LMFDB - Embedded newform 775.2.bf.c.349.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(349,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([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("775.349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.bf (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:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.9
Character	$\chi$	$=$	775.349
Dual form			775.2.bf.c.624.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29445 + 0.420591i) q^{2} +(-2.99486 + 0.973089i) q^{3} +(-0.119342 - 0.0867070i) q^{4} -4.28595 q^{6} +(0.538593 - 0.741309i) q^{7} +(-1.71804 - 2.36467i) q^{8} +(5.59523 - 4.06517i) q^{9} +O(q^{10})$	\(q+(1.29445 + 0.420591i) q^{2} +(-2.99486 + 0.973089i) q^{3} +(-0.119342 - 0.0867070i) q^{4} -4.28595 q^{6} +(0.538593 - 0.741309i) q^{7} +(-1.71804 - 2.36467i) q^{8} +(5.59523 - 4.06517i) q^{9} +(4.53839 + 3.29733i) q^{11} +(0.441786 + 0.143545i) q^{12} +(-1.82252 + 0.592172i) q^{13} +(1.00897 - 0.733057i) q^{14} +(-1.13817 - 3.50294i) q^{16} +(-1.35276 - 1.86192i) q^{17} +(8.95250 - 2.90884i) q^{18} +(-1.97142 + 6.06741i) q^{19} +(-0.891650 + 2.74422i) q^{21} +(4.48787 + 6.17702i) q^{22} +(2.17057 + 2.98754i) q^{23} +(7.44631 + 5.41006i) q^{24} -2.60821 q^{26} +(-7.24839 + 9.97655i) q^{27} +(-0.128554 + 0.0417696i) q^{28} +(-0.643286 + 1.97983i) q^{29} +(5.54716 - 0.478553i) q^{31} +0.832724i q^{32} +(-16.8004 - 5.45879i) q^{33} +(-0.967971 - 2.97911i) q^{34} -1.02023 q^{36} +8.06343i q^{37} +(-5.10379 + 7.02476i) q^{38} +(4.88195 - 3.54694i) q^{39} +(-0.782302 + 2.40768i) q^{41} +(-2.30838 + 3.17722i) q^{42} +(9.06681 + 2.94598i) q^{43} +(-0.255718 - 0.787020i) q^{44} +(1.55316 + 4.78013i) q^{46} +(-3.96894 + 1.28959i) q^{47} +(6.81735 + 9.38327i) q^{48} +(1.90366 + 5.85887i) q^{49} +(5.86314 + 4.25982i) q^{51} +(0.268848 + 0.0873542i) q^{52} +(4.54466 + 6.25519i) q^{53} +(-13.5787 + 9.86549i) q^{54} -2.67828 q^{56} -20.0894i q^{57} +(-1.66540 + 2.29222i) q^{58} +(-3.04742 - 9.37899i) q^{59} -6.81609 q^{61} +(7.38177 + 1.71362i) q^{62} -6.33727i q^{63} +(-2.62658 + 8.08380i) q^{64} +(-19.4513 - 14.1322i) q^{66} +0.414188i q^{67} +0.339499i q^{68} +(-9.40770 - 6.83509i) q^{69} +(4.68617 - 3.40470i) q^{71} +(-19.2256 - 6.24678i) q^{72} +(3.71605 - 5.11470i) q^{73} +(-3.39140 + 10.4377i) q^{74} +(0.761360 - 0.553160i) q^{76} +(4.88869 - 1.58843i) q^{77} +(7.81123 - 2.53802i) q^{78} +(8.59071 - 6.24151i) q^{79} +(5.58827 - 17.1989i) q^{81} +(-2.02529 + 2.78758i) q^{82} +(9.55223 + 3.10371i) q^{83} +(0.344354 - 0.250188i) q^{84} +(10.4974 + 7.62683i) q^{86} -6.55529i q^{87} -16.3967i q^{88} +(-1.86543 - 1.35532i) q^{89} +(-0.542612 + 1.66999i) q^{91} -0.544743i q^{92} +(-16.1473 + 6.83108i) q^{93} -5.67996 q^{94} +(-0.810314 - 2.49389i) q^{96} +(6.67401 - 9.18599i) q^{97} +8.38465i q^{98} +38.7976 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{4} - 32 q^{6} + 12 q^{9}+O(q^{10}) $ 48 * q + 12 * q^4 - 32 * q^6 + 12 * q^9	$ 48 q + 12 q^{4} - 32 q^{6} + 12 q^{9} + 2 q^{11} - 12 q^{14} - 48 q^{16} - 4 q^{19} - 20 q^{21} + 64 q^{24} + 44 q^{26} - 30 q^{29} + 12 q^{31} + 40 q^{34} - 116 q^{36} + 20 q^{39} - 48 q^{41} - 82 q^{44} + 96 q^{46} + 46 q^{49} + 52 q^{51} - 22 q^{54} - 96 q^{56} - 20 q^{59} - 80 q^{61} - 18 q^{64} - 4 q^{66} - 128 q^{69} - 14 q^{71} + 2 q^{74} + 86 q^{76} - 62 q^{79} + 68 q^{81} - 226 q^{84} - 44 q^{86} - 26 q^{89} + 108 q^{91} + 20 q^{94} + 202 q^{96} + 340 q^{99}+O(q^{100}) $ 48 * q + 12 * q^4 - 32 * q^6 + 12 * q^9 + 2 * q^11 - 12 * q^14 - 48 * q^16 - 4 * q^19 - 20 * q^21 + 64 * q^24 + 44 * q^26 - 30 * q^29 + 12 * q^31 + 40 * q^34 - 116 * q^36 + 20 * q^39 - 48 * q^41 - 82 * q^44 + 96 * q^46 + 46 * q^49 + 52 * q^51 - 22 * q^54 - 96 * q^56 - 20 * q^59 - 80 * q^61 - 18 * q^64 - 4 * q^66 - 128 * q^69 - 14 * q^71 + 2 * q^74 + 86 * q^76 - 62 * q^79 + 68 * q^81 - 226 * q^84 - 44 * q^86 - 26 * q^89 + 108 * q^91 + 20 * q^94 + 202 * q^96 + 340 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.29445	+	0.420591i	0.915311	+	0.297403i	0.728542	−	0.685001i	$-0.240198\pi$
$2$	1.29445	+	0.420591i	0.915311	+	0.297403i	0.186769	+	0.982404i	$0.440198\pi$
$3$	−2.99486	+	0.973089i	−1.72908	+	0.561813i	−0.993317	−	0.115422i	$-0.963178\pi$
$3$	−2.99486	+	0.973089i	−1.72908	+	0.561813i	−0.735767	+	0.677235i	$0.763178\pi$
$4$	−0.119342	−	0.0867070i	−0.0596710	−	0.0433535i
$5$		0			0
$5$		0			0
$6$	−4.28595			−1.74973
$7$	0.538593	−	0.741309i	0.203569	−	0.280189i	−0.695010	−	0.719000i	$-0.744600\pi$
$7$	0.538593	−	0.741309i	0.203569	−	0.280189i	0.898579	+	0.438811i	$0.144600\pi$
$8$	−1.71804	−	2.36467i	−0.607417	−	0.836038i
$9$	5.59523	−	4.06517i	1.86508	−	1.35506i
$10$		0			0
$11$	4.53839	+	3.29733i	1.36838	+	0.994183i	0.997862	+	0.0653556i	$0.0208182\pi$
$11$	4.53839	+	3.29733i	1.36838	+	0.994183i	0.370513	+	0.928827i	$0.379182\pi$
$12$	0.441786	+	0.143545i	0.127533	+	0.0414379i
$13$	−1.82252	+	0.592172i	−0.505476	+	0.164239i	−0.550644	−	0.834740i	$-0.685618\pi$
$13$	−1.82252	+	0.592172i	−0.505476	+	0.164239i	0.0451681	+	0.998979i	$0.485618\pi$
$14$	1.00897	−	0.733057i	0.269658	−	0.195918i
$15$		0			0
$16$	−1.13817	−	3.50294i	−0.284544	−	0.875735i
$17$	−1.35276	−	1.86192i	−0.328093	−	0.451581i	0.612824	−	0.790220i	$-0.290034\pi$
$17$	−1.35276	−	1.86192i	−0.328093	−	0.451581i	−0.940917	+	0.338639i	$0.890034\pi$
$18$	8.95250	−	2.90884i	2.11012	−	0.685621i
$19$	−1.97142	+	6.06741i	−0.452275	+	1.39196i	0.422031	+	0.906582i	$0.361317\pi$
$19$	−1.97142	+	6.06741i	−0.452275	+	1.39196i	−0.874305	+	0.485377i	$0.838683\pi$
$20$		0			0
$21$	−0.891650	+	2.74422i	−0.194574	+	0.598837i
$22$	4.48787	+	6.17702i	0.956816	+	1.31694i
$23$	2.17057	+	2.98754i	0.452596	+	0.622944i	0.972953	−	0.231004i	$-0.0742011\pi$
$23$	2.17057	+	2.98754i	0.452596	+	0.622944i	−0.520357	+	0.853949i	$0.674201\pi$
$24$	7.44631	+	5.41006i	1.51997	+	1.10432i
$25$		0			0
$26$	−2.60821			−0.511512
$27$	−7.24839	+	9.97655i	−1.39495	+	1.91999i
$28$	−0.128554	+	0.0417696i	−0.0242943	+	0.00789371i
$29$	−0.643286	+	1.97983i	−0.119455	+	0.367645i	−0.992850	−	0.119367i	$-0.961913\pi$
$29$	−0.643286	+	1.97983i	−0.119455	+	0.367645i	0.873395	+	0.487012i	$0.161913\pi$
$30$		0			0
$31$	5.54716	−	0.478553i	0.996299	−	0.0859507i
$31$	5.54716	−	0.478553i	0.996299	−	0.0859507i
$32$			0.832724i			0.147206i
$33$	−16.8004	−	5.45879i	−2.92458	−	0.950253i
$34$	−0.967971	−	2.97911i	−0.166006	−	0.510913i
$35$		0			0
$36$	−1.02023			−0.170038
$37$			8.06343i			1.32562i	0.748788	+	0.662810i	$0.230636\pi$
$37$			8.06343i			1.32562i	−0.748788	+	0.662810i	$0.769364\pi$
$38$	−5.10379	+	7.02476i	−0.827944	+	1.13957i
$39$	4.88195	−	3.54694i	0.781738	−	0.567966i
$40$		0			0
$41$	−0.782302	+	2.40768i	−0.122175	+	0.376016i	−0.993376	−	0.114911i	$-0.963342\pi$
$41$	−0.782302	+	2.40768i	−0.122175	+	0.376016i	0.871201	+	0.490927i	$0.163342\pi$
$42$	−2.30838	+	3.17722i	−0.356191	+	0.490255i
$43$	9.06681	+	2.94598i	1.38268	+	0.449258i	0.903548	−	0.428487i	$-0.140953\pi$
$43$	9.06681	+	2.94598i	1.38268	+	0.449258i	0.479127	+	0.877746i	$0.340953\pi$
$44$	−0.255718	−	0.787020i	−0.0385510	−	0.118648i
$45$		0			0
$46$	1.55316	+	4.78013i	0.229001	+	0.704791i
$47$	−3.96894	+	1.28959i	−0.578929	+	0.188106i	−0.583821	−	0.811883i	$-0.698443\pi$
$47$	−3.96894	+	1.28959i	−0.578929	+	0.188106i	0.00489158	+	0.999988i	$0.498443\pi$
$48$	6.81735	+	9.38327i	0.983999	+	1.35436i
$49$	1.90366	+	5.85887i	0.271952	+	0.836981i
$50$		0			0
$51$	5.86314	+	4.25982i	0.821004	+	0.596494i
$52$	0.268848	+	0.0873542i	0.0372826	+	0.0121138i
$53$	4.54466	+	6.25519i	0.624258	+	0.859217i	0.997654	−	0.0684548i	$-0.0218069\pi$
$53$	4.54466	+	6.25519i	0.624258	+	0.859217i	−0.373396	+	0.927672i	$0.621807\pi$
$54$	−13.5787	+	9.86549i	−1.84782	+	1.34252i
$55$		0			0
$56$	−2.67828			−0.357900
$57$		−	20.0894i		−	2.66091i
$58$	−1.66540	+	2.29222i	−0.218677	+	0.300983i
$59$	−3.04742	−	9.37899i	−0.396740	−	1.22104i	−0.927598	−	0.373580i	$-0.878130\pi$
$59$	−3.04742	−	9.37899i	−0.396740	−	1.22104i	0.530858	−	0.847461i	$-0.321870\pi$
$60$		0			0
$61$	−6.81609			−0.872711			−0.436355	−	0.899774i	$-0.643731\pi$
$61$	−6.81609			−0.872711			−0.436355	+	0.899774i	$0.643731\pi$
$62$	7.38177	+	1.71362i	0.937486	+	0.217630i
$63$		−	6.33727i		−	0.798421i
$64$	−2.62658	+	8.08380i	−0.328323	+	1.01047i
$65$		0			0
$66$	−19.4513	−	14.1322i	−2.39429	−	1.73956i
$67$			0.414188i			0.0506011i	0.999680	+	0.0253006i	$0.00805428\pi$
$67$			0.414188i			0.0506011i	−0.999680	+	0.0253006i	$0.991946\pi$
$68$			0.339499i			0.0411703i
$69$	−9.40770	−	6.83509i	−1.13255	−	0.822849i
$70$		0			0
$71$	4.68617	−	3.40470i	0.556146	−	0.404064i	−0.273901	−	0.961758i	$-0.588314\pi$
$71$	4.68617	−	3.40470i	0.556146	−	0.404064i	0.830046	+	0.557694i	$0.188314\pi$
$72$	−19.2256	−	6.24678i	−2.26576	−	0.736190i
$73$	3.71605	−	5.11470i	0.434931	−	0.598631i	−0.534145	−	0.845393i	$-0.679367\pi$
$73$	3.71605	−	5.11470i	0.434931	−	0.598631i	0.969076	+	0.246762i	$0.0793665\pi$
$74$	−3.39140	+	10.4377i	−0.394243	+	1.21335i
$75$		0			0
$76$	0.761360	−	0.553160i	0.0873340	−	0.0634518i
$77$	4.88869	−	1.58843i	0.557117	−	0.181018i
$78$	7.81123	−	2.53802i	0.884448	−	0.287374i
$79$	8.59071	−	6.24151i	0.966530	−	0.702225i	0.0118721	−	0.999930i	$-0.496221\pi$
$79$	8.59071	−	6.24151i	0.966530	−	0.702225i	0.954658	+	0.297704i	$0.0962209\pi$
$80$		0			0
$81$	5.58827	−	17.1989i	0.620919	−	1.91099i
$82$	−2.02529	+	2.78758i	−0.223656	+	0.307836i
$83$	9.55223	+	3.10371i	1.04849	+	0.340676i	0.782077	−	0.623182i	$-0.214160\pi$
$83$	9.55223	+	3.10371i	1.04849	+	0.340676i	0.266416	+	0.963858i	$0.414160\pi$
$84$	0.344354	−	0.250188i	0.0375721	−	0.0272977i
$85$		0			0
$86$	10.4974	+	7.62683i	1.13197	+	0.822422i
$87$		−	6.55529i		−	0.702800i
$88$		−	16.3967i		−	1.74790i
$89$	−1.86543	−	1.35532i	−0.197735	−	0.143663i	0.484512	−	0.874785i	$-0.338997\pi$
$89$	−1.86543	−	1.35532i	−0.197735	−	0.143663i	−0.682247	+	0.731122i	$0.738997\pi$
$90$		0			0
$91$	−0.542612	+	1.66999i	−0.0568812	+	0.175062i
$92$		−	0.544743i		−	0.0567933i
$93$	−16.1473	+	6.83108i	−1.67440	+	0.708350i
$94$	−5.67996			−0.585843
$95$		0			0
$96$	−0.810314	−	2.49389i	−0.0827024	−	0.254532i
$97$	6.67401	−	9.18599i	0.677643	−	0.932696i	−0.322260	−	0.946651i	$-0.604442\pi$
$97$	6.67401	−	9.18599i	0.677643	−	0.932696i	0.999903	+	0.0139556i	$0.00444236\pi$
$98$			8.38465i			0.846977i
$99$	38.7976			3.89930
$100$		0			0
$101$	−3.83286	+	2.78473i	−0.381383	+	0.277091i	−0.761915	−	0.647676i	$-0.775741\pi$
$101$	−3.83286	+	2.78473i	−0.381383	+	0.277091i	0.380532	+	0.924768i	$0.375741\pi$
$102$	5.79787	+	7.98009i	0.574075	+	0.790147i
$103$	−1.17363	−	0.381335i	−0.115641	−	0.0375740i	0.250625	−	0.968084i	$-0.419364\pi$
$103$	−1.17363	−	0.381335i	−0.115641	−	0.0375740i	−0.366266	+	0.930510i	$0.619364\pi$
$104$	4.53144	+	3.29229i	0.444345	+	0.322835i
$105$		0			0
$106$	3.25194	+	10.0085i	0.315857	+	0.972107i
$107$	7.55250	+	10.3951i	0.730127	+	1.00493i	0.999126	+	0.0417936i	$0.0133072\pi$
$107$	7.55250	+	10.3951i	0.730127	+	1.00493i	−0.268999	+	0.963140i	$0.586693\pi$
$108$	1.73007	−	0.562135i	0.166476	−	0.0540915i
$109$	−0.325129	−	1.00064i	−0.0311417	−	0.0958444i	0.934278	−	0.356547i	$-0.116046\pi$
$109$	−0.325129	−	1.00064i	−0.0311417	−	0.0958444i	−0.965419	+	0.260702i	$0.916046\pi$
$110$		0			0
$111$	−7.84643	−	24.1488i	−0.744750	−	2.29211i
$112$	−3.20978	−	1.04292i	−0.303295	−	0.0985466i
$113$	−7.23572	+	9.95912i	−0.680680	+	0.936875i	−0.999942	−	0.0107913i	$-0.996565\pi$
$113$	−7.23572	+	9.95912i	−0.680680	+	0.936875i	0.319262	+	0.947666i	$0.396565\pi$
$114$	8.44941	−	26.0046i	0.791360	−	2.43556i
$115$		0			0
$116$	0.248436	−	0.180499i	0.0230667	−	0.0167589i
$117$	−7.79013	+	10.7222i	−0.720198	+	0.991267i
$118$		−	13.4223i		−	1.23562i
$119$	−2.10884			−0.193317
$120$		0			0
$121$	6.32538	+	19.4675i	0.575034	+	1.76977i
$122$	−8.82306	−	2.86678i	−0.798802	−	0.259546i
$123$		−	7.97190i		−	0.718802i
$124$	−0.703503	−	0.423866i	−0.0631765	−	0.0380643i
$125$		0			0
$126$	2.66540	−	8.20325i	0.237453	−	0.730804i
$127$	0.439500	−	0.142802i	0.0389993	−	0.0126716i	−0.289452	−	0.957192i	$-0.593473\pi$
$127$	0.439500	−	0.142802i	0.0389993	−	0.0126716i	0.328452	+	0.944521i	$0.393473\pi$
$128$	−5.82101	+	8.01194i	−0.514510	+	0.708162i
$129$	−30.0205			−2.64316
$130$		0			0
$131$	3.15547	+	2.29258i	0.275694	+	0.200304i	0.717037	−	0.697035i	$-0.245498\pi$
$131$	3.15547	+	2.29258i	0.275694	+	0.200304i	−0.441343	+	0.897339i	$0.645498\pi$
$132$	1.53168	+	2.10818i	0.133316	+	0.183493i
$133$	3.43603	+	4.72929i	0.297942	+	0.410082i
$134$	−0.174204	+	0.536144i	−0.0150489	+	0.0463158i
$135$		0			0
$136$	−2.07873	+	6.39768i	−0.178250	+	0.548596i
$137$	−10.8607	+	3.52887i	−0.927895	+	0.301491i	−0.733702	−	0.679472i	$-0.762209\pi$
$137$	−10.8607	+	3.52887i	−0.927895	+	0.301491i	−0.194193	+	0.980963i	$0.562209\pi$
$138$	−9.30298	−	12.8044i	−0.791922	−	1.08999i
$139$	2.91380	+	8.96774i	0.247145	+	0.760634i	0.995276	+	0.0970833i	$0.0309513\pi$
$139$	2.91380	+	8.96774i	0.247145	+	0.760634i	−0.748131	+	0.663551i	$0.769049\pi$
$140$		0			0
$141$	10.6315	−	7.72426i	0.895337	−	0.650500i
$142$	7.49797	−	2.43624i	0.629216	−	0.204445i
$143$	−10.2239	−	3.32194i	−0.854964	−	0.277795i
$144$	−20.6084	−	14.9729i	−1.71737	−	1.24774i
$145$		0			0
$146$	6.96142	−	5.05777i	0.576131	−	0.418584i
$147$	−11.4024	−	15.6941i	−0.940454	−	1.29442i
$148$	0.699156	−	0.962306i	0.0574703	−	0.0791010i
$149$	16.3472			1.33922			0.669608	−	0.742715i	$-0.266462\pi$
$149$	16.3472			1.33922			0.669608	+	0.742715i	$0.266462\pi$
$150$		0			0
$151$	−2.41419	−	1.75402i	−0.196464	−	0.142740i	0.485204	−	0.874401i	$-0.338745\pi$
$151$	−2.41419	−	1.75402i	−0.196464	−	0.142740i	−0.681668	+	0.731661i	$0.738745\pi$
$152$	17.7344	−	5.76226i	1.43845	−	0.467381i
$153$	−15.1380	−	4.91864i	−1.22384	−	0.397649i
$154$	6.99621			0.563771
$155$		0			0
$156$	−0.890167			−0.0712704
$157$	−7.89548	−	2.56540i	−0.630128	−	0.204741i	−0.0234963	−	0.999724i	$-0.507480\pi$
$157$	−7.89548	−	2.56540i	−0.630128	−	0.204741i	−0.606632	+	0.794983i	$0.707480\pi$
$158$	13.7453	−	4.46613i	1.09352	−	0.355306i
$159$	−19.6975	−	14.3111i	−1.56211	−	1.13494i
$160$		0			0
$161$	3.38374			0.266676
$162$	14.4674	−	19.9127i	1.13667	−	1.56449i
$163$	−13.4314	−	18.4867i	−1.05203	−	1.44799i	−0.887037	−	0.461698i	$-0.847240\pi$
$163$	−13.4314	−	18.4867i	−1.05203	−	1.44799i	−0.164992	−	0.986295i	$-0.552760\pi$
$164$	0.302124	−	0.219506i	0.0235919	−	0.0171405i
$165$		0			0
$166$	11.0594	+	8.03516i	0.858379	+	0.623649i
$167$	14.2283	+	4.62307i	1.10102	+	0.357744i	0.802496	−	0.596657i	$-0.203505\pi$
$167$	14.2283	+	4.62307i	1.10102	+	0.357744i	0.298526	+	0.954401i	$0.403505\pi$
$168$	8.02106	−	2.60620i	0.618838	−	0.201073i
$169$	−7.54632	+	5.48272i	−0.580486	+	0.421748i
$170$		0			0
$171$	13.6345	+	41.9627i	1.04266	+	3.20897i
$172$	−0.826613	−	1.13774i	−0.0630287	−	0.0867515i
$173$	−2.56469	+	0.833317i	−0.194990	+	0.0633560i	−0.404884	−	0.914368i	$-0.632688\pi$
$173$	−2.56469	+	0.833317i	−0.194990	+	0.0633560i	0.209894	+	0.977724i	$0.432688\pi$
$174$	2.75709	−	8.48546i	0.209015	−	0.643281i
$175$		0			0
$176$	6.38488	−	19.6506i	0.481278	−	1.48122i
$177$	18.2532	+	25.1234i	1.37199	+	1.88839i
$178$	−1.84467	−	2.53896i	−0.138264	−	0.190303i
$179$	−19.7892	−	14.3777i	−1.47911	−	1.07464i	−0.977841	−	0.209348i	$-0.932866\pi$
$179$	−19.7892	−	14.3777i	−1.47911	−	1.07464i	−0.501271	−	0.865290i	$-0.667134\pi$
$180$		0			0
$181$	−18.9958			−1.41194			−0.705972	−	0.708239i	$-0.749490\pi$
$181$	−18.9958			−1.41194			−0.705972	+	0.708239i	$0.749490\pi$
$182$	−1.40476	+	1.93349i	−0.104128	+	0.143320i
$183$	20.4132	−	6.63266i	1.50899	−	0.490301i
$184$	3.33543	−	10.2654i	0.245891	−	0.756775i
$185$		0			0
$186$	−23.7749	+	2.05106i	−1.74326	+	0.150391i
$187$		−	12.9106i		−	0.944117i
$188$	0.585477	+	0.190233i	0.0427003	+	0.0138742i
$189$	3.49178	+	10.7466i	0.253990	+	0.781700i
$190$		0			0
$191$	−22.8593			−1.65404			−0.827021	−	0.562171i	$-0.809966\pi$
$191$	−22.8593			−1.65404			−0.827021	+	0.562171i	$0.809966\pi$
$192$		−	26.7657i		−	1.93165i
$193$	7.50709	−	10.3326i	0.540372	−	0.743759i	−0.448294	−	0.893886i	$-0.647968\pi$
$193$	7.50709	−	10.3326i	0.540372	−	0.743759i	0.988667	+	0.150127i	$0.0479683\pi$
$194$	12.5027	−	9.08373i	0.897640	−	0.652174i
$195$		0			0
$196$	0.280818	−	0.864270i	0.0200585	−	0.0617336i
$197$	10.7751	−	14.8306i	0.767693	−	1.05664i	−0.228842	−	0.973464i	$-0.573494\pi$
$197$	10.7751	−	14.8306i	0.767693	−	1.05664i	0.996535	−	0.0831754i	$-0.0265062\pi$
$198$	50.2213	+	16.3179i	3.56907	+	1.15966i
$199$	7.21304	+	22.1995i	0.511319	+	1.57368i	0.789881	+	0.613260i	$0.210142\pi$
$199$	7.21304	+	22.1995i	0.511319	+	1.57368i	−0.278562	+	0.960418i	$0.589858\pi$
$200$		0			0
$201$	−0.403042	−	1.24043i	−0.0284284	−	0.0874935i
$202$	−6.13265	+	1.99262i	−0.431492	+	0.140200i
$203$	1.12120	+	1.54320i	0.0786926	+	0.108311i
$204$	−0.330363	−	1.01675i	−0.0231300	−	0.0711868i
$205$		0			0
$206$	−1.35881	−	0.987234i	−0.0946729	−	0.0687839i
$207$	24.2897	+	7.89221i	1.68825	+	0.548546i
$208$	4.14869	+	5.71018i	0.287660	+	0.395930i
$209$	−28.9533	+	21.0358i	−2.00274	+	1.45508i
$210$		0			0
$211$	−4.87701			−0.335747			−0.167874	−	0.985809i	$-0.553690\pi$
$211$	−4.87701			−0.335747			−0.167874	+	0.985809i	$0.553690\pi$
$212$		−	1.14056i		−	0.0783341i
$213$	−10.7213	+	14.7567i	−0.734614	+	1.01111i
$214$	5.40420	+	16.6324i	0.369424	+	1.13697i
$215$		0			0
$216$	36.0443			2.45250
$217$	2.63290	−	4.36991i	0.178733	−	0.296649i
$218$		−	1.43203i		−	0.0969891i
$219$	−6.15199	+	18.9339i	−0.415713	+	1.27943i
$220$		0			0
$221$	3.56801	+	2.59231i	0.240010	+	0.174378i
$222$		−	34.5595i		−	2.31948i
$223$			10.8420i			0.726032i	0.931783	+	0.363016i	$0.118253\pi$
$223$			10.8420i			0.726032i	−0.931783	+	0.363016i	$0.881747\pi$
$224$	0.617306	+	0.448499i	0.0412455	+	0.0299666i
$225$		0			0
$226$	−13.5550	+	9.84826i	−0.901663	+	0.655096i
$227$	−5.25714	−	1.70815i	−0.348929	−	0.113374i	0.129309	−	0.991604i	$-0.458724\pi$
$227$	−5.25714	−	1.70815i	−0.348929	−	0.113374i	−0.478238	+	0.878231i	$0.658724\pi$
$228$	−1.74189	+	2.39751i	−0.115360	+	0.158779i
$229$	3.15229	−	9.70174i	0.208309	−	0.641109i	−0.791252	−	0.611490i	$-0.790571\pi$
$229$	3.15229	−	9.70174i	0.208309	−	0.641109i	0.999561	−	0.0296192i	$-0.00942947\pi$
$230$		0			0
$231$	−13.0952	+	9.51425i	−0.861604	+	0.625992i
$232$	5.78684	−	1.88026i	0.379924	−	0.123445i
$233$	−8.61352	+	2.79870i	−0.564290	+	0.183349i	−0.577251	−	0.816567i	$-0.695874\pi$
$233$	−8.61352	+	2.79870i	−0.564290	+	0.183349i	0.0129605	+	0.999916i	$0.495874\pi$
$234$	−14.5936	+	10.6028i	−0.954010	+	0.693129i
$235$		0			0
$236$	−0.449540	+	1.38354i	−0.0292625	+	0.0900608i
$237$	−19.6544	+	27.0520i	−1.27669	+	1.75722i
$238$	−2.72978	−	0.886960i	−0.176946	−	0.0574931i
$239$	9.64391	−	7.00671i	0.623813	−	0.453226i	−0.230439	−	0.973087i	$-0.574016\pi$
$239$	9.64391	−	7.00671i	0.623813	−	0.453226i	0.854251	+	0.519860i	$0.174016\pi$
$240$		0			0
$241$	−14.1964	−	10.3143i	−0.914473	−	0.664404i	0.0276690	−	0.999617i	$-0.491192\pi$
$241$	−14.1964	−	10.3143i	−0.914473	−	0.664404i	−0.942142	+	0.335213i	$0.891192\pi$
$242$			27.8600i			1.79091i
$243$			19.9512i			1.27987i
$244$	0.813446	+	0.591003i	0.0520755	+	0.0378351i
$245$		0			0
$246$	3.35291	−	10.3192i	0.213774	−	0.657928i
$247$		−	12.2254i		−	0.777882i
$248$	−10.6618	−	12.2951i	−0.677028	−	0.780737i
$249$	−31.6278			−2.00433
$250$		0			0
$251$	7.48819	+	23.0463i	0.472650	+	1.45467i	0.849100	+	0.528231i	$0.177145\pi$
$251$	7.48819	+	23.0463i	0.472650	+	1.45467i	−0.376450	+	0.926437i	$0.622855\pi$
$252$	−0.549486	+	0.756303i	−0.0346144	+	0.0476426i
$253$			20.7157i			1.30238i
$254$	0.628970			0.0394651
$255$		0			0
$256$	2.84824	−	2.06937i	0.178015	−	0.129336i
$257$	−3.24142	−	4.46143i	−0.202194	−	0.278296i	0.695864	−	0.718174i	$-0.255022\pi$
$257$	−3.24142	−	4.46143i	−0.202194	−	0.278296i	−0.898058	+	0.439878i	$0.855022\pi$
$258$	−38.8599	−	12.6264i	−2.41931	−	0.786082i
$259$	5.97750	+	4.34290i	0.371423	+	0.269855i
$260$		0			0
$261$	4.44902	+	13.6927i	0.275387	+	0.847555i
$262$	3.12034	+	4.29478i	0.192775	+	0.265332i
$263$	−7.52489	+	2.44499i	−0.464005	+	0.150764i	−0.531684	−	0.846943i	$-0.678441\pi$
$263$	−7.52489	+	2.44499i	−0.464005	+	0.150764i	0.0676792	+	0.997707i	$0.478441\pi$
$264$	15.9555	+	49.1059i	0.981992	+	3.02226i
$265$		0			0
$266$	2.45866	+	7.56697i	0.150750	+	0.463961i
$267$	6.90555	+	2.24375i	0.422613	+	0.137315i
$268$	0.0359130	−	0.0494300i	0.00219374	−	0.00301942i
$269$	−0.166570	+	0.512649i	−0.0101559	+	0.0312568i	−0.956006	−	0.293347i	$-0.905231\pi$
$269$	−0.166570	+	0.512649i	−0.0101559	+	0.0312568i	0.945850	+	0.324604i	$0.105231\pi$
$270$		0			0
$271$	10.5152	−	7.63975i	0.638754	−	0.464082i	−0.220668	−	0.975349i	$-0.570824\pi$
$271$	10.5152	−	7.63975i	0.638754	−	0.464082i	0.859422	+	0.511267i	$0.170824\pi$
$272$	−4.98250	+	6.85783i	−0.302109	+	0.415817i
$273$		−	5.52939i		−	0.334654i
$274$	−15.5428			−0.938977
$275$		0			0
$276$	0.530083	+	1.63143i	0.0319072	+	0.0982004i
$277$	−1.21278	−	0.394056i	−0.0728689	−	0.0236765i	0.272356	−	0.962197i	$-0.412197\pi$
$277$	−1.21278	−	0.394056i	−0.0728689	−	0.0236765i	−0.345225	+	0.938520i	$0.612197\pi$
$278$			12.8338i			0.769718i
$279$	29.0923	−	25.2278i	1.74171	−	1.51035i
$280$		0			0
$281$	3.36754	−	10.3642i	0.200891	−	0.618278i	−0.798967	−	0.601375i	$-0.794620\pi$
$281$	3.36754	−	10.3642i	0.200891	−	0.618278i	0.999857	−	0.0169022i	$-0.00538040\pi$
$282$	17.0107	−	5.52711i	1.01297	−	0.329135i
$283$	6.08069	−	8.36935i	0.361460	−	0.497506i	−0.589095	−	0.808064i	$-0.700516\pi$
$283$	6.08069	−	8.36935i	0.361460	−	0.497506i	0.950555	+	0.310557i	$0.100516\pi$
$284$	−0.854468			−0.0507034
$285$		0			0
$286$	−11.8371	−	8.60014i	−0.699941	−	0.508537i
$287$	1.36349	+	1.87668i	0.0804843	+	0.110777i
$288$	3.38517	+	4.65928i	0.199473	+	0.274551i
$289$	3.61652	−	11.1305i	0.212736	−	0.654736i
$290$		0			0
$291$	−11.0489	+	34.0052i	−0.647701	+	1.99342i
$292$	−0.886962	+	0.288191i	−0.0519055	+	0.0168651i
$293$	11.2835	+	15.5304i	0.659190	+	0.907297i	0.999454	−	0.0330331i	$-0.0105167\pi$
$293$	11.2835	+	15.5304i	0.659190	+	0.907297i	−0.340265	+	0.940330i	$0.610517\pi$
$294$	−8.15901	−	25.1108i	−0.475843	−	1.46449i
$295$		0			0
$296$	19.0674	−	13.8533i	1.10827	−	0.805204i
$297$	−65.7920	+	21.3771i	−3.81764	+	1.24043i
$298$	21.1606	+	6.87549i	1.22580	+	0.398286i
$299$	−5.72504	−	4.15949i	−0.331088	−	0.240549i
$300$		0			0
$301$	7.06720	−	5.13462i	0.407347	−	0.295955i
$302$	−2.38732	−	3.28586i	−0.137375	−	0.189080i
$303$	8.76907	−	12.0696i	0.503770	−	0.693380i
$304$	23.4976			1.34768
$305$		0			0
$306$	−17.5266	−	12.7338i	−1.00193	−	0.727945i
$307$	9.10984	−	2.95997i	0.519926	−	0.168934i	−0.0372856	−	0.999305i	$-0.511871\pi$
$307$	9.10984	−	2.95997i	0.519926	−	0.168934i	0.557212	+	0.830370i	$0.311871\pi$
$308$	−0.721154	−	0.234317i	−0.0410915	−	0.0133515i
$309$	3.88593			0.221063
$310$		0			0
$311$	0.0597943			0.00339063			0.00169531	−	0.999999i	$-0.499460\pi$
$311$	0.0597943			0.00339063			0.00169531	+	0.999999i	$0.499460\pi$
$312$	−16.7747	−	5.45044i	−0.949682	−	0.308570i
$313$	9.25752	−	3.00795i	0.523266	−	0.170019i	−0.0354611	−	0.999371i	$-0.511290\pi$
$313$	9.25752	−	3.00795i	0.523266	−	0.170019i	0.558727	+	0.829352i	$0.311290\pi$
$314$	−9.14129	−	6.64153i	−0.515873	−	0.374804i
$315$		0			0
$316$	−1.56642			−0.0881178
$317$	−3.85337	+	5.30371i	−0.216427	+	0.297886i	−0.903402	−	0.428795i	$-0.858938\pi$
$317$	−3.85337	+	5.30371i	−0.216427	+	0.297886i	0.686975	+	0.726681i	$0.258938\pi$
$318$	−19.4782	−	26.8095i	−1.09228	−	1.50340i
$319$	−9.44763	+	6.86411i	−0.528966	+	0.384316i
$320$		0			0
$321$	−32.7340	−	23.7827i	−1.82704	−	1.32742i
$322$	4.38007	+	1.42317i	0.244092	+	0.0793102i
$323$	13.9639	−	4.53713i	0.776970	−	0.252453i
$324$	−2.15818	+	1.56801i	−0.119899	+	0.0871117i
$325$		0			0
$326$	−9.61086	−	29.5792i	−0.532297	−	1.63824i
$327$	1.94743	+	2.68041i	0.107693	+	0.148227i
$328$	7.03739	−	2.28659i	0.388575	−	0.126256i
$329$	−1.18166	+	3.63677i	−0.0651470	+	0.200502i
$330$		0			0
$331$	−3.02132	+	9.29868i	−0.166067	+	0.511101i	−0.999113	−	0.0421017i	$-0.986595\pi$
$331$	−3.02132	+	9.29868i	−0.166067	+	0.511101i	0.833046	+	0.553203i	$0.186595\pi$
$332$	−0.870869	−	1.19865i	−0.0477951	−	0.0657844i
$333$	32.7792	+	45.1168i	1.79629	+	2.47238i
$334$	16.4734	+	11.9686i	0.901384	+	0.654894i
$335$		0			0
$336$	10.6277			0.579788
$337$	3.54190	−	4.87501i	0.192940	−	0.265559i	−0.701577	−	0.712594i	$-0.747520\pi$
$337$	3.54190	−	4.87501i	0.192940	−	0.265559i	0.894516	+	0.447035i	$0.147520\pi$
$338$	−12.0743	+	3.92317i	−0.656754	+	0.213392i
$339$	11.9789	−	36.8672i	0.650603	−	2.00235i
$340$		0			0
$341$	26.7531	+	16.1190i	1.44876	+	0.872891i
$342$			60.0530i			3.24729i
$343$	11.4688	+	3.72643i	0.619255	+	0.201208i
$344$	−8.61081	−	26.5013i	−0.464264	−	1.42886i
$345$		0			0
$346$	−3.67033			−0.197318
$347$			19.0290i			1.02153i	0.859720	+	0.510765i	$0.170638\pi$
$347$			19.0290i			1.02153i	−0.859720	+	0.510765i	$0.829362\pi$
$348$	−0.568389	+	0.782321i	−0.0304689	+	0.0419368i
$349$	14.0832	−	10.2321i	0.753859	−	0.547710i	−0.143162	−	0.989699i	$-0.545727\pi$
$349$	14.0832	−	10.2321i	0.753859	−	0.547710i	0.897021	+	0.441989i	$0.145727\pi$
$350$		0			0
$351$	7.30248	−	22.4747i	0.389778	−	1.19961i
$352$	−2.74577	+	3.77922i	−0.146350	+	0.201433i
$353$	−11.3506	−	3.68802i	−0.604129	−	0.196293i	−0.00904788	−	0.999959i	$-0.502880\pi$
$353$	−11.3506	−	3.68802i	−0.604129	−	0.196293i	−0.595081	+	0.803666i	$0.702880\pi$
$354$	13.0611	+	40.1979i	0.694190	+	2.13650i
$355$		0			0
$356$	0.105109	+	0.323492i	0.00557076	+	0.0171450i
$357$	6.31569	−	2.05209i	0.334262	−	0.108608i
$358$	−19.5689	−	26.9343i	−1.03425	−	1.42352i
$359$	9.86202	+	30.3522i	0.520497	+	1.60193i	0.773052	+	0.634343i	$0.218729\pi$
$359$	9.86202	+	30.3522i	0.520497	+	1.60193i	−0.252554	+	0.967583i	$0.581271\pi$
$360$		0			0
$361$	−17.5556	−	12.7549i	−0.923978	−	0.671310i
$362$	−24.5890	−	7.98945i	−1.29237	−	0.419916i
$363$	−37.8872	−	52.1473i	−1.98856	−	2.73702i
$364$	0.209556	−	0.152252i	0.0109837	−	0.00798015i
$365$		0			0
$366$	29.2135			1.52701
$367$			16.2510i			0.848293i	0.905593	+	0.424147i	$0.139426\pi$
$367$			16.2510i			0.848293i	−0.905593	+	0.424147i	$0.860574\pi$
$368$	7.99467	−	11.0037i	0.416751	−	0.573609i
$369$	5.41047	+	16.6517i	0.281658	+	0.866853i
$370$		0			0
$371$	7.08476			0.367822
$372$	2.51935	+	0.584849i	0.130622	+	0.0303230i
$373$		−	21.1742i		−	1.09636i	−0.836360	−	0.548180i	$-0.815321\pi$
$373$		−	21.1742i		−	1.09636i	0.836360	−	0.548180i	$-0.184679\pi$
$374$	5.43008	−	16.7121i	0.280783	−	0.864160i
$375$		0			0
$376$	9.86823	+	7.16969i	0.508915	+	0.369748i
$377$		−	3.98921i		−	0.205455i
$378$			15.3795i			0.791036i
$379$	−5.43943	−	3.95198i	−0.279405	−	0.203000i	0.439253	−	0.898363i	$-0.355243\pi$
$379$	−5.43943	−	3.95198i	−0.279405	−	0.203000i	−0.718658	+	0.695364i	$0.755243\pi$
$380$		0			0
$381$	−1.17728	+	0.855345i	−0.0603140	+	0.0438207i
$382$	−29.5901	−	9.61442i	−1.51396	−	0.491916i
$383$	10.8951	−	14.9958i	0.556714	−	0.766251i	−0.434190	−	0.900821i	$-0.642965\pi$
$383$	10.8951	−	14.9958i	0.556714	−	0.766251i	0.990904	+	0.134571i	$0.0429655\pi$
$384$	9.63679	−	29.6590i	0.491776	−	1.51353i
$385$		0			0
$386$	14.0633	−	10.2176i	0.715805	−	0.520062i
$387$	62.7068	−	20.3747i	3.18757	−	1.03570i
$388$	−1.59298	+	0.517590i	−0.0808713	+	0.0262767i
$389$	−2.34427	+	1.70321i	−0.118859	+	0.0863562i	−0.645627	−	0.763653i	$-0.723404\pi$
$389$	−2.34427	+	1.70321i	−0.118859	+	0.0863562i	0.526768	+	0.850009i	$0.323404\pi$
$390$		0			0
$391$	2.62628	−	8.08285i	0.132817	−	0.408767i
$392$	10.5838	−	14.5673i	0.534560	−	0.735759i
$393$	−11.6811	−	3.79541i	−0.589232	−	0.191453i
$394$	20.1854	−	14.6655i	1.01693	−	0.738839i
$395$		0			0
$396$	−4.63018	−	3.36402i	−0.232675	−	0.169048i
$397$		−	21.8732i		−	1.09778i	−0.835894	−	0.548891i	$-0.815050\pi$
$397$		−	21.8732i		−	1.09778i	0.835894	−	0.548891i	$-0.184950\pi$
$398$			31.7697i			1.59247i
$399$	−14.8925	−	10.8200i	−0.745555	−	0.541678i
$400$		0			0
$401$	−1.69586	+	5.21933i	−0.0846874	+	0.260641i	−0.984429	−	0.175782i	$-0.943755\pi$
$401$	−1.69586	+	5.21933i	−0.0846874	+	0.260641i	0.899742	+	0.436423i	$0.143755\pi$
$402$		−	1.77519i		−	0.0885385i
$403$	−9.82641	+	4.15705i	−0.489489	+	0.207077i
$404$	0.698877			0.0347704
$405$		0			0
$406$	0.802275	+	2.46915i	0.0398162	+	0.122542i
$407$	−26.5878	+	36.5950i	−1.31791	+	1.81394i
$408$		−	21.1829i		−	1.04871i
$409$	−20.9396			−1.03540			−0.517698	−	0.855563i	$-0.673211\pi$
$409$	−20.9396			−1.03540			−0.517698	+	0.855563i	$0.673211\pi$
$410$		0			0
$411$	29.0925	−	21.1369i	1.43503	−	1.04261i
$412$	0.106999	+	0.147271i	0.00527145	+	0.00725553i
$413$	−8.59406	−	2.79238i	−0.422886	−	0.137404i
$414$	28.1223	+	20.4321i	1.38214	+	1.00418i
$415$		0			0
$416$	−0.493116	−	1.51765i	−0.0241770	−	0.0744091i
$417$	−17.4528	−	24.0218i	−0.854669	−	1.17635i
$418$	−46.3259	+	15.0522i	−2.26588	+	0.736228i
$419$	−0.278033	−	0.855696i	−0.0135828	−	0.0418035i	0.944035	−	0.329844i	$-0.106996\pi$
$419$	−0.278033	−	0.855696i	−0.0135828	−	0.0418035i	−0.957618	+	0.288041i	$0.906996\pi$
$420$		0			0
$421$	−7.08975	−	21.8200i	−0.345533	−	1.06344i	−0.961298	−	0.275512i	$-0.911153\pi$
$421$	−7.08975	−	21.8200i	−0.345533	−	1.06344i	0.615765	−	0.787930i	$-0.288847\pi$
$422$	−6.31302	−	2.05122i	−0.307313	−	0.0998521i
$423$	−16.9647	+	23.3500i	−0.824854	+	1.13531i
$424$	6.98360	−	21.4933i	0.339153	−	1.04381i
$425$		0			0
$426$	−20.0847	+	14.5924i	−0.973107	+	0.707004i
$427$	−3.67110	+	5.05283i	−0.177657	+	0.244524i
$428$		−	1.89543i		−	0.0916190i
$429$	33.8516			1.63437
$430$		0			0
$431$	−10.6468	−	32.7676i	−0.512840	−	1.57836i	−0.787177	−	0.616727i	$-0.788458\pi$
$431$	−10.6468	−	32.7676i	−0.512840	−	1.57836i	0.274337	−	0.961634i	$-0.411542\pi$
$432$	43.1972	+	14.0356i	2.07833	+	0.675289i
$433$		−	0.131862i		−	0.00633687i	−0.999995	−	0.00316844i	$-0.998991\pi$
$433$		−	0.131862i		−	0.00633687i	0.999995	−	0.00316844i	$-0.00100855\pi$
$434$	5.24609	−	4.54923i	0.251821	−	0.218370i
$435$		0			0
$436$	−0.0479614	+	0.147610i	−0.00229693	+	0.00706924i
$437$	−22.4057	+	7.28005i	−1.07181	+	0.348252i
$438$	−15.9268	+	21.9214i	−0.761013	+	1.04744i
$439$	−27.8217			−1.32786			−0.663929	−	0.747795i	$-0.731112\pi$
$439$	−27.8217			−1.32786			−0.663929	+	0.747795i	$0.731112\pi$
$440$		0			0
$441$	34.4688	+	25.0430i	1.64137	+	1.19252i
$442$	3.52829	+	4.85627i	0.167824	+	0.230989i
$443$	13.7389	+	18.9099i	0.652753	+	0.898437i	0.999215	−	0.0396273i	$-0.0126170\pi$
$443$	13.7389	+	18.9099i	0.652753	+	0.898437i	−0.346462	+	0.938064i	$0.612617\pi$
$444$	−1.15747	+	3.56231i	−0.0549309	+	0.169060i
$445$		0			0
$446$	−4.56003	+	14.0343i	−0.215924	+	0.664545i
$447$	−48.9576	+	15.9073i	−2.31562	+	0.752389i
$448$	4.57794	+	6.30099i	0.216287	+	0.297694i
$449$	1.68488	+	5.18553i	0.0795145	+	0.244721i	0.982910	−	0.184089i	$-0.0589333\pi$
$449$	1.68488	+	5.18553i	0.0795145	+	0.244721i	−0.903395	+	0.428809i	$0.858933\pi$
$450$		0			0
$451$	−11.4893	+	8.34746i	−0.541010	+	0.393067i
$452$	1.72705	−	0.561153i	0.0812337	−	0.0263944i
$453$	8.93699	+	2.90380i	0.419896	+	0.136433i
$454$	−6.08665	−	4.42221i	−0.285661	−	0.207545i
$455$		0			0
$456$	−47.5049	+	34.5143i	−2.22462	+	1.61628i
$457$	−19.4836	−	26.8169i	−0.911404	−	1.25444i	−0.966685	−	0.255969i	$-0.917606\pi$
$457$	−19.4836	−	26.8169i	−0.911404	−	1.25444i	0.0552814	−	0.998471i	$-0.482394\pi$
$458$	8.16093	−	11.2325i	0.381335	−	0.524863i
$459$	28.3808			1.32470
$460$		0			0
$461$	5.65240	+	4.10671i	0.263259	+	0.191269i	0.711582	−	0.702603i	$-0.247979\pi$
$461$	5.65240	+	4.10671i	0.263259	+	0.191269i	−0.448324	+	0.893871i	$0.647979\pi$
$462$	−20.9527	+	6.80794i	−0.974807	+	0.316734i
$463$	18.7991	+	6.10820i	0.873668	+	0.283872i	0.711326	−	0.702863i	$-0.248095\pi$
$463$	18.7991	+	6.10820i	0.873668	+	0.283872i	0.162342	+	0.986734i	$0.448095\pi$
$464$	7.66740			0.355950
$465$		0			0
$466$	−12.3268			−0.571029
$467$	15.9082	+	5.16887i	0.736142	+	0.239187i	0.653007	−	0.757351i	$-0.273507\pi$
$467$	15.9082	+	5.16887i	0.736142	+	0.239187i	0.0831341	+	0.996538i	$0.473507\pi$
$468$	1.85938	−	0.604149i	0.0859499	−	0.0279268i
$469$	0.307041	+	0.223079i	0.0141779	+	0.0103008i
$470$		0			0
$471$	26.1422			1.20457
$472$	−16.9427	+	23.3196i	−0.779850	+	1.07337i
$473$	31.4348	+	43.2663i	1.44537	+	1.98939i
$474$	−36.8194	+	26.7508i	−1.69117	+	1.22871i
$475$		0			0
$476$	0.251674	+	0.182852i	0.0115354	+	0.00838099i
$477$	50.8569	+	16.5244i	2.32858	+	0.756601i
$478$	15.4305	−	5.01366i	0.705773	−	0.229320i
$479$	3.37161	−	2.44962i	0.154053	−	0.111926i	−0.508089	−	0.861305i	$-0.669648\pi$
$479$	3.37161	−	2.44962i	0.154053	−	0.111926i	0.662141	+	0.749379i	$0.269648\pi$
$480$		0			0
$481$	−4.77494	−	14.6957i	−0.217718	−	0.670068i
$482$	−14.0384	−	19.3222i	−0.639432	−	0.880103i
$483$	−10.1338	+	3.29268i	−0.461106	+	0.149822i
$484$	0.933087	−	2.87175i	0.0424130	−	0.130534i
$485$		0			0
$486$	−8.39127	+	25.8257i	−0.380636	+	1.17148i
$487$	−3.82291	−	5.26178i	−0.173232	−	0.238434i	0.713569	−	0.700585i	$-0.247078\pi$
$487$	−3.82291	−	5.26178i	−0.173232	−	0.238434i	−0.886801	+	0.462151i	$0.847078\pi$
$488$	11.7103	+	16.1178i	0.530100	+	0.729620i
$489$	58.2144	+	42.2952i	2.63255	+	1.91266i
$490$		0			0
$491$	25.5391			1.15256			0.576282	−	0.817251i	$-0.304503\pi$
$491$	25.5391			1.15256			0.576282	+	0.817251i	$0.304503\pi$
$492$	−0.691220	+	0.951383i	−0.0311626	+	0.0428917i
$493$	4.55649	−	1.48049i	0.205214	−	0.0666780i
$494$	5.14188	−	15.8251i	0.231344	−	0.712004i
$495$		0			0
$496$	−7.98998	−	18.8867i	−0.358761	−	0.848038i
$497$		−	5.30765i		−	0.238081i
$498$	−40.9404	−	13.3023i	−1.83458	−	0.596092i
$499$	−2.83976	−	8.73989i	−0.127125	−	0.391251i	0.867157	−	0.498035i	$-0.165945\pi$
$499$	−2.83976	−	8.73989i	−0.127125	−	0.391251i	−0.994282	+	0.106783i	$0.965945\pi$
$500$		0			0
$501$	−47.1106			−2.10474
$502$			32.9816i			1.47204i
$503$	14.6683	−	20.1892i	0.654029	−	0.900193i	−0.345237	−	0.938516i	$-0.612201\pi$
$503$	14.6683	−	20.1892i	0.654029	−	0.900193i	0.999265	+	0.0383223i	$0.0122014\pi$
$504$	−14.9856	+	10.8877i	−0.667511	+	0.484975i
$505$		0			0
$506$	−8.71283	+	26.8153i	−0.387333	+	1.19209i
$507$	17.2650	−	23.7632i	0.766765	−	1.05536i
$508$	−0.0648328	−	0.0210654i	−0.00287649	−	0.000934628i
$509$	2.71759	+	8.36389i	0.120455	+	0.370723i	0.993046	−	0.117729i	$-0.0375616\pi$
$509$	2.71759	+	8.36389i	0.120455	+	0.370723i	−0.872590	+	0.488453i	$0.837562\pi$
$510$		0			0
$511$	−1.79014	−	5.50949i	−0.0791912	−	0.243725i
$512$	23.3945	−	7.60132i	1.03390	−	0.335934i
$513$	−46.2422	−	63.6469i	−2.04164	−	2.81008i
$514$	−2.31940	−	7.13839i	−0.102305	−	0.314861i
$515$		0			0
$516$	3.58271	+	2.60299i	0.157720	+	0.114590i
$517$	−22.2648	−	7.23426i	−0.979204	−	0.318163i
$518$	5.91096	+	8.13573i	0.259712	+	0.357464i
$519$	6.86999	−	4.99134i	0.301559	−	0.219095i
$520$		0			0
$521$	21.3783			0.936602			0.468301	−	0.883569i	$-0.344866\pi$
$521$	21.3783			0.936602			0.468301	+	0.883569i	$0.344866\pi$
$522$			19.5956i			0.857678i
$523$	−23.5819	+	32.4578i	−1.03117	+	1.41928i	−0.127099	+	0.991890i	$0.540567\pi$
$523$	−23.5819	+	32.4578i	−1.03117	+	1.41928i	−0.904068	+	0.427389i	$0.859433\pi$
$524$	−0.177797	−	0.547202i	−0.00776709	−	0.0239046i
$525$		0			0
$526$	−10.7689			−0.469546
$527$	−8.39501	−	9.68098i	−0.365692	−	0.421710i
$528$			65.0640i			2.83155i
$529$	2.89340	−	8.90497i	0.125800	−	0.387173i
$530$		0			0
$531$	−55.1783	−	40.0894i	−2.39453	−	1.73973i
$532$		−	0.862332i		−	0.0373868i
$533$		−	4.85129i		−	0.210133i
$534$	7.99515	+	5.80882i	0.345984	+	0.251372i
$535$		0			0
$536$	0.979419	−	0.711590i	0.0423045	−	0.0307360i
$537$	73.2566	+	23.8025i	3.16125	+	1.02715i
$538$	−0.431231	+	0.593539i	−0.0185917	+	0.0255893i
$539$	−10.6791	+	32.8668i	−0.459980	+	1.41567i
$540$		0			0
$541$	32.6156	−	23.6966i	1.40225	−	1.01880i	0.407860	−	0.913045i	$-0.366275\pi$
$541$	32.6156	−	23.6966i	1.40225	−	1.01880i	0.994393	−	0.105751i	$-0.0337248\pi$
$542$	16.8246	−	5.46664i	0.722677	−	0.234812i
$543$	56.8897	−	18.4846i	2.44137	−	0.793249i
$544$	1.55046	−	1.12648i	0.0664755	−	0.0482973i
$545$		0			0
$546$	2.32561	−	7.15750i	0.0995270	−	0.306313i
$547$	−16.2644	+	22.3860i	−0.695416	+	0.957157i	0.304573	+	0.952489i	$0.401486\pi$
$547$	−16.2644	+	22.3860i	−0.695416	+	0.957157i	−0.999989	+	0.00466864i	$0.998514\pi$
$548$	1.60212	+	0.520560i	0.0684391	+	0.0222372i
$549$	−38.1376	+	27.7086i	−1.62767	+	1.18257i
$550$		0			0
$551$	−10.7442	−	7.80615i	−0.457720	−	0.332553i
$552$			33.9891i			1.44667i
$553$		−	9.73001i		−	0.413762i
$554$	−1.40414	−	1.02017i	−0.0596563	−	0.0433428i
$555$		0			0
$556$	0.429828	−	1.32288i	0.0182288	−	0.0561024i
$557$			15.4033i			0.652657i	0.945256	+	0.326329i	$0.105812\pi$
$557$			15.4033i			0.652657i	−0.945256	+	0.326329i	$0.894188\pi$
$558$	48.2689	−	20.4201i	2.04339	−	0.864450i
$559$	−18.2689			−0.772694
$560$		0			0
$561$	12.5632	+	38.6654i	0.530417	+	1.63246i
$562$	8.71819	−	11.9996i	0.367755	−	0.506171i
$563$		−	1.02980i		−	0.0434009i	−0.999765	−	0.0217005i	$-0.993092\pi$
$563$		−	1.02980i		−	0.0434009i	0.999765	−	0.0217005i	$-0.00690802\pi$
$564$	−1.93854			−0.0816271
$565$		0			0
$566$	11.3912	−	8.27619i	0.478808	−	0.347874i
$567$	−9.73992	−	13.4058i	−0.409038	−	0.562993i
$568$	−16.1020	−	5.23186i	−0.675625	−	0.219524i
$569$	10.0268	+	7.28492i	0.420347	+	0.305400i	0.777777	−	0.628540i	$-0.216347\pi$
$569$	10.0268	+	7.28492i	0.420347	+	0.305400i	−0.357431	+	0.933940i	$0.616347\pi$
$570$		0			0
$571$	−1.51723	−	4.66955i	−0.0634941	−	0.195415i	0.914277	−	0.405089i	$-0.132760\pi$
$571$	−1.51723	−	4.66955i	−0.0634941	−	0.195415i	−0.977771	+	0.209675i	$0.932760\pi$
$572$	0.932103	+	1.28293i	0.0389732	+	0.0536420i
$573$	68.4605	−	22.2442i	2.85998	−	0.929263i
$574$	0.975649	+	3.00274i	0.0407228	+	0.125332i
$575$		0			0
$576$	18.1657	+	55.9083i	0.756904	+	2.32951i
$577$	−15.9849	−	5.19382i	−0.665461	−	0.216221i	−0.0432422	−	0.999065i	$-0.513769\pi$
$577$	−15.9849	−	5.19382i	−0.665461	−	0.216221i	−0.622219	+	0.782843i	$0.713769\pi$
$578$	9.36277	−	12.8868i	0.389440	−	0.536018i
$579$	−12.4281	+	38.2498i	−0.516495	+	1.58961i
$580$		0			0
$581$	7.44557	−	5.40952i	0.308894	−	0.224425i
$582$	−28.6045	+	39.3707i	−1.18569	+	1.63197i
$583$			43.3738i			1.79636i
$584$	−18.4789			−0.764663
$585$		0			0
$586$	8.07393	+	24.8490i	0.333531	+	1.02650i
$587$	38.5388	+	12.5220i	1.59067	+	0.516839i	0.964776	−	0.263072i	$-0.0847356\pi$
$587$	38.5388	+	12.5220i	1.59067	+	0.516839i	0.625891	+	0.779911i	$0.284736\pi$
$588$			2.86163i			0.118012i
$589$	−8.03220	+	34.6003i	−0.330961	+	1.42568i
$590$		0			0
$591$	−17.8384	+	54.9008i	−0.733772	+	2.25832i
$592$	28.2457	−	9.17759i	1.16089	−	0.377197i
$593$	−25.1238	+	34.5799i	−1.03171	+	1.42003i	−0.128055	+	0.991767i	$0.540873\pi$
$593$	−25.1238	+	34.5799i	−1.03171	+	1.42003i	−0.903656	+	0.428260i	$0.859127\pi$
$594$	−94.1551			−3.86323
$595$		0			0
$596$	−1.95091	−	1.41742i	−0.0799124	−	0.0580597i
$597$	−43.2041	−	59.4654i	−1.76823	−	2.43376i
$598$	−5.66131	−	7.79213i	−0.231508	−	0.318644i
$599$	−1.73669	+	5.34499i	−0.0709594	+	0.218391i	−0.980247	−	0.197778i	$-0.936627\pi$
$599$	−1.73669	+	5.34499i	−0.0709594	+	0.218391i	0.909287	+	0.416169i	$0.136627\pi$
$600$		0			0
$601$	−6.95038	+	21.3911i	−0.283512	+	0.872560i	0.703329	+	0.710864i	$0.251696\pi$
$601$	−6.95038	+	21.3911i	−0.283512	+	0.872560i	−0.986841	+	0.161695i	$0.948304\pi$
$602$	11.3077	−	3.67409i	0.460867	−	0.149745i
$603$	1.68375	+	2.31748i	0.0685674	+	0.0943750i
$604$	0.136029	+	0.418655i	0.00553496	+	0.0170348i
$605$		0			0
$606$	16.4274	−	11.9352i	0.667319	−	0.484836i
$607$	16.7700	−	5.44889i	0.680671	−	0.221164i	0.0517821	−	0.998658i	$-0.483510\pi$
$607$	16.7700	−	5.44889i	0.680671	−	0.221164i	0.628889	+	0.777495i	$0.283510\pi$
$608$	−5.05247	−	1.64165i	−0.204905	−	0.0665776i
$609$	−4.85949	−	3.53063i	−0.196917	−	0.143068i
$610$		0			0
$611$	6.46981	−	4.70059i	0.261740	−	0.190165i
$612$	1.38012	+	1.89957i	0.0557881	+	0.0767858i
$613$	21.6484	−	29.7965i	0.874372	−	1.20347i	−0.103577	−	0.994621i	$-0.533029\pi$
$613$	21.6484	−	29.7965i	0.874372	−	1.20347i	0.977948	−	0.208848i	$-0.0669713\pi$
$614$	13.0371			0.526136
$615$		0			0
$616$	−12.1551	−	8.83117i	−0.489741	−	0.355818i
$617$	−3.16290	+	1.02769i	−0.127333	+	0.0413731i	−0.371991	−	0.928237i	$-0.621325\pi$
$617$	−3.16290	+	1.02769i	−0.127333	+	0.0413731i	0.244657	+	0.969610i	$0.421325\pi$
$618$	5.03012	+	1.63438i	0.202341	+	0.0657446i
$619$	−12.2404			−0.491982			−0.245991	−	0.969272i	$-0.579113\pi$
$619$	−12.2404			−0.491982			−0.245991	+	0.969272i	$0.579113\pi$
$620$		0			0
$621$	−45.5385			−1.82740
$622$	0.0774005	+	0.0251489i	0.00310348	+	0.00100838i
$623$	−2.00942	+	0.652899i	−0.0805056	+	0.0261578i
$624$	−17.9812	−	13.0641i	−0.719826	−	0.522984i
$625$		0			0
$626$	13.2485			0.529515
$627$	66.2414	−	91.1735i	2.64543	−	3.64112i
$628$	0.719825	+	0.990754i	0.0287241	+	0.0395354i
$629$	15.0134	−	10.9079i	0.598625	−	0.434926i
$630$		0			0
$631$	30.3909	+	22.0803i	1.20984	+	0.879001i	0.995216	−	0.0976951i	$-0.0311470\pi$
$631$	30.3909	+	22.0803i	1.20984	+	0.879001i	0.214625	+	0.976696i	$0.431147\pi$
$632$	−29.5183	−	9.59107i	−1.17417	−	0.381512i
$633$	14.6060	−	4.74576i	0.580535	−	0.188627i
$634$	−7.21867	+	5.24467i	−0.286690	+	0.208292i
$635$		0			0
$636$	1.10987	+	3.41582i	0.0440091	+	0.135446i
$637$	−6.93891	−	9.55060i	−0.274930	−	0.378408i
$638$	−15.1164	+	4.91162i	−0.598465	+	0.194453i
$639$	12.3795	−	38.1002i	0.489725	−	1.50722i
$640$		0			0
$641$	2.20975	−	6.80091i	0.0872799	−	0.268620i	−0.897885	−	0.440230i	$-0.854897\pi$
$641$	2.20975	−	6.80091i	0.0872799	−	0.268620i	0.985165	+	0.171610i	$0.0548969\pi$
$642$	−32.3697	−	44.5530i	−1.27753	−	1.75837i
$643$	−19.5344	−	26.8868i	−0.770363	−	1.06031i	−0.996281	−	0.0861670i	$-0.972538\pi$
$643$	−19.5344	−	26.8868i	−0.770363	−	1.06031i	0.225918	−	0.974146i	$-0.427462\pi$
$644$	−0.403823	−	0.293394i	−0.0159128	−	0.0115614i
$645$		0			0
$646$	19.9837			0.786249
$647$	9.77225	−	13.4503i	0.384187	−	0.528788i	−0.572501	−	0.819904i	$-0.694027\pi$
$647$	9.77225	−	13.4503i	0.384187	−	0.528788i	0.956688	+	0.291117i	$0.0940267\pi$
$648$	−50.2707	+	16.3339i	−1.97482	+	0.641657i
$649$	17.0953	−	52.6139i	0.671048	−	2.06527i
$650$		0			0
$651$	−3.63287	+	15.6493i	−0.142383	+	0.613345i
$652$			3.37084i			0.132012i
$653$	−32.0372	−	10.4095i	−1.25371	−	0.407356i	−0.394462	−	0.918912i	$-0.629069\pi$
$653$	−32.0372	−	10.4095i	−1.25371	−	0.407356i	−0.859250	+	0.511556i	$0.829069\pi$
$654$	1.39349	+	4.28872i	0.0544897	+	0.167702i
$655$		0			0
$656$	9.32434			0.364054
$657$		−	43.7244i		−	1.70585i
$658$	−3.05919	+	4.21061i	−0.119260	+	0.164147i
$659$	−12.4643	+	9.05581i	−0.485538	+	0.352764i	−0.803466	−	0.595351i	$-0.797013\pi$
$659$	−12.4643	+	9.05581i	−0.485538	+	0.352764i	0.317928	+	0.948115i	$0.397013\pi$
$660$		0			0
$661$	0.797817	−	2.45543i	0.0310315	−	0.0955050i	−0.934341	−	0.356380i	$-0.884011\pi$
$661$	0.797817	−	2.45543i	0.0310315	−	0.0955050i	0.965373	+	0.260875i	$0.0840109\pi$
$662$	−7.82187	+	10.7659i	−0.304006	+	0.418428i
$663$	−13.2082	−	4.29161i	−0.512965	−	0.166672i
$664$	−9.07182	−	27.9202i	−0.352055	−	1.08351i
$665$		0			0
$666$	23.4552	+	72.1878i	0.908872	+	2.79722i
$667$	−7.31111	+	2.37552i	−0.283087	+	0.0919807i
$668$	−1.29719	−	1.78542i	−0.0501897	−	0.0690801i
$669$	−10.5502	−	32.4702i	−0.407895	−	1.25537i
$670$		0			0
$671$	−30.9341	−	22.4749i	−1.19420	−	0.867634i
$672$	−2.28517	−	0.742498i	−0.0881525	−	0.0286425i
$673$	−8.78514	−	12.0917i	−0.338642	−	0.466101i	0.605402	−	0.795920i	$-0.293012\pi$
$673$	−8.78514	−	12.0917i	−0.338642	−	0.466101i	−0.944044	+	0.329819i	$0.893012\pi$
$674$	6.63518	−	4.82074i	0.255578	−	0.185688i
$675$		0			0
$676$	1.37598			0.0529224
$677$			9.58212i			0.368271i	0.982901	+	0.184135i	$0.0589485\pi$
$677$			9.58212i			0.368271i	−0.982901	+	0.184135i	$0.941052\pi$
$678$	31.0120	−	42.6843i	1.19101	−	1.63928i
$679$	−3.21509	−	9.89501i	−0.123384	−	0.379736i
$680$		0			0
$681$	17.4066			0.667022
$682$	27.8509	+	32.1172i	1.06647	+	1.22983i
$683$			42.9429i			1.64317i	0.570089	+	0.821583i	$0.306909\pi$
$683$			42.9429i			1.64317i	−0.570089	+	0.821583i	$0.693091\pi$
$684$	2.01129	−	6.19012i	0.0769037	−	0.236685i
$685$		0			0
$686$	13.2784	+	9.64731i	0.506971	+	0.368336i
$687$			32.1228i			1.22556i
$688$		−	35.1135i		−	1.33869i
$689$	−11.9869	−	8.70898i	−0.456664	−	0.331786i
$690$		0			0
$691$	16.0878	−	11.6885i	0.612010	−	0.444651i	−0.238111	−	0.971238i	$-0.576528\pi$
$691$	16.0878	−	11.6885i	0.612010	−	0.444651i	0.850122	+	0.526586i	$0.176528\pi$
$692$	0.378329	+	0.122927i	0.0143819	+	0.00467297i
$693$	20.8961	−	28.7610i	0.793777	−	1.09254i
$694$	−8.00343	+	24.6320i	−0.303806	+	0.935019i
$695$		0			0
$696$	−15.5011	+	11.2622i	−0.587568	+	0.426893i
$697$	5.54116	−	1.80043i	0.209886	−	0.0681962i
$698$	22.5335	−	7.32158i	0.852906	−	0.277126i
$699$	23.0729	−	16.7634i	0.872697	−	0.634051i
$700$		0			0
$701$	4.81083	−	14.8062i	0.181702	−	0.559223i	−0.818174	−	0.574971i	$-0.805013\pi$
$701$	4.81083	−	14.8062i	0.181702	−	0.559223i	0.999876	+	0.0157487i	$0.00501318\pi$
$702$	18.9053	−	26.0210i	0.713536	−	0.982098i
$703$	−48.9241	−	15.8964i	−1.84521	−	0.599544i
$704$	−38.5754	+	28.0267i	−1.45387	+	1.05630i
$705$		0			0
$706$	−13.1415	−	9.54788i	−0.494588	−	0.359339i
$707$			4.34117i			0.163266i
$708$		−	4.58095i		−	0.172163i
$709$	−34.1492	−	24.8109i	−1.28250	−	0.931792i	−0.282876	−	0.959157i	$-0.591288\pi$
$709$	−34.1492	−	24.8109i	−1.28250	−	0.931792i	−0.999626	+	0.0273649i	$0.991288\pi$
$710$		0			0
$711$	22.6942	−	69.8455i	0.851098	−	2.61941i
$712$			6.73962i			0.252578i
$713$	13.4702	+	15.5336i	0.504463	+	0.581738i
$714$	9.03841			0.338254
$715$		0			0
$716$	1.11503	+	3.43172i	0.0416708	+	0.128249i
$717$	−22.0640	+	30.3685i	−0.823995	+	1.13413i
$718$			43.4371i			1.62106i
$719$	46.3827			1.72978			0.864891	−	0.501960i	$-0.167387\pi$
$719$	46.3827			1.72978			0.864891	+	0.501960i	$0.167387\pi$
$720$		0			0
$721$	−0.914795	+	0.664637i	−0.0340687	+	0.0247524i
$722$	−17.3602	−	23.8942i	−0.646078	−	0.889251i
$723$	52.5531	+	17.0755i	1.95447	+	0.635046i
$724$	2.26699	+	1.64707i	0.0842522	+	0.0612128i
$725$		0			0
$726$	−27.1103	−	83.4369i	−1.00616	−	3.09663i
$727$	8.99188	+	12.3763i	0.333491	+	0.459010i	0.942526	−	0.334133i	$-0.108443\pi$
$727$	8.99188	+	12.3763i	0.333491	+	0.459010i	−0.609036	+	0.793143i	$0.708443\pi$
$728$	4.88121	−	1.58600i	0.180910	−	0.0587811i
$729$	−2.64945	−	8.15416i	−0.0981277	−	0.302006i
$730$		0			0
$731$	−6.78005	−	20.8668i	−0.250769	−	0.771788i
$732$	−3.01126	−	0.978416i	−0.111299	−	0.0361633i
$733$	4.57555	−	6.29770i	0.169002	−	0.232611i	−0.716112	−	0.697985i	$-0.754080\pi$
$733$	4.57555	−	6.29770i	0.169002	−	0.232611i	0.885114	+	0.465374i	$0.154080\pi$
$734$	−6.83501	+	21.0360i	−0.252285	+	0.776452i
$735$		0			0
$736$	−2.48779	+	1.80749i	−0.0917013	+	0.0666249i
$737$	−1.36571	+	1.87975i	−0.0503067	+	0.0692413i
$738$			23.8303i			0.877206i
$739$	1.12482			0.0413773			0.0206887	−	0.999786i	$-0.493414\pi$
$739$	1.12482			0.0413773			0.0206887	+	0.999786i	$0.493414\pi$
$740$		0			0
$741$	11.8964	+	36.6133i	0.437024	+	1.34502i
$742$	9.17083	+	2.97978i	0.336672	+	0.109391i
$743$			37.3958i			1.37192i	0.727639	+	0.685960i	$0.240618\pi$
$743$			37.3958i			1.37192i	−0.727639	+	0.685960i	$0.759382\pi$
$744$	43.8949	+	26.4470i	1.60927	+	0.969595i
$745$		0			0
$746$	8.90569	−	27.4089i	0.326060	−	1.00351i
$747$	66.0640	−	21.4655i	2.41716	−	0.785382i
$748$	−1.11944	+	1.54078i	−0.0409308	+	0.0563364i
$749$	11.7737			0.430202
$750$		0			0
$751$	−43.0328	−	31.2652i	−1.57029	−	1.14088i	−0.926878	−	0.375362i	$-0.877518\pi$
$751$	−43.0328	−	31.2652i	−1.57029	−	1.14088i	−0.643412	−	0.765520i	$-0.722482\pi$
$752$	9.03469	+	12.4352i	0.329461	+	0.453464i
$753$	−44.8522	−	61.7337i	−1.63450	−	2.24970i
$754$	1.67782	−	5.16381i	0.0611028	−	0.188055i
$755$		0			0
$756$	0.515089	−	1.58528i	0.0187336	−	0.0576562i
$757$	20.4386	−	6.64091i	0.742854	−	0.241368i	0.0869504	−	0.996213i	$-0.472288\pi$
$757$	20.4386	−	6.64091i	0.742854	−	0.241368i	0.655903	+	0.754845i	$0.272288\pi$
$758$	−5.37888	−	7.40340i	−0.195370	−	0.268903i
$759$	−20.1582	−	62.0406i	−0.731697	−	2.25193i
$760$		0			0
$761$	−22.9004	+	16.6381i	−0.830138	+	0.603130i	−0.919598	−	0.392860i	$-0.871486\pi$
$761$	−22.9004	+	16.6381i	−0.830138	+	0.603130i	0.0894604	+	0.995990i	$0.471486\pi$
$762$	−1.88368	+	0.612044i	−0.0682384	+	0.0221720i
$763$	−0.916900	−	0.297919i	−0.0331940	−	0.0107854i
$764$	2.72808	+	1.98206i	0.0986984	+	0.0717086i
$765$		0			0
$766$	20.4102	−	14.8289i	0.737451	−	0.535790i
$767$	11.1080	+	15.2888i	0.401085	+	0.552046i
$768$	−6.51641	+	8.96907i	−0.235141	+	0.323643i
$769$	8.29866			0.299257			0.149629	−	0.988742i	$-0.452192\pi$
$769$	8.29866			0.299257			0.149629	+	0.988742i	$0.452192\pi$
$770$		0			0
$771$	14.0490	+	10.2072i	0.505961	+	0.367602i
$772$	−1.79182	+	0.582199i	−0.0644891	+	0.0209538i
$773$	−12.2249	−	3.97213i	−0.439701	−	0.142867i	0.0807968	−	0.996731i	$-0.474254\pi$
$773$	−12.2249	−	3.97213i	−0.439701	−	0.142867i	−0.520498	+	0.853863i	$0.674254\pi$
$774$	89.7400			3.22564
$775$		0			0
$776$	−33.1881			−1.19138
$777$	−22.1278	−	7.18976i	−0.793830	−	0.257931i
$778$	−3.75088	+	1.21874i	−0.134476	+	0.0436938i
$779$	−13.0661	−	9.49308i	−0.468142	−	0.340125i
$780$		0			0
$781$	32.4941			1.16273
$782$	6.79914	−	9.35822i	0.243137	−	0.334649i
$783$	−15.0891	−	20.7683i	−0.539240	−	0.742200i
$784$	18.3566	−	13.3368i	0.655592	−	0.476315i
$785$		0			0
$786$	−13.5242	−	9.82590i	−0.482392	−	0.350478i
$787$	11.0908	+	3.60362i	0.395345	+	0.128455i	0.499941	−	0.866059i	$-0.333355\pi$
$787$	11.0908	+	3.60362i	0.395345	+	0.128455i	−0.104596	+	0.994515i	$0.533355\pi$
$788$	−2.57184	+	0.835642i	−0.0916181	+	0.0297685i
$789$	20.1568	−	14.6448i	0.717601	−	0.521368i
$790$		0			0
$791$	3.48568	+	10.7278i	0.123937	+	0.381437i
$792$	−66.6556	−	91.7436i	−2.36850	−	3.25997i
$793$	12.4224	−	4.03630i	0.441134	−	0.143333i
$794$	9.19965	−	28.3136i	0.326483	−	1.00481i
$795$		0			0
$796$	1.06403	−	3.27475i	0.0377136	−	0.116070i
$797$	−3.13553	−	4.31568i	−0.111066	−	0.152869i	0.749865	−	0.661591i	$-0.230118\pi$
$797$	−3.13553	−	4.31568i	−0.111066	−	0.152869i	−0.860931	+	0.508721i	$0.830118\pi$
$798$	−14.7267	−	20.2695i	−0.521319	−	0.717534i
$799$	7.77013	+	5.64533i	0.274887	+	0.199717i
$800$		0			0
$801$	−15.9471			−0.563464
$802$	−4.39041	+	6.04288i	−0.155031	+	0.213381i
$803$	33.7298	−	10.9595i	1.19030	−	0.386751i
$804$	−0.0594546	+	0.182983i	−0.00209680	+	0.00645330i
$805$		0			0
$806$	−14.4682	+	1.24817i	−0.509620	+	0.0439649i
$807$		−	1.69740i		−	0.0597513i
$808$	13.1700	+	4.27918i	0.463318	+	0.150541i
$809$	5.06021	+	15.5737i	0.177908	+	0.547543i	0.999754	−	0.0221653i	$-0.00705600\pi$
$809$	5.06021	+	15.5737i	0.177908	+	0.547543i	−0.821847	+	0.569709i	$0.807056\pi$
$810$		0			0
$811$	35.0584			1.23107			0.615534	−	0.788110i	$-0.288940\pi$
$811$	35.0584			1.23107			0.615534	+	0.788110i	$0.288940\pi$
$812$		−	0.281384i		−	0.00987463i
$813$	−24.0574	+	33.1122i	−0.843731	+	1.16130i
$814$	−49.8079	+	36.1876i	−1.74577	+	1.26837i
$815$		0			0
$816$	8.24862	−	25.3867i	0.288760	−	0.888711i
$817$	−35.7490	+	49.2042i	−1.25070	+	1.72144i
$818$	−27.1051	−	8.80700i	−0.947709	−	0.307929i
$819$	3.75276	+	11.5498i	0.131132	+	0.403582i
$820$		0			0
$821$	−7.94004	−	24.4369i	−0.277109	−	0.852855i	−0.988654	−	0.150214i	$-0.952004\pi$
$821$	−7.94004	−	24.4369i	−0.277109	−	0.852855i	0.711544	−	0.702641i	$-0.247996\pi$
$822$	46.5486	−	15.1246i	1.62357	−	0.527530i
$823$	4.04173	+	5.56297i	0.140886	+	0.193913i	0.873629	−	0.486592i	$-0.161760\pi$
$823$	4.04173	+	5.56297i	0.140886	+	0.193913i	−0.732743	+	0.680505i	$0.761760\pi$
$824$	1.11460	+	3.43039i	0.0388290	+	0.119503i
$825$		0			0
$826$	−9.95009	−	7.22916i	−0.346208	−	0.251535i
$827$	−33.1261	−	10.7633i	−1.15191	−	0.374278i	−0.330046	−	0.943965i	$-0.607064\pi$
$827$	−33.1261	−	10.7633i	−1.15191	−	0.374278i	−0.821862	+	0.569687i	$0.807064\pi$
$828$	−2.21447	−	3.04796i	−0.0769583	−	0.105924i
$829$	9.87637	−	7.17560i	0.343021	−	0.249219i	−0.402915	−	0.915238i	$-0.632003\pi$
$829$	9.87637	−	7.17560i	0.343021	−	0.249219i	0.745935	+	0.666019i	$0.232003\pi$
$830$		0			0
$831$	4.01556			0.139298
$832$		−	16.2883i		−	0.564694i
$833$	8.33352	−	11.4701i	0.288739	−	0.397416i
$834$	−12.4884	−	38.4353i	−0.432438	−	1.33091i
$835$		0			0
$836$	5.27930			0.182588
$837$	−35.4337	+	58.8103i	−1.22477	+	2.03278i
$838$		−	1.22459i		−	0.0423028i
$839$	2.12550	−	6.54162i	0.0733804	−	0.225842i	−0.907639	−	0.419752i	$-0.862117\pi$
$839$	2.12550	−	6.54162i	0.0733804	−	0.225842i	0.981019	+	0.193910i	$0.0621171\pi$
$840$		0			0
$841$	19.9556	+	14.4986i	0.688124	+	0.499951i
$842$		−	31.2267i		−	1.07614i
$843$			34.3163i			1.18192i
$844$	0.582032	+	0.422871i	0.0200344	+	0.0145558i
$845$		0			0
$846$	−31.7807	+	23.0900i	−1.09264	+	0.793852i
$847$	17.8383	+	5.79600i	0.612930	+	0.199153i
$848$	16.7390	−	23.0392i	0.574818	−	0.791169i
$849$	−10.0667	+	30.9821i	−0.345488	+	1.06330i
$850$		0			0
$851$	−24.0898	+	17.5023i	−0.825787	+	0.599970i
$852$	2.55901	−	0.831474i	0.0876703	−	0.0284858i
$853$	−19.1978	+	6.23773i	−0.657319	+	0.213576i	−0.618639	−	0.785676i	$-0.712315\pi$
$853$	−19.1978	+	6.23773i	−0.657319	+	0.213576i	−0.0386804	+	0.999252i	$0.512315\pi$
$854$	−6.87721	+	4.99659i	−0.235333	+	0.170980i
$855$		0			0
$856$	11.6056	−	35.7184i	0.396671	−	1.22083i
$857$	−3.83293	+	5.27558i	−0.130931	+	0.180210i	−0.869449	−	0.494023i	$-0.835526\pi$
$857$	−3.83293	+	5.27558i	−0.130931	+	0.180210i	0.738518	+	0.674233i	$0.235526\pi$
$858$	43.8191	+	14.2377i	1.49596	+	0.486066i
$859$	6.94602	−	5.04658i	0.236995	−	0.172187i	−0.462948	−	0.886385i	$-0.653208\pi$
$859$	6.94602	−	5.04658i	0.236995	−	0.172187i	0.699944	+	0.714198i	$0.253208\pi$
$860$		0			0
$861$	−5.90965	−	4.29361i	−0.201400	−	0.146326i
$862$		−	46.8939i		−	1.59721i
$863$		−	46.4756i		−	1.58205i	−0.611786	−	0.791023i	$-0.709549\pi$
$863$		−	46.4756i		−	1.58205i	0.611786	−	0.791023i	$-0.290451\pi$
$864$	−8.30771	−	6.03590i	−0.282634	−	0.205346i
$865$		0			0
$866$	0.0554598	−	0.170688i	0.00188460	−	0.00580021i
$867$			36.8535i			1.25161i
$868$	−0.693118	+	0.293222i	−0.0235260	+	0.00995261i
$869$	59.5683			2.02072
$870$		0			0
$871$	−0.245270	−	0.754865i	−0.00831067	−	0.0255776i
$872$	−1.80761	+	2.48797i	−0.0612136	+	0.0842532i
$873$		−	78.5288i		−	2.65780i
$874$	−32.0649			−1.08461
$875$		0			0
$876$	2.37589	−	1.72619i	0.0802739	−	0.0583224i
$877$	−25.0753	−	34.5132i	−0.846732	−	1.16543i	−0.984573	−	0.174972i	$-0.944016\pi$
$877$	−25.0753	−	34.5132i	−0.846732	−	1.16543i	0.137841	−	0.990454i	$-0.455984\pi$
$878$	−36.0137	−	11.7016i	−1.21540	−	0.394909i
$879$	−48.9050	−	35.5316i	−1.64952	−	1.19845i
$880$		0			0
$881$	6.10369	+	18.7852i	0.205639	+	0.632891i	0.999687	+	0.0250354i	$0.00796985\pi$
$881$	6.10369	+	18.7852i	0.205639	+	0.632891i	−0.794048	+	0.607855i	$0.792030\pi$
$882$	34.0851	+	46.9140i	1.14770	+	1.57968i
$883$	−4.60925	+	1.49764i	−0.155114	+	0.0503995i	−0.385545	−	0.922689i	$-0.625986\pi$
$883$	−4.60925	+	1.49764i	−0.155114	+	0.0503995i	0.230431	+	0.973089i	$0.425986\pi$
$884$	−0.201042	−	0.618743i	−0.00676176	−	0.0208106i
$885$		0			0
$886$	9.83086	+	30.2563i	0.330274	+	1.01648i
$887$	−33.3422	−	10.8335i	−1.11952	−	0.363754i	−0.309936	−	0.950757i	$-0.600308\pi$
$887$	−33.3422	−	10.8335i	−1.11952	−	0.363754i	−0.809585	+	0.587003i	$0.800308\pi$
$888$	−43.6237	+	60.0428i	−1.46391	+	2.01491i
$889$	0.130851	−	0.402718i	0.00438860	−	0.0135067i
$890$		0			0
$891$	82.0722	−	59.6290i	2.74952	−	1.99765i
$892$	0.940076	−	1.29390i	0.0314761	−	0.0433231i
$893$		−	26.6235i		−	0.890921i
$894$	−70.0634			−2.34327
$895$		0			0
$896$	2.80417	+	8.63035i	0.0936807	+	0.288320i
$897$	21.1933	+	6.88611i	0.707622	+	0.229920i
$898$			7.42104i			0.247643i
$899$	−2.62095	+	11.2903i	−0.0874137	+	0.376552i
$900$		0			0
$901$	5.49880	−	16.9236i	0.183192	−	0.563806i
$902$	−18.3831	+	5.97304i	−0.612091	+	0.198880i
$903$	−16.1688	+	22.2545i	−0.538065	+	0.740583i
$904$	35.9813			1.19672
$905$		0			0
$906$	10.3471	+	7.51763i	0.343760	+	0.249756i
$907$	−12.7723	−	17.5796i	−0.424098	−	0.583721i	0.542488	−	0.840064i	$-0.317483\pi$
$907$	−12.7723	−	17.5796i	−0.424098	−	0.583721i	−0.966586	+	0.256343i	$0.917483\pi$
$908$	0.479289	+	0.659685i	0.0159058	+	0.0218924i
$909$	−10.1253	+	31.1625i	−0.335835	+	1.03359i
$910$		0			0
$911$	−1.34474	+	4.13869i	−0.0445533	+	0.137121i	−0.970859	−	0.239653i	$-0.922966\pi$
$911$	−1.34474	+	4.13869i	−0.0445533	+	0.137121i	0.926305	+	0.376773i	$0.122966\pi$
$912$	−70.3720	+	22.8652i	−2.33025	+	0.757144i
$913$	33.1178	+	45.5827i	1.09604	+	1.50857i
$914$	−13.9415	−	42.9076i	−0.461144	−	1.41926i
$915$		0			0
$916$	−1.21741	+	0.884500i	−0.0402243	+	0.0292247i
$917$	3.39902	−	1.10441i	0.112246	−	0.0364708i
$918$	36.7374	+	11.9367i	1.21252	+	0.393970i
$919$	−33.2493	−	24.1571i	−1.09679	−	0.796868i	−0.116261	−	0.993219i	$-0.537091\pi$
$919$	−33.2493	−	24.1571i	−1.09679	−	0.796868i	−0.980534	+	0.196351i	$0.937091\pi$
$920$		0			0
$921$	−24.4024	+	17.7294i	−0.804086	+	0.584203i
$922$	5.58948	+	7.69326i	0.184080	+	0.253364i
$923$	−6.52446	+	8.98014i	−0.214755	+	0.295585i
$924$	2.38777			0.0785517
$925$		0			0
$926$	21.7653	+	15.8135i	0.715254	+	0.519662i
$927$	−8.11692	+	2.63735i	−0.266595	+	0.0866218i
$928$	−1.64865	−	0.535679i	−0.0541196	−	0.0175845i
$929$	19.8163			0.650152			0.325076	−	0.945688i	$-0.394610\pi$
$929$	19.8163			0.650152			0.325076	+	0.945688i	$0.394610\pi$
$930$		0			0
$931$	−39.3010			−1.28804
$932$	1.27062	+	0.412850i	0.0416206	+	0.0135233i
$933$	−0.179076	+	0.0581852i	−0.00586267	+	0.00190490i
$934$	18.4183	+	13.3816i	0.602664	+	0.437861i
$935$		0			0
$936$	38.7382			1.26620
$937$	25.1647	−	34.6362i	0.822094	−	1.13152i	−0.167249	−	0.985915i	$-0.553488\pi$
$937$	25.1647	−	34.6362i	0.822094	−	1.13152i	0.989343	−	0.145601i	$-0.0465116\pi$
$938$	0.303623	+	0.417902i	0.00991366	+	0.0136450i
$939$	−24.7980	+	18.0168i	−0.809251	+	0.587955i
$940$		0			0
$941$	−20.5084	−	14.9002i	−0.668554	−	0.485733i	0.200987	−	0.979594i	$-0.435585\pi$
$941$	−20.5084	−	14.9002i	−0.668554	−	0.485733i	−0.869541	+	0.493861i	$0.835585\pi$
$942$	33.8397	+	10.9952i	1.10256	+	0.358242i
$943$	−8.89106	+	2.88888i	−0.289533	+	0.0940749i
$944$	−29.3856	+	21.3499i	−0.956419	+	0.694879i
$945$		0			0
$946$	22.4932	+	69.2270i	0.731318	+	2.25076i
$947$	18.0761	+	24.8796i	0.587395	+	0.808480i	0.994482	−	0.104910i	$-0.0334554\pi$
$947$	18.0761	+	24.8796i	0.587395	+	0.808480i	−0.407087	+	0.913389i	$0.633455\pi$
$948$	4.69120	−	1.52426i	0.152363	−	0.0495057i
$949$	−3.74378	+	11.5222i	−0.121528	+	0.374026i
$950$		0			0
$951$	6.37932	−	19.6335i	0.206864	−	0.636661i
$952$	3.62307	+	4.98673i	0.117424	+	0.161621i
$953$	−19.1384	−	26.3418i	−0.619955	−	0.853294i	0.377395	−	0.926052i	$-0.376820\pi$
$953$	−19.1384	−	26.3418i	−0.619955	−	0.853294i	−0.997350	+	0.0727581i	$0.976820\pi$
$954$	58.8815	+	42.7799i	1.90636	+	1.38505i
$955$		0			0
$956$	−1.75845			−0.0568725
$957$	21.6149	−	29.7504i	0.698712	−	0.961695i
$958$	5.39465	−	1.75283i	0.174293	−	0.0566313i
$959$	−3.23353	+	9.95178i	−0.104416	+	0.321360i
$960$		0			0
$961$	30.5420	−	5.30923i	0.985225	−	0.171265i
$962$		−	21.0311i		−	0.678071i
$963$	84.5159	+	27.4609i	2.72349	+	0.884915i
$964$	0.799908	+	2.46186i	0.0257633	+	0.0792913i
$965$		0			0
$966$	−14.5026			−0.466613
$967$		−	29.4715i		−	0.947741i	−0.880595	−	0.473870i	$-0.842857\pi$
$967$		−	29.4715i		−	0.947741i	0.880595	−	0.473870i	$-0.157143\pi$
$968$	35.1671	−	48.4033i	1.13031	−	1.55574i
$969$	−37.4048	+	27.1762i	−1.20161	+	0.873024i
$970$		0			0
$971$	−15.8132	+	48.6679i	−0.507468	+	1.56183i	0.289113	+	0.957295i	$0.406640\pi$
$971$	−15.8132	+	48.6679i	−0.507468	+	1.56183i	−0.796581	+	0.604532i	$0.793360\pi$
$972$	1.72991	−	2.38101i	0.0554868	−	0.0763710i
$973$	8.21722	+	2.66994i	0.263432	+	0.0855943i
$974$	−2.73549	−	8.41896i	−0.0876506	−	0.269761i
$975$		0			0
$976$	7.75790	+	23.8764i	0.248324	+	0.764264i
$977$	−1.34541	+	0.437149i	−0.0430433	+	0.0139856i	−0.330460	−	0.943820i	$-0.607204\pi$
$977$	−1.34541	+	0.437149i	−0.0430433	+	0.0139856i	0.287416	+	0.957806i	$0.407204\pi$
$978$	57.5664	+	79.2333i	1.84077	+	2.53360i
$979$	−3.99713	−	12.3019i	−0.127749	−	0.393170i
$980$		0			0
$981$	−5.88697	−	4.27713i	−0.187956	−	0.136558i
$982$	33.0590	+	10.7415i	1.05495	+	0.342775i
$983$	0.348286	+	0.479375i	0.0111086	+	0.0152897i	0.814535	−	0.580114i	$-0.196992\pi$
$983$	0.348286	+	0.479375i	0.0111086	+	0.0152897i	−0.803427	+	0.595404i	$0.796992\pi$
$984$	−18.8509	+	13.6960i	−0.600946	+	0.436613i
$985$		0			0
$986$	6.52081			0.207665
$987$		−	12.0415i		−	0.383285i
$988$	−1.06003	+	1.45900i	−0.0337239	+	0.0464170i
$989$	10.8789	+	33.4819i	0.345930	+	1.06466i
$990$		0			0
$991$	−61.1371			−1.94208			−0.971042	−	0.238909i	$-0.923210\pi$
$991$	−61.1371			−1.94208			−0.971042	+	0.238909i	$0.923210\pi$
$992$	0.398503	+	4.61925i	0.0126525	+	0.146661i
$993$		−	30.7882i		−	0.977036i
$994$	2.23235	−	6.87046i	0.0708058	−	0.217918i
$995$		0			0
$996$	3.77452	+	2.74235i	0.119600	+	0.0868947i
$997$			21.4914i			0.680640i	0.940310	+	0.340320i	$0.110535\pi$
$997$			21.4914i			0.680640i	−0.940310	+	0.340320i	$0.889465\pi$
$998$		−	12.5077i		−	0.395924i
$999$	−80.4452	−	58.4468i	−2.54517	−	1.84918i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.bf.c.349.9		48
5.2	odd	4		775.2.k.d.101.2		24
5.3	odd	4		155.2.h.b.101.5	yes	24
5.4	even	2	inner	775.2.bf.c.349.4		48
31.4	even	5	inner	775.2.bf.c.624.4		48
155.4	even	10	inner	775.2.bf.c.624.9		48
155.33	odd	20		4805.2.a.u.1.9		12
155.97	odd	20		775.2.k.d.376.2		24
155.128	odd	20		155.2.h.b.66.5	✓	24
155.153	even	20		4805.2.a.v.1.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.h.b.66.5	✓	24	155.128	odd	20
155.2.h.b.101.5	yes	24	5.3	odd	4
775.2.k.d.101.2		24	5.2	odd	4
775.2.k.d.376.2		24	155.97	odd	20
775.2.bf.c.349.4		48	5.4	even	2	inner
775.2.bf.c.349.9		48	1.1	even	1	trivial
775.2.bf.c.624.4		48	31.4	even	5	inner
775.2.bf.c.624.9		48	155.4	even	10	inner
4805.2.a.u.1.9		12	155.33	odd	20
4805.2.a.v.1.9		12	155.153	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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.bf (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.29445 + 0.420591i) q^{2} +(-2.99486 + 0.973089i) q^{3} +(-0.119342 - 0.0867070i) q^{4} -4.28595 q^{6} +(0.538593 - 0.741309i) q^{7} +(-1.71804 - 2.36467i) q^{8} +(5.59523 - 4.06517i) q^{9} +O(q^{10})\)	\(q+(1.29445 + 0.420591i) q^{2} +(-2.99486 + 0.973089i) q^{3} +(-0.119342 - 0.0867070i) q^{4} -4.28595 q^{6} +(0.538593 - 0.741309i) q^{7} +(-1.71804 - 2.36467i) q^{8} +(5.59523 - 4.06517i) q^{9} +(4.53839 + 3.29733i) q^{11} +(0.441786 + 0.143545i) q^{12} +(-1.82252 + 0.592172i) q^{13} +(1.00897 - 0.733057i) q^{14} +(-1.13817 - 3.50294i) q^{16} +(-1.35276 - 1.86192i) q^{17} +(8.95250 - 2.90884i) q^{18} +(-1.97142 + 6.06741i) q^{19} +(-0.891650 + 2.74422i) q^{21} +(4.48787 + 6.17702i) q^{22} +(2.17057 + 2.98754i) q^{23} +(7.44631 + 5.41006i) q^{24} -2.60821 q^{26} +(-7.24839 + 9.97655i) q^{27} +(-0.128554 + 0.0417696i) q^{28} +(-0.643286 + 1.97983i) q^{29} +(5.54716 - 0.478553i) q^{31} +0.832724i q^{32} +(-16.8004 - 5.45879i) q^{33} +(-0.967971 - 2.97911i) q^{34} -1.02023 q^{36} +8.06343i q^{37} +(-5.10379 + 7.02476i) q^{38} +(4.88195 - 3.54694i) q^{39} +(-0.782302 + 2.40768i) q^{41} +(-2.30838 + 3.17722i) q^{42} +(9.06681 + 2.94598i) q^{43} +(-0.255718 - 0.787020i) q^{44} +(1.55316 + 4.78013i) q^{46} +(-3.96894 + 1.28959i) q^{47} +(6.81735 + 9.38327i) q^{48} +(1.90366 + 5.85887i) q^{49} +(5.86314 + 4.25982i) q^{51} +(0.268848 + 0.0873542i) q^{52} +(4.54466 + 6.25519i) q^{53} +(-13.5787 + 9.86549i) q^{54} -2.67828 q^{56} -20.0894i q^{57} +(-1.66540 + 2.29222i) q^{58} +(-3.04742 - 9.37899i) q^{59} -6.81609 q^{61} +(7.38177 + 1.71362i) q^{62} -6.33727i q^{63} +(-2.62658 + 8.08380i) q^{64} +(-19.4513 - 14.1322i) q^{66} +0.414188i q^{67} +0.339499i q^{68} +(-9.40770 - 6.83509i) q^{69} +(4.68617 - 3.40470i) q^{71} +(-19.2256 - 6.24678i) q^{72} +(3.71605 - 5.11470i) q^{73} +(-3.39140 + 10.4377i) q^{74} +(0.761360 - 0.553160i) q^{76} +(4.88869 - 1.58843i) q^{77} +(7.81123 - 2.53802i) q^{78} +(8.59071 - 6.24151i) q^{79} +(5.58827 - 17.1989i) q^{81} +(-2.02529 + 2.78758i) q^{82} +(9.55223 + 3.10371i) q^{83} +(0.344354 - 0.250188i) q^{84} +(10.4974 + 7.62683i) q^{86} -6.55529i q^{87} -16.3967i q^{88} +(-1.86543 - 1.35532i) q^{89} +(-0.542612 + 1.66999i) q^{91} -0.544743i q^{92} +(-16.1473 + 6.83108i) q^{93} -5.67996 q^{94} +(-0.810314 - 2.49389i) q^{96} +(6.67401 - 9.18599i) q^{97} +8.38465i q^{98} +38.7976 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{4} - 32 q^{6} + 12 q^{9}+O(q^{10}) \) 48 * q + 12 * q^4 - 32 * q^6 + 12 * q^9	\( 48 q + 12 q^{4} - 32 q^{6} + 12 q^{9} + 2 q^{11} - 12 q^{14} - 48 q^{16} - 4 q^{19} - 20 q^{21} + 64 q^{24} + 44 q^{26} - 30 q^{29} + 12 q^{31} + 40 q^{34} - 116 q^{36} + 20 q^{39} - 48 q^{41} - 82 q^{44} + 96 q^{46} + 46 q^{49} + 52 q^{51} - 22 q^{54} - 96 q^{56} - 20 q^{59} - 80 q^{61} - 18 q^{64} - 4 q^{66} - 128 q^{69} - 14 q^{71} + 2 q^{74} + 86 q^{76} - 62 q^{79} + 68 q^{81} - 226 q^{84} - 44 q^{86} - 26 q^{89} + 108 q^{91} + 20 q^{94} + 202 q^{96} + 340 q^{99}+O(q^{100}) \) 48 * q + 12 * q^4 - 32 * q^6 + 12 * q^9 + 2 * q^11 - 12 * q^14 - 48 * q^16 - 4 * q^19 - 20 * q^21 + 64 * q^24 + 44 * q^26 - 30 * q^29 + 12 * q^31 + 40 * q^34 - 116 * q^36 + 20 * q^39 - 48 * q^41 - 82 * q^44 + 96 * q^46 + 46 * q^49 + 52 * q^51 - 22 * q^54 - 96 * q^56 - 20 * q^59 - 80 * q^61 - 18 * q^64 - 4 * q^66 - 128 * q^69 - 14 * q^71 + 2 * q^74 + 86 * q^76 - 62 * q^79 + 68 * q^81 - 226 * q^84 - 44 * q^86 - 26 * q^89 + 108 * q^91 + 20 * q^94 + 202 * q^96 + 340 * q^99

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