LMFDB - Embedded newform 525.3.c.b.176.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,3,Mod(176,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("525.176");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	525.c (of order $2$, degree $1$, 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:	$14.3052138789$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 46x^{14} + 823x^{12} + 7252x^{10} + 32831x^{8} + 71486x^{6} + 60809x^{4} + 15680x^{2} + 576 $ x^16 + 46x^14 + 823x^12 + 7252x^10 + 32831x^8 + 71486x^6 + 60809x^4 + 15680*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			176.5
Root			$-2.02253i$ of defining polynomial
Character	$\chi$	$=$	525.176
Dual form			525.3.c.b.176.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.02253i q^{2} +(-2.91626 - 0.703870i) q^{3} -0.0906451 q^{4} +(-1.42360 + 5.89823i) q^{6} -2.64575 q^{7} -7.90680i q^{8} +(8.00914 + 4.10533i) q^{9} +O(q^{10})$	\(q-2.02253i q^{2} +(-2.91626 - 0.703870i) q^{3} -0.0906451 q^{4} +(-1.42360 + 5.89823i) q^{6} -2.64575 q^{7} -7.90680i q^{8} +(8.00914 + 4.10533i) q^{9} -11.6583i q^{11} +(0.264344 + 0.0638023i) q^{12} +20.3660 q^{13} +5.35112i q^{14} -16.3544 q^{16} -9.92200i q^{17} +(8.30318 - 16.1988i) q^{18} -4.91979 q^{19} +(7.71570 + 1.86226i) q^{21} -23.5793 q^{22} +11.4646i q^{23} +(-5.56536 + 23.0583i) q^{24} -41.1909i q^{26} +(-20.4671 - 17.6096i) q^{27} +0.239824 q^{28} -37.5101i q^{29} -21.2282 q^{31} +1.45004i q^{32} +(-8.20592 + 33.9986i) q^{33} -20.0676 q^{34} +(-0.725989 - 0.372128i) q^{36} -57.1939 q^{37} +9.95044i q^{38} +(-59.3924 - 14.3350i) q^{39} -20.2428i q^{41} +(3.76649 - 15.6053i) q^{42} -5.88954 q^{43} +1.05677i q^{44} +23.1876 q^{46} +74.5051i q^{47} +(47.6936 + 11.5113i) q^{48} +7.00000 q^{49} +(-6.98379 + 28.9351i) q^{51} -1.84607 q^{52} -88.2001i q^{53} +(-35.6160 + 41.3954i) q^{54} +20.9194i q^{56} +(14.3474 + 3.46289i) q^{57} -75.8655 q^{58} +71.6589i q^{59} -26.0462 q^{61} +42.9347i q^{62} +(-21.1902 - 10.8617i) q^{63} -62.4847 q^{64} +(68.7633 + 16.5967i) q^{66} -76.4691 q^{67} +0.899380i q^{68} +(8.06960 - 33.4338i) q^{69} +47.1551i q^{71} +(32.4601 - 63.3267i) q^{72} +135.859 q^{73} +115.677i q^{74} +0.445954 q^{76} +30.8449i q^{77} +(-28.9930 + 120.123i) q^{78} -98.2712 q^{79} +(47.2925 + 65.7603i) q^{81} -40.9418 q^{82} -55.8693i q^{83} +(-0.699390 - 0.168805i) q^{84} +11.9118i q^{86} +(-26.4022 + 109.389i) q^{87} -92.1798 q^{88} -105.666i q^{89} -53.8833 q^{91} -1.03921i q^{92} +(61.9069 + 14.9419i) q^{93} +150.689 q^{94} +(1.02064 - 4.22870i) q^{96} -61.8996 q^{97} -14.1577i q^{98} +(47.8612 - 93.3728i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 - 28 * q^4 - 28 * q^6 + 22 * q^9	$ 16 q - 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9} - 12 q^{12} + 92 q^{16} + 52 q^{18} - 16 q^{19} - 14 q^{21} - 16 q^{22} + 128 q^{24} + 148 q^{27} - 112 q^{28} - 72 q^{31} + 4 q^{33} - 176 q^{34} - 76 q^{36} + 40 q^{37} + 90 q^{39} - 280 q^{43} + 72 q^{46} + 172 q^{48} + 112 q^{49} + 38 q^{51} + 88 q^{52} + 208 q^{54} + 36 q^{57} + 24 q^{58} - 56 q^{61} + 56 q^{63} - 44 q^{64} - 260 q^{66} + 120 q^{67} + 60 q^{69} - 376 q^{72} + 208 q^{73} + 144 q^{76} + 228 q^{78} - 204 q^{79} + 458 q^{81} + 384 q^{82} - 84 q^{84} + 324 q^{87} - 168 q^{88} - 28 q^{91} - 108 q^{93} + 984 q^{94} + 40 q^{96} - 728 q^{97} - 166 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 - 28 * q^4 - 28 * q^6 + 22 * q^9 - 12 * q^12 + 92 * q^16 + 52 * q^18 - 16 * q^19 - 14 * q^21 - 16 * q^22 + 128 * q^24 + 148 * q^27 - 112 * q^28 - 72 * q^31 + 4 * q^33 - 176 * q^34 - 76 * q^36 + 40 * q^37 + 90 * q^39 - 280 * q^43 + 72 * q^46 + 172 * q^48 + 112 * q^49 + 38 * q^51 + 88 * q^52 + 208 * q^54 + 36 * q^57 + 24 * q^58 - 56 * q^61 + 56 * q^63 - 44 * q^64 - 260 * q^66 + 120 * q^67 + 60 * q^69 - 376 * q^72 + 208 * q^73 + 144 * q^76 + 228 * q^78 - 204 * q^79 + 458 * q^81 + 384 * q^82 - 84 * q^84 + 324 * q^87 - 168 * q^88 - 28 * q^91 - 108 * q^93 + 984 * q^94 + 40 * q^96 - 728 * q^97 - 166 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$		−	2.02253i		−	1.01127i	−0.862748	−	0.505634i	$-0.831259\pi$
$2$		−	2.02253i		−	1.01127i	0.862748	−	0.505634i	$-0.168741\pi$
$3$	−2.91626	−	0.703870i	−0.972086	−	0.234623i
$3$	−2.91626	−	0.703870i	−0.972086	−	0.234623i
$4$	−0.0906451			−0.0226613
$5$		0			0
$5$		0			0
$6$	−1.42360	+	5.89823i	−0.237267	+	0.983039i
$7$	−2.64575			−0.377964
$7$	−2.64575			−0.377964
$8$		−	7.90680i		−	0.988351i
$9$	8.00914	+	4.10533i	0.889904	+	0.456148i
$10$		0			0
$11$		−	11.6583i		−	1.05984i	−0.848046	−	0.529922i	$-0.822221\pi$
$11$		−	11.6583i		−	1.05984i	0.848046	−	0.529922i	$-0.177779\pi$
$12$	0.264344	+	0.0638023i	0.0220287	+	0.00531686i
$13$	20.3660			1.56661			0.783306	−	0.621636i	$-0.213532\pi$
$13$	20.3660			1.56661			0.783306	+	0.621636i	$0.213532\pi$
$14$			5.35112i			0.382223i
$15$		0			0
$16$	−16.3544			−1.02215
$17$		−	9.92200i		−	0.583647i	−0.956472	−	0.291824i	$-0.905738\pi$
$17$		−	9.92200i		−	0.583647i	0.956472	−	0.291824i	$-0.0942620\pi$
$18$	8.30318	−	16.1988i	0.461288	−	0.899931i
$19$	−4.91979			−0.258936			−0.129468	−	0.991584i	$-0.541327\pi$
$19$	−4.91979			−0.258936			−0.129468	+	0.991584i	$0.541327\pi$
$20$		0			0
$21$	7.71570	+	1.86226i	0.367414	+	0.0886792i
$22$	−23.5793			−1.07179
$23$			11.4646i			0.498462i	0.968444	+	0.249231i	$0.0801779\pi$
$23$			11.4646i			0.498462i	−0.968444	+	0.249231i	$0.919822\pi$
$24$	−5.56536	+	23.0583i	−0.231890	+	0.960762i
$25$		0			0
$26$		−	41.1909i		−	1.58426i
$27$	−20.4671	−	17.6096i	−0.758041	−	0.652207i
$28$	0.239824			0.00856515
$29$		−	37.5101i		−	1.29345i	−0.762722	−	0.646726i	$-0.776138\pi$
$29$		−	37.5101i		−	1.29345i	0.762722	−	0.646726i	$-0.223862\pi$
$30$		0			0
$31$	−21.2282			−0.684780			−0.342390	−	0.939558i	$-0.611236\pi$
$31$	−21.2282			−0.684780			−0.342390	+	0.939558i	$0.611236\pi$
$32$			1.45004i			0.0453139i
$33$	−8.20592	+	33.9986i	−0.248664	+	1.03026i
$34$	−20.0676			−0.590223
$35$		0			0
$36$	−0.725989	−	0.372128i	−0.0201663	−	0.0103369i
$37$	−57.1939			−1.54578			−0.772890	−	0.634540i	$-0.781190\pi$
$37$	−57.1939			−1.54578			−0.772890	+	0.634540i	$0.781190\pi$
$38$			9.95044i			0.261854i
$39$	−59.3924	−	14.3350i	−1.52288	−	0.367564i
$40$		0			0
$41$		−	20.2428i		−	0.493728i	−0.969050	−	0.246864i	$-0.920600\pi$
$41$		−	20.2428i		−	0.493728i	0.969050	−	0.246864i	$-0.0794001\pi$
$42$	3.76649	−	15.6053i	0.0896784	−	0.371554i
$43$	−5.88954			−0.136966			−0.0684830	−	0.997652i	$-0.521816\pi$
$43$	−5.88954			−0.136966			−0.0684830	+	0.997652i	$0.521816\pi$
$44$			1.05677i			0.0240174i
$45$		0			0
$46$	23.1876			0.504078
$47$			74.5051i			1.58521i	0.609733	+	0.792607i	$0.291277\pi$
$47$			74.5051i			1.58521i	−0.609733	+	0.792607i	$0.708723\pi$
$48$	47.6936	+	11.5113i	0.993616	+	0.239820i
$49$	7.00000			0.142857
$50$		0			0
$51$	−6.98379	+	28.9351i	−0.136937	+	0.567355i
$52$	−1.84607			−0.0355014
$53$		−	88.2001i		−	1.66415i	−0.554661	−	0.832077i	$-0.687152\pi$
$53$		−	88.2001i		−	1.66415i	0.554661	−	0.832077i	$-0.312848\pi$
$54$	−35.6160	+	41.3954i	−0.659556	+	0.766582i
$55$		0			0
$56$			20.9194i			0.373561i
$57$	14.3474	+	3.46289i	0.251708	+	0.0607524i
$58$	−75.8655			−1.30803
$59$			71.6589i			1.21456i	0.794489	+	0.607279i	$0.207739\pi$
$59$			71.6589i			1.21456i	−0.794489	+	0.607279i	$0.792261\pi$
$60$		0			0
$61$	−26.0462			−0.426987			−0.213494	−	0.976944i	$-0.568484\pi$
$61$	−26.0462			−0.426987			−0.213494	+	0.976944i	$0.568484\pi$
$62$			42.9347i			0.692496i
$63$	−21.1902	−	10.8617i	−0.336352	−	0.172408i
$64$	−62.4847			−0.976323
$65$		0			0
$66$	68.7633	+	16.5967i	1.04187	+	0.251466i
$67$	−76.4691			−1.14133			−0.570665	−	0.821183i	$-0.693315\pi$
$67$	−76.4691			−1.14133			−0.570665	+	0.821183i	$0.693315\pi$
$68$			0.899380i			0.0132262i
$69$	8.06960	−	33.4338i	0.116951	−	0.484548i
$70$		0			0
$71$			47.1551i			0.664156i	0.943252	+	0.332078i	$0.107750\pi$
$71$			47.1551i			0.664156i	−0.943252	+	0.332078i	$0.892250\pi$
$72$	32.4601	−	63.3267i	0.450834	−	0.879537i
$73$	135.859			1.86109			0.930544	−	0.366179i	$-0.119334\pi$
$73$	135.859			1.86109			0.930544	+	0.366179i	$0.119334\pi$
$74$			115.677i			1.56320i
$75$		0			0
$76$	0.445954			0.00586782
$77$			30.8449i			0.400584i
$78$	−28.9930	+	120.123i	−0.371705	+	1.54004i
$79$	−98.2712			−1.24394			−0.621969	−	0.783041i	$-0.713667\pi$
$79$	−98.2712			−1.24394			−0.621969	+	0.783041i	$0.713667\pi$
$80$		0			0
$81$	47.2925	+	65.7603i	0.583858	+	0.811856i
$82$	−40.9418			−0.499291
$83$		−	55.8693i		−	0.673124i	−0.941661	−	0.336562i	$-0.890736\pi$
$83$		−	55.8693i		−	0.673124i	0.941661	−	0.336562i	$-0.109264\pi$
$84$	−0.699390	−	0.168805i	−0.00832607	−	0.00200958i
$85$		0			0
$86$			11.9118i			0.138509i
$87$	−26.4022	+	109.389i	−0.303474	+	1.25735i
$88$	−92.1798			−1.04750
$89$		−	105.666i		−	1.18726i	−0.804740	−	0.593628i	$-0.797695\pi$
$89$		−	105.666i		−	1.18726i	0.804740	−	0.593628i	$-0.202305\pi$
$90$		0			0
$91$	−53.8833			−0.592124
$92$		−	1.03921i		−	0.0112958i
$93$	61.9069	+	14.9419i	0.665666	+	0.160665i
$94$	150.689			1.60308
$95$		0			0
$96$	1.02064	−	4.22870i	0.0106317	−	0.0440490i
$97$	−61.8996			−0.638141			−0.319070	−	0.947731i	$-0.603371\pi$
$97$	−61.8996			−0.638141			−0.319070	+	0.947731i	$0.603371\pi$
$98$		−	14.1577i		−	0.144467i
$99$	47.8612	−	93.3728i	0.483446	−	0.943160i
$100$		0			0
$101$		−	11.1708i		−	0.110602i	−0.998470	−	0.0553011i	$-0.982388\pi$
$101$		−	11.1708i		−	0.110602i	0.998470	−	0.0553011i	$-0.0176119\pi$
$102$	58.5223	+	14.1250i	0.573748	+	0.138480i
$103$	−38.6092			−0.374846			−0.187423	−	0.982279i	$-0.560014\pi$
$103$	−38.6092			−0.374846			−0.187423	+	0.982279i	$0.560014\pi$
$104$		−	161.030i		−	1.54836i
$105$		0			0
$106$	−178.388			−1.68290
$107$		−	196.812i		−	1.83936i	−0.392668	−	0.919680i	$-0.628448\pi$
$107$		−	196.812i		−	1.83936i	0.392668	−	0.919680i	$-0.371552\pi$
$108$	1.85524	+	1.59622i	0.0171782	+	0.0147798i
$109$	47.3856			0.434730			0.217365	−	0.976090i	$-0.430254\pi$
$109$	47.3856			0.434730			0.217365	+	0.976090i	$0.430254\pi$
$110$		0			0
$111$	166.792	+	40.2570i	1.50263	+	0.362676i
$112$	43.2696			0.386336
$113$		−	64.2642i		−	0.568710i	−0.958719	−	0.284355i	$-0.908221\pi$
$113$		−	64.2642i		−	0.568710i	0.958719	−	0.284355i	$-0.0917794\pi$
$114$	7.00381	−	29.0181i	0.0614369	−	0.254544i
$115$		0			0
$116$			3.40011i			0.0293113i
$117$	163.114	+	83.6090i	1.39413	+	0.714607i
$118$	144.933			1.22824
$119$			26.2511i			0.220598i
$120$		0			0
$121$	−14.9157			−0.123271
$122$			52.6794i			0.431798i
$123$	−14.2483	+	59.0334i	−0.115840	+	0.479946i
$124$	1.92423			0.0155180
$125$		0			0
$126$	−21.9681	+	42.8579i	−0.174350	+	0.340142i
$127$	88.6515			0.698044			0.349022	−	0.937115i	$-0.386514\pi$
$127$	88.6515			0.698044			0.349022	+	0.937115i	$0.386514\pi$
$128$			132.178i			1.03264i
$129$	17.1754	+	4.14547i	0.133143	+	0.0321354i
$130$		0			0
$131$			116.606i			0.890121i	0.895501	+	0.445060i	$0.146818\pi$
$131$			116.606i			0.890121i	−0.895501	+	0.445060i	$0.853182\pi$
$132$	0.743826	−	3.08180i	0.00563504	−	0.0233470i
$133$	13.0165			0.0978686
$134$			154.661i			1.15419i
$135$		0			0
$136$	−78.4513			−0.576848
$137$			80.7032i			0.589075i	0.955640	+	0.294537i	$0.0951655\pi$
$137$			80.7032i			0.589075i	−0.955640	+	0.294537i	$0.904834\pi$
$138$	−67.6211	−	16.3211i	−0.490008	−	0.118268i
$139$	194.771			1.40123			0.700616	−	0.713538i	$-0.252909\pi$
$139$	194.771			1.40123			0.700616	+	0.713538i	$0.252909\pi$
$140$		0			0
$141$	52.4418	−	217.276i	0.371928	−	1.54097i
$142$	95.3727			0.671639
$143$		−	237.432i		−	1.66037i
$144$	−130.984	−	67.1401i	−0.909613	−	0.466251i
$145$		0			0
$146$		−	274.780i		−	1.88206i
$147$	−20.4138	−	4.92709i	−0.138869	−	0.0335176i
$148$	5.18434			0.0350293
$149$		−	251.636i		−	1.68883i	−0.535690	−	0.844415i	$-0.679948\pi$
$149$		−	251.636i		−	1.68883i	0.535690	−	0.844415i	$-0.320052\pi$
$150$		0			0
$151$	138.915			0.919969			0.459984	−	0.887927i	$-0.347855\pi$
$151$	138.915			0.919969			0.459984	+	0.887927i	$0.347855\pi$
$152$			38.8998i			0.255920i
$153$	40.7331	−	79.4667i	0.266229	−	0.519390i
$154$	62.3849			0.405097
$155$		0			0
$156$	5.38363	+	1.29940i	0.0345104	+	0.00832946i
$157$	25.8481			0.164638			0.0823189	−	0.996606i	$-0.473767\pi$
$157$	25.8481			0.164638			0.0823189	+	0.996606i	$0.473767\pi$
$158$			198.757i			1.25795i
$159$	−62.0814	+	257.214i	−0.390449	+	1.61770i
$160$		0			0
$161$		−	30.3326i		−	0.188401i
$162$	133.003	−	95.6507i	0.821003	−	0.590436i
$163$	−94.9187			−0.582323			−0.291162	−	0.956674i	$-0.594042\pi$
$163$	−94.9187			−0.582323			−0.291162	+	0.956674i	$0.594042\pi$
$164$			1.83491i			0.0111885i
$165$		0			0
$166$	−112.998			−0.680708
$167$		−	325.029i		−	1.94628i	−0.230206	−	0.973142i	$-0.573940\pi$
$167$		−	325.029i		−	1.94628i	0.230206	−	0.973142i	$-0.426060\pi$
$168$	14.7246	−	61.0065i	0.0876462	−	0.363134i
$169$	245.772			1.45427
$170$		0			0
$171$	−39.4032	−	20.1974i	−0.230428	−	0.118113i
$172$	0.533857			0.00310382
$173$			97.5515i			0.563881i	0.959432	+	0.281941i	$0.0909781\pi$
$173$			97.5515i			0.563881i	−0.959432	+	0.281941i	$0.909022\pi$
$174$	221.244	+	53.3994i	1.27151	+	0.306893i
$175$		0			0
$176$			190.664i			1.08332i
$177$	50.4385	−	208.976i	0.284963	−	1.18065i
$178$	−213.713			−1.20063
$179$			172.813i			0.965435i	0.875776	+	0.482718i	$0.160350\pi$
$179$			172.813i			0.965435i	−0.875776	+	0.482718i	$0.839650\pi$
$180$		0			0
$181$	−8.15596			−0.0450606			−0.0225303	−	0.999746i	$-0.507172\pi$
$181$	−8.15596			−0.0450606			−0.0225303	+	0.999746i	$0.507172\pi$
$182$			108.981i			0.598795i
$183$	75.9575	+	18.3331i	0.415069	+	0.100181i
$184$	90.6486			0.492655
$185$		0			0
$186$	30.2205	−	125.209i	0.162476	−	0.673166i
$187$	−115.674			−0.618575
$188$		−	6.75352i		−	0.0359230i
$189$	54.1508	+	46.5906i	0.286512	+	0.246511i
$190$		0			0
$191$		−	119.244i		−	0.624313i	−0.950031	−	0.312156i	$-0.898949\pi$
$191$		−	119.244i		−	0.624313i	0.950031	−	0.312156i	$-0.101051\pi$
$192$	182.222	+	43.9811i	0.949071	+	0.229068i
$193$	−137.385			−0.711838			−0.355919	−	0.934517i	$-0.615832\pi$
$193$	−137.385			−0.711838			−0.355919	+	0.934517i	$0.615832\pi$
$194$			125.194i			0.645331i
$195$		0			0
$196$	−0.634515			−0.00323732
$197$		−	202.161i		−	1.02620i	−0.858330	−	0.513098i	$-0.828498\pi$
$197$		−	202.161i		−	1.02620i	0.858330	−	0.513098i	$-0.171502\pi$
$198$	−188.850	−	96.8008i	−0.953787	−	0.488893i
$199$	59.0561			0.296764			0.148382	−	0.988930i	$-0.452593\pi$
$199$	59.0561			0.296764			0.148382	+	0.988930i	$0.452593\pi$
$200$		0			0
$201$	223.004	+	53.8243i	1.10947	+	0.267783i
$202$	−22.5934			−0.111848
$203$			99.2425i			0.488879i
$204$	0.633046	−	2.62283i	0.00310317	−	0.0128570i
$205$		0			0
$206$			78.0884i			0.379070i
$207$	−47.0661	+	91.8218i	−0.227373	+	0.443583i
$208$	−333.072			−1.60131
$209$			57.3563i			0.274432i
$210$		0			0
$211$	13.5306			0.0641261			0.0320630	−	0.999486i	$-0.489792\pi$
$211$	13.5306			0.0641261			0.0320630	+	0.999486i	$0.489792\pi$
$212$			7.99490i			0.0377118i
$213$	33.1910	−	137.516i	0.155826	−	0.645617i
$214$	−398.058			−1.86008
$215$		0			0
$216$	−139.236	+	161.829i	−0.644610	+	0.749210i
$217$	56.1645			0.258823
$218$		−	95.8389i		−	0.439628i
$219$	−396.201	−	95.6274i	−1.80914	−	0.436655i
$220$		0			0
$221$		−	202.071i		−	0.914349i
$222$	81.4212	−	337.343i	0.366762	−	1.51956i
$223$	342.401			1.53543			0.767715	−	0.640792i	$-0.221394\pi$
$223$	342.401			1.53543			0.767715	+	0.640792i	$0.221394\pi$
$224$		−	3.83645i		−	0.0171270i
$225$		0			0
$226$	−129.977			−0.575117
$227$			15.4878i			0.0682283i	0.999418	+	0.0341141i	$0.0108610\pi$
$227$			15.4878i			0.0682283i	−0.999418	+	0.0341141i	$0.989139\pi$
$228$	−1.30052	−	0.313894i	−0.00570403	−	0.00137673i
$229$	−178.803			−0.780798			−0.390399	−	0.920646i	$-0.627663\pi$
$229$	−178.803			−0.780798			−0.390399	+	0.920646i	$0.627663\pi$
$230$		0			0
$231$	21.7108	−	89.9518i	0.0939862	−	0.389402i
$232$	−296.585			−1.27838
$233$			415.344i			1.78259i	0.453422	+	0.891296i	$0.350203\pi$
$233$			415.344i			1.78259i	−0.453422	+	0.891296i	$0.649797\pi$
$234$	169.102	−	329.903i	0.722659	−	1.40984i
$235$		0			0
$236$		−	6.49552i		−	0.0275234i
$237$	286.584	+	69.1701i	1.20922	+	0.291857i
$238$	53.0938			0.223083
$239$		−	204.961i		−	0.857577i	−0.903405	−	0.428788i	$-0.858941\pi$
$239$		−	204.961i		−	0.857577i	0.903405	−	0.428788i	$-0.141059\pi$
$240$		0			0
$241$	−75.9054			−0.314960			−0.157480	−	0.987522i	$-0.550337\pi$
$241$	−75.9054			−0.314960			−0.157480	+	0.987522i	$0.550337\pi$
$242$			30.1676i			0.124659i
$243$	−91.6305	−	225.062i	−0.377080	−	0.926181i
$244$	2.36096			0.00967607
$245$		0			0
$246$	119.397	+	28.8177i	0.485354	+	0.117145i
$247$	−100.196			−0.405653
$248$			167.847i			0.676803i
$249$	−39.3247	+	162.929i	−0.157930	+	0.654335i
$250$		0			0
$251$			25.9960i			0.103570i	0.998658	+	0.0517849i	$0.0164910\pi$
$251$			25.9960i			0.103570i	−0.998658	+	0.0517849i	$0.983509\pi$
$252$	1.92079	+	0.984558i	0.00762216	+	0.00390698i
$253$	133.658			0.528292
$254$		−	179.301i		−	0.705908i
$255$		0			0
$256$	17.3950			0.0679491
$257$			244.092i			0.949775i	0.880047	+	0.474887i	$0.157511\pi$
$257$			244.092i			0.949775i	−0.880047	+	0.474887i	$0.842489\pi$
$258$	8.38435	−	34.7379i	0.0324975	−	0.134643i
$259$	151.321			0.584250
$260$		0			0
$261$	153.992	−	300.424i	0.590006	−	1.15105i
$262$	235.839			0.900150
$263$			98.5645i			0.374770i	0.982287	+	0.187385i	$0.0600012\pi$
$263$			98.5645i			0.374770i	−0.982287	+	0.187385i	$0.939999\pi$
$264$	268.820	+	64.8826i	1.01826	+	0.245767i
$265$		0			0
$266$		−	26.3264i		−	0.0989714i
$267$	−74.3749	+	308.149i	−0.278558	+	1.15412i
$268$	6.93155			0.0258640
$269$			32.3831i			0.120383i	0.998187	+	0.0601917i	$0.0191712\pi$
$269$			32.3831i			0.120383i	−0.998187	+	0.0601917i	$0.980829\pi$
$270$		0			0
$271$	251.624			0.928501			0.464251	−	0.885704i	$-0.346324\pi$
$271$	251.624			0.928501			0.464251	+	0.885704i	$0.346324\pi$
$272$			162.268i			0.596574i
$273$	157.138	+	37.9268i	0.575596	+	0.138926i
$274$	163.225			0.595712
$275$		0			0
$276$	−0.731470	+	3.03061i	−0.00265025	+	0.0109805i
$277$	319.412			1.15311			0.576556	−	0.817058i	$-0.304396\pi$
$277$	319.412			1.15311			0.576556	+	0.817058i	$0.304396\pi$
$278$		−	393.932i		−	1.41702i
$279$	−170.019	−	87.1488i	−0.609389	−	0.312361i
$280$		0			0
$281$			234.200i			0.833450i	0.909033	+	0.416725i	$0.136822\pi$
$281$			234.200i			0.833450i	−0.909033	+	0.416725i	$0.863178\pi$
$282$	−439.448	−	106.065i	−1.55833	−	0.376119i
$283$	430.416			1.52091			0.760453	−	0.649393i	$-0.224977\pi$
$283$	430.416			1.52091			0.760453	+	0.649393i	$0.224977\pi$
$284$		−	4.27437i		−	0.0150506i
$285$		0			0
$286$	−480.215			−1.67907
$287$			53.5575i			0.186612i
$288$	−5.95291	+	11.6136i	−0.0206698	+	0.0403250i
$289$	190.554			0.659356
$290$		0			0
$291$	180.515	+	43.5693i	0.620328	+	0.149723i
$292$	−12.3150			−0.0421746
$293$			359.848i			1.22815i	0.789247	+	0.614075i	$0.210471\pi$
$293$			359.848i			1.22815i	−0.789247	+	0.614075i	$0.789529\pi$
$294$	−9.96520	+	41.2876i	−0.0338952	+	0.140434i
$295$		0			0
$296$			452.221i			1.52777i
$297$	−205.298	+	238.611i	−0.691238	+	0.803405i
$298$	−508.942			−1.70786
$299$			233.488i			0.780897i
$300$		0			0
$301$	15.5822			0.0517683
$302$		−	280.961i		−	0.930334i
$303$	−7.86280	+	32.5770i	−0.0259498	+	0.107515i
$304$	80.4600			0.264671
$305$		0			0
$306$	−160.724	−	82.3841i	−0.525242	−	0.269229i
$307$	−146.927			−0.478590			−0.239295	−	0.970947i	$-0.576916\pi$
$307$	−146.927			−0.478590			−0.239295	+	0.970947i	$0.576916\pi$
$308$		−	2.79594i		−	0.00907773i
$309$	112.594	+	27.1758i	0.364383	+	0.0879476i
$310$		0			0
$311$			18.9887i			0.0610570i	0.999534	+	0.0305285i	$0.00971903\pi$
$311$			18.9887i			0.0610570i	−0.999534	+	0.0305285i	$0.990281\pi$
$312$	−113.344	+	469.604i	−0.363282	+	1.50514i
$313$	253.927			0.811268			0.405634	−	0.914036i	$-0.367051\pi$
$313$	253.927			0.811268			0.405634	+	0.914036i	$0.367051\pi$
$314$		−	52.2787i		−	0.166493i
$315$		0			0
$316$	8.90780			0.0281892
$317$			576.396i			1.81829i	0.416485	+	0.909143i	$0.363262\pi$
$317$			576.396i			1.81829i	−0.416485	+	0.909143i	$0.636738\pi$
$318$	520.225	+	125.562i	1.63593	+	0.394848i
$319$	−437.304			−1.37086
$320$		0			0
$321$	−138.530	+	573.954i	−0.431557	+	1.78802i
$322$	−61.3486			−0.190524
$323$			48.8141i			0.151127i
$324$	−4.28683	−	5.96085i	−0.0132310	−	0.0183977i
$325$		0			0
$326$			191.976i			0.588884i
$327$	−138.189	−	33.3533i	−0.422595	−	0.101998i
$328$	−160.056			−0.487976
$329$		−	197.122i		−	0.599155i
$330$		0			0
$331$	246.809			0.745646			0.372823	−	0.927903i	$-0.378390\pi$
$331$	246.809			0.745646			0.372823	+	0.927903i	$0.378390\pi$
$332$			5.06427i			0.0152538i
$333$	−458.073	−	234.800i	−1.37560	−	0.705104i
$334$	−657.383			−1.96821
$335$		0			0
$336$	−126.185	−	30.4561i	−0.375552	−	0.0906433i
$337$	137.732			0.408701			0.204351	−	0.978898i	$-0.434492\pi$
$337$	137.732			0.408701			0.204351	+	0.978898i	$0.434492\pi$
$338$		−	497.083i		−	1.47066i
$339$	−45.2336	+	187.411i	−0.133432	+	0.552835i
$340$		0			0
$341$			247.484i			0.725761i
$342$	−40.8498	+	79.6944i	−0.119444	+	0.233025i
$343$	−18.5203			−0.0539949
$344$			46.5674i			0.135370i
$345$		0			0
$346$	197.301			0.570235
$347$		−	445.192i		−	1.28298i	−0.767133	−	0.641488i	$-0.778318\pi$
$347$		−	445.192i		−	1.28298i	0.767133	−	0.641488i	$-0.221682\pi$
$348$	2.39323	−	9.91559i	0.00687710	−	0.0284931i
$349$	483.226			1.38460			0.692301	−	0.721609i	$-0.256597\pi$
$349$	483.226			1.38460			0.692301	+	0.721609i	$0.256597\pi$
$350$		0			0
$351$	−416.832	−	358.636i	−1.18756	−	1.02176i
$352$	16.9050			0.0480257
$353$		−	229.392i		−	0.649835i	−0.945742	−	0.324917i	$-0.894664\pi$
$353$		−	229.392i		−	0.649835i	0.945742	−	0.324917i	$-0.105336\pi$
$354$	−422.661	−	102.014i	−1.19396	−	0.288174i
$355$		0			0
$356$			9.57808i			0.0269047i
$357$	18.4774	−	76.5552i	0.0517574	−	0.214440i
$358$	349.520			0.976313
$359$			33.5036i			0.0933247i	0.998911	+	0.0466624i	$0.0148585\pi$
$359$			33.5036i			0.0933247i	−0.998911	+	0.0466624i	$0.985142\pi$
$360$		0			0
$361$	−336.796			−0.932952
$362$			16.4957i			0.0455683i
$363$	43.4982	+	10.4987i	0.119830	+	0.0289221i
$364$	4.88425			0.0134183
$365$		0			0
$366$	37.0794	−	153.627i	0.101310	−	0.419745i
$367$	−466.167			−1.27021			−0.635105	−	0.772426i	$-0.719043\pi$
$367$	−466.167			−1.27021			−0.635105	+	0.772426i	$0.719043\pi$
$368$		−	187.497i		−	0.509502i
$369$	83.1036	−	162.128i	0.225213	−	0.439370i
$370$		0			0
$371$			233.356i			0.628991i
$372$	−5.61156	−	1.35441i	−0.0150848	−	0.00364088i
$373$	583.312			1.56384			0.781920	−	0.623379i	$-0.214241\pi$
$373$	583.312			1.56384			0.781920	+	0.623379i	$0.214241\pi$
$374$			233.954i			0.625545i
$375$		0			0
$376$	589.097			1.56675
$377$		−	763.930i		−	2.02634i
$378$	94.2311	−	109.522i	0.249289	−	0.289741i
$379$	−320.826			−0.846507			−0.423253	−	0.906011i	$-0.639112\pi$
$379$	−320.826			−0.846507			−0.423253	+	0.906011i	$0.639112\pi$
$380$		0			0
$381$	−258.531	−	62.3991i	−0.678559	−	0.163777i
$382$	−241.175			−0.631347
$383$			636.582i			1.66209i	0.556203	+	0.831046i	$0.312258\pi$
$383$			636.582i			1.66209i	−0.556203	+	0.831046i	$0.687742\pi$
$384$	93.0358	−	385.464i	0.242281	−	1.00381i
$385$		0			0
$386$			277.865i			0.719858i
$387$	−47.1701	−	24.1785i	−0.121887	−	0.0624767i
$388$	5.61090			0.0144611
$389$		−	67.4908i		−	0.173498i	−0.996230	−	0.0867491i	$-0.972352\pi$
$389$		−	67.4908i		−	0.173498i	0.996230	−	0.0867491i	$-0.0276478\pi$
$390$		0			0
$391$	113.752			0.290926
$392$		−	55.3476i		−	0.141193i
$393$	82.0753	−	340.053i	0.208843	−	0.865274i
$394$	−408.877			−1.03776
$395$		0			0
$396$	−4.33838	+	8.46378i	−0.0109555	+	0.0213732i
$397$	−567.020			−1.42826			−0.714131	−	0.700012i	$-0.753178\pi$
$397$	−567.020			−1.42826			−0.714131	+	0.700012i	$0.753178\pi$
$398$		−	119.443i		−	0.300108i
$399$	−37.9596	−	9.16194i	−0.0951368	−	0.0229623i
$400$		0			0
$401$		−	151.329i		−	0.377378i	−0.982037	−	0.188689i	$-0.939576\pi$
$401$		−	151.329i		−	0.377378i	0.982037	−	0.188689i	$-0.0604238\pi$
$402$	108.861	−	451.033i	0.270800	−	1.12197i
$403$	−432.333			−1.07279
$404$			1.01258i			0.00250638i
$405$		0			0
$406$	200.721			0.494387
$407$			666.783i			1.63829i
$408$	228.784	+	55.2195i	0.560746	+	0.135342i
$409$	557.799			1.36381			0.681906	−	0.731440i	$-0.261151\pi$
$409$	557.799			1.36381			0.681906	+	0.731440i	$0.261151\pi$
$410$		0			0
$411$	56.8045	−	235.352i	0.138211	−	0.572631i
$412$	3.49973			0.00849449
$413$		−	189.592i		−	0.459059i
$414$	185.713	+	95.1928i	0.448581	+	0.229934i
$415$		0			0
$416$			29.5315i			0.0709893i
$417$	−568.004	−	137.094i	−1.36212	−	0.328762i
$418$	116.005			0.277524
$419$			217.458i			0.518992i	0.965744	+	0.259496i	$0.0835564\pi$
$419$			217.458i			0.518992i	−0.965744	+	0.259496i	$0.916444\pi$
$420$		0			0
$421$	344.111			0.817366			0.408683	−	0.912676i	$-0.365988\pi$
$421$	344.111			0.817366			0.408683	+	0.912676i	$0.365988\pi$
$422$		−	27.3661i		−	0.0648486i
$423$	−305.868	+	596.721i	−0.723092	+	1.41069i
$424$	−697.381			−1.64477
$425$		0			0
$426$	−278.132	−	67.1300i	−0.652891	−	0.157582i
$427$	68.9118			0.161386
$428$			17.8400i			0.0416822i
$429$	−167.121	+	692.414i	−0.389560	+	1.61402i
$430$		0			0
$431$		−	733.518i		−	1.70190i	−0.525248	−	0.850949i	$-0.676027\pi$
$431$		−	733.518i		−	1.70190i	0.525248	−	0.850949i	$-0.323973\pi$
$432$	334.726	+	287.994i	0.774829	+	0.666652i
$433$	−489.197			−1.12978			−0.564892	−	0.825165i	$-0.691082\pi$
$433$	−489.197			−1.12978			−0.564892	+	0.825165i	$0.691082\pi$
$434$		−	113.595i		−	0.261739i
$435$		0			0
$436$	−4.29527			−0.00985153
$437$		−	56.4035i		−	0.129070i
$438$	−193.410	+	801.331i	−0.441574	+	1.82952i
$439$	−787.369			−1.79355			−0.896775	−	0.442486i	$-0.854097\pi$
$439$	−787.369			−1.79355			−0.896775	+	0.442486i	$0.854097\pi$
$440$		0			0
$441$	56.0639	+	28.7373i	0.127129	+	0.0651640i
$442$	−408.696			−0.924651
$443$		−	351.199i		−	0.792773i	−0.918084	−	0.396387i	$-0.870264\pi$
$443$		−	351.199i		−	0.792773i	0.918084	−	0.396387i	$-0.129736\pi$
$444$	−15.1189	−	3.64910i	−0.0340515	−	0.00821869i
$445$		0			0
$446$		−	692.517i		−	1.55273i
$447$	−177.119	+	733.835i	−0.396239	+	1.64169i
$448$	165.319			0.369016
$449$			85.6820i			0.190828i	0.995438	+	0.0954142i	$0.0304176\pi$
$449$			85.6820i			0.190828i	−0.995438	+	0.0954142i	$0.969582\pi$
$450$		0			0
$451$	−235.997			−0.523275
$452$			5.82523i			0.0128877i
$453$	−405.113	−	97.7782i	−0.894289	−	0.215846i
$454$	31.3247			0.0689970
$455$		0			0
$456$	27.3804	−	113.442i	0.0600447	−	0.248776i
$457$	442.093			0.967381			0.483691	−	0.875239i	$-0.339296\pi$
$457$	442.093			0.967381			0.483691	+	0.875239i	$0.339296\pi$
$458$			361.635i			0.789596i
$459$	−174.722	+	203.075i	−0.380659	+	0.442428i
$460$		0			0
$461$		−	386.251i		−	0.837854i	−0.908020	−	0.418927i	$-0.862406\pi$
$461$		−	386.251i		−	0.837854i	0.908020	−	0.418927i	$-0.137594\pi$
$462$	−181.931	−	43.9109i	−0.393789	−	0.0950452i
$463$	300.426			0.648868			0.324434	−	0.945908i	$-0.394826\pi$
$463$	300.426			0.648868			0.324434	+	0.945908i	$0.394826\pi$
$464$			613.454i			1.32210i
$465$		0			0
$466$	840.047			1.80268
$467$			29.5201i			0.0632123i	0.999500	+	0.0316062i	$0.0100622\pi$
$467$			29.5201i			0.0632123i	−0.999500	+	0.0316062i	$0.989938\pi$
$468$	−14.7855	−	7.57875i	−0.0315928	−	0.0161939i
$469$	202.318			0.431382
$470$		0			0
$471$	−75.3798	−	18.1937i	−0.160042	−	0.0386278i
$472$	566.593			1.20041
$473$			68.6619i			0.145163i
$474$	139.899	−	579.626i	0.295145	−	1.22284i
$475$		0			0
$476$		−	2.37954i		−	0.00499903i
$477$	362.091	−	706.407i	0.759100	−	1.48094i
$478$	−414.540			−0.867239
$479$			183.487i			0.383063i	0.981486	+	0.191531i	$0.0613454\pi$
$479$			183.487i			0.383063i	−0.981486	+	0.191531i	$0.938655\pi$
$480$		0			0
$481$	−1164.81			−2.42164
$482$			153.521i			0.318509i
$483$	−21.3502	+	88.4576i	−0.0442032	+	0.183142i
$484$	1.35204			0.00279347
$485$		0			0
$486$	−455.195	+	185.326i	−0.936616	+	0.381329i
$487$	529.580			1.08743			0.543717	−	0.839269i	$-0.317016\pi$
$487$	529.580			1.08743			0.543717	+	0.839269i	$0.317016\pi$
$488$			205.942i			0.422013i
$489$	276.807	+	66.8104i	0.566068	+	0.136627i
$490$		0			0
$491$		−	640.468i		−	1.30442i	−0.758040	−	0.652208i	$-0.773843\pi$
$491$		−	640.468i		−	1.30442i	0.758040	−	0.652208i	$-0.226157\pi$
$492$	1.29154	−	5.35108i	0.00262508	−	0.0108762i
$493$	−372.176			−0.754920
$494$			202.650i			0.410223i
$495$		0			0
$496$	347.174			0.699947
$497$		−	124.761i		−	0.251027i
$498$	329.530	+	79.5355i	0.661707	+	0.159710i
$499$	121.650			0.243788			0.121894	−	0.992543i	$-0.461103\pi$
$499$	121.650			0.243788			0.121894	+	0.992543i	$0.461103\pi$
$500$		0			0
$501$	−228.778	+	947.870i	−0.456643	+	1.89196i
$502$	52.5778			0.104737
$503$		−	524.536i		−	1.04281i	−0.853308	−	0.521407i	$-0.825407\pi$
$503$		−	524.536i		−	1.04281i	0.853308	−	0.521407i	$-0.174593\pi$
$504$	−85.8812	+	167.547i	−0.170399	+	0.332434i
$505$		0			0
$506$		−	270.328i		−	0.534245i
$507$	−716.736	−	172.992i	−1.41368	−	0.341206i
$508$	−8.03582			−0.0158185
$509$		−	572.981i		−	1.12570i	−0.826559	−	0.562849i	$-0.809705\pi$
$509$		−	572.981i		−	1.12570i	0.826559	−	0.562849i	$-0.190295\pi$
$510$		0			0
$511$	−359.450			−0.703425
$512$			493.528i			0.963923i
$513$	100.694	+	86.6355i	0.196284	+	0.168880i
$514$	493.685			0.960476
$515$		0			0
$516$	−1.55687	−	0.375766i	−0.00301718	−	0.000728229i
$517$	868.602			1.68008
$518$		−	306.051i		−	0.590833i
$519$	68.6635	−	284.485i	0.132300	−	0.548141i
$520$		0			0
$521$		−	247.906i		−	0.475827i	−0.971286	−	0.237913i	$-0.923537\pi$
$521$		−	247.906i		−	0.475827i	0.971286	−	0.237913i	$-0.0764634\pi$
$522$	−607.617	−	311.453i	−1.16402	−	0.596654i
$523$	431.945			0.825898			0.412949	−	0.910754i	$-0.364499\pi$
$523$	431.945			0.825898			0.412949	+	0.910754i	$0.364499\pi$
$524$		−	10.5697i		−	0.0201713i
$525$		0			0
$526$	199.350			0.378992
$527$			210.626i			0.399670i
$528$	134.203	−	556.025i	0.254171	−	1.05308i
$529$	397.562			0.751535
$530$		0			0
$531$	−294.183	+	573.926i	−0.554018	+	1.08084i
$532$	−1.17988			−0.00221783
$533$		−	412.265i		−	0.773480i
$534$	623.242	+	150.426i	1.16712	+	0.281696i
$535$		0			0
$536$			604.626i			1.12803i
$537$	121.638	−	503.967i	0.226513	−	0.938486i
$538$	65.4960			0.121740
$539$		−	81.6080i		−	0.151406i
$540$		0			0
$541$	961.822			1.77786			0.888930	−	0.458044i	$-0.151450\pi$
$541$	961.822			1.77786			0.888930	+	0.458044i	$0.151450\pi$
$542$		−	508.918i		−	0.938963i
$543$	23.7849	+	5.74073i	0.0438028	+	0.0105723i
$544$	14.3873			0.0264473
$545$		0			0
$546$	76.7082	−	317.816i	0.140491	−	0.582081i
$547$	82.6144			0.151032			0.0755159	−	0.997145i	$-0.475940\pi$
$547$	82.6144			0.151032			0.0755159	+	0.997145i	$0.475940\pi$
$548$		−	7.31535i		−	0.0133492i
$549$	−208.608	−	106.928i	−0.379978	−	0.194769i
$550$		0			0
$551$			184.542i			0.334922i
$552$	−264.355	−	63.8048i	−0.478904	−	0.115588i
$553$	260.001			0.470165
$554$		−	646.022i		−	1.16610i
$555$		0			0
$556$	−17.6551			−0.0317537
$557$		−	576.766i		−	1.03549i	−0.855536	−	0.517743i	$-0.826772\pi$
$557$		−	576.766i		−	1.03549i	0.855536	−	0.517743i	$-0.173228\pi$
$558$	−176.261	+	343.870i	−0.315881	+	0.616255i
$559$	−119.946			−0.214573
$560$		0			0
$561$	337.334	+	81.4191i	0.601309	+	0.145132i
$562$	473.677			0.842841
$563$		−	486.496i		−	0.864115i	−0.901846	−	0.432057i	$-0.857788\pi$
$563$		−	486.496i		−	0.864115i	0.901846	−	0.432057i	$-0.142212\pi$
$564$	−4.75359	+	19.6950i	−0.00842836	+	0.0349202i
$565$		0			0
$566$		−	870.532i		−	1.53804i
$567$	−125.124	−	173.985i	−0.220678	−	0.306853i
$568$	372.846			0.656419
$569$			355.587i			0.624934i	0.949929	+	0.312467i	$0.101155\pi$
$569$			355.587i			0.624934i	−0.949929	+	0.312467i	$0.898845\pi$
$570$		0			0
$571$	104.407			0.182849			0.0914244	−	0.995812i	$-0.470858\pi$
$571$	104.407			0.182849			0.0914244	+	0.995812i	$0.470858\pi$
$572$			21.5221i			0.0376260i
$573$	−83.9321	+	347.746i	−0.146478	+	0.606886i
$574$	108.322			0.188714
$575$		0			0
$576$	−500.448	−	256.520i	−0.868834	−	0.445348i
$577$	502.560			0.870987			0.435494	−	0.900192i	$-0.356574\pi$
$577$	502.560			0.870987			0.435494	+	0.900192i	$0.356574\pi$
$578$		−	385.402i		−	0.666785i
$579$	400.649	+	96.7009i	0.691968	+	0.167014i
$580$		0			0
$581$			147.816i			0.254417i
$582$	88.1203	−	365.099i	0.151410	−	0.627317i
$583$	−1028.26			−1.76374
$584$		−	1074.21i		−	1.83941i
$585$		0			0
$586$	727.805			1.24199
$587$			361.958i			0.616623i	0.951285	+	0.308312i	$0.0997639\pi$
$587$			361.958i			0.616623i	−0.951285	+	0.308312i	$0.900236\pi$
$588$	1.85041	+	0.446616i	0.00314696	+	0.000759551i
$589$	104.438			0.177314
$590$		0			0
$591$	−142.295	+	589.553i	−0.240769	+	0.997551i
$592$	935.369			1.58002
$593$			761.082i			1.28344i	0.766938	+	0.641722i	$0.221780\pi$
$593$			761.082i			1.28344i	−0.766938	+	0.641722i	$0.778220\pi$
$594$	482.600	+	415.222i	0.812457	+	0.699027i
$595$		0			0
$596$			22.8095i			0.0382710i
$597$	−172.223	−	41.5678i	−0.288481	−	0.0696278i
$598$	472.238			0.789695
$599$		−	534.644i		−	0.892560i	−0.894893	−	0.446280i	$-0.852748\pi$
$599$		−	534.644i		−	0.892560i	0.894893	−	0.446280i	$-0.147252\pi$
$600$		0			0
$601$	−237.242			−0.394746			−0.197373	−	0.980328i	$-0.563241\pi$
$601$	−237.242			−0.394746			−0.197373	+	0.980328i	$0.563241\pi$
$602$		−	31.5156i		−	0.0523515i
$603$	−612.452	−	313.931i	−1.01567	−	0.520615i
$604$	−12.5920			−0.0208477
$605$		0			0
$606$	65.8881	+	15.9028i	0.108726	+	0.0262422i
$607$	−530.470			−0.873921			−0.436961	−	0.899481i	$-0.643945\pi$
$607$	−530.470			−0.873921			−0.436961	+	0.899481i	$0.643945\pi$
$608$		−	7.13390i		−	0.0117334i
$609$	69.8537	−	289.417i	0.114702	−	0.475233i
$610$		0			0
$611$			1517.37i			2.48342i
$612$	−3.69226	+	7.20326i	−0.00603310	+	0.0117700i
$613$	−313.472			−0.511374			−0.255687	−	0.966760i	$-0.582302\pi$
$613$	−313.472			−0.511374			−0.255687	+	0.966760i	$0.582302\pi$
$614$			297.165i			0.483982i
$615$		0			0
$616$	243.885			0.395917
$617$			752.431i			1.21950i	0.792594	+	0.609750i	$0.208730\pi$
$617$			752.431i			1.21950i	−0.792594	+	0.609750i	$0.791270\pi$
$618$	54.9640	−	227.726i	0.0889385	−	0.368488i
$619$	−157.272			−0.254074			−0.127037	−	0.991898i	$-0.540547\pi$
$619$	−157.272			−0.254074			−0.127037	+	0.991898i	$0.540547\pi$
$620$		0			0
$621$	201.888	−	234.648i	0.325101	−	0.377855i
$622$	38.4053			0.0617449
$623$			279.565i			0.448741i
$624$	971.325	+	234.439i	1.55661	+	0.375704i
$625$		0			0
$626$		−	513.576i		−	0.820409i
$627$	40.3713	−	167.266i	0.0643881	−	0.266772i
$628$	−2.34300			−0.00373090
$629$			567.478i			0.902190i
$630$		0			0
$631$	−481.330			−0.762806			−0.381403	−	0.924409i	$-0.624559\pi$
$631$	−481.330			−0.762806			−0.381403	+	0.924409i	$0.624559\pi$
$632$			777.011i			1.22945i
$633$	−39.4588	−	9.52378i	−0.0623361	−	0.0150455i
$634$	1165.78			1.83877
$635$		0			0
$636$	5.62737	−	23.3152i	0.00884807	−	0.0366591i
$637$	142.562			0.223802
$638$			884.462i			1.38630i
$639$	−193.587	+	377.671i	−0.302953	+	0.591035i
$640$		0			0
$641$			91.6756i			0.143020i	0.997440	+	0.0715098i	$0.0227817\pi$
$641$			91.6756i			0.143020i	−0.997440	+	0.0715098i	$0.977218\pi$
$642$	1160.84	+	280.181i	1.80816	+	0.436419i
$643$	983.203			1.52909			0.764544	−	0.644572i	$-0.222964\pi$
$643$	983.203			1.52909			0.764544	+	0.644572i	$0.222964\pi$
$644$			2.74950i			0.00426940i
$645$		0			0
$646$	98.7282			0.152830
$647$		−	146.732i		−	0.226788i	−0.993550	−	0.113394i	$-0.963828\pi$
$647$		−	146.732i		−	0.226788i	0.993550	−	0.113394i	$-0.0361722\pi$
$648$	519.954	−	373.933i	0.802398	−	0.577056i
$649$	835.420			1.28724
$650$		0			0
$651$	−163.790	−	39.5325i	−0.251598	−	0.0607258i
$652$	8.60391			0.0131962
$653$		−	589.430i		−	0.902649i	−0.892360	−	0.451324i	$-0.850952\pi$
$653$		−	589.430i		−	0.902649i	0.892360	−	0.451324i	$-0.149048\pi$
$654$	−67.4581	+	279.491i	−0.103147	+	0.427356i
$655$		0			0
$656$			331.059i			0.504663i
$657$	1088.12	+	557.748i	1.65619	+	0.848932i
$658$	−398.686			−0.605905
$659$			27.8483i			0.0422584i	0.999777	+	0.0211292i	$0.00672613\pi$
$659$			27.8483i			0.0422584i	−0.999777	+	0.0211292i	$0.993274\pi$
$660$		0			0
$661$	60.5008			0.0915292			0.0457646	−	0.998952i	$-0.485428\pi$
$661$	60.5008			0.0915292			0.0457646	+	0.998952i	$0.485428\pi$
$662$		−	499.179i		−	0.754047i
$663$	−142.232	+	589.292i	−0.214527	+	0.888826i
$664$	−441.748			−0.665282
$665$		0			0
$666$	−474.891	+	926.469i	−0.713049	+	1.39109i
$667$	430.040			0.644737
$668$			29.4623i			0.0441052i
$669$	−998.529	−	241.005i	−1.49257	−	0.360247i
$670$		0			0
$671$			303.654i			0.452540i
$672$	−2.70036	+	11.1881i	−0.00401840	+	0.0166490i
$673$	−1111.43			−1.65145			−0.825727	−	0.564070i	$-0.809235\pi$
$673$	−1111.43			−1.65145			−0.825727	+	0.564070i	$0.809235\pi$
$674$		−	278.568i		−	0.413306i
$675$		0			0
$676$	−22.2781			−0.0329557
$677$		−	703.912i		−	1.03975i	−0.854242	−	0.519876i	$-0.825978\pi$
$677$		−	703.912i		−	1.03975i	0.854242	−	0.519876i	$-0.174022\pi$
$678$	379.045	+	91.4865i	0.559064	+	0.134936i
$679$	163.771			0.241194
$680$		0			0
$681$	10.9014	−	45.1665i	0.0160079	−	0.0663238i
$682$	500.546			0.733938
$683$			828.212i			1.21261i	0.795233	+	0.606305i	$0.207349\pi$
$683$			828.212i			1.21261i	−0.795233	+	0.606305i	$0.792651\pi$
$684$	3.57171	+	1.83079i	0.00522180	+	0.00267659i
$685$		0			0
$686$			37.4579i			0.0546033i
$687$	521.435	+	125.854i	0.759003	+	0.183193i
$688$	96.3196			0.139999
$689$		−	1796.28i		−	2.60708i
$690$		0			0
$691$	287.201			0.415631			0.207816	−	0.978168i	$-0.433365\pi$
$691$	287.201			0.415631			0.207816	+	0.978168i	$0.433365\pi$
$692$		−	8.84256i		−	0.0127783i
$693$	−126.629	+	247.041i	−0.182725	+	0.356481i
$694$	−900.417			−1.29743
$695$		0			0
$696$	864.919	+	208.757i	1.24270	+	0.299939i
$697$	−200.849			−0.288163
$698$		−	977.341i		−	1.40020i
$699$	292.348	−	1211.25i	0.418237	−	1.73283i
$700$		0			0
$701$		−	285.350i		−	0.407061i	−0.979069	−	0.203531i	$-0.934758\pi$
$701$		−	285.350i		−	0.407061i	0.979069	−	0.203531i	$-0.0652416\pi$
$702$	−725.354	+	843.057i	−1.03327	+	1.20094i
$703$	281.382			0.400258
$704$			728.465i			1.03475i
$705$		0			0
$706$	−463.952			−0.657156
$707$			29.5552i			0.0418037i
$708$	−4.57200	+	18.9426i	−0.00645763	+	0.0267551i
$709$	522.639			0.737149			0.368575	−	0.929598i	$-0.379846\pi$
$709$	522.639			0.737149			0.368575	+	0.929598i	$0.379846\pi$
$710$		0			0
$711$	−787.067	−	403.436i	−1.10699	−	0.567420i
$712$	−835.479			−1.17343
$713$		−	243.373i		−	0.341337i
$714$	−154.835	−	37.3711i	−0.216856	−	0.0523405i
$715$		0			0
$716$		−	15.6646i		−	0.0218780i
$717$	−144.266	+	597.719i	−0.201207	+	0.833639i
$718$	67.7622			0.0943763
$719$		−	640.717i		−	0.891123i	−0.895251	−	0.445561i	$-0.853004\pi$
$719$		−	640.717i		−	0.891123i	0.895251	−	0.445561i	$-0.146996\pi$
$720$		0			0
$721$	102.150			0.141679
$722$			681.181i			0.943464i
$723$	221.360	+	53.4275i	0.306169	+	0.0738970i
$724$	0.739297			0.00102113
$725$		0			0
$726$	21.2340	−	87.9765i	0.0292480	−	0.121180i
$727$	−466.941			−0.642285			−0.321142	−	0.947031i	$-0.604067\pi$
$727$	−466.941			−0.642285			−0.321142	+	0.947031i	$0.604067\pi$
$728$			426.044i			0.585226i
$729$	108.804	+	720.835i	0.149251	+	0.988799i
$730$		0			0
$731$			58.4360i			0.0799398i
$732$	−6.88518	−	1.66181i	−0.00940598	−	0.00227023i
$733$	−418.565			−0.571030			−0.285515	−	0.958374i	$-0.592165\pi$
$733$	−418.565			−0.571030			−0.285515	+	0.958374i	$0.592165\pi$
$734$			942.839i			1.28452i
$735$		0			0
$736$	−16.6242			−0.0225872
$737$			891.499i			1.20963i
$738$	−327.909	−	168.080i	−0.444321	−	0.227750i
$739$	112.745			0.152565			0.0762824	−	0.997086i	$-0.475695\pi$
$739$	112.745			0.152565			0.0762824	+	0.997086i	$0.475695\pi$
$740$		0			0
$741$	292.198	+	70.5250i	0.394329	+	0.0951755i
$742$	471.970			0.636078
$743$		−	195.638i		−	0.263308i	−0.991296	−	0.131654i	$-0.957971\pi$
$743$		−	195.638i		−	0.263308i	0.991296	−	0.131654i	$-0.0420288\pi$
$744$	118.143	−	489.486i	0.158794	−	0.657911i
$745$		0			0
$746$		−	1179.77i		−	1.58146i
$747$	229.362	−	447.465i	0.307044	−	0.599016i
$748$	10.4852			0.0140177
$749$			520.714i			0.695213i
$750$		0			0
$751$	−216.850			−0.288748			−0.144374	−	0.989523i	$-0.546117\pi$
$751$	−216.850			−0.288748			−0.144374	+	0.989523i	$0.546117\pi$
$752$		−	1218.48i		−	1.62032i
$753$	18.2978	−	75.8111i	0.0242999	−	0.100679i
$754$	−1545.07			−2.04917
$755$		0			0
$756$	−4.90851	−	4.22321i	−0.00649273	−	0.00558626i
$757$	944.974			1.24831			0.624157	−	0.781299i	$-0.285442\pi$
$757$	944.974			1.24831			0.624157	+	0.781299i	$0.285442\pi$
$758$			648.882i			0.856044i
$759$	−389.781	−	94.0778i	−0.513546	−	0.123950i
$760$		0			0
$761$			438.658i			0.576424i	0.957567	+	0.288212i	$0.0930607\pi$
$761$			438.658i			0.576424i	−0.957567	+	0.288212i	$0.906939\pi$
$762$	−126.204	+	522.887i	−0.165622	+	0.686204i
$763$	−125.370			−0.164312
$764$			10.8089i			0.0141477i
$765$		0			0
$766$	1287.51			1.68082
$767$			1459.40i			1.90274i
$768$	−50.7283	−	12.2438i	−0.0660524	−	0.0159424i
$769$	−265.037			−0.344651			−0.172325	−	0.985040i	$-0.555128\pi$
$769$	−265.037			−0.344651			−0.172325	+	0.985040i	$0.555128\pi$
$770$		0			0
$771$	171.809	−	711.836i	0.222839	−	0.923263i
$772$	12.4532			0.0161311
$773$			500.020i			0.646856i	0.946253	+	0.323428i	$0.104835\pi$
$773$			500.020i			0.646856i	−0.946253	+	0.323428i	$0.895165\pi$
$774$	−48.9018	+	95.4031i	−0.0631807	+	0.123260i
$775$		0			0
$776$			489.428i			0.630707i
$777$	−441.290	−	106.510i	−0.567941	−	0.137079i
$778$	−136.502			−0.175453
$779$			99.5904i			0.127844i
$780$		0			0
$781$	549.748			0.703902
$782$		−	230.067i		−	0.294204i
$783$	−660.538	+	767.723i	−0.843599	+	0.980490i
$784$	−114.481			−0.146021
$785$		0			0
$786$	−687.768	−	166.000i	−0.875023	−	0.211196i
$787$	−466.854			−0.593207			−0.296603	−	0.955001i	$-0.595854\pi$
$787$	−466.854			−0.593207			−0.296603	+	0.955001i	$0.595854\pi$
$788$			18.3249i			0.0232549i
$789$	69.3765	−	287.440i	0.0879297	−	0.364309i
$790$		0			0
$791$			170.027i			0.214952i
$792$	−738.281	−	378.429i	−0.932173	−	0.477814i
$793$	−530.456			−0.668924
$794$			1146.82i			1.44435i
$795$		0			0
$796$	−5.35314			−0.00672505
$797$		−	1227.75i		−	1.54046i	−0.637763	−	0.770232i	$-0.720140\pi$
$797$		−	1227.75i		−	1.54046i	0.637763	−	0.770232i	$-0.279860\pi$
$798$	−18.5303	+	76.7745i	−0.0232210	+	0.0962087i
$799$	739.239			0.925206
$800$		0			0
$801$	433.793	−	846.292i	0.541564	−	1.05654i
$802$	−306.067			−0.381630
$803$		−	1583.89i		−	1.97246i
$804$	−20.2142	−	4.87891i	−0.0251420	−	0.00606829i
$805$		0			0
$806$			874.407i			1.08487i
$807$	22.7935	−	94.4376i	0.0282447	−	0.117023i
$808$	−88.3254			−0.109314
$809$		−	327.028i		−	0.404237i	−0.979361	−	0.202119i	$-0.935217\pi$
$809$		−	327.028i		−	0.404237i	0.979361	−	0.202119i	$-0.0647826\pi$
$810$		0			0
$811$	1069.52			1.31877			0.659384	−	0.751807i	$-0.270817\pi$
$811$	1069.52			1.31877			0.659384	+	0.751807i	$0.270817\pi$
$812$		−	8.99584i		−	0.0110786i
$813$	−733.800	−	177.110i	−0.902584	−	0.217848i
$814$	1348.59			1.65675
$815$		0			0
$816$	114.216	−	473.216i	0.139970	−	0.579921i
$817$	28.9753			0.0354654
$818$		−	1128.17i		−	1.37918i
$819$	−431.558	−	221.209i	−0.526933	−	0.270096i
$820$		0			0
$821$			184.485i			0.224707i	0.993668	+	0.112354i	$0.0358389\pi$
$821$			184.485i			0.224707i	−0.993668	+	0.112354i	$0.964161\pi$
$822$	−476.007	−	114.889i	−0.579083	−	0.139768i
$823$	739.393			0.898412			0.449206	−	0.893428i	$-0.351707\pi$
$823$	739.393			0.898412			0.449206	+	0.893428i	$0.351707\pi$
$824$			305.275i			0.370479i
$825$		0			0
$826$	−383.455			−0.464232
$827$		−	1253.54i		−	1.51577i	−0.652388	−	0.757885i	$-0.726233\pi$
$827$		−	1253.54i		−	1.51577i	0.652388	−	0.757885i	$-0.273767\pi$
$828$	4.26631	−	8.32319i	0.00515255	−	0.0100522i
$829$	−1566.71			−1.88988			−0.944941	−	0.327240i	$-0.893881\pi$
$829$	−1566.71			−1.88988			−0.944941	+	0.327240i	$0.893881\pi$
$830$		0			0
$831$	−931.488	−	224.824i	−1.12092	−	0.270547i
$832$	−1272.56			−1.52952
$833$		−	69.4540i		−	0.0833782i
$834$	−277.276	+	1148.81i	−0.332466	+	1.37747i
$835$		0			0
$836$		−	5.19906i		−	0.00621898i
$837$	434.479	+	373.820i	0.519091	+	0.446619i
$838$	439.815			0.524839
$839$			836.567i			0.997100i	0.866861	+	0.498550i	$0.166134\pi$
$839$			836.567i			0.997100i	−0.866861	+	0.498550i	$0.833866\pi$
$840$		0			0
$841$	−566.010			−0.673020
$842$		−	695.977i		−	0.826576i
$843$	164.846	−	682.987i	0.195547	−	0.810186i
$844$	−1.22648			−0.00145318
$845$		0			0
$846$	1206.89	+	618.629i	1.42658	+	0.731239i
$847$	39.4633			0.0465919
$848$			1442.46i			1.70101i
$849$	−1255.21	−	302.957i	−1.47845	−	0.356840i
$850$		0			0
$851$		−	655.706i		−	0.770513i
$852$	−3.00860	+	12.4652i	−0.00353122	+	0.0146305i
$853$	361.497			0.423794			0.211897	−	0.977292i	$-0.432036\pi$
$853$	361.497			0.423794			0.211897	+	0.977292i	$0.432036\pi$
$854$		−	139.377i		−	0.163204i
$855$		0			0
$856$	−1556.15			−1.81793
$857$		−	106.923i		−	0.124764i	−0.998052	−	0.0623820i	$-0.980130\pi$
$857$		−	106.923i		−	0.124764i	0.998052	−	0.0623820i	$-0.0198697\pi$
$858$	1400.43	+	338.009i	1.63220	+	0.393950i
$859$	−290.602			−0.338302			−0.169151	−	0.985590i	$-0.554103\pi$
$859$	−290.602			−0.338302			−0.169151	+	0.985590i	$0.554103\pi$
$860$		0			0
$861$	37.6975	−	156.188i	0.0437834	−	0.181403i
$862$	−1483.57			−1.72107
$863$		−	74.3624i		−	0.0861673i	−0.999071	−	0.0430837i	$-0.986282\pi$
$863$		−	74.3624i		−	0.0861673i	0.999071	−	0.0430837i	$-0.0137182\pi$
$864$	25.5347	−	29.6782i	0.0295540	−	0.0343497i
$865$		0			0
$866$			989.417i			1.14251i
$867$	−555.705	−	134.125i	−0.640951	−	0.154700i
$868$	−5.09104			−0.00586525
$869$			1145.67i			1.31838i
$870$		0			0
$871$	−1557.37			−1.78802
$872$		−	374.668i		−	0.429666i
$873$	−495.763	−	254.119i	−0.567884	−	0.291087i
$874$	−114.078			−0.130524
$875$		0			0
$876$	35.9137	+	8.66815i	0.0409974	+	0.00989514i
$877$	1221.03			1.39228			0.696138	−	0.717908i	$-0.254900\pi$
$877$	1221.03			1.39228			0.696138	+	0.717908i	$0.254900\pi$
$878$			1592.48i			1.81376i
$879$	253.286	−	1049.41i	0.288153	−	1.19387i
$880$		0			0
$881$		−	946.113i		−	1.07391i	−0.843611	−	0.536954i	$-0.819575\pi$
$881$		−	946.113i		−	1.07391i	0.843611	−	0.536954i	$-0.180425\pi$
$882$	58.1222	−	113.391i	0.0658982	−	0.128562i
$883$	866.198			0.980971			0.490486	−	0.871449i	$-0.336819\pi$
$883$	866.198			0.980971			0.490486	+	0.871449i	$0.336819\pi$
$884$			18.3167i			0.0207203i
$885$		0			0
$886$	−710.311			−0.801706
$887$		−	814.659i		−	0.918443i	−0.888322	−	0.459222i	$-0.848128\pi$
$887$		−	814.659i		−	0.918443i	0.888322	−	0.459222i	$-0.151872\pi$
$888$	318.304	−	1318.79i	0.358451	−	1.48513i
$889$	−234.550			−0.263836
$890$		0			0
$891$	766.653	−	551.350i	0.860441	−	0.618799i
$892$	−31.0369			−0.0347948
$893$		−	366.549i		−	0.410469i
$894$	1484.21	+	358.229i	1.66019	+	0.400703i
$895$		0			0
$896$		−	349.709i		−	0.390300i
$897$	164.345	−	680.912i	0.183217	−	0.759099i
$898$	173.295			0.192979
$899$			796.272i			0.885731i
$900$		0			0
$901$	−875.122			−0.971278
$902$			477.312i			0.529171i
$903$	−45.4419	−	10.9679i	−0.0503232	−	0.0121460i
$904$	−508.124			−0.562084
$905$		0			0
$906$	−197.760	+	819.355i	−0.218278	+	0.904365i
$907$	−374.381			−0.412768			−0.206384	−	0.978471i	$-0.566170\pi$
$907$	−374.381			−0.412768			−0.206384	+	0.978471i	$0.566170\pi$
$908$		−	1.40389i		−	0.00154614i
$909$	45.8599	−	89.4686i	0.0504509	−	0.0984252i
$910$		0			0
$911$			586.070i			0.643326i	0.946854	+	0.321663i	$0.104242\pi$
$911$			586.070i			0.643326i	−0.946854	+	0.321663i	$0.895758\pi$
$912$	−234.642	−	56.6333i	−0.257283	−	0.0620979i
$913$	−651.340			−0.713407
$914$		−	894.149i		−	0.978281i
$915$		0			0
$916$	16.2076			0.0176939
$917$		−	308.510i		−	0.336434i
$918$	410.725	+	353.382i	0.447413	+	0.384948i
$919$	−903.038			−0.982632			−0.491316	−	0.870982i	$-0.663484\pi$
$919$	−903.038			−0.982632			−0.491316	+	0.870982i	$0.663484\pi$
$920$		0			0
$921$	428.478	+	103.418i	0.465231	+	0.112288i
$922$	−781.206			−0.847295
$923$			960.358i			1.04047i
$924$	−1.96798	+	8.15369i	−0.00212985	+	0.00882434i
$925$		0			0
$926$		−	607.621i		−	0.656179i
$927$	−309.226	−	158.503i	−0.333577	−	0.170985i
$928$	54.3913			0.0586113
$929$			1184.88i			1.27543i	0.770271	+	0.637717i	$0.220121\pi$
$929$			1184.88i			1.27543i	−0.770271	+	0.637717i	$0.779879\pi$
$930$		0			0
$931$	−34.4385			−0.0369909
$932$		−	37.6489i		−	0.0403958i
$933$	13.3656	−	55.3760i	0.0143254	−	0.0593526i
$934$	59.7055			0.0639245
$935$		0			0
$936$	661.080	−	1289.71i	0.706282	−	1.37789i
$937$	−802.075			−0.856003			−0.428002	−	0.903778i	$-0.640782\pi$
$937$	−802.075			−0.856003			−0.428002	+	0.903778i	$0.640782\pi$
$938$		−	409.196i		−	0.436243i
$939$	−740.517	−	178.731i	−0.788623	−	0.190342i
$940$		0			0
$941$		−	379.438i		−	0.403229i	−0.979465	−	0.201614i	$-0.935381\pi$
$941$		−	379.438i		−	0.403229i	0.979465	−	0.201614i	$-0.0646188\pi$
$942$	−36.7974	+	152.458i	−0.0390631	+	0.161845i
$943$	232.077			0.246105
$944$		−	1171.94i		−	1.24146i
$945$		0			0
$946$	138.871			0.146798
$947$		−	611.809i		−	0.646050i	−0.946391	−	0.323025i	$-0.895300\pi$
$947$		−	611.809i		−	0.646050i	0.946391	−	0.323025i	$-0.104700\pi$
$948$	−25.9774	−	6.26993i	−0.0274024	−	0.00661385i
$949$	2766.91			2.91560
$950$		0			0
$951$	405.708	−	1680.92i	0.426612	−	1.76753i
$952$	207.563			0.218028
$953$		−	410.950i		−	0.431217i	−0.976480	−	0.215609i	$-0.930826\pi$
$953$		−	410.950i		−	0.431217i	0.976480	−	0.215609i	$-0.0691735\pi$
$954$	−1428.73	−	732.341i	−1.49762	−	0.767653i
$955$		0			0
$956$			18.5787i			0.0194338i
$957$	1275.29	+	307.805i	1.33259	+	0.321635i
$958$	371.109			0.387379
$959$		−	213.521i		−	0.222649i
$960$		0			0
$961$	−510.364			−0.531076
$962$			2355.86i			2.44892i
$963$	807.977	−	1576.29i	0.839021	−	1.63685i
$964$	6.88045			0.00713740
$965$		0			0
$966$	178.909	+	43.1814i	0.185206	+	0.0447013i
$967$	−1368.83			−1.41555			−0.707773	−	0.706440i	$-0.750300\pi$
$967$	−1368.83			−1.41555			−0.707773	+	0.706440i	$0.750300\pi$
$968$			117.936i			0.121835i
$969$	34.3588	−	142.355i	0.0354580	−	0.146909i
$970$		0			0
$971$			918.521i			0.945954i	0.881075	+	0.472977i	$0.156821\pi$
$971$			918.521i			0.945954i	−0.881075	+	0.472977i	$0.843179\pi$
$972$	8.30585	+	20.4007i	0.00854511	+	0.0209884i
$973$	−515.316			−0.529616
$974$		−	1071.09i		−	1.09969i
$975$		0			0
$976$	425.969			0.436444
$977$			1327.47i			1.35872i	0.733807	+	0.679358i	$0.237742\pi$
$977$			1327.47i			1.35872i	−0.733807	+	0.679358i	$0.762258\pi$
$978$	135.126	−	559.853i	0.138166	−	0.572446i
$979$	−1231.88			−1.25831
$980$		0			0
$981$	379.517	+	194.533i	0.386868	+	0.198301i
$982$	−1295.37			−1.31911
$983$		−	1045.07i		−	1.06314i	−0.847015	−	0.531570i	$-0.821602\pi$
$983$		−	1045.07i		−	1.06314i	0.847015	−	0.531570i	$-0.178398\pi$
$984$	466.765	+	112.659i	0.474355	+	0.114491i
$985$		0			0
$986$			752.738i			0.763426i
$987$	−138.748	+	574.858i	−0.140576	+	0.582430i
$988$	9.08229			0.00919260
$989$		−	67.5213i		−	0.0682723i
$990$		0			0
$991$	−636.280			−0.642058			−0.321029	−	0.947069i	$-0.604029\pi$
$991$	−636.280			−0.642058			−0.321029	+	0.947069i	$0.604029\pi$
$992$		−	30.7818i		−	0.0310300i
$993$	−719.758	−	173.721i	−0.724832	−	0.174946i
$994$	−252.333			−0.253856
$995$		0			0
$996$	3.56459	−	14.7687i	0.00357890	−	0.0148280i
$997$	−607.263			−0.609090			−0.304545	−	0.952498i	$-0.598504\pi$
$997$	−607.263			−0.609090			−0.304545	+	0.952498i	$0.598504\pi$
$998$		−	246.042i		−	0.246535i
$999$	1170.59	+	1007.16i	1.17176	+	1.00817i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.c.b.176.5		16
3.2	odd	2	inner	525.3.c.b.176.12		16
5.2	odd	4		525.3.f.b.449.23		32
5.3	odd	4		525.3.f.b.449.9		32
5.4	even	2		105.3.c.a.71.12	yes	16
15.2	even	4		525.3.f.b.449.10		32
15.8	even	4		525.3.f.b.449.24		32
15.14	odd	2		105.3.c.a.71.5	✓	16
20.19	odd	2		1680.3.l.a.1121.3		16
60.59	even	2		1680.3.l.a.1121.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.c.a.71.5	✓	16	15.14	odd	2
105.3.c.a.71.12	yes	16	5.4	even	2
525.3.c.b.176.5		16	1.1	even	1	trivial
525.3.c.b.176.12		16	3.2	odd	2	inner
525.3.f.b.449.9		32	5.3	odd	4
525.3.f.b.449.10		32	15.2	even	4
525.3.f.b.449.23		32	5.2	odd	4
525.3.f.b.449.24		32	15.8	even	4
1680.3.l.a.1121.3		16	20.19	odd	2
1680.3.l.a.1121.4		16	60.59	even	2

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	525.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.02253i q^{2} +(-2.91626 - 0.703870i) q^{3} -0.0906451 q^{4} +(-1.42360 + 5.89823i) q^{6} -2.64575 q^{7} -7.90680i q^{8} +(8.00914 + 4.10533i) q^{9} +O(q^{10})\)	\(q-2.02253i q^{2} +(-2.91626 - 0.703870i) q^{3} -0.0906451 q^{4} +(-1.42360 + 5.89823i) q^{6} -2.64575 q^{7} -7.90680i q^{8} +(8.00914 + 4.10533i) q^{9} -11.6583i q^{11} +(0.264344 + 0.0638023i) q^{12} +20.3660 q^{13} +5.35112i q^{14} -16.3544 q^{16} -9.92200i q^{17} +(8.30318 - 16.1988i) q^{18} -4.91979 q^{19} +(7.71570 + 1.86226i) q^{21} -23.5793 q^{22} +11.4646i q^{23} +(-5.56536 + 23.0583i) q^{24} -41.1909i q^{26} +(-20.4671 - 17.6096i) q^{27} +0.239824 q^{28} -37.5101i q^{29} -21.2282 q^{31} +1.45004i q^{32} +(-8.20592 + 33.9986i) q^{33} -20.0676 q^{34} +(-0.725989 - 0.372128i) q^{36} -57.1939 q^{37} +9.95044i q^{38} +(-59.3924 - 14.3350i) q^{39} -20.2428i q^{41} +(3.76649 - 15.6053i) q^{42} -5.88954 q^{43} +1.05677i q^{44} +23.1876 q^{46} +74.5051i q^{47} +(47.6936 + 11.5113i) q^{48} +7.00000 q^{49} +(-6.98379 + 28.9351i) q^{51} -1.84607 q^{52} -88.2001i q^{53} +(-35.6160 + 41.3954i) q^{54} +20.9194i q^{56} +(14.3474 + 3.46289i) q^{57} -75.8655 q^{58} +71.6589i q^{59} -26.0462 q^{61} +42.9347i q^{62} +(-21.1902 - 10.8617i) q^{63} -62.4847 q^{64} +(68.7633 + 16.5967i) q^{66} -76.4691 q^{67} +0.899380i q^{68} +(8.06960 - 33.4338i) q^{69} +47.1551i q^{71} +(32.4601 - 63.3267i) q^{72} +135.859 q^{73} +115.677i q^{74} +0.445954 q^{76} +30.8449i q^{77} +(-28.9930 + 120.123i) q^{78} -98.2712 q^{79} +(47.2925 + 65.7603i) q^{81} -40.9418 q^{82} -55.8693i q^{83} +(-0.699390 - 0.168805i) q^{84} +11.9118i q^{86} +(-26.4022 + 109.389i) q^{87} -92.1798 q^{88} -105.666i q^{89} -53.8833 q^{91} -1.03921i q^{92} +(61.9069 + 14.9419i) q^{93} +150.689 q^{94} +(1.02064 - 4.22870i) q^{96} -61.8996 q^{97} -14.1577i q^{98} +(47.8612 - 93.3728i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 - 28 * q^4 - 28 * q^6 + 22 * q^9	\( 16 q - 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9} - 12 q^{12} + 92 q^{16} + 52 q^{18} - 16 q^{19} - 14 q^{21} - 16 q^{22} + 128 q^{24} + 148 q^{27} - 112 q^{28} - 72 q^{31} + 4 q^{33} - 176 q^{34} - 76 q^{36} + 40 q^{37} + 90 q^{39} - 280 q^{43} + 72 q^{46} + 172 q^{48} + 112 q^{49} + 38 q^{51} + 88 q^{52} + 208 q^{54} + 36 q^{57} + 24 q^{58} - 56 q^{61} + 56 q^{63} - 44 q^{64} - 260 q^{66} + 120 q^{67} + 60 q^{69} - 376 q^{72} + 208 q^{73} + 144 q^{76} + 228 q^{78} - 204 q^{79} + 458 q^{81} + 384 q^{82} - 84 q^{84} + 324 q^{87} - 168 q^{88} - 28 q^{91} - 108 q^{93} + 984 q^{94} + 40 q^{96} - 728 q^{97} - 166 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 - 28 * q^4 - 28 * q^6 + 22 * q^9 - 12 * q^12 + 92 * q^16 + 52 * q^18 - 16 * q^19 - 14 * q^21 - 16 * q^22 + 128 * q^24 + 148 * q^27 - 112 * q^28 - 72 * q^31 + 4 * q^33 - 176 * q^34 - 76 * q^36 + 40 * q^37 + 90 * q^39 - 280 * q^43 + 72 * q^46 + 172 * q^48 + 112 * q^49 + 38 * q^51 + 88 * q^52 + 208 * q^54 + 36 * q^57 + 24 * q^58 - 56 * q^61 + 56 * q^63 - 44 * q^64 - 260 * q^66 + 120 * q^67 + 60 * q^69 - 376 * q^72 + 208 * q^73 + 144 * q^76 + 228 * q^78 - 204 * q^79 + 458 * q^81 + 384 * q^82 - 84 * q^84 + 324 * q^87 - 168 * q^88 - 28 * q^91 - 108 * q^93 + 984 * q^94 + 40 * q^96 - 728 * q^97 - 166 * q^99

Introduction

L-functions

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