$	−3.61803	+	14.3844i	−0.202571	+	0.805370i
$320$		0			0
$321$	−0.190983	−	0.138757i	−0.0106596	−	0.00774468i
$322$	25.2623	+	8.20820i	1.40781	+	0.457425i
$323$	−0.502029	+	0.163119i	−0.0279336	+	0.00907618i
$324$	0.500000	−	0.363271i	0.0277778	−	0.0201817i
$325$		0			0
$326$	−7.63525	−	23.4989i	−0.422878	−	1.30148i
$327$		0			0
$328$	−7.81272	+	10.7533i	−0.431385	+	0.593751i
$329$	1.85410			0.102220
$330$		0			0
$331$	−22.5967			−1.24203			−0.621015	−	0.783799i	$-0.713279\pi$
$331$	−22.5967			−1.24203			−0.621015	+	0.783799i	$0.713279\pi$
$332$	4.61653	−	6.35410i	0.253365	−	0.348727i
$333$	−4.02874	−	1.30902i	−0.220774	−	0.0717337i
$334$	9.51722	+	29.2910i	0.520759	+	1.60273i
$335$		0			0
$336$	11.7812	−	8.55951i	0.642715	−	0.466959i
$337$	−13.0373	+	4.23607i	−0.710186	+	0.230753i	−0.641763	−	0.766903i	$-0.721797\pi$
$337$	−13.0373	+	4.23607i	−0.710186	+	0.230753i	−0.0684228	+	0.997656i	$0.521797\pi$
$338$	39.8384	+	12.9443i	2.16692	+	0.704076i
$339$	−10.2812	−	7.46969i	−0.558396	−	0.405698i
$340$		0			0
$341$	4.76393	+	11.8617i	0.257981	+	0.642347i
$342$			1.38197i			0.0747282i
$343$	−8.81678	+	12.1353i	−0.476061	+	0.655242i
$344$	1.21885	−	3.75123i	0.0657158	−	0.202253i
$345$		0			0
$346$	−23.0623	+	16.7557i	−1.23984	+	0.900794i
$347$	−1.79611	−	2.47214i	−0.0964203	−	0.132711i	0.758081	−	0.652160i	$-0.226137\pi$
$347$	−1.79611	−	2.47214i	−0.0964203	−	0.132711i	−0.854501	+	0.519449i	$0.826137\pi$
$348$	2.62866	−	0.854102i	0.140911	−	0.0457847i
$349$	−9.30902	+	28.6502i	−0.498300	+	1.53361i	0.313449	+	0.949605i	$0.398515\pi$
$349$	−9.30902	+	28.6502i	−0.498300	+	1.53361i	−0.811750	+	0.584006i	$0.801485\pi$
$350$		0			0
$351$	6.23607			0.332857
$352$	−5.96361	+	9.50000i	−0.317861	+	0.506352i
$353$		−	1.52786i		−	0.0813200i	−0.999173	−	0.0406600i	$-0.987054\pi$
$353$		−	1.52786i		−	0.0813200i	0.999173	−	0.0406600i	$-0.0129460\pi$
$354$	−6.97214	−	5.06555i	−0.370565	−	0.269231i
$355$		0			0
$356$	1.80902	+	5.56758i	0.0958777	+	0.295081i
$357$	−1.08981	−	1.50000i	−0.0576791	−	0.0793884i
$358$	−2.12663	−	2.92705i	−0.112396	−	0.154699i
$359$	5.32624	+	16.3925i	0.281108	+	0.865162i	0.987538	+	0.157379i	$0.0503044\pi$
$359$	5.32624	+	16.3925i	0.281108	+	0.865162i	−0.706430	+	0.707783i	$0.749696\pi$
$360$		0			0
$361$	14.7812	+	10.7391i	0.777955	+	0.565218i
$362$			13.7984i			0.725226i
$363$	1.48584	+	10.8992i	0.0779864	+	0.572059i
$364$	−11.5623			−0.606029
$365$		0			0
$366$	0.572949	−	1.76336i	0.0299485	−	0.0921721i
$367$	−13.8496	+	4.50000i	−0.722942	+	0.234898i	−0.647298	−	0.762237i	$-0.724101\pi$
$367$	−13.8496	+	4.50000i	−0.722942	+	0.234898i	−0.0756437	+	0.997135i	$0.524101\pi$
$368$	−15.6129	−	21.4894i	−0.813880	−	1.12021i
$369$	4.80902	−	3.49396i	0.250347	−	0.181888i
$370$		0			0
$371$	−6.84346	+	21.0620i	−0.355295	+	1.09348i
$372$	1.40008	−	1.92705i	0.0725910	−	0.0999129i
$373$			22.4164i			1.16068i	0.814375	+	0.580339i	$0.197080\pi$
$373$			22.4164i			1.16068i	−0.814375	+	0.580339i	$0.802920\pi$
$374$	2.80902	+	1.76336i	0.145251	+	0.0911810i
$375$		0			0
$376$	−1.11803	−	0.812299i	−0.0576582	−	0.0418911i
$377$	26.5236	+	8.61803i	1.36603	+	0.443851i
$378$	−4.61653	+	1.50000i	−0.237448	+	0.0771517i
$379$	22.9894	−	16.7027i	1.18088	−	0.857962i	0.188613	−	0.982052i	$-0.439601\pi$
$379$	22.9894	−	16.7027i	1.18088	−	0.857962i	0.992271	+	0.124089i	$0.0396009\pi$
$380$		0			0
$381$	3.00000	+	9.23305i	0.153695	+	0.473024i
$382$	−2.26538	−	0.736068i	−0.115907	−	0.0376605i
$383$	−5.22455	+	7.19098i	−0.266962	+	0.367442i	−0.921361	−	0.388707i	$-0.872922\pi$
$383$	−5.22455	+	7.19098i	−0.266962	+	0.367442i	0.654399	+	0.756149i	$0.272922\pi$
$384$	−13.6180			−0.694942
$385$		0			0
$386$	2.52786			0.128665
$387$	−1.03681	+	1.42705i	−0.0527042	+	0.0725411i
$388$	8.83702	+	2.87132i	0.448632	+	0.145769i
$389$	2.86475	+	8.81678i	0.145248	+	0.447028i	0.997043	−	0.0768476i	$-0.0244855\pi$
$389$	2.86475	+	8.81678i	0.145248	+	0.447028i	−0.851795	+	0.523876i	$0.824485\pi$
$390$		0			0
$391$	−2.73607	+	1.98787i	−0.138369	+	0.100531i
$392$	−4.25325	+	1.38197i	−0.214822	+	0.0697998i
$393$	−13.1760	−	4.28115i	−0.664643	−	0.215956i
$394$	34.8435	+	25.3153i	1.75539	+	1.27536i
$395$		0			0
$396$	1.57295	−	1.31433i	0.0790437	−	0.0660475i
$397$			25.2918i			1.26936i	0.772776	+	0.634679i	$0.218868\pi$
$397$			25.2918i			1.26936i	−0.772776	+	0.634679i	$0.781132\pi$
$398$	−3.13068	+	4.30902i	−0.156927	+	0.215992i
$399$	0.791796	−	2.43690i	0.0396394	−	0.121997i
$400$		0			0
$401$	12.0623	−	8.76378i	0.602363	−	0.437642i	−0.244354	−	0.969686i	$-0.578576\pi$
$401$	12.0623	−	8.76378i	0.602363	−	0.437642i	0.846717	+	0.532044i	$0.178576\pi$
$402$	10.0453	+	13.8262i	0.501017	+	0.689590i
$403$	22.8581	−	7.42705i	1.13864	−	0.369968i
$404$	0.572949	−	1.76336i	0.0285053	−	0.0877302i
$405$		0			0
$406$	−21.7082			−1.07736
$407$	−13.6251	−	3.42705i	−0.675369	−	0.169873i
$408$			1.38197i			0.0684175i
$409$	−23.4164	−	17.0130i	−1.15787	−	0.841240i	−0.168360	−	0.985726i	$-0.553847\pi$
$409$	−23.4164	−	17.0130i	−1.15787	−	0.841240i	−0.989507	+	0.144486i	$0.953847\pi$
$410$		0			0
$411$	−0.454915	−	1.40008i	−0.0224393	−	0.0690611i
$412$	−2.17963	−	3.00000i	−0.107383	−	0.147799i
$413$	9.39205	+	12.9271i	0.462153	+	0.636099i
$414$	2.73607	+	8.42075i	0.134470	+	0.413857i
$415$		0			0
$416$	17.0623	+	12.3965i	0.836548	+	0.607788i
$417$		−	5.85410i		−	0.286677i
$418$	0.310271	+	4.57295i	0.0151758	+	0.223670i
$419$	21.5066			1.05067			0.525333	−	0.850897i	$-0.323941\pi$
$419$	21.5066			1.05067			0.525333	+	0.850897i	$0.323941\pi$
$420$		0			0
$421$	−1.15248	+	3.54696i	−0.0561682	+	0.172868i	−0.975205	−	0.221304i	$-0.928969\pi$
$421$	−1.15248	+	3.54696i	−0.0561682	+	0.172868i	0.919037	+	0.394172i	$0.128969\pi$
$422$	17.3435	−	5.63525i	0.844270	−	0.274320i
$423$	0.363271	+	0.500000i	0.0176629	+	0.0243108i
$424$	13.3541	−	9.70232i	0.648533	−	0.471186i
$425$		0			0
$426$	7.28115	−	22.4091i	0.352773	−	1.08572i
$427$	−2.02063	+	2.78115i	−0.0977849	+	0.134589i
$428$			0.145898i			0.00705225i
$429$	20.6353	−	1.40008i	0.996279	−	0.0675967i
$430$		0			0
$431$	1.20820	+	0.877812i	0.0581971	+	0.0422827i	0.616503	−	0.787352i	$-0.288549\pi$
$431$	1.20820	+	0.877812i	0.0581971	+	0.0422827i	−0.558306	+	0.829635i	$0.688549\pi$
$432$	4.61653	+	1.50000i	0.222113	+	0.0721688i
$433$	5.70634	−	1.85410i	0.274229	−	0.0891025i	−0.168674	−	0.985672i	$-0.553949\pi$
$433$	5.70634	−	1.85410i	0.274229	−	0.0891025i	0.442903	+	0.896569i	$0.353949\pi$
$434$	−15.1353	+	10.9964i	−0.726515	+	0.527844i
$435$		0			0
$436$		0			0
$437$	−4.44501	−	1.44427i	−0.212634	−	0.0690889i
$438$	1.17557	−	1.61803i	0.0561709	−	0.0773127i
$439$	−16.7082			−0.797439			−0.398720	−	0.917073i	$-0.630545\pi$
$439$	−16.7082			−0.797439			−0.398720	+	0.917073i	$0.630545\pi$
$440$		0			0
$441$	2.00000			0.0952381
$442$	3.66547	−	5.04508i	0.174349	−	0.239970i
$443$	−0.832544	−	0.270510i	−0.0395553	−	0.0128523i	0.289172	−	0.957277i	$-0.406620\pi$
$443$	−0.832544	−	0.270510i	−0.0395553	−	0.0128523i	−0.328728	+	0.944425i	$0.606620\pi$
$444$	0.809017	+	2.48990i	0.0383942	+	0.118165i
$445$		0			0
$446$	16.6353	−	12.0862i	0.787702	−	0.572299i
$447$	14.2658	−	4.63525i	0.674751	−	0.219240i
$448$	12.0862	+	3.92705i	0.571020	+	0.185536i
$449$	−12.5623	−	9.12705i	−0.592852	−	0.430732i	0.250483	−	0.968121i	$-0.419411\pi$
$449$	−12.5623	−	9.12705i	−0.592852	−	0.430732i	−0.843334	+	0.537389i	$0.819411\pi$
$450$		0			0
$451$	15.1287	−	12.6412i	0.712382	−	0.595253i
$452$			7.85410i			0.369426i
$453$	1.17557	−	1.61803i	0.0552331	−	0.0760219i
$454$	−5.44427	+	16.7557i	−0.255512	+	0.786386i
$455$		0			0
$456$	−1.54508	+	1.12257i	−0.0723552	+	0.0525692i
$457$	19.2784	+	26.5344i	0.901806	+	1.24123i	0.969889	+	0.243549i	$0.0783117\pi$
$457$	19.2784	+	26.5344i	0.901806	+	1.24123i	−0.0680830	+	0.997680i	$0.521688\pi$
$458$	−15.3884	+	5.00000i	−0.719054	+	0.233635i
$459$	0.190983	−	0.587785i	0.00891432	−	0.0274355i
$460$		0			0
$461$	−9.90983			−0.461547			−0.230773	−	0.973008i	$-0.574126\pi$
$461$	−9.90983			−0.461547			−0.230773	+	0.973008i	$0.574126\pi$
$462$	−14.9394	+	6.00000i	−0.695043	+	0.279145i
$463$			8.79837i			0.408895i	0.978878	+	0.204448i	$0.0655398\pi$
$463$			8.79837i			0.408895i	−0.978878	+	0.204448i	$0.934460\pi$
$464$	17.5623	+	12.7598i	0.815310	+	0.592357i
$465$		0			0
$466$	4.33688	+	13.3475i	0.200902	+	0.618313i
$467$	−8.36775	−	11.5172i	−0.387213	−	0.532953i	0.570264	−	0.821461i	$-0.306841\pi$
$467$	−8.36775	−	11.5172i	−0.387213	−	0.532953i	−0.957478	+	0.288508i	$0.906841\pi$
$468$	−2.26538	−	3.11803i	−0.104717	−	0.144131i
$469$	−9.79180	−	30.1360i	−0.452143	−	1.39155i
$470$		0			0
$471$	−7.85410	−	5.70634i	−0.361898	−	0.262934i
$472$		−	11.9098i		−	0.548194i
$473$	−3.11044	+	4.95492i	−0.143018	+	0.227827i
$474$	−0.854102			−0.0392302
$475$		0			0
$476$	−0.354102	+	1.08981i	−0.0162302	+	0.0499515i
$477$	−7.02067	+	2.28115i	−0.321454	+	0.104447i
$478$	16.7027	+	22.9894i	0.763966	+	1.05151i
$479$	−13.6803	+	9.93935i	−0.625071	+	0.454140i	−0.854689	−	0.519140i	$-0.826252\pi$
$479$	−13.6803	+	9.93935i	−0.625071	+	0.454140i	0.229618	+	0.973281i	$0.426252\pi$
$480$		0			0
$481$	−8.16312	+	25.1235i	−0.372206	+	1.14553i
$482$	−16.2865	+	22.4164i	−0.741829	+	1.02104i
$483$		−	16.4164i		−	0.746972i
$484$	4.90983	−	4.70228i	0.223174	−	0.213740i
$485$		0			0
$486$	−1.30902	−	0.951057i	−0.0593782	−	0.0431408i
$487$	−37.2627	−	12.1074i	−1.68853	−	0.548638i	−0.701998	−	0.712179i	$-0.747709\pi$
$487$	−37.2627	−	12.1074i	−1.68853	−	0.548638i	−0.986537	+	0.163540i	$0.947709\pi$
$488$	2.43690	−	0.791796i	0.110313	−	0.0358429i
$489$	−12.3541	+	8.97578i	−0.558672	+	0.405899i
$490$		0			0
$491$	−8.10081	−	24.9317i	−0.365585	−	1.12515i	−0.949614	−	0.313421i	$-0.898525\pi$
$491$	−8.10081	−	24.9317i	−0.365585	−	1.12515i	0.584030	−	0.811732i	$-0.301475\pi$
$492$	−3.49396	−	1.13525i	−0.157520	−	0.0511812i
$493$	1.62460	−	2.23607i	0.0731682	−	0.100707i
$494$	8.61803			0.387744
$495$		0			0
$496$	18.7082			0.840023
$497$	−25.6785	+	35.3435i	−1.15184	+	1.58537i
$498$	−19.5559	−	6.35410i	−0.876322	−	0.284734i
$499$	−0.791796	−	2.43690i	−0.0354457	−	0.109091i	0.931768	−	0.363054i	$-0.118266\pi$
$499$	−0.791796	−	2.43690i	−0.0354457	−	0.109091i	−0.967214	+	0.253963i	$0.918266\pi$
$500$		0			0
$501$	15.3992	−	11.1882i	0.687985	−	0.499850i
$502$	25.8500	−	8.39919i	1.15374	−	0.374874i
$503$	−28.5972	−	9.29180i	−1.27509	−	0.414301i	−0.408239	−	0.912875i	$-0.633857\pi$
$503$	−28.5972	−	9.29180i	−1.27509	−	0.414301i	−0.866847	+	0.498574i	$0.833857\pi$
$504$	−5.42705	−	3.94298i	−0.241740	−	0.175634i
$505$		0			0
$506$	10.9443	+	27.2501i	0.486532	+	1.21142i
$507$		−	25.8885i		−	1.14975i
$508$	3.52671	−	4.85410i	0.156473	−	0.215366i
$509$	−6.60739	+	20.3355i	−0.292867	+	0.901353i	0.691062	+	0.722796i	$0.257143\pi$
$509$	−6.60739	+	20.3355i	−0.292867	+	0.901353i	−0.983929	+	0.178558i	$0.942857\pi$
$510$		0			0
$511$	−3.00000	+	2.17963i	−0.132712	+	0.0964210i
$512$	−3.11044	−	4.28115i	−0.137463	−	0.189202i
$513$	0.812299	−	0.263932i	0.0358639	−	0.0116529i
$514$	13.6631	−	42.0508i	0.602654	−	1.85478i
$515$		0			0
$516$	1.09017			0.0479921
$517$	1.31433	+	1.57295i	0.0578041	+	0.0691782i
$518$		−	20.5623i		−	0.903456i
$519$	14.2533	+	10.3556i	0.625650	+	0.454561i
$520$		0			0
$521$	12.0000	+	36.9322i	0.525730	+	1.61803i	0.762869	+	0.646553i	$0.223790\pi$
$521$	12.0000	+	36.9322i	0.525730	+	1.61803i	−0.237139	+	0.971476i	$0.576210\pi$
$522$	−4.25325	−	5.85410i	−0.186160	−	0.256227i
$523$	−20.5600	−	28.2984i	−0.899025	−	1.23740i	−0.970778	−	0.239979i	$-0.922859\pi$
$523$	−20.5600	−	28.2984i	−0.899025	−	1.23740i	0.0717533	−	0.997422i	$-0.477141\pi$
$524$	2.64590	+	8.14324i	0.115587	+	0.355739i
$525$		0			0
$526$	0.881966	+	0.640786i	0.0384555	+	0.0279396i
$527$		−	2.38197i		−	0.103760i
$528$	15.6129	+	3.92705i	0.679466	+	0.170903i
$529$	−6.94427			−0.301925
$530$		0			0
$531$	−1.64590	+	5.06555i	−0.0714259	+	0.219826i
$532$	−1.50609	+	0.489357i	−0.0652971	+	0.0212163i
$533$	−21.7885	−	29.9894i	−0.943767	−	1.29898i
$534$	12.3992	−	9.00854i	0.536565	−	0.389838i
$535$		0			0
$536$	−7.29837	+	22.4621i	−0.315242	+	0.970214i
$537$	−1.31433	+	1.80902i	−0.0567174	+	0.0780648i
$538$			39.5967i			1.70714i
$539$	6.61803	−	0.449028i	0.285059	−	0.0193410i
$540$		0			0
$541$	0.454915	+	0.330515i	0.0195583	+	0.0142100i	0.597521	−	0.801853i	$-0.296152\pi$
$541$	0.454915	+	0.330515i	0.0195583	+	0.0142100i	−0.577963	+	0.816063i	$0.696152\pi$
$542$	−9.64932	−	3.13525i	−0.414474	−	0.134671i
$543$	8.11048	−	2.63525i	0.348054	−	0.113090i
$544$	1.69098	−	1.22857i	0.0725003	−	0.0526745i
$545$		0			0
$546$	9.35410	+	28.7890i	0.400319	+	1.23205i
$547$	−18.4333	−	5.98936i	−0.788153	−	0.256086i	−0.112836	−	0.993614i	$-0.535993\pi$
$547$	−18.4333	−	5.98936i	−0.788153	−	0.256086i	−0.675317	+	0.737527i	$0.735993\pi$
$548$	−0.534785	+	0.736068i	−0.0228449	+	0.0314433i
$549$	−1.14590			−0.0489057
$550$		0			0
$551$	3.81966			0.162723
$552$	−7.19218	+	9.89919i	−0.306120	+	0.421337i
$553$	1.50609	+	0.489357i	0.0640453	+	0.0208096i
$554$	−5.21885	−	16.0620i	−0.221728	−	0.682407i
$555$		0			0
$556$	−2.92705	+	2.12663i	−0.124135	+	0.0901891i
$557$	24.8132	−	8.06231i	1.05137	−	0.341611i	0.268164	−	0.963373i	$-0.413583\pi$
$557$	24.8132	−	8.06231i	1.05137	−	0.341611i	0.783206	+	0.621762i	$0.213583\pi$
$558$	−5.93085	−	1.92705i	−0.251073	−	0.0815786i
$559$	8.89919	+	6.46564i	0.376396	+	0.273467i
$560$		0			0
$561$	0.500000	−	1.98787i	0.0211100	−	0.0839279i
$562$			8.47214i			0.357375i
$563$	15.8047	−	21.7533i	0.666088	−	0.916792i	−0.333575	−	0.942723i	$-0.608255\pi$
$563$	15.8047	−	21.7533i	0.666088	−	0.916792i	0.999664	+	0.0259316i	$0.00825520\pi$
$564$	0.118034	−	0.363271i	0.00497013	−	0.0152965i
$565$		0			0
$566$	29.0344	−	21.0948i	1.22041	−	0.886679i
$567$	1.76336	+	2.42705i	0.0740540	+	0.101927i
$568$	30.9686	−	10.0623i	1.29941	−	0.422205i
$569$	−10.5279	+	32.4014i	−0.441351	+	1.35834i	0.445085	+	0.895488i	$0.353173\pi$
$569$	−10.5279	+	32.4014i	−0.441351	+	1.35834i	−0.886436	+	0.462851i	$0.846827\pi$
$570$		0			0
$571$	−25.6869			−1.07496			−0.537482	−	0.843275i	$-0.680624\pi$
$571$	−25.6869			−1.07496			−0.537482	+	0.843275i	$0.680624\pi$
$572$	−8.19624	−	9.80902i	−0.342702	−	0.410136i
$573$			1.47214i			0.0614994i
$574$	23.3435	+	16.9600i	0.974337	+	0.707897i
$575$		0			0
$576$	1.30902	+	4.02874i	0.0545424	+	0.167864i
$577$	8.95554	+	12.3262i	0.372824	+	0.513148i	0.953666	−	0.300868i	$-0.0972765\pi$
$577$	8.95554	+	12.3262i	0.372824	+	0.513148i	−0.580842	+	0.814016i	$0.697277\pi$
$578$	15.8047	+	21.7533i	0.657388	+	0.904818i
$579$	−0.482779	−	1.48584i	−0.0200636	−	0.0617495i
$580$		0			0
$581$	30.8435	+	22.4091i	1.27960	+	0.929685i
$582$		−	24.3262i		−	1.00836i
$583$	−22.7194	+	9.12461i	−0.940940	+	0.377903i
$584$	2.76393			0.114372
$585$		0			0
$586$	8.97214	−	27.6134i	0.370636	−	1.14070i
$587$	23.1154	−	7.51064i	0.954074	−	0.309997i	0.209704	−	0.977765i	$-0.432750\pi$
$587$	23.1154	−	7.51064i	0.954074	−	0.309997i	0.744370	+	0.667767i	$0.232750\pi$
$588$	−0.726543	−	1.00000i	−0.0299621	−	0.0412393i
$589$	2.66312	−	1.93487i	0.109732	−	0.0797249i
$590$		0			0
$591$	8.22542	−	25.3153i	0.338349	−	1.04133i
$592$	−12.0862	+	16.6353i	−0.496741	+	0.683705i
$593$		−	29.2148i		−	1.19971i	−0.800110	−	0.599854i	$-0.795225\pi$
$593$		−	29.2148i		−	1.19971i	0.800110	−	0.599854i	$-0.204775\pi$
$594$	−4.54508	−	2.85317i	−0.186487	−	0.117067i
$595$		0			0
$596$	−7.50000	−	5.44907i	−0.307212	−	0.223203i
$597$	3.13068	+	1.01722i	0.128130	+	0.0416321i
$598$	52.5124	−	17.0623i	2.14739	−	0.697730i
$599$	−17.5623	+	12.7598i	−0.717576	+	0.521350i	−0.885609	−	0.464432i	$-0.846259\pi$
$599$	−17.5623	+	12.7598i	−0.717576	+	0.521350i	0.168033	+	0.985781i	$0.446259\pi$
$600$		0			0
$601$	−6.12868	−	18.8621i	−0.249994	−	0.769402i	−0.994775	−	0.102093i	$-0.967446\pi$
$601$	−6.12868	−	18.8621i	−0.249994	−	0.769402i	0.744781	−	0.667309i	$-0.232554\pi$
$602$	−8.14324	−	2.64590i	−0.331894	−	0.107839i
$603$	6.20837	−	8.54508i	0.252824	−	0.347983i
$604$	−1.23607			−0.0502949
$605$		0			0
$606$	−4.85410			−0.197184
$607$	1.36733	−	1.88197i	0.0554981	−	0.0763866i	−0.780366	−	0.625323i	$-0.784967\pi$
$607$	1.36733	−	1.88197i	0.0554981	−	0.0763866i	0.835864	+	0.548937i	$0.184967\pi$
$608$	2.74717	+	0.892609i	0.111412	+	0.0362001i
$609$	4.14590	+	12.7598i	0.168000	+	0.517052i
$610$		0			0
$611$	3.11803	−	2.26538i	0.126142	−	0.0916476i
$612$	−0.363271	+	0.118034i	−0.0146844	+	0.00477124i
$613$	3.18368	+	1.03444i	0.128588	+	0.0417807i	0.372604	−	0.927990i	$-0.378465\pi$
$613$	3.18368	+	1.03444i	0.128588	+	0.0417807i	−0.244016	+	0.969771i	$0.578465\pi$
$614$	−25.6074	−	18.6049i	−1.03343	−	0.750831i
$615$		0			0
$616$	−18.8435	−	11.8290i	−0.759225	−	0.476602i
$617$		−	46.4164i		−	1.86865i	−0.356417	−	0.934327i	$-0.616002\pi$
$617$		−	46.4164i		−	1.86865i	0.356417	−	0.934327i	$-0.383998\pi$
$618$	−5.70634	+	7.85410i	−0.229543	+	0.315938i
$619$	9.63525	−	29.6543i	0.387274	−	1.19191i	−0.547544	−	0.836777i	$-0.684437\pi$
$619$	9.63525	−	29.6543i	0.387274	−	1.19191i	0.934817	−	0.355129i	$-0.115563\pi$
$620$		0			0
$621$	4.42705	−	3.21644i	0.177651	−	0.129071i
$622$	10.9106	+	15.0172i	0.437477	+	0.602136i
$623$	−27.0256	+	8.78115i	−1.08276	+	0.351809i
$624$	9.35410	−	28.7890i	0.374464	−	1.15248i
$625$		0			0
$626$	−45.0344			−1.79994
$627$	2.62866	−	1.05573i	0.104978	−	0.0421617i
$628$			6.00000i			0.239426i
$629$	2.11803	+	1.53884i	0.0844515	+	0.0613576i
$630$		0			0
$631$	3.93363	+	12.1065i	0.156595	+	0.481951i	0.998319	−	0.0579577i	$-0.0184589\pi$
$631$	3.93363	+	12.1065i	0.156595	+	0.481951i	−0.841724	+	0.539908i	$0.818459\pi$
$632$	−0.693786	−	0.954915i	−0.0275973	−	0.0379845i
$633$	−6.62464	−	9.11803i	−0.263306	−	0.362409i
$634$	−12.6803	−	39.0261i	−0.503601	−	1.54992i
$635$		0			0
$636$	3.69098	+	2.68166i	0.146357	+	0.106335i
$637$		−	12.4721i		−	0.494164i
$638$	−15.3884	−	18.4164i	−0.609233	−	0.729113i
$639$	−14.5623			−0.576076
$640$		0			0
$641$	−2.08359	+	6.41264i	−0.0822969	+	0.253284i	−0.983736	−	0.179623i	$-0.942512\pi$
$641$	−2.08359	+	6.41264i	−0.0822969	+	0.253284i	0.901439	+	0.432907i	$0.142512\pi$
$642$	0.363271	−	0.118034i	0.0143372	−	0.00465843i
$643$	10.8374	+	14.9164i	0.427386	+	0.588246i	0.967351	−	0.253442i	$-0.0815626\pi$
$643$	10.8374	+	14.9164i	0.427386	+	0.588246i	−0.539965	+	0.841687i	$0.681563\pi$
$644$	−8.20820	+	5.96361i	−0.323449	+	0.234999i
$645$		0			0
$646$	0.263932	−	0.812299i	0.0103843	−	0.0319595i
$647$	−1.88187	+	2.59017i	−0.0739839	+	0.101830i	−0.844405	−	0.535705i	$-0.820046\pi$
$647$	−1.88187	+	2.59017i	−0.0739839	+	0.101830i	0.770421	+	0.637535i	$0.220046\pi$
$648$		−	2.23607i		−	0.0878410i
$649$	−4.30902	+	17.1315i	−0.169144	+	0.672471i
$650$		0			0
$651$	9.35410	+	6.79615i	0.366616	+	0.266362i
$652$	8.97578	+	2.91641i	0.351519	+	0.114215i
$653$	−20.8905	+	6.78773i	−0.817508	+	0.265624i	−0.687774	−	0.725924i	$-0.741412\pi$
$653$	−20.8905	+	6.78773i	−0.817508	+	0.265624i	−0.129734	+	0.991549i	$0.541412\pi$
$654$		0			0
$655$		0			0
$656$	−8.91641	−	27.4419i	−0.348127	−	1.07143i
$657$	−1.17557	−	0.381966i	−0.0458634	−	0.0149019i
$658$	−1.76336	+	2.42705i	−0.0687428	+	0.0946163i
$659$	−20.6525			−0.804506			−0.402253	−	0.915528i	$-0.631773\pi$
$659$	−20.6525			−0.804506			−0.402253	+	0.915528i	$0.631773\pi$
$660$		0			0
$661$	−21.0902			−0.820313			−0.410156	−	0.912015i	$-0.634526\pi$
$661$	−21.0902			−0.820313			−0.410156	+	0.912015i	$0.634526\pi$
$662$	21.4908	−	29.5795i	0.835263	−	1.14964i
$663$	−3.66547	−	1.19098i	−0.142355	−	0.0462539i
$664$	−8.78115	−	27.0256i	−0.340775	−	1.04880i
$665$		0			0
$666$	5.54508	−	4.02874i	0.214868	−	0.156111i
$667$	23.2744	−	7.56231i	0.901188	−	0.292814i
$668$	−11.1882	−	3.63525i	−0.432883	−	0.140652i
$669$	−10.2812	−	7.46969i	−0.397492	−	0.288795i
$670$		0			0
$671$	−3.79180	+	0.257270i	−0.146381	+	0.00993180i
$672$			10.1459i			0.391387i
$673$	−8.47375	+	11.6631i	−0.326639	+	0.449580i	−0.940480	−	0.339850i	$-0.889624\pi$
$673$	−8.47375	+	11.6631i	−0.326639	+	0.449580i	0.613841	+	0.789430i	$0.289624\pi$
$674$	6.85410	−	21.0948i	0.264010	−	0.812540i
$675$		0			0
$676$	−12.9443	+	9.40456i	−0.497857	+	0.361714i
$677$	13.2088	+	18.1803i	0.507655	+	0.698727i	0.983522	−	0.180790i	$-0.0578655\pi$
$677$	13.2088	+	18.1803i	0.507655	+	0.698727i	−0.475867	+	0.879517i	$0.657866\pi$
$678$	19.5559	−	6.35410i	0.751040	−	0.244028i
$679$	−13.9377	+	42.8958i	−0.534880	+	1.64619i
$680$		0			0
$681$	10.8885			0.417250
$682$	−20.0579	−	5.04508i	−0.768058	−	0.193186i
$683$		−	38.8885i		−	1.48803i	−0.668164	−	0.744014i	$-0.732919\pi$
$683$		−	38.8885i		−	1.48803i	0.668164	−	0.744014i	$-0.267081\pi$
$684$	−0.427051	−	0.310271i	−0.0163287	−	0.0118635i
$685$		0			0
$686$	−7.50000	−	23.0826i	−0.286351	−	0.881299i
$687$	5.87785	+	8.09017i	0.224254	+	0.308659i
$688$	5.03280	+	6.92705i	0.191874	+	0.264091i
$689$	14.2254	+	43.7814i	0.541946	+	1.66794i
$690$		0			0
$691$	32.1246	+	23.3399i	1.22208	+	0.887892i	0.996271	−	0.0862806i	$-0.0274981\pi$
$691$	32.1246	+	23.3399i	1.22208	+	0.887892i	0.225807	+	0.974172i	$0.427498\pi$
$692$		−	10.8885i		−	0.413920i
$693$	6.37988	+	7.63525i	0.242352	+	0.290039i
$694$	4.94427			0.187682
$695$		0			0
$696$	3.09017	−	9.51057i	0.117133	−	0.360497i
$697$	−3.49396	+	1.13525i	−0.132343	+	0.0430008i
$698$	−28.6502	−	39.4336i	−1.08443	−	1.49258i
$699$	7.01722	−	5.09831i	0.265416	−	0.192836i
$700$		0			0
$701$	15.3541	−	47.2551i	0.579916	−	1.78480i	−0.0388752	−	0.999244i	$-0.512377\pi$
$701$	15.3541	−	47.2551i	0.579916	−	1.78480i	0.618792	−	0.785555i	$-0.287623\pi$
$702$	−5.93085	+	8.16312i	−0.223846	+	0.308097i
$703$			3.61803i			0.136457i
$704$	5.23607	+	13.0373i	0.197342	+	0.491361i
$705$		0			0
$706$	2.00000	+	1.45309i	0.0752710	+	0.0546876i
$707$	8.55951	+	2.78115i	0.321913	+	0.104596i
$708$	3.13068	−	1.01722i	0.117658	−	0.0382295i
$709$	5.06231	−	3.67798i	0.190119	−	0.138129i	−0.488654	−	0.872478i	$-0.662512\pi$
$709$	5.06231	−	3.67798i	0.190119	−	0.138129i	0.678773	+	0.734348i	$0.262512\pi$
$710$		0			0
$711$	0.163119	+	0.502029i	0.00611744	+	0.0188275i
$712$	20.1437	+	6.54508i	0.754917	+	0.245287i
$713$	12.3965	−	17.0623i	0.464252	−	0.638988i
$714$	3.00000			0.112272
$715$		0			0
$716$	1.38197			0.0516465
$717$	10.3229	−	14.2082i	0.385514	−	0.530615i
$718$	−26.5236	−	8.61803i	−0.989851	−	0.321622i
$719$	8.78115	+	27.0256i	0.327482	+	1.00789i	0.970308	+	0.241873i	$0.0777618\pi$
$719$	8.78115	+	27.0256i	0.327482	+	1.00789i	−0.642826	+	0.766012i	$0.722238\pi$
$720$		0			0
$721$	14.5623	−	10.5801i	0.542329	−	0.394025i
$722$	−28.1154	+	9.13525i	−1.04635	+	0.339979i
$723$	16.2865	+	5.29180i	0.605700	+	0.196804i
$724$	−4.26393	−	3.09793i	−0.158468	−	0.115134i
$725$		0			0
$726$	−15.6803	−	8.42075i	−0.581952	−	0.312523i
$727$		−	32.1459i		−	1.19223i	−0.802901	−	0.596113i	$-0.796711\pi$
$727$		−	32.1459i		−	1.19223i	0.802901	−	0.596113i	$-0.203289\pi$
$728$	−24.5887	+	33.8435i	−0.911318	+	1.25432i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$		0			0
$731$	0.881966	−	0.640786i	0.0326207	−	0.0237003i
$732$	0.416272	+	0.572949i	0.0153858	+	0.0211768i
$733$	23.1029	−	7.50658i	0.853324	−	0.277262i	0.150486	−	0.988612i	$-0.451916\pi$
$733$	23.1029	−	7.50658i	0.853324	−	0.277262i	0.702838	+	0.711350i	$0.251916\pi$
$734$	7.28115	−	22.4091i	0.268752	−	0.827134i
$735$		0			0
$736$	18.5066			0.682162
$737$	18.6251	−	29.6697i	0.686064	−	1.09290i
$738$			9.61803i			0.354045i
$739$	−20.2254	−	14.6946i	−0.744004	−	0.540551i	0.149958	−	0.988692i	$-0.452086\pi$
$739$	−20.2254	−	14.6946i	−0.744004	−	0.540551i	−0.893963	+	0.448142i	$0.852086\pi$
$740$		0			0
$741$	−1.64590	−	5.06555i	−0.0604636	−	0.186088i
$742$	−21.0620	−	28.9894i	−0.773210	−	1.06423i
$743$	−7.53521	−	10.3713i	−0.276440	−	0.380487i	0.648111	−	0.761546i	$-0.275559\pi$
$743$	−7.53521	−	10.3713i	−0.276440	−	0.380487i	−0.924551	+	0.381059i	$0.875559\pi$
$744$	−2.66312	−	8.19624i	−0.0976347	−	0.300489i
$745$		0			0
$746$	−29.3435	−	21.3193i	−1.07434	−	0.780554i
$747$			12.7082i			0.464969i
$748$	−1.17557	+	0.472136i	−0.0429831	+	0.0172630i
$749$	−0.708204			−0.0258772
$750$		0			0
$751$	−16.3541	+	50.3328i	−0.596770	+	1.83667i	−0.0510571	+	0.998696i	$0.516259\pi$
$751$	−16.3541	+	50.3328i	−0.596770	+	1.83667i	−0.545713	+	0.837972i	$0.683741\pi$
$752$	2.85317	−	0.927051i	0.104044	−	0.0338061i
$753$	−9.87384	−	13.5902i	−0.359823	−	0.495253i
$754$	−36.5066	+	26.5236i	−1.32949	+	0.965932i
$755$		0			0
$756$	0.572949	−	1.76336i	0.0208380	−	0.0641326i
$757$	9.37181	−	12.8992i	0.340624	−	0.468829i	−0.603999	−	0.796985i	$-0.706427\pi$
$757$	9.37181	−	12.8992i	0.340624	−	0.468829i	0.944624	+	0.328156i	$0.106427\pi$
$758$			45.9787i			1.67002i
$759$	13.9271	−	11.6372i	0.505520	−	0.422403i
$760$		0			0
$761$	−3.95492	−	2.87341i	−0.143366	−	0.104161i	0.513791	−	0.857916i	$-0.328241\pi$
$761$	−3.95492	−	2.87341i	−0.143366	−	0.104161i	−0.657156	+	0.753754i	$0.728241\pi$
$762$	−14.9394	−	4.85410i	−0.541197	−	0.175846i
$763$		0			0
$764$	0.736068	−	0.534785i	0.0266300	−	0.0193478i
$765$		0			0
$766$	−4.44427	−	13.6781i	−0.160578	−	0.494208i
$767$	31.5891	+	10.2639i	1.14062	+	0.370609i
$768$	7.97172	−	10.9721i	0.287655	−	0.395923i
$769$	47.6869			1.71963			0.859817	−	0.510602i	$-0.170577\pi$
$769$	47.6869			1.71963			0.859817	+	0.510602i	$0.170577\pi$
$770$		0			0
$771$	−27.3262			−0.984130
$772$	−0.567541	+	0.781153i	−0.0204262	+	0.0281143i
$773$	46.8388	+	15.2188i	1.68467	+	0.547384i	0.985809	−	0.167870i	$-0.0536887\pi$
$773$	46.8388	+	15.2188i	1.68467	+	0.547384i	0.698865	+	0.715253i	$0.253689\pi$
$774$	−0.881966	−	2.71441i	−0.0317016	−	0.0975675i
$775$		0			0
$776$	27.1976	−	19.7602i	0.976336	−	0.709349i
$777$	−12.0862	+	3.92705i	−0.433591	+	0.140882i
$778$	−14.2658	−	4.63525i	−0.511455	−	0.166182i
$779$	−4.10739	−	2.98419i	−0.147163	−	0.106920i
$780$		0			0
$781$	−48.1869	+	3.26944i	−1.72426	+	0.116990i
$782$		−	5.47214i		−	0.195683i
$783$	−2.62866	+	3.61803i	−0.0939405	+	0.129298i
$784$	3.00000	−	9.23305i	0.107143	−	0.329752i
$785$		0			0
$786$	18.1353	−	13.1760i	0.646863	−	0.469974i
$787$	−13.9353	−	19.1803i	−0.496741	−	0.683705i	0.484873	−	0.874585i	$-0.338866\pi$
$787$	−13.9353	−	19.1803i	−0.496741	−	0.683705i	−0.981613	+	0.190880i	$0.938866\pi$
$788$	−15.6457	+	5.08359i	−0.557355	+	0.181095i
$789$	0.208204	−	0.640786i	0.00741226	−	0.0228126i
$790$		0			0
$791$	−38.1246			−1.35556
$792$	−0.502029	−	7.39919i	−0.0178388	−	0.262919i
$793$			7.14590i			0.253758i
$794$	−33.1074	−	24.0539i	−1.17494	−	0.853642i
$795$		0			0
$796$	−0.628677	−	1.93487i	−0.0222829	−	0.0685796i
$797$	8.95554	+	12.3262i	0.317221	+	0.436618i	0.937616	−	0.347672i	$-0.113028\pi$
$797$	8.95554	+	12.3262i	0.317221	+	0.436618i	−0.620395	+	0.784290i	$0.713028\pi$
$798$	2.43690	+	3.35410i	0.0862652	+	0.118734i
$799$	−0.118034	−	0.363271i	−0.00417574	−	0.0128516i
$800$		0			0
$801$	−7.66312	−	5.56758i	−0.270763	−	0.196721i
$802$			24.1246i			0.851870i
$803$	−3.97574	−	1.00000i	−0.140301	−	0.0352892i
$804$	−6.52786			−0.230220
$805$		0			0
$806$	−12.0172	+	36.9852i	−0.423289	+	1.30275i
$807$	23.2744	−	7.56231i	0.819297	−	0.266206i
$808$	−3.94298	−	5.42705i	−0.138714	−	0.190923i
$809$	20.4894	−	14.8864i	0.720367	−	0.523378i	−0.166134	−	0.986103i	$-0.553128\pi$
$809$	20.4894	−	14.8864i	0.720367	−	0.523378i	0.886502	+	0.462726i	$0.153128\pi$
$810$		0			0
$811$	14.1353	−	43.5038i	0.496356	−	1.52763i	−0.318477	−	0.947931i	$-0.603171\pi$
$811$	14.1353	−	43.5038i	0.496356	−	1.52763i	0.814833	−	0.579696i	$-0.196829\pi$
$812$	4.87380	−	6.70820i	0.171037	−	0.235412i
$813$			6.27051i			0.219916i
$814$	17.4443	−	14.5761i	0.611421	−	0.510893i
$815$		0			0
$816$	−2.42705	−	1.76336i	−0.0849638	−	0.0617298i
$817$	1.43284	+	0.465558i	0.0501287	+	0.0162878i
$818$	44.5407	−	14.4721i	1.55733	−	0.506006i
$819$	15.1353	−	10.9964i	0.528869	−	0.384246i
$820$		0			0
$821$	4.19756	+	12.9188i	0.146496	+	0.450868i	0.997200	−	0.0747763i	$-0.0238243\pi$
$821$	4.19756	+	12.9188i	0.146496	+	0.450868i	−0.850704	+	0.525644i	$0.823824\pi$
$822$	2.26538	+	0.736068i	0.0790144	+	0.0256733i
$823$	−15.5927	+	21.4615i	−0.543527	+	0.748101i	−0.989116	−	0.147137i	$-0.952994\pi$
$823$	−15.5927	+	21.4615i	−0.543527	+	0.748101i	0.445589	+	0.895238i	$0.352994\pi$
$824$	−13.4164			−0.467383
$825$		0			0
$826$	−25.8541			−0.899579
$827$	−7.56796	+	10.4164i	−0.263164	+	0.362214i	−0.920067	−	0.391761i	$-0.871866\pi$
$827$	−7.56796	+	10.4164i	−0.263164	+	0.362214i	0.656903	+	0.753975i	$0.271866\pi$
$828$	−3.21644	−	1.04508i	−0.111779	−	0.0363192i
$829$	13.1910	+	40.5977i	0.458142	+	1.41002i	0.867407	+	0.497600i	$0.165785\pi$
$829$	13.1910	+	40.5977i	0.458142	+	1.41002i	−0.409265	+	0.912416i	$0.634215\pi$
$830$		0			0
$831$	−8.44427	+	6.13512i	−0.292929	+	0.212825i
$832$	25.1235	−	8.16312i	0.871001	−	0.283005i
$833$	−1.17557	−	0.381966i	−0.0407311	−	0.0132343i
$834$	7.66312	+	5.56758i	0.265352	+	0.192790i
$835$		0			0
$836$	−1.48278	−	0.930812i	−0.0512830	−	0.0321928i
$837$			3.85410i			0.133217i
$838$	−20.4540	+	28.1525i	−0.706571	+	0.972511i
$839$	7.19756	−	22.1518i	0.248487	−	0.764766i	−0.746556	−	0.665323i	$-0.768294\pi$
$839$	7.19756	−	22.1518i	0.248487	−	0.764766i	0.995043	−	0.0994428i	$-0.0317060\pi$
$840$		0			0
$841$	7.28115	−	5.29007i	0.251074	−	0.182416i
$842$	−3.54696	−	4.88197i	−0.122236	−	0.168244i
$843$	4.97980	−	1.61803i	0.171513	−	0.0557281i
$844$	−2.15248	+	6.62464i	−0.0740913	+	0.228029i
$845$		0			0
$846$	−1.00000			−0.0343807
$847$	22.8254	+	23.8328i	0.784289	+	0.818905i
$848$			35.8328i			1.23050i
$849$	−17.9443	−	13.0373i	−0.615846	−	0.447438i
$850$		0			0
$851$	7.16312	+	22.0458i	0.245549	+	0.755721i
$852$	5.29007	+	7.28115i	0.181235	+	0.249448i
$853$	−4.66953	−	6.42705i	−0.159882	−	0.220058i	0.721559	−	0.692353i	$-0.243426\pi$
$853$	−4.66953	−	6.42705i	−0.159882	−	0.220058i	−0.881441	+	0.472295i	$0.843426\pi$
$854$	−1.71885	−	5.29007i	−0.0588177	−	0.181022i
$855$		0			0
$856$	0.427051	+	0.310271i	0.0145963	+	0.0106048i
$857$			41.7214i			1.42517i	0.701584	+	0.712587i	$0.252477\pi$
$857$			41.7214i			1.42517i	−0.701584	+	0.712587i	$0.747523\pi$
$858$	−17.7926	+	28.3435i	−0.607428	+	0.967630i
$859$	−42.8885			−1.46334			−0.731669	−	0.681660i	$-0.761258\pi$
$859$	−42.8885			−1.46334			−0.731669	+	0.681660i	$0.761258\pi$
$860$		0			0
$861$	5.51064	−	16.9600i	0.187802	−	0.577996i
$862$	−2.29814	+	0.746711i	−0.0782750	+	0.0254331i
$863$	14.0413	+	19.3262i	0.477973	+	0.657873i	0.978114	−	0.208071i	$-0.0667185\pi$
$863$	14.0413	+	19.3262i	0.477973	+	0.657873i	−0.500141	+	0.865944i	$0.666719\pi$
$864$	−2.73607	+	1.98787i	−0.0930829	+	0.0676287i
$865$		0			0
$866$	−3.00000	+	9.23305i	−0.101944	+	0.313752i
$867$	9.76784	−	13.4443i	0.331733	−	0.456591i
$868$		−	7.14590i		−	0.242548i
$869$	0.652476	+	1.62460i	0.0221337	+	0.0551107i
$870$		0			0
$871$	−53.2877	−	38.7158i	−1.80559	−	1.31183i
$872$		0			0
$873$	−14.2986	+	4.64590i	−0.483934	+	0.157240i
$874$	6.11803	−	4.44501i	0.206946	−	0.150355i
$875$		0			0
$876$	0.236068	+	0.726543i	0.00797600	+	0.0245476i
$877$	19.4172	+	6.30902i	0.655671	+	0.213040i	0.617913	−	0.786247i	$-0.287978\pi$
$877$	19.4172	+	6.30902i	0.655671	+	0.213040i	0.0377579	+	0.999287i	$0.487978\pi$
$878$	15.8904	−	21.8713i	0.536277	−	0.738121i
$879$	−17.9443			−0.605245
$880$		0			0
$881$	25.0902			0.845309			0.422655	−	0.906291i	$-0.361098\pi$
$881$	25.0902			0.845309			0.422655	+	0.906291i	$0.361098\pi$
$882$	−1.90211	+	2.61803i	−0.0640475	+	0.0881538i
$883$	35.5851	+	11.5623i	1.19753	+	0.389103i	0.838853	−	0.544358i	$-0.183226\pi$
$883$	35.5851	+	11.5623i	1.19753	+	0.389103i	0.358681	+	0.933460i	$0.383226\pi$
$884$	0.736068	+	2.26538i	0.0247566	+	0.0761931i
$885$		0			0
$886$	1.14590	−	0.832544i	0.0384972	−	0.0279699i
$887$	2.85317	−	0.927051i	0.0958001	−	0.0311273i	−0.260725	−	0.965413i	$-0.583962\pi$
$887$	2.85317	−	0.927051i	0.0958001	−	0.0311273i	0.356525	+	0.934286i	$0.383962\pi$
$888$	9.00854	+	2.92705i	0.302307	+	0.0982254i
$889$	23.5623	+	17.1190i	0.790254	+	0.574153i
$890$		0			0
$891$	−0.809017	+	3.21644i	−0.0271031	+	0.107755i
$892$			7.85410i			0.262975i
$893$	0.310271	−	0.427051i	0.0103828	−	0.0142907i
$894$	−7.50000	+	23.0826i	−0.250838	+	0.771999i
$895$		0			0
$896$	−33.0517	+	24.0134i	−1.10418	+	0.802233i
$897$	−20.0579	−	27.6074i	−0.669715	−	0.921784i
$898$	23.8949	−	7.76393i	0.797384	−	0.259086i
$899$	−5.32624	+	16.3925i	−0.177640	+	0.546720i
$900$		0			0
$901$	4.56231			0.151992
$902$	2.15938	+	31.8262i	0.0718996	+	1.05970i
$903$			5.29180i			0.176100i
$904$	22.9894	+	16.7027i	0.764615	+	0.555525i
$905$		0			0
$906$	1.00000	+	3.07768i	0.0332228	+	0.102249i
$907$	2.33863	+	3.21885i	0.0776529	+	0.106880i	0.846077	−	0.533061i	$-0.178959\pi$
$907$	2.33863	+	3.21885i	0.0776529	+	0.106880i	−0.768424	+	0.639942i	$0.778959\pi$
$908$	−3.95550	−	5.44427i	−0.131268	−	0.180675i
$909$	0.927051	+	2.85317i	0.0307483	+	0.0946337i
$910$		0			0
$911$	−29.0795	−	21.1275i	−0.963448	−	0.699986i	−0.00949880	−	0.999955i	$-0.503024\pi$
$911$	−29.0795	−	21.1275i	−0.963448	−	0.699986i	−0.953949	+	0.299969i	$0.903024\pi$
$912$		−	4.14590i		−	0.137284i
$913$	2.85317	+	42.0517i	0.0944261	+	1.39171i
$914$	−53.0689			−1.75536
$915$		0			0
$916$	1.90983	−	5.87785i	0.0631026	−	0.194210i
$917$	−39.5281	+	12.8435i	−1.30533	+	0.424128i
$918$	0.587785	+	0.809017i	0.0193998	+	0.0267015i
$919$	−37.9894	+	27.6009i	−1.25315	+	0.910469i	−0.998400	−	0.0565371i	$-0.981994\pi$
$919$	−37.9894	+	27.6009i	−1.25315	+	0.910469i	−0.254753	+	0.967006i	$0.581994\pi$
$920$		0			0
$921$	−6.04508	+	18.6049i	−0.199192	+	0.613051i
$922$	9.42481	−	12.9721i	0.310390	−	0.427215i
$923$			90.8115i			2.98910i
$924$	1.50000	−	5.96361i	0.0493464	−	0.196188i
$925$		0			0
$926$	−11.5172	−	8.36775i	−0.378479	−	0.274981i
$927$	5.70634	+	1.85410i	0.187421	+	0.0608967i
$928$	−14.3844	+	4.67376i	−0.472190	+	0.153424i
$929$	2.33688	−	1.69784i	0.0766706	−	0.0557044i	−0.548790	−	0.835960i	$-0.684911\pi$
$929$	2.33688	−	1.69784i	0.0766706	−	0.0557044i	0.625460	+	0.780256i	$0.284911\pi$
$930$		0			0
$931$	−0.527864	−	1.62460i	−0.0173000	−	0.0532441i
$932$	−5.09831	−	1.65654i	−0.167001	−	0.0542618i
$933$	6.74315	−	9.28115i	0.220761	−	0.303851i
$934$	23.0344			0.753710
$935$		0			0
$936$	−13.9443			−0.455783
$937$	−19.1599	+	26.3713i	−0.625926	+	0.861514i	−0.997768	−	0.0667827i	$-0.978727\pi$
$937$	−19.1599	+	26.3713i	−0.625926	+	0.861514i	0.371841	+	0.928296i	$0.378727\pi$
$938$	48.7612	+	15.8435i	1.59211	+	0.517307i
$939$	8.60081	+	26.4706i	0.280677	+	0.863835i
$940$		0			0
$941$	−27.2082	+	19.7679i	−0.886962	+	0.644416i	−0.935084	−	0.354426i	$-0.884676\pi$
$941$	−27.2082	+	19.7679i	−0.886962	+	0.644416i	0.0481221	+	0.998841i	$0.484676\pi$
$942$	14.9394	−	4.85410i	0.486752	−	0.158155i
$943$	−30.9358	−	10.0517i	−1.00741	−	0.327327i
$944$	20.9164	+	15.1967i	0.680771	+	0.494609i
$945$		0			0
$946$	−3.52786	−	8.78402i	−0.114701	−	0.285593i
$947$		−	2.67376i		−	0.0868856i	−0.999056	−	0.0434428i	$-0.986167\pi$
$947$		−	2.67376i		−	0.0868856i	0.999056	−	0.0434428i	$-0.0138326\pi$
$948$	0.191758	−	0.263932i	0.00622801	−	0.00857211i
$949$	−2.38197	+	7.33094i	−0.0773219	+	0.237972i
$950$		0			0
$951$	−20.5172	+	14.9066i	−0.665316	+	0.483381i
$952$	2.43690	+	3.35410i	0.0789803	+	0.108707i
$953$	−57.2349	+	18.5967i	−1.85402	+	0.602408i	−0.857961	+	0.513714i	$0.828269\pi$
$953$	−57.2349	+	18.5967i	−1.85402	+	0.602408i	−0.996059	+	0.0886937i	$0.971731\pi$
$954$	3.69098	−	11.3597i	0.119500	−	0.367783i
$955$		0			0
$956$	−10.8541			−0.351047
$957$	−7.88597	+	12.5623i	−0.254917	+	0.406082i
$958$		−	27.3607i		−	0.883983i
$959$	−3.57295	−	2.59590i	−0.115377	−	0.0838260i
$960$		0			0
$961$	−4.98936	−	15.3557i	−0.160947	−	0.495344i
$962$	−25.1235	−	34.5795i	−0.810014	−	1.11489i
$963$	−0.138757	−	0.190983i	−0.00447139	−	0.00615434i
$964$	−3.27051	−	10.0656i	−0.105336	−	0.324191i
$965$		0			0
$966$	21.4894	+	15.6129i	0.691409	+	0.502338i
$967$		−	25.6869i		−	0.826036i	−0.910723	−	0.413018i	$-0.864475\pi$
$967$		−	25.6869i		−	0.826036i	0.910723	−	0.413018i	$-0.135525\pi$
$968$	−3.32244	−	24.3713i	−0.106787	−	0.783324i
$969$	−0.527864			−0.0169574
$970$		0			0
$971$	−10.4377	+	32.1239i	−0.334962	+	1.03091i	0.631779	+	0.775148i	$0.282325\pi$
$971$	−10.4377	+	32.1239i	−0.334962	+	1.03091i	−0.966741	+	0.255757i	$0.917675\pi$
$972$	0.587785	−	0.190983i	0.0188532	−	0.00612578i
$973$	−10.3229	−	14.2082i	−0.330936	−	0.455494i
$974$	51.2877	−	37.2627i	1.64336	−	1.19397i
$975$		0			0
$976$	−1.71885	+	5.29007i	−0.0550190	+	0.169331i
$977$	29.0135	−	39.9336i	0.928223	−	1.27759i	−0.0323250	−	0.999477i	$-0.510291\pi$
$977$	29.0135	−	39.9336i	0.928223	−	1.27759i	0.960548	−	0.278113i	$-0.0897088\pi$
$978$		−	24.7082i		−	0.790081i
$979$	−26.6074	−	16.7027i	−0.850376	−	0.533822i
$980$		0			0
$981$		0			0
$982$	40.3404	+	13.1074i	1.28731	+	0.418274i
$983$	−33.5770	+	10.9098i	−1.07094	+	0.347970i	−0.790854	−	0.612005i	$-0.790363\pi$
$983$	−33.5770	+	10.9098i	−1.07094	+	0.347970i	−0.280086	+	0.959975i	$0.590363\pi$
$984$	−10.7533	+	7.81272i	−0.342802	+	0.249060i
$985$		0			0
$986$	1.38197	+	4.25325i	0.0440108	+	0.135451i
$987$	1.76336	+	0.572949i	0.0561282	+	0.0182372i
$988$	−1.93487	+	2.66312i	−0.0615564	+	0.0847251i
$989$	9.65248			0.306931
$990$		0			0
$991$	−12.2705			−0.389786			−0.194893	−	0.980825i	$-0.562436\pi$
$991$	−12.2705			−0.389786			−0.194893	+	0.980825i	$0.562436\pi$
$992$	−7.66145	+	10.5451i	−0.243251	+	0.334807i
$993$	−21.4908	−	6.98278i	−0.681989	−	0.221592i
$994$	−21.8435	−	67.2273i	−0.692832	−	2.13232i
$995$		0			0
$996$	6.35410	−	4.61653i	0.201337	−	0.146280i
$997$	32.3157	−	10.5000i	1.02345	−	0.332538i	0.251251	−	0.967922i	$-0.419158\pi$
$997$	32.3157	−	10.5000i	1.02345	−	0.332538i	0.772197	+	0.635384i	$0.219158\pi$
$998$	3.94298	+	1.28115i	0.124813	+	0.0405542i
$999$	−3.42705	−	2.48990i	−0.108427	−	0.0787769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.bx.b.499.1		8
5.2	odd	4		33.2.e.a.4.1	✓	4
5.3	odd	4		825.2.n.f.301.1		4
5.4	even	2	inner	825.2.bx.b.499.2		8
11.3	even	5	inner	825.2.bx.b.124.2		8
15.2	even	4		99.2.f.b.37.1		4
20.7	even	4		528.2.y.f.433.1		4
45.2	even	12		891.2.n.a.433.1		8
45.7	odd	12		891.2.n.d.433.1		8
45.22	odd	12		891.2.n.d.136.1		8
45.32	even	12		891.2.n.a.136.1		8
55.2	even	20		363.2.e.c.148.1		4
55.3	odd	20		825.2.n.f.751.1		4
55.7	even	20		363.2.e.c.130.1		4
55.14	even	10	inner	825.2.bx.b.124.1		8
55.17	even	20		363.2.a.e.1.1		2
55.27	odd	20		363.2.a.h.1.2		2
55.28	even	20		9075.2.a.bv.1.2		2
55.32	even	4		363.2.e.j.202.1		4
55.37	odd	20		363.2.e.h.130.1		4
55.38	odd	20		9075.2.a.x.1.1		2
55.42	odd	20		363.2.e.h.148.1		4
55.47	odd	20		33.2.e.a.25.1	yes	4
55.52	even	20		363.2.e.j.124.1		4
165.17	odd	20		1089.2.a.s.1.2		2
165.47	even	20		99.2.f.b.91.1		4
165.137	even	20		1089.2.a.m.1.1		2
220.27	even	20		5808.2.a.bl.1.2		2
220.47	even	20		528.2.y.f.289.1		4
220.127	odd	20		5808.2.a.bm.1.2		2
495.47	even	60		891.2.n.a.190.1		8
495.157	odd	60		891.2.n.d.784.1		8
495.212	even	60		891.2.n.a.784.1		8
495.322	odd	60		891.2.n.d.190.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.a.4.1	✓	4	5.2	odd	4
33.2.e.a.25.1	yes	4	55.47	odd	20
99.2.f.b.37.1		4	15.2	even	4
99.2.f.b.91.1		4	165.47	even	20
363.2.a.e.1.1		2	55.17	even	20
363.2.a.h.1.2		2	55.27	odd	20
363.2.e.c.130.1		4	55.7	even	20
363.2.e.c.148.1		4	55.2	even	20
363.2.e.h.130.1		4	55.37	odd	20
363.2.e.h.148.1		4	55.42	odd	20
363.2.e.j.124.1		4	55.52	even	20
363.2.e.j.202.1		4	55.32	even	4
528.2.y.f.289.1		4	220.47	even	20
528.2.y.f.433.1		4	20.7	even	4
825.2.n.f.301.1		4	5.3	odd	4
825.2.n.f.751.1		4	55.3	odd	20
825.2.bx.b.124.1		8	55.14	even	10	inner
825.2.bx.b.124.2		8	11.3	even	5	inner
825.2.bx.b.499.1		8	1.1	even	1	trivial
825.2.bx.b.499.2		8	5.4	even	2	inner
891.2.n.a.136.1		8	45.32	even	12
891.2.n.a.190.1		8	495.47	even	60
891.2.n.a.433.1		8	45.2	even	12
891.2.n.a.784.1		8	495.212	even	60
891.2.n.d.136.1		8	45.22	odd	12
891.2.n.d.190.1		8	495.322	odd	60
891.2.n.d.433.1		8	45.7	odd	12
891.2.n.d.784.1		8	495.157	odd	60
1089.2.a.m.1.1		2	165.137	even	20
1089.2.a.s.1.2		2	165.17	odd	20
5808.2.a.bl.1.2		2	220.27	even	20
5808.2.a.bm.1.2		2	220.127	odd	20
9075.2.a.x.1.1		2	55.38	odd	20
9075.2.a.bv.1.2		2	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+(-0.951057 + 1.30902i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.190983 - 0.587785i) q^{4} +(-1.30902 + 0.951057i) q^{6} +(2.85317 - 0.927051i) q^{7} +(-2.12663 - 0.690983i) q^{8} +(0.809017 + 0.587785i) q^{9} +(2.80902 + 1.76336i) q^{11} -0.618034i q^{12} +(3.66547 - 5.04508i) q^{13} +(-1.50000 + 4.61653i) q^{14} +(3.92705 - 2.85317i) q^{16} +(-0.363271 - 0.500000i) q^{17} +(-1.53884 + 0.500000i) q^{18} +(0.263932 - 0.812299i) q^{19} +3.00000 q^{21} +(-4.97980 + 2.00000i) q^{22} -5.47214i q^{23} +(-1.80902 - 1.31433i) q^{24} +(3.11803 + 9.59632i) q^{26} +(0.587785 + 0.809017i) q^{27} +(-1.08981 - 1.50000i) q^{28} +(1.38197 + 4.25325i) q^{29} +(3.11803 + 2.26538i) q^{31} +3.38197i q^{32} +(2.12663 + 2.54508i) q^{33} +1.00000 q^{34} +(0.190983 - 0.587785i) q^{36} +(-4.02874 + 1.30902i) q^{37} +(0.812299 + 1.11803i) q^{38} +(5.04508 - 3.66547i) q^{39} +(1.83688 - 5.65334i) q^{41} +(-2.85317 + 3.92705i) q^{42} +1.76393i q^{43} +(0.500000 - 1.98787i) q^{44} +(7.16312 + 5.20431i) q^{46} +(0.587785 + 0.190983i) q^{47} +(4.61653 - 1.50000i) q^{48} +(1.61803 - 1.17557i) q^{49} +(-0.190983 - 0.587785i) q^{51} +(-3.66547 - 1.19098i) q^{52} +(-4.33901 + 5.97214i) q^{53} -1.61803 q^{54} -6.70820 q^{56} +(0.502029 - 0.690983i) q^{57} +(-6.88191 - 2.23607i) q^{58} +(1.64590 + 5.06555i) q^{59} +(-0.927051 + 0.673542i) q^{61} +(-5.93085 + 1.92705i) q^{62} +(2.85317 + 0.927051i) q^{63} +(3.42705 + 2.48990i) q^{64} +(-5.35410 + 0.363271i) q^{66} -10.5623i q^{67} +(-0.224514 + 0.309017i) q^{68} +(1.69098 - 5.20431i) q^{69} +(-11.7812 + 8.55951i) q^{71} +(-1.31433 - 1.80902i) q^{72} +(-1.17557 + 0.381966i) q^{73} +(2.11803 - 6.51864i) q^{74} -0.527864 q^{76} +(9.64932 + 2.42705i) q^{77} +10.0902i q^{78} +(0.427051 + 0.310271i) q^{79} +(0.309017 + 0.951057i) q^{81} +(5.65334 + 7.78115i) q^{82} +(7.46969 + 10.2812i) q^{83} +(-0.572949 - 1.76336i) q^{84} +(-2.30902 - 1.67760i) q^{86} +4.47214i q^{87} +(-4.75528 - 5.69098i) q^{88} -9.47214 q^{89} +(5.78115 - 17.7926i) q^{91} +(-3.21644 + 1.04508i) q^{92} +(2.26538 + 3.11803i) q^{93} +(-0.809017 + 0.587785i) q^{94} +(-1.04508 + 3.21644i) q^{96} +(-8.83702 + 12.1631i) q^{97} +3.23607i q^{98} +(1.23607 + 3.07768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{4} - 6 q^{6} + 2 q^{9} + 18 q^{11} - 12 q^{14} + 18 q^{16} + 20 q^{19} + 24 q^{21} - 10 q^{24} + 16 q^{26} + 20 q^{29} + 16 q^{31} + 8 q^{34} + 6 q^{36} + 18 q^{39} + 46 q^{41} + 4 q^{44} + 26 q^{46}+ \cdots - 8 q^{99}+O(q^{100}) \) 8 * q - 6 * q^4 - 6 * q^6 + 2 * q^9 + 18 * q^11 - 12 * q^14 + 18 * q^16 + 20 * q^19 + 24 * q^21 - 10 * q^24 + 16 * q^26 + 20 * q^29 + 16 * q^31 + 8 * q^34 + 6 * q^36 + 18 * q^39 + 46 * q^41 + 4 * q^44 + 26 * q^46 + 4 * q^49 - 6 * q^51 - 4 * q^54 + 40 * q^59 + 6 * q^61 + 14 * q^64 - 16 * q^66 + 18 * q^69 - 54 * q^71 + 8 * q^74 - 40 * q^76 - 10 * q^79 - 2 * q^81 - 18 * q^84 - 14 * q^86 - 40 * q^89 + 6 * q^91 - 2 * q^94 + 14 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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