LMFDB - Embedded newform 525.3.c.a.176.4

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:	$4$
Coefficient field:	4.0.65856.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 14x^{2} + 21 $ x^4 + 14*x^2 + 21
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			176.4
Root			$3.50592i$ of defining polynomial
Character	$\chi$	$=$	525.176
Dual form			525.3.c.a.176.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.50592i q^{2} +(-0.822876 - 2.88494i) q^{3} -8.29150 q^{4} +(10.1144 - 2.88494i) q^{6} -2.64575 q^{7} -15.0457i q^{8} +(-7.64575 + 4.74789i) q^{9} +O(q^{10})$	\(q+3.50592i q^{2} +(-0.822876 - 2.88494i) q^{3} -8.29150 q^{4} +(10.1144 - 2.88494i) q^{6} -2.64575 q^{7} -15.0457i q^{8} +(-7.64575 + 4.74789i) q^{9} -7.01185i q^{11} +(6.82288 + 23.9205i) q^{12} +11.6458 q^{13} -9.27580i q^{14} +19.5830 q^{16} -4.52791i q^{17} +(-16.6458 - 26.8054i) q^{18} +16.2288 q^{19} +(2.17712 + 7.63283i) q^{21} +24.5830 q^{22} +25.5635i q^{23} +(-43.4059 + 12.3807i) q^{24} +40.8291i q^{26} +(19.9889 + 18.1506i) q^{27} +21.9373 q^{28} +9.49579i q^{29} +28.7085 q^{31} +8.47380i q^{32} +(-20.2288 + 5.76988i) q^{33} +15.8745 q^{34} +(63.3948 - 39.3672i) q^{36} +33.0405 q^{37} +56.8968i q^{38} +(-9.58301 - 33.5973i) q^{39} +67.1946i q^{41} +(-26.7601 + 7.63283i) q^{42} +24.1255 q^{43} +58.1388i q^{44} -89.6235 q^{46} +33.0153i q^{47} +(-16.1144 - 56.4958i) q^{48} +7.00000 q^{49} +(-13.0627 + 3.72591i) q^{51} -96.5608 q^{52} +15.1877i q^{53} +(-63.6346 + 70.0795i) q^{54} +39.8071i q^{56} +(-13.3542 - 46.8190i) q^{57} -33.2915 q^{58} +92.3960i q^{59} -57.5203 q^{61} +100.650i q^{62} +(20.2288 - 12.5617i) q^{63} +48.6235 q^{64} +(-20.2288 - 70.9205i) q^{66} -15.1660 q^{67} +37.5432i q^{68} +(73.7490 - 21.0355i) q^{69} -70.5584i q^{71} +(71.4353 + 115.036i) q^{72} +76.7895 q^{73} +115.838i q^{74} -134.561 q^{76} +18.5516i q^{77} +(117.790 - 33.5973i) q^{78} +127.247 q^{79} +(35.9150 - 72.6024i) q^{81} -235.579 q^{82} -74.2844i q^{83} +(-18.0516 - 63.2876i) q^{84} +84.5821i q^{86} +(27.3948 - 7.81385i) q^{87} -105.498 q^{88} -127.377i q^{89} -30.8118 q^{91} -211.959i q^{92} +(-23.6235 - 82.8223i) q^{93} -115.749 q^{94} +(24.4464 - 6.97288i) q^{96} +23.1660 q^{97} +24.5415i q^{98} +(33.2915 + 53.6108i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 12 q^{4} + 14 q^{6} - 20 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 12 * q^4 + 14 * q^6 - 20 * q^9	$ 4 q + 2 q^{3} - 12 q^{4} + 14 q^{6} - 20 q^{9} + 22 q^{12} + 36 q^{13} + 36 q^{16} - 56 q^{18} + 12 q^{19} + 14 q^{21} + 56 q^{22} - 126 q^{24} - 10 q^{27} + 56 q^{28} + 136 q^{31} - 28 q^{33} + 116 q^{36} - 16 q^{37} + 4 q^{39} - 70 q^{42} + 160 q^{43} - 168 q^{46} - 38 q^{48} + 28 q^{49} - 84 q^{51} - 164 q^{52} - 154 q^{54} - 64 q^{57} - 112 q^{58} - 156 q^{61} + 28 q^{63} + 4 q^{64} - 28 q^{66} + 24 q^{67} + 168 q^{69} + 32 q^{73} - 316 q^{76} + 196 q^{78} + 128 q^{79} - 68 q^{81} - 392 q^{82} - 14 q^{84} - 28 q^{87} - 168 q^{88} - 28 q^{91} + 96 q^{93} - 336 q^{94} - 98 q^{96} + 8 q^{97} + 112 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 12 * q^4 + 14 * q^6 - 20 * q^9 + 22 * q^12 + 36 * q^13 + 36 * q^16 - 56 * q^18 + 12 * q^19 + 14 * q^21 + 56 * q^22 - 126 * q^24 - 10 * q^27 + 56 * q^28 + 136 * q^31 - 28 * q^33 + 116 * q^36 - 16 * q^37 + 4 * q^39 - 70 * q^42 + 160 * q^43 - 168 * q^46 - 38 * q^48 + 28 * q^49 - 84 * q^51 - 164 * q^52 - 154 * q^54 - 64 * q^57 - 112 * q^58 - 156 * q^61 + 28 * q^63 + 4 * q^64 - 28 * q^66 + 24 * q^67 + 168 * q^69 + 32 * q^73 - 316 * q^76 + 196 * q^78 + 128 * q^79 - 68 * q^81 - 392 * q^82 - 14 * q^84 - 28 * q^87 - 168 * q^88 - 28 * q^91 + 96 * q^93 - 336 * q^94 - 98 * q^96 + 8 * q^97 + 112 * 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 $

$2$			3.50592i			1.75296i	0.481436	+	0.876481i	$0.340115\pi$
$2$			3.50592i			1.75296i	−0.481436	+	0.876481i	$0.659885\pi$
$3$	−0.822876	−	2.88494i	−0.274292	−	0.961646i
$3$	−0.822876	−	2.88494i	−0.274292	−	0.961646i
$4$	−8.29150			−2.07288
$5$		0			0
$5$		0			0
$6$	10.1144	−	2.88494i	1.68573	−	0.480823i
$7$	−2.64575			−0.377964
$7$	−2.64575			−0.377964
$8$		−	15.0457i		−	1.88071i
$9$	−7.64575	+	4.74789i	−0.849528	+	0.527544i
$10$		0			0
$11$		−	7.01185i		−	0.637441i	−0.947849	−	0.318720i	$-0.896747\pi$
$11$		−	7.01185i		−	0.637441i	0.947849	−	0.318720i	$-0.103253\pi$
$12$	6.82288	+	23.9205i	0.568573	+	1.99337i
$13$	11.6458			0.895827			0.447914	−	0.894077i	$-0.352167\pi$
$13$	11.6458			0.895827			0.447914	+	0.894077i	$0.352167\pi$
$14$		−	9.27580i		−	0.662557i
$15$		0			0
$16$	19.5830			1.22394
$17$		−	4.52791i		−	0.266348i	−0.991093	−	0.133174i	$-0.957483\pi$
$17$		−	4.52791i		−	0.266348i	0.991093	−	0.133174i	$-0.0425169\pi$
$18$	−16.6458	−	26.8054i	−0.924764	−	1.48919i
$19$	16.2288			0.854145			0.427073	−	0.904217i	$-0.359545\pi$
$19$	16.2288			0.854145			0.427073	+	0.904217i	$0.359545\pi$
$20$		0			0
$21$	2.17712	+	7.63283i	0.103673	+	0.363468i
$22$	24.5830			1.11741
$23$			25.5635i			1.11145i	0.831365	+	0.555727i	$0.187560\pi$
$23$			25.5635i			1.11145i	−0.831365	+	0.555727i	$0.812440\pi$
$24$	−43.4059	+	12.3807i	−1.80858	+	0.515864i
$25$		0			0
$26$			40.8291i			1.57035i
$27$	19.9889	+	18.1506i	0.740329	+	0.672245i
$28$	21.9373			0.783473
$29$			9.49579i			0.327441i	0.986507	+	0.163720i	$0.0523495\pi$
$29$			9.49579i			0.327441i	−0.986507	+	0.163720i	$0.947650\pi$
$30$		0			0
$31$	28.7085			0.926081			0.463040	−	0.886337i	$-0.346759\pi$
$31$	28.7085			0.926081			0.463040	+	0.886337i	$0.346759\pi$
$32$			8.47380i			0.264806i
$33$	−20.2288	+	5.76988i	−0.612993	+	0.174845i
$34$	15.8745			0.466897
$35$		0			0
$36$	63.3948	−	39.3672i	1.76097	−	1.09353i
$37$	33.0405			0.892987			0.446493	−	0.894787i	$-0.352673\pi$
$37$	33.0405			0.892987			0.446493	+	0.894787i	$0.352673\pi$
$38$			56.8968i			1.49728i
$39$	−9.58301	−	33.5973i	−0.245718	−	0.861469i
$40$		0			0
$41$			67.1946i			1.63889i	0.573156	+	0.819446i	$0.305719\pi$
$41$			67.1946i			1.63889i	−0.573156	+	0.819446i	$0.694281\pi$
$42$	−26.7601	+	7.63283i	−0.637146	+	0.181734i
$43$	24.1255			0.561058			0.280529	−	0.959846i	$-0.409490\pi$
$43$	24.1255			0.561058			0.280529	+	0.959846i	$0.409490\pi$
$44$			58.1388i			1.32134i
$45$		0			0
$46$	−89.6235			−1.94834
$47$			33.0153i			0.702452i	0.936291	+	0.351226i	$0.114235\pi$
$47$			33.0153i			0.702452i	−0.936291	+	0.351226i	$0.885765\pi$
$48$	−16.1144	−	56.4958i	−0.335716	−	1.17700i
$49$	7.00000			0.142857
$50$		0			0
$51$	−13.0627	+	3.72591i	−0.256132	+	0.0730570i
$52$	−96.5608			−1.85694
$53$			15.1877i			0.286561i	0.989682	+	0.143281i	$0.0457651\pi$
$53$			15.1877i			0.286561i	−0.989682	+	0.143281i	$0.954235\pi$
$54$	−63.6346	+	70.0795i	−1.17842	+	1.29777i
$55$		0			0
$56$			39.8071i			0.710842i
$57$	−13.3542	−	46.8190i	−0.234285	−	0.821386i
$58$	−33.2915			−0.573991
$59$			92.3960i			1.56603i	0.622000	+	0.783017i	$0.286320\pi$
$59$			92.3960i			1.56603i	−0.622000	+	0.783017i	$0.713680\pi$
$60$		0			0
$61$	−57.5203			−0.942955			−0.471478	−	0.881878i	$-0.656279\pi$
$61$	−57.5203			−0.942955			−0.471478	+	0.881878i	$0.656279\pi$
$62$			100.650i			1.62338i
$63$	20.2288	−	12.5617i	0.321091	−	0.199393i
$64$	48.6235			0.759743
$65$		0			0
$66$	−20.2288	−	70.9205i	−0.306496	−	1.07455i
$67$	−15.1660			−0.226358			−0.113179	−	0.993575i	$-0.536103\pi$
$67$	−15.1660			−0.226358			−0.113179	+	0.993575i	$0.536103\pi$
$68$			37.5432i			0.552106i
$69$	73.7490	−	21.0355i	1.06883	−	0.304863i
$70$		0			0
$71$		−	70.5584i		−	0.993781i	−0.867813	−	0.496890i	$-0.834475\pi$
$71$		−	70.5584i		−	0.993781i	0.867813	−	0.496890i	$-0.165525\pi$
$72$	71.4353	+	115.036i	0.992157	+	1.59772i
$73$	76.7895			1.05191			0.525956	−	0.850512i	$-0.323708\pi$
$73$	76.7895			1.05191			0.525956	+	0.850512i	$0.323708\pi$
$74$			115.838i			1.56537i
$75$		0			0
$76$	−134.561			−1.77054
$77$			18.5516i			0.240930i
$78$	117.790	−	33.5973i	1.51012	−	0.430734i
$79$	127.247			1.61072			0.805361	−	0.592785i	$-0.201971\pi$
$79$	127.247			1.61072			0.805361	+	0.592785i	$0.201971\pi$
$80$		0			0
$81$	35.9150	−	72.6024i	0.443395	−	0.896326i
$82$	−235.579			−2.87292
$83$		−	74.2844i		−	0.894992i	−0.894286	−	0.447496i	$-0.852316\pi$
$83$		−	74.2844i		−	0.894992i	0.894286	−	0.447496i	$-0.147684\pi$
$84$	−18.0516	−	63.2876i	−0.214900	−	0.753424i
$85$		0			0
$86$			84.5821i			0.983513i
$87$	27.3948	−	7.81385i	0.314882	−	0.0898144i
$88$	−105.498			−1.19884
$89$		−	127.377i		−	1.43121i	−0.698507	−	0.715603i	$-0.746152\pi$
$89$		−	127.377i		−	1.43121i	0.698507	−	0.715603i	$-0.253848\pi$
$90$		0			0
$91$	−30.8118			−0.338591
$92$		−	211.959i		−	2.30391i
$93$	−23.6235	−	82.8223i	−0.254016	−	0.890562i
$94$	−115.749			−1.23137
$95$		0			0
$96$	24.4464	−	6.97288i	0.254650	−	0.0726342i
$97$	23.1660			0.238825			0.119412	−	0.992845i	$-0.461899\pi$
$97$	23.1660			0.238825			0.119412	+	0.992845i	$0.461899\pi$
$98$			24.5415i			0.250423i
$99$	33.2915	+	53.6108i	0.336278	+	0.541524i
$100$		0			0
$101$		−	134.907i		−	1.33571i	−0.744290	−	0.667857i	$-0.767212\pi$
$101$		−	134.907i		−	1.33571i	0.744290	−	0.667857i	$-0.232788\pi$
$102$	−13.0627	−	45.7970i	−0.128066	−	0.448990i
$103$	119.749			1.16261			0.581306	−	0.813685i	$-0.302542\pi$
$103$	119.749			1.16261			0.581306	+	0.813685i	$0.302542\pi$
$104$		−	175.218i		−	1.68479i
$105$		0			0
$106$	−53.2470			−0.502331
$107$			77.8544i			0.727611i	0.931475	+	0.363806i	$0.118523\pi$
$107$			77.8544i			0.727611i	−0.931475	+	0.363806i	$0.881477\pi$
$108$	−165.738	−	150.496i	−1.53461	−	1.39348i
$109$	−36.5385			−0.335216			−0.167608	−	0.985854i	$-0.553604\pi$
$109$	−36.5385			−0.335216			−0.167608	+	0.985854i	$0.553604\pi$
$110$		0			0
$111$	−27.1882	−	95.3199i	−0.244939	−	0.858738i
$112$	−51.8118			−0.462605
$113$		−	21.7596i		−	0.192563i	−0.995354	−	0.0962815i	$-0.969305\pi$
$113$		−	21.7596i		−	0.192563i	0.995354	−	0.0962815i	$-0.0306949\pi$
$114$	164.144	−	46.8190i	1.43986	−	0.410693i
$115$		0			0
$116$		−	78.7343i		−	0.678744i
$117$	−89.0405	+	55.2928i	−0.761030	+	0.472588i
$118$	−323.933			−2.74520
$119$			11.9797i			0.100670i
$120$		0			0
$121$	71.8340			0.593669
$122$		−	201.662i		−	1.65296i
$123$	193.852	−	55.2928i	1.57603	−	0.449535i
$124$	−238.037			−1.91965
$125$		0			0
$126$	44.0405	+	70.9205i	0.349528	+	0.562861i
$127$	15.4170			0.121394			0.0606968	−	0.998156i	$-0.480668\pi$
$127$	15.4170			0.121394			0.0606968	+	0.998156i	$0.480668\pi$
$128$			204.366i			1.59661i
$129$	−19.8523	−	69.6006i	−0.153894	−	0.539539i
$130$		0			0
$131$			183.110i			1.39779i	0.715226	+	0.698893i	$0.246324\pi$
$131$			183.110i			1.39779i	−0.715226	+	0.698893i	$0.753676\pi$
$132$	167.727	−	47.8410i	1.27066	−	0.362432i
$133$	−42.9373			−0.322836
$134$		−	53.1709i		−	0.396798i
$135$		0			0
$136$	−68.1255			−0.500923
$137$		−	33.0153i		−	0.240987i	−0.992714	−	0.120494i	$-0.961552\pi$
$137$		−	33.0153i		−	0.240987i	0.992714	−	0.120494i	$-0.0384477\pi$
$138$	73.7490	+	258.558i	0.534413	+	1.87361i
$139$	64.6418			0.465049			0.232525	−	0.972591i	$-0.425301\pi$
$139$	64.6418			0.465049			0.232525	+	0.972591i	$0.425301\pi$
$140$		0			0
$141$	95.2470	−	27.1675i	0.675511	−	0.192677i
$142$	247.373			1.74206
$143$		−	81.6582i		−	0.571037i
$144$	−149.727	+	92.9780i	−1.03977	+	0.645681i
$145$		0			0
$146$			269.218i			1.84396i
$147$	−5.76013	−	20.1946i	−0.0391846	−	0.137378i
$148$	−273.956			−1.85105
$149$			195.736i			1.31366i	0.754037	+	0.656832i	$0.228104\pi$
$149$			195.736i			1.31366i	−0.754037	+	0.656832i	$0.771896\pi$
$150$		0			0
$151$	102.251			0.677159			0.338579	−	0.940938i	$-0.390054\pi$
$151$	102.251			0.677159			0.338579	+	0.940938i	$0.390054\pi$
$152$		−	244.173i		−	1.60640i
$153$	21.4980	+	34.6193i	0.140510	+	0.226270i
$154$	−65.0405			−0.422341
$155$		0			0
$156$	79.4575	+	278.572i	0.509343	+	1.78572i
$157$	−104.723			−0.667025			−0.333512	−	0.942746i	$-0.608234\pi$
$157$	−104.723			−0.667025			−0.333512	+	0.942746i	$0.608234\pi$
$158$			446.118i			2.82353i
$159$	43.8157	−	12.4976i	0.275570	−	0.0786014i
$160$		0			0
$161$		−	67.6345i		−	0.420090i
$162$	254.539	+	125.915i	1.57123	+	0.777255i
$163$	70.9595			0.435334			0.217667	−	0.976023i	$-0.430155\pi$
$163$	70.9595			0.435334			0.217667	+	0.976023i	$0.430155\pi$
$164$		−	557.144i		−	3.39722i
$165$		0			0
$166$	260.435			1.56889
$167$			206.992i			1.23947i	0.784811	+	0.619735i	$0.212760\pi$
$167$			206.992i			1.23947i	−0.784811	+	0.619735i	$0.787240\pi$
$168$	114.841	−	32.7563i	0.683578	−	0.194978i
$169$	−33.3765			−0.197494
$170$		0			0
$171$	−124.081	+	77.0524i	−0.725620	+	0.450599i
$172$	−200.037			−1.16300
$173$		−	108.464i		−	0.626958i	−0.949595	−	0.313479i	$-0.898506\pi$
$173$		−	108.464i		−	0.626958i	0.949595	−	0.313479i	$-0.101494\pi$
$174$	27.3948	+	96.0440i	0.157441	+	0.551977i
$175$		0			0
$176$		−	137.313i		−	0.780188i
$177$	266.557	−	76.0304i	1.50597	−	0.429550i
$178$	446.575			2.50885
$179$			159.357i			0.890261i	0.895466	+	0.445131i	$0.146843\pi$
$179$			159.357i			0.890261i	−0.895466	+	0.445131i	$0.853157\pi$
$180$		0			0
$181$	−233.889			−1.29220			−0.646102	−	0.763251i	$-0.723602\pi$
$181$	−233.889			−1.29220			−0.646102	+	0.763251i	$0.723602\pi$
$182$		−	108.024i		−	0.593537i
$183$	47.3320	+	165.942i	0.258645	+	0.906789i
$184$	384.620			2.09032
$185$		0			0
$186$	290.369	−	82.8223i	1.56112	−	0.445281i
$187$	−31.7490			−0.169781
$188$		−	273.746i		−	1.45610i
$189$	−52.8856	−	48.0220i	−0.279818	−	0.254085i
$190$		0			0
$191$		−	288.210i		−	1.50895i	−0.656328	−	0.754476i	$-0.727891\pi$
$191$		−	288.210i		−	1.50895i	0.656328	−	0.754476i	$-0.272109\pi$
$192$	−40.0111	−	140.276i	−0.208391	−	0.730604i
$193$	−77.1216			−0.399594			−0.199797	−	0.979837i	$-0.564028\pi$
$193$	−77.1216			−0.399594			−0.199797	+	0.979837i	$0.564028\pi$
$194$			81.2183i			0.418651i
$195$		0			0
$196$	−58.0405			−0.296125
$197$			136.433i			0.692554i	0.938132	+	0.346277i	$0.112554\pi$
$197$			136.433i			0.692554i	−0.938132	+	0.346277i	$0.887446\pi$
$198$	−187.956	+	116.717i	−0.949270	+	0.589482i
$199$	86.5830			0.435090			0.217545	−	0.976050i	$-0.430195\pi$
$199$	86.5830			0.435090			0.217545	+	0.976050i	$0.430195\pi$
$200$		0			0
$201$	12.4797	+	43.7530i	0.0620883	+	0.217677i
$202$	472.974			2.34145
$203$		−	25.1235i		−	0.123761i
$204$	108.310	−	30.8934i	0.530930	−	0.151438i
$205$		0			0
$206$			419.831i			2.03801i
$207$	−121.373	−	195.452i	−0.586341	−	0.944212i
$208$	228.059			1.09644
$209$		−	113.794i		−	0.544467i
$210$		0			0
$211$	19.4170			0.0920237			0.0460118	−	0.998941i	$-0.485349\pi$
$211$	19.4170			0.0920237			0.0460118	+	0.998941i	$0.485349\pi$
$212$		−	125.929i		−	0.594005i
$213$	−203.557	+	58.0608i	−0.955666	+	0.272586i
$214$	−272.952			−1.27547
$215$		0			0
$216$	273.088	−	300.746i	1.26430	−	1.39234i
$217$	−75.9555			−0.350026
$218$		−	128.101i		−	0.587621i
$219$	−63.1882	−	221.533i	−0.288531	−	1.01157i
$220$		0			0
$221$		−	52.7309i		−	0.238601i
$222$	334.184	−	95.3199i	1.50533	−	0.429369i
$223$	−175.041			−0.784935			−0.392468	−	0.919766i	$-0.628378\pi$
$223$	−175.041			−0.784935			−0.392468	+	0.919766i	$0.628378\pi$
$224$		−	22.4196i		−	0.100087i
$225$		0			0
$226$	76.2876			0.337556
$227$			177.574i			0.782264i	0.920335	+	0.391132i	$0.127916\pi$
$227$			177.574i			0.782264i	−0.920335	+	0.391132i	$0.872084\pi$
$228$	110.727	+	388.200i	0.485644	+	1.70263i
$229$	40.8118			0.178217			0.0891087	−	0.996022i	$-0.471598\pi$
$229$	40.8118			0.178217			0.0891087	+	0.996022i	$0.471598\pi$
$230$		0			0
$231$	53.5203	−	15.2657i	0.231689	−	0.0660851i
$232$	142.871			0.615821
$233$		−	387.696i		−	1.66393i	−0.554828	−	0.831965i	$-0.687216\pi$
$233$		−	387.696i		−	1.66393i	0.554828	−	0.831965i	$-0.312784\pi$
$234$	−193.852	−	312.169i	−0.828429	−	1.33406i
$235$		0			0
$236$		−	766.102i		−	3.24619i
$237$	−104.708	−	367.100i	−0.441808	−	1.54895i
$238$	−42.0000			−0.176471
$239$		−	49.5229i		−	0.207209i	−0.994619	−	0.103604i	$-0.966962\pi$
$239$		−	49.5229i		−	0.207209i	0.994619	−	0.103604i	$-0.0330376\pi$
$240$		0			0
$241$	325.247			1.34957			0.674786	−	0.738013i	$-0.264236\pi$
$241$	325.247			1.34957			0.674786	+	0.738013i	$0.264236\pi$
$242$			251.845i			1.04068i
$243$	−239.007	−	43.8699i	−0.983569	−	0.180535i
$244$	476.929			1.95463
$245$		0			0
$246$	193.852	+	679.631i	0.788017	+	2.76273i
$247$	188.996			0.765166
$248$		−	431.939i		−	1.74169i
$249$	−214.306	+	61.1268i	−0.860666	+	0.245489i
$250$		0			0
$251$		−	263.732i		−	1.05073i	−0.850878	−	0.525364i	$-0.823929\pi$
$251$		−	263.732i		−	1.05073i	0.850878	−	0.525364i	$-0.176071\pi$
$252$	−167.727	+	104.156i	−0.665582	+	0.413316i
$253$	179.247			0.708486
$254$			54.0508i			0.212798i
$255$		0			0
$256$	−521.996			−2.03905
$257$			151.181i			0.588252i	0.955767	+	0.294126i	$0.0950286\pi$
$257$			151.181i			0.588252i	−0.955767	+	0.294126i	$0.904971\pi$
$258$	244.014	−	69.6006i	0.945792	−	0.269770i
$259$	−87.4170			−0.337517
$260$		0			0
$261$	−45.0850	−	72.6024i	−0.172739	−	0.278170i
$262$	−641.970			−2.45027
$263$		−	114.389i		−	0.434941i	−0.976067	−	0.217470i	$-0.930219\pi$
$263$		−	114.389i		−	0.434941i	0.976067	−	0.217470i	$-0.0697805\pi$
$264$	86.8118	+	304.355i	0.328832	+	1.15286i
$265$		0			0
$266$		−	150.535i		−	0.565920i
$267$	−367.476	+	104.816i	−1.37631	+	0.392568i
$268$	125.749			0.469213
$269$			4.76170i			0.0177015i	0.999961	+	0.00885074i	$0.00281731\pi$
$269$			4.76170i			0.0177015i	−0.999961	+	0.00885074i	$0.997183\pi$
$270$		0			0
$271$	−518.701			−1.91402			−0.957012	−	0.290048i	$-0.906329\pi$
$271$	−518.701			−1.91402			−0.957012	+	0.290048i	$0.906329\pi$
$272$		−	88.6701i		−	0.325993i
$273$	25.3542	+	88.8901i	0.0928727	+	0.325605i
$274$	115.749			0.422442
$275$		0			0
$276$	−611.490	+	174.416i	−2.21554	+	0.631943i
$277$	121.085			0.437130			0.218565	−	0.975822i	$-0.429862\pi$
$277$	121.085			0.437130			0.218565	+	0.975822i	$0.429862\pi$
$278$			226.629i			0.815213i
$279$	−219.498	+	136.305i	−0.786731	+	0.488548i
$280$		0			0
$281$			407.255i			1.44931i	0.689113	+	0.724654i	$0.258000\pi$
$281$			407.255i			1.44931i	−0.689113	+	0.724654i	$0.742000\pi$
$282$	95.2470	+	333.929i	0.337755	+	1.18415i
$283$	398.634			1.40860			0.704300	−	0.709902i	$-0.251261\pi$
$283$	398.634			1.40860			0.704300	+	0.709902i	$0.251261\pi$
$284$			585.036i			2.05998i
$285$		0			0
$286$	286.288			1.00101
$287$		−	177.780i		−	0.619443i
$288$	−40.2327	−	64.7886i	−0.139697	−	0.224960i
$289$	268.498			0.929059
$290$		0			0
$291$	−19.0627	−	66.8325i	−0.0655077	−	0.229665i
$292$	−636.701			−2.18048
$293$		−	2.53426i		−	0.00864935i	−0.999991	−	0.00432468i	$-0.998623\pi$
$293$		−	2.53426i		−	0.00864935i	0.999991	−	0.00432468i	$-0.00137659\pi$
$294$	70.8006	−	20.1946i	0.240819	−	0.0686890i
$295$		0			0
$296$		−	497.117i		−	1.67945i
$297$	127.269	−	140.159i	0.428516	−	0.471916i
$298$	−686.235			−2.30280
$299$			297.706i			0.995671i
$300$		0			0
$301$	−63.8301			−0.212060
$302$			358.484i			1.18703i
$303$	−389.199	+	111.012i	−1.28448	+	0.366375i
$304$	317.808			1.04542
$305$		0			0
$306$	−121.373	+	75.3705i	−0.396642	+	0.246309i
$307$	−86.2366			−0.280901			−0.140451	−	0.990088i	$-0.544855\pi$
$307$	−86.2366			−0.280901			−0.140451	+	0.990088i	$0.544855\pi$
$308$		−	153.821i		−	0.499418i
$309$	−98.5385	−	345.469i	−0.318895	−	1.11802i
$310$		0			0
$311$			151.777i			0.488028i	0.969772	+	0.244014i	$0.0784643\pi$
$311$			151.777i			0.488028i	−0.969772	+	0.244014i	$0.921536\pi$
$312$	−505.494	+	144.183i	−1.62017	+	0.462125i
$313$	−318.118			−1.01635			−0.508175	−	0.861254i	$-0.669680\pi$
$313$	−318.118			−1.01635			−0.508175	+	0.861254i	$0.669680\pi$
$314$		−	367.150i		−	1.16927i
$315$		0			0
$316$	−1055.07			−3.33883
$317$		−	364.020i		−	1.14833i	−0.818740	−	0.574164i	$-0.805327\pi$
$317$		−	364.020i		−	1.14833i	0.818740	−	0.574164i	$-0.194673\pi$
$318$	43.8157	+	153.615i	0.137785	+	0.483064i
$319$	66.5830			0.208724
$320$		0			0
$321$	224.605	−	64.0645i	0.699705	−	0.199578i
$322$	237.122			0.736402
$323$		−	73.4823i		−	0.227500i
$324$	−297.790	+	601.983i	−0.919104	+	1.85797i
$325$		0			0
$326$			248.779i			0.763124i
$327$	30.0667	+	105.412i	0.0919470	+	0.322359i
$328$	1010.99			3.08228
$329$		−	87.3502i		−	0.265502i
$330$		0			0
$331$	154.369			0.466370			0.233185	−	0.972432i	$-0.425085\pi$
$331$	154.369			0.466370			0.233185	+	0.972432i	$0.425085\pi$
$332$			615.929i			1.85521i
$333$	−252.620	+	156.873i	−0.758617	+	0.471090i
$334$	−725.697			−2.17274
$335$		0			0
$336$	42.6346	+	149.474i	0.126889	+	0.444862i
$337$	−403.041			−1.19597			−0.597983	−	0.801509i	$-0.704031\pi$
$337$	−403.041			−1.19597			−0.597983	+	0.801509i	$0.704031\pi$
$338$		−	117.015i		−	0.346199i
$339$	−62.7752	+	17.9055i	−0.185178	+	0.0528185i
$340$		0			0
$341$		−	201.300i		−	0.590321i
$342$	−270.140	−	435.019i	−0.789883	−	1.27198i
$343$	−18.5203			−0.0539949
$344$		−	362.984i		−	1.05519i
$345$		0			0
$346$	380.265			1.09903
$347$			471.242i			1.35805i	0.734117	+	0.679023i	$0.237596\pi$
$347$			471.242i			1.35805i	−0.734117	+	0.679023i	$0.762404\pi$
$348$	−227.144	+	64.7886i	−0.652712	+	0.186174i
$349$	−364.516			−1.04446			−0.522230	−	0.852805i	$-0.674900\pi$
$349$	−364.516			−1.04446			−0.522230	+	0.852805i	$0.674900\pi$
$350$		0			0
$351$	232.786	+	211.377i	0.663207	+	0.602215i
$352$	59.4170			0.168798
$353$			86.3420i			0.244595i	0.992493	+	0.122297i	$0.0390262\pi$
$353$			86.3420i			0.244595i	−0.992493	+	0.122297i	$0.960974\pi$
$354$	266.557	+	934.528i	0.752985	+	2.63991i
$355$		0			0
$356$			1056.15i			2.96671i
$357$	34.5608	−	9.85782i	0.0968089	−	0.0276129i
$358$	−558.693			−1.56059
$359$			372.068i			1.03640i	0.855259	+	0.518200i	$0.173398\pi$
$359$			372.068i			1.03640i	−0.855259	+	0.518200i	$0.826602\pi$
$360$		0			0
$361$	−97.6275			−0.270436
$362$		−	819.997i		−	2.26518i
$363$	−59.1104	−	207.237i	−0.162839	−	0.570900i
$364$	255.476			0.701857
$365$		0			0
$366$	−581.782	+	165.942i	−1.58957	+	0.453395i
$367$	161.786			0.440833			0.220416	−	0.975406i	$-0.429258\pi$
$367$	161.786			0.440833			0.220416	+	0.975406i	$0.429258\pi$
$368$			500.609i			1.36035i
$369$	−319.033	−	513.753i	−0.864587	−	1.39228i
$370$		0			0
$371$		−	40.1830i		−	0.108310i
$372$	195.875	+	686.721i	0.526544	+	1.84602i
$373$	−378.251			−1.01408			−0.507039	−	0.861923i	$-0.669260\pi$
$373$	−378.251			−1.01408			−0.507039	+	0.861923i	$0.669260\pi$
$374$		−	111.310i		−	0.297619i
$375$		0			0
$376$	496.737			1.32111
$377$			110.586i			0.293330i
$378$	168.361	−	185.413i	0.445401	−	0.490510i
$379$	−50.7974			−0.134030			−0.0670151	−	0.997752i	$-0.521348\pi$
$379$	−50.7974			−0.134030			−0.0670151	+	0.997752i	$0.521348\pi$
$380$		0			0
$381$	−12.6863	−	44.4771i	−0.0332973	−	0.116738i
$382$	1010.44			2.64514
$383$		−	113.381i		−	0.296034i	−0.988985	−	0.148017i	$-0.952711\pi$
$383$		−	113.381i		−	0.296034i	0.988985	−	0.148017i	$-0.0472891\pi$
$384$	589.582	−	168.167i	1.53537	−	0.437936i
$385$		0			0
$386$		−	270.382i		−	0.700472i
$387$	−184.458	+	114.545i	−0.476634	+	0.295983i
$388$	−192.081			−0.495054
$389$		−	725.584i		−	1.86526i	−0.360841	−	0.932628i	$-0.617510\pi$
$389$		−	725.584i		−	1.86526i	0.360841	−	0.932628i	$-0.382490\pi$
$390$		0			0
$391$	115.749			0.296033
$392$		−	105.320i		−	0.268673i
$393$	528.261	−	150.677i	1.34418	−	0.383402i
$394$	−478.324			−1.21402
$395$		0			0
$396$	−276.037	−	444.514i	−0.697062	−	1.12251i
$397$	94.3464			0.237648			0.118824	−	0.992915i	$-0.462088\pi$
$397$	94.3464			0.237648			0.118824	+	0.992915i	$0.462088\pi$
$398$			303.553i			0.762697i
$399$	35.3320	+	123.871i	0.0885514	+	0.310455i
$400$		0			0
$401$		−	677.665i		−	1.68994i	−0.534815	−	0.844969i	$-0.679619\pi$
$401$		−	677.665i		−	1.68994i	0.534815	−	0.844969i	$-0.320381\pi$
$402$	−153.395	+	43.7530i	−0.381579	+	0.108838i
$403$	334.332			0.829608
$404$			1118.58i			2.76877i
$405$		0			0
$406$	88.0810			0.216948
$407$		−	231.675i		−	0.569226i
$408$	56.0588	+	196.538i	0.137399	+	0.481711i
$409$	17.3647			0.0424564			0.0212282	−	0.999775i	$-0.493242\pi$
$409$	17.3647			0.0424564			0.0212282	+	0.999775i	$0.493242\pi$
$410$		0			0
$411$	−95.2470	+	27.1675i	−0.231745	+	0.0661009i
$412$	−992.899			−2.40995
$413$		−	244.457i		−	0.591905i
$414$	685.239	−	425.523i	1.65517	−	1.02783i
$415$		0			0
$416$			98.6838i			0.237221i
$417$	−53.1922	−	186.488i	−0.127559	−	0.447213i
$418$	398.952			0.954430
$419$			136.071i			0.324752i	0.986729	+	0.162376i	$0.0519157\pi$
$419$			136.071i			0.324752i	−0.986729	+	0.162376i	$0.948084\pi$
$420$		0			0
$421$	423.992			1.00711			0.503554	−	0.863964i	$-0.332026\pi$
$421$	423.992			1.00711			0.503554	+	0.863964i	$0.332026\pi$
$422$			68.0745i			0.161314i
$423$	−156.753	−	252.427i	−0.370574	−	0.596753i
$424$	228.510			0.538938
$425$		0			0
$426$	−203.557	−	713.655i	−0.477833	−	1.67525i
$427$	152.184			0.356404
$428$		−	645.530i		−	1.50825i
$429$	−235.579	+	67.1946i	−0.549135	+	0.156631i
$430$		0			0
$431$			340.244i			0.789430i	0.918804	+	0.394715i	$0.129157\pi$
$431$			340.244i			0.789430i	−0.918804	+	0.394715i	$0.870843\pi$
$432$	391.442	+	355.443i	0.906117	+	0.822786i
$433$	−159.166			−0.367589			−0.183794	−	0.982965i	$-0.558838\pi$
$433$	−159.166			−0.367589			−0.183794	+	0.982965i	$0.558838\pi$
$434$		−	266.294i		−	0.613581i
$435$		0			0
$436$	302.959			0.694861
$437$			414.863i			0.949343i
$438$	776.678	−	221.533i	1.77324	−	0.505783i
$439$	128.073			0.291738			0.145869	−	0.989304i	$-0.453402\pi$
$439$	128.073			0.291738			0.145869	+	0.989304i	$0.453402\pi$
$440$		0			0
$441$	−53.5203	+	33.2353i	−0.121361	+	0.0753634i
$442$	184.871			0.418259
$443$			197.340i			0.445463i	0.974880	+	0.222731i	$0.0714973\pi$
$443$			197.340i			0.445463i	−0.974880	+	0.222731i	$0.928503\pi$
$444$	225.431	+	790.345i	0.507728	+	1.78006i
$445$		0			0
$446$		−	613.679i		−	1.37596i
$447$	564.686	−	161.066i	1.26328	−	0.360327i
$448$	−128.646			−0.287156
$449$			148.101i			0.329847i	0.986306	+	0.164923i	$0.0527377\pi$
$449$			148.101i			0.329847i	−0.986306	+	0.164923i	$0.947262\pi$
$450$		0			0
$451$	471.158			1.04470
$452$			180.420i			0.399159i
$453$	−84.1398	−	294.988i	−0.185739	−	0.651187i
$454$	−622.561			−1.37128
$455$		0			0
$456$	−704.423	+	200.924i	−1.54479	+	0.440622i
$457$	122.214			0.267428			0.133714	−	0.991020i	$-0.457310\pi$
$457$	122.214			0.267428			0.133714	+	0.991020i	$0.457310\pi$
$458$			143.083i			0.312408i
$459$	82.1843	−	90.5079i	0.179051	−	0.197185i
$460$		0			0
$461$			602.089i			1.30605i	0.757337	+	0.653025i	$0.226500\pi$
$461$			602.089i			1.30605i	−0.757337	+	0.653025i	$0.773500\pi$
$462$	53.5203	+	187.638i	0.115845	+	0.406143i
$463$	637.061			1.37594			0.687971	−	0.725738i	$-0.258502\pi$
$463$	637.061			1.37594			0.687971	+	0.725738i	$0.258502\pi$
$464$			185.956i			0.400767i
$465$		0			0
$466$	1359.23			2.91681
$467$			767.706i			1.64391i	0.569553	+	0.821955i	$0.307116\pi$
$467$			767.706i			1.64391i	−0.569553	+	0.821955i	$0.692884\pi$
$468$	738.280	−	458.460i	1.57752	−	0.979616i
$469$	40.1255			0.0855554
$470$		0			0
$471$	86.1739	+	302.119i	0.182959	+	0.641442i
$472$	1390.16			2.94526
$473$		−	169.164i		−	0.357641i
$474$	1287.02	−	367.100i	2.71524	−	0.774473i
$475$		0			0
$476$		−	99.3299i		−	0.208676i
$477$	−72.1097	−	116.122i	−0.151173	−	0.243442i
$478$	173.624			0.363229
$479$			393.855i			0.822245i	0.911580	+	0.411122i	$0.134863\pi$
$479$			393.855i			0.822245i	−0.911580	+	0.411122i	$0.865137\pi$
$480$		0			0
$481$	384.782			0.799962
$482$			1140.29i			2.36575i
$483$	−195.122	+	55.6548i	−0.403978	+	0.115227i
$484$	−595.612			−1.23060
$485$		0			0
$486$	153.805	−	837.941i	0.316470	−	1.72416i
$487$	−573.409			−1.17743			−0.588716	−	0.808340i	$-0.700366\pi$
$487$	−573.409			−1.17743			−0.588716	+	0.808340i	$0.700366\pi$
$488$			865.432i			1.77343i
$489$	−58.3908	−	204.714i	−0.119409	−	0.418638i
$490$		0			0
$491$		−	170.796i		−	0.347853i	−0.984759	−	0.173927i	$-0.944354\pi$
$491$		−	170.796i		−	0.347853i	0.984759	−	0.173927i	$-0.0556455\pi$
$492$	−1607.33	+	458.460i	−3.26692	+	0.931830i
$493$	42.9961			0.0872131
$494$			662.606i			1.34131i
$495$		0			0
$496$	562.199			1.13347
$497$			186.680i			0.375614i
$498$	−214.306	−	751.340i	−0.430333	−	1.50871i
$499$	−847.814			−1.69903			−0.849513	−	0.527567i	$-0.823104\pi$
$499$	−847.814			−1.69903			−0.849513	+	0.527567i	$0.823104\pi$
$500$		0			0
$501$	597.158	−	170.328i	1.19193	−	0.339977i
$502$	924.626			1.84188
$503$		−	197.624i		−	0.392891i	−0.980515	−	0.196445i	$-0.937060\pi$
$503$		−	197.624i		−	0.392891i	0.980515	−	0.196445i	$-0.0629398\pi$
$504$	−189.000	−	304.355i	−0.375000	−	0.603880i
$505$		0			0
$506$			628.427i			1.24195i
$507$	27.4647	+	96.2891i	0.0541710	+	0.189919i
$508$	−127.830			−0.251634
$509$			491.448i			0.965516i	0.875754	+	0.482758i	$0.160365\pi$
$509$			491.448i			0.965516i	−0.875754	+	0.482758i	$0.839635\pi$
$510$		0			0
$511$	−203.166			−0.397585
$512$		−	1012.62i		−	1.97777i
$513$	324.395	+	294.562i	0.632348	+	0.574194i
$514$	−530.029			−1.03118
$515$		0			0
$516$	164.605	+	577.093i	0.319002	+	1.11840i
$517$	231.498			0.447772
$518$		−	306.477i		−	0.591655i
$519$	−312.911	+	89.2521i	−0.602912	+	0.171969i
$520$		0			0
$521$			870.010i			1.66988i	0.550338	+	0.834942i	$0.314499\pi$
$521$			870.010i			1.66988i	−0.550338	+	0.834942i	$0.685501\pi$
$522$	254.539	−	158.064i	0.487622	−	0.302806i
$523$	−798.707			−1.52716			−0.763582	−	0.645710i	$-0.776561\pi$
$523$	−798.707			−1.52716			−0.763582	+	0.645710i	$0.776561\pi$
$524$		−	1518.26i		−	2.89744i
$525$		0			0
$526$	401.041			0.762434
$527$		−	129.989i		−	0.246659i
$528$	−396.140	+	112.992i	−0.750265	+	0.213999i
$529$	−124.490			−0.235331
$530$		0			0
$531$	−438.686	−	706.437i	−0.826151	−	1.33039i
$532$	356.014			0.669200
$533$			782.531i			1.46816i
$534$	−367.476	−	1288.34i	−0.688157	−	2.41263i
$535$		0			0
$536$			228.183i			0.425714i
$537$	459.735	−	131.131i	0.856117	−	0.244191i
$538$	−16.6941			−0.0310300
$539$		−	49.0829i		−	0.0910630i
$540$		0			0
$541$	−736.243			−1.36089			−0.680446	−	0.732798i	$-0.738214\pi$
$541$	−736.243			−1.36089			−0.680446	+	0.732798i	$0.738214\pi$
$542$		−	1818.52i		−	3.35521i
$543$	192.461	+	674.755i	0.354441	+	1.24264i
$544$	38.3686			0.0705305
$545$		0			0
$546$	−311.642	+	88.8901i	−0.570773	+	0.162802i
$547$	228.952			0.418559			0.209279	−	0.977856i	$-0.432888\pi$
$547$	228.952			0.418559			0.209279	+	0.977856i	$0.432888\pi$
$548$			273.746i			0.499537i
$549$	439.786	−	273.100i	0.801067	−	0.497450i
$550$		0			0
$551$			154.105i			0.279682i
$552$	−316.494	−	1109.60i	−0.573359	−	2.01015i
$553$	−336.664			−0.608796
$554$			424.515i			0.766272i
$555$		0			0
$556$	−535.978			−0.963989
$557$		−	906.288i		−	1.62709i	−0.581503	−	0.813544i	$-0.697535\pi$
$557$		−	906.288i		−	1.62709i	0.581503	−	0.813544i	$-0.302465\pi$
$558$	−477.875	−	769.543i	−0.856406	−	1.37911i
$559$	280.959			0.502611
$560$		0			0
$561$	26.1255	+	91.5940i	0.0465695	+	0.163269i
$562$	−1427.81			−2.54058
$563$			458.616i			0.814593i	0.913296	+	0.407297i	$0.133529\pi$
$563$			458.616i			0.814593i	−0.913296	+	0.407297i	$0.866471\pi$
$564$	−789.741	+	225.259i	−1.40025	+	0.399396i
$565$		0			0
$566$			1397.58i			2.46922i
$567$	−95.0222	+	192.088i	−0.167588	+	0.338779i
$568$	−1061.60			−1.86901
$569$		−	577.428i		−	1.01481i	−0.861707	−	0.507406i	$-0.830605\pi$
$569$		−	577.428i		−	1.01481i	0.861707	−	0.507406i	$-0.169395\pi$
$570$		0			0
$571$	−103.122			−0.180598			−0.0902991	−	0.995915i	$-0.528782\pi$
$571$	−103.122			−0.180598			−0.0902991	+	0.995915i	$0.528782\pi$
$572$			677.069i			1.18369i
$573$	−831.468	+	237.161i	−1.45108	+	0.413893i
$574$	623.284			1.08586
$575$		0			0
$576$	−371.763	+	230.859i	−0.645423	+	0.400797i
$577$	676.583			1.17259			0.586294	−	0.810099i	$-0.300586\pi$
$577$	676.583			1.17259			0.586294	+	0.810099i	$0.300586\pi$
$578$			941.334i			1.62860i
$579$	63.4615	+	222.491i	0.109605	+	0.384268i
$580$		0			0
$581$			196.538i			0.338275i
$582$	234.310	−	66.8325i	0.402594	−	0.114833i
$583$	106.494			0.182666
$584$		−	1155.35i		−	1.97834i
$585$		0			0
$586$	8.88492			0.0151620
$587$		−	158.683i		−	0.270329i	−0.990823	−	0.135164i	$-0.956844\pi$
$587$		−	158.683i		−	0.270329i	0.990823	−	0.135164i	$-0.0431563\pi$
$588$	47.7601	+	167.443i	0.0812247	+	0.284768i
$589$	465.903			0.791007
$590$		0			0
$591$	393.601	−	112.267i	0.665992	−	0.189962i
$592$	647.033			1.09296
$593$			935.371i			1.57735i	0.614807	+	0.788677i	$0.289234\pi$
$593$			935.371i			1.57735i	−0.614807	+	0.788677i	$0.710766\pi$
$594$	491.387	+	446.196i	0.827251	+	0.751172i
$595$		0			0
$596$		−	1622.94i		−	2.72306i
$597$	−71.2470	−	249.787i	−0.119342	−	0.418403i
$598$	−1043.73			−1.74537
$599$			73.7665i			0.123149i	0.998102	+	0.0615747i	$0.0196122\pi$
$599$			73.7665i			0.123149i	−0.998102	+	0.0615747i	$0.980388\pi$
$600$		0			0
$601$	−934.280			−1.55454			−0.777271	−	0.629166i	$-0.783397\pi$
$601$	−934.280			−1.55454			−0.777271	+	0.629166i	$0.783397\pi$
$602$		−	223.783i		−	0.371733i
$603$	115.956	−	72.0066i	0.192298	−	0.119414i
$604$	−847.814			−1.40367
$605$		0			0
$606$	−389.199	−	1364.50i	−0.642242	−	2.25165i
$607$	181.608			0.299189			0.149595	−	0.988747i	$-0.452203\pi$
$607$	181.608			0.299189			0.149595	+	0.988747i	$0.452203\pi$
$608$			137.519i			0.226183i
$609$	−72.4797	+	20.6735i	−0.119014	+	0.0339466i
$610$		0			0
$611$			384.488i			0.629276i
$612$	−178.251	−	287.046i	−0.291260	−	0.469029i
$613$	897.940			1.46483			0.732414	−	0.680859i	$-0.238394\pi$
$613$	897.940			1.46483			0.732414	+	0.680859i	$0.238394\pi$
$614$		−	302.339i		−	0.492409i
$615$		0			0
$616$	279.122			0.453119
$617$		−	1169.69i		−	1.89576i	−0.318622	−	0.947882i	$-0.603220\pi$
$617$		−	1169.69i		−	1.89576i	0.318622	−	0.947882i	$-0.396780\pi$
$618$	1211.19	−	345.469i	1.95985	−	0.559011i
$619$	1208.97			1.95310			0.976548	−	0.215301i	$-0.0690734\pi$
$619$	1208.97			1.95310			0.976548	+	0.215301i	$0.0690734\pi$
$620$		0			0
$621$	−463.992	+	510.985i	−0.747169	+	0.822842i
$622$	−532.118			−0.855495
$623$			337.009i			0.540945i
$624$	−187.664	−	657.936i	−0.300744	−	1.05438i
$625$		0			0
$626$		−	1115.30i		−	1.78162i
$627$	−328.288	+	93.6380i	−0.523585	+	0.149343i
$628$	868.310			1.38266
$629$		−	149.604i		−	0.237845i
$630$		0			0
$631$	901.223			1.42825			0.714123	−	0.700020i	$-0.246826\pi$
$631$	901.223			1.42825			0.714123	+	0.700020i	$0.246826\pi$
$632$		−	1914.52i		−	3.02930i
$633$	−15.9778	−	56.0169i	−0.0252413	−	0.0884942i
$634$	1276.23			2.01298
$635$		0			0
$636$	−363.298	+	103.624i	−0.571223	+	0.162931i
$637$	81.5203			0.127975
$638$			233.435i			0.365886i
$639$	335.004	+	539.472i	0.524263	+	0.844245i
$640$		0			0
$641$			528.629i			0.824694i	0.911027	+	0.412347i	$0.135291\pi$
$641$			528.629i			0.824694i	−0.911027	+	0.412347i	$0.864709\pi$
$642$	224.605	+	787.449i	0.349852	+	1.22656i
$643$	−33.4392			−0.0520050			−0.0260025	−	0.999662i	$-0.508278\pi$
$643$	−33.4392			−0.0520050			−0.0260025	+	0.999662i	$0.508278\pi$
$644$			560.792i			0.870795i
$645$		0			0
$646$	257.624			0.398798
$647$			786.308i			1.21531i	0.794200	+	0.607657i	$0.207890\pi$
$647$			786.308i			1.21531i	−0.794200	+	0.607657i	$0.792110\pi$
$648$	−1092.35	−	540.366i	−1.68573	−	0.833898i
$649$	647.867			0.998254
$650$		0			0
$651$	62.5020	+	219.127i	0.0960092	+	0.336601i
$652$	−588.361			−0.902394
$653$			385.807i			0.590823i	0.955370	+	0.295412i	$0.0954568\pi$
$653$			385.807i			0.590823i	−0.955370	+	0.295412i	$0.904543\pi$
$654$	−369.565	+	105.412i	−0.565084	+	0.161180i
$655$		0			0
$656$			1315.87i			2.00590i
$657$	−587.114	+	364.588i	−0.893628	+	0.554929i
$658$	306.243			0.465415
$659$		−	97.2583i		−	0.147585i	−0.997274	−	0.0737924i	$-0.976490\pi$
$659$		−	97.2583i		−	0.147585i	0.997274	−	0.0737924i	$-0.0235102\pi$
$660$		0			0
$661$	−961.505			−1.45462			−0.727311	−	0.686309i	$-0.759230\pi$
$661$	−961.505			−1.45462			−0.727311	+	0.686309i	$0.759230\pi$
$662$			541.205i			0.817530i
$663$	−152.125	+	43.3910i	−0.229450	+	0.0654464i
$664$	−1117.66			−1.68322
$665$		0			0
$666$	−549.984	−	885.665i	−0.825802	−	1.32983i
$667$	−242.745			−0.363936
$668$		−	1716.27i		−	2.56927i
$669$	144.037	+	504.981i	0.215301	+	0.754830i
$670$		0			0
$671$			403.323i			0.601078i
$672$	−64.6791	+	18.4485i	−0.0962487	+	0.0274531i
$673$	1089.81			1.61933			0.809663	−	0.586895i	$-0.199650\pi$
$673$	1089.81			1.61933			0.809663	+	0.586895i	$0.199650\pi$
$674$		−	1413.03i		−	2.09648i
$675$		0			0
$676$	276.741			0.409380
$677$		−	1252.56i		−	1.85016i	−0.379771	−	0.925080i	$-0.623997\pi$
$677$		−	1252.56i		−	1.85016i	0.379771	−	0.925080i	$-0.376003\pi$
$678$	−62.7752	−	220.085i	−0.0925888	−	0.324609i
$679$	−61.2915			−0.0902673
$680$		0			0
$681$	512.290	−	146.121i	0.752262	−	0.214569i
$682$	705.741			1.03481
$683$		−	341.097i		−	0.499409i	−0.968322	−	0.249705i	$-0.919666\pi$
$683$		−	341.097i		−	0.499409i	0.968322	−	0.249705i	$-0.0803335\pi$
$684$	1028.82	−	638.880i	1.50412	−	0.934035i
$685$		0			0
$686$		−	64.9306i		−	0.0946510i
$687$	−33.5830	−	117.739i	−0.0488836	−	0.171382i
$688$	472.450			0.686700
$689$			176.873i			0.256709i
$690$		0			0
$691$	−783.667			−1.13411			−0.567053	−	0.823682i	$-0.691916\pi$
$691$	−783.667			−1.13411			−0.567053	+	0.823682i	$0.691916\pi$
$692$			899.327i			1.29961i
$693$	−88.0810	−	141.841i	−0.127101	−	0.204677i
$694$	−1652.14			−2.38060
$695$		0			0
$696$	−117.565	−	412.173i	−0.168915	−	0.592203i
$697$	304.251			0.436515
$698$		−	1277.97i		−	1.83090i
$699$	−1118.48	+	319.025i	−1.60011	+	0.456402i
$700$		0			0
$701$		−	1331.76i		−	1.89979i	−0.312562	−	0.949897i	$-0.601187\pi$
$701$		−	1331.76i		−	1.89979i	0.312562	−	0.949897i	$-0.398813\pi$
$702$	−741.073	+	816.129i	−1.05566	+	1.16258i
$703$	536.207			0.762740
$704$		−	340.941i		−	0.484291i
$705$		0			0
$706$	−302.708			−0.428766
$707$			356.930i			0.504852i
$708$	−2210.16	+	630.406i	−3.12169	+	0.890404i
$709$	763.963			1.07752			0.538761	−	0.842459i	$-0.318893\pi$
$709$	763.963			1.07752			0.538761	+	0.842459i	$0.318893\pi$
$710$		0			0
$711$	−972.899	+	604.155i	−1.36835	+	0.849726i
$712$	−1916.48			−2.69168
$713$			733.888i			1.02930i
$714$	34.5608	+	121.167i	0.0484045	+	0.169702i
$715$		0			0
$716$		−	1321.31i		−	1.84540i
$717$	−142.871	+	40.7512i	−0.199262	+	0.0568357i
$718$	−1304.44			−1.81677
$719$		−	623.715i		−	0.867476i	−0.901039	−	0.433738i	$-0.857194\pi$
$719$		−	623.715i		−	0.867476i	0.901039	−	0.433738i	$-0.142806\pi$
$720$		0			0
$721$	−316.826			−0.439426
$722$		−	342.274i		−	0.474064i
$723$	−267.638	−	938.318i	−0.370177	−	1.29781i
$724$	1939.29			2.67858
$725$		0			0
$726$	726.556	−	207.237i	1.00077	−	0.285450i
$727$	−678.494			−0.933279			−0.466640	−	0.884448i	$-0.654536\pi$
$727$	−678.494			−0.933279			−0.466640	+	0.884448i	$0.654536\pi$
$728$			463.584i			0.636791i
$729$	70.1111	+	725.621i	0.0961744	+	0.995364i
$730$		0			0
$731$		−	109.238i		−	0.149436i
$732$	−392.454	−	1375.91i	−0.536139	−	1.87966i
$733$	394.966			0.538835			0.269417	−	0.963023i	$-0.413169\pi$
$733$	394.966			0.538835			0.269417	+	0.963023i	$0.413169\pi$
$734$			567.208i			0.772763i
$735$		0			0
$736$	−216.620			−0.294320
$737$			106.342i			0.144290i
$738$	1801.18	−	1118.50i	2.44062	−	1.51559i
$739$	292.199			0.395397			0.197699	−	0.980263i	$-0.436653\pi$
$739$	292.199			0.395397			0.197699	+	0.980263i	$0.436653\pi$
$740$		0			0
$741$	−155.520	−	545.242i	−0.209879	−	0.735819i
$742$	140.878			0.189863
$743$		−	383.452i		−	0.516086i	−0.966133	−	0.258043i	$-0.916922\pi$
$743$		−	383.452i		−	0.516086i	0.966133	−	0.258043i	$-0.0830776\pi$
$744$	−1246.12	+	355.432i	−1.67489	+	0.477731i
$745$		0			0
$746$		−	1326.12i		−	1.77764i
$747$	352.694	+	567.960i	0.472147	+	0.760321i
$748$	263.247			0.351935
$749$		−	205.983i		−	0.275011i
$750$		0			0
$751$	−696.332			−0.927206			−0.463603	−	0.886043i	$-0.653444\pi$
$751$	−696.332			−0.927206			−0.463603	+	0.886043i	$0.653444\pi$
$752$			646.538i			0.859758i
$753$	−760.852	+	217.019i	−1.01043	+	0.288206i
$754$	−387.705			−0.514197
$755$		0			0
$756$	438.501	+	398.174i	0.580028	+	0.526686i
$757$	−967.357			−1.27788			−0.638941	−	0.769256i	$-0.720627\pi$
$757$	−967.357			−1.27788			−0.638941	+	0.769256i	$0.720627\pi$
$758$		−	178.092i		−	0.234950i
$759$	−147.498	−	517.117i	−0.194332	−	0.681313i
$760$		0			0
$761$			89.7059i			0.117879i	0.998262	+	0.0589395i	$0.0187719\pi$
$761$			89.7059i			0.117879i	−0.998262	+	0.0589395i	$0.981228\pi$
$762$	155.933	−	44.4771i	0.204637	−	0.0583689i
$763$	96.6719			0.126700
$764$			2389.69i			3.12787i
$765$		0			0
$766$	397.506			0.518937
$767$			1076.02i			1.40290i
$768$	429.538	+	1505.93i	0.559294	+	1.96084i
$769$	926.219			1.20445			0.602223	−	0.798328i	$-0.294282\pi$
$769$	926.219			1.20445			0.602223	+	0.798328i	$0.294282\pi$
$770$		0			0
$771$	436.148	−	124.403i	0.565691	−	0.161353i
$772$	639.454			0.828308
$773$			424.125i			0.548674i	0.961634	+	0.274337i	$0.0884584\pi$
$773$			424.125i			0.548674i	−0.961634	+	0.274337i	$0.911542\pi$
$774$	−401.587	−	646.694i	−0.518846	−	0.835522i
$775$		0			0
$776$		−	348.548i		−	0.449160i
$777$	71.9333	+	252.193i	0.0925783	+	0.324572i
$778$	2543.84			3.26972
$779$			1090.48i			1.39985i
$780$		0			0
$781$	−494.745			−0.633476
$782$			405.807i			0.518935i
$783$	−172.354	+	189.810i	−0.220120	+	0.242414i
$784$	137.081			0.174848
$785$		0			0
$786$	528.261	+	1852.04i	0.672088	+	2.35629i
$787$	155.889			0.198080			0.0990399	−	0.995083i	$-0.468423\pi$
$787$	155.889			0.198080			0.0990399	+	0.995083i	$0.468423\pi$
$788$		−	1131.24i		−	1.43558i
$789$	−330.006	+	94.1282i	−0.418259	+	0.119301i
$790$		0			0
$791$			57.5705i			0.0727820i
$792$	806.612	−	500.893i	1.01845	−	0.632441i
$793$	−669.867			−0.844725
$794$			330.771i			0.416588i
$795$		0			0
$796$	−717.903			−0.901888
$797$		−	719.191i		−	0.902373i	−0.892430	−	0.451186i	$-0.851001\pi$
$797$		−	719.191i		−	0.902373i	0.892430	−	0.451186i	$-0.148999\pi$
$798$	−434.284	+	123.871i	−0.544215	+	0.155227i
$799$	149.490			0.187097
$800$		0			0
$801$	604.774	+	973.895i	0.755023	+	1.21585i
$802$	2375.84			2.96240
$803$		−	538.437i		−	0.670531i
$804$	−103.476	−	362.778i	−0.128701	−	0.451217i
$805$		0			0
$806$			1172.14i			1.45427i
$807$	13.7372	−	3.91828i	0.0170226	−	0.00485537i
$808$	−2029.77			−2.51209
$809$			212.244i			0.262353i	0.991359	+	0.131176i	$0.0418755\pi$
$809$			212.244i			0.262353i	−0.991359	+	0.131176i	$0.958125\pi$
$810$		0			0
$811$	1058.66			1.30538			0.652690	−	0.757625i	$-0.273641\pi$
$811$	1058.66			1.30538			0.652690	+	0.757625i	$0.273641\pi$
$812$			208.311i			0.256541i
$813$	426.826	+	1496.42i	0.525001	+	1.84061i
$814$	812.235			0.997832
$815$		0			0
$816$	−255.808	+	72.9645i	−0.313490	+	0.0894172i
$817$	391.527			0.479225
$818$			60.8792i			0.0744244i
$819$	235.579	−	146.291i	0.287642	−	0.178621i
$820$		0			0
$821$		−	818.571i		−	0.997042i	−0.866878	−	0.498521i	$-0.833877\pi$
$821$		−	818.571i		−	0.997042i	0.866878	−	0.498521i	$-0.166123\pi$
$822$	−95.2470	−	333.929i	−0.115872	−	0.406240i
$823$	−206.850			−0.251336			−0.125668	−	0.992072i	$-0.540107\pi$
$823$	−206.850			−0.251336			−0.125668	+	0.992072i	$0.540107\pi$
$824$		−	1801.71i		−	2.18654i
$825$		0			0
$826$	857.047			1.03759
$827$		−	438.639i		−	0.530398i	−0.964194	−	0.265199i	$-0.914562\pi$
$827$		−	438.639i		−	0.530398i	0.964194	−	0.265199i	$-0.0854376\pi$
$828$	1006.36	+	1620.59i	1.21541	+	1.95723i
$829$	654.804			0.789872			0.394936	−	0.918709i	$-0.370767\pi$
$829$	654.804			0.789872			0.394936	+	0.918709i	$0.370767\pi$
$830$		0			0
$831$	−99.6379	−	349.323i	−0.119901	−	0.420364i
$832$	566.257			0.680598
$833$		−	31.6954i		−	0.0380497i
$834$	653.812	−	186.488i	0.783947	−	0.223606i
$835$		0			0
$836$			943.520i			1.12861i
$837$	573.851	+	521.077i	0.685604	+	0.622553i
$838$	−477.055			−0.569278
$839$		−	50.9710i		−	0.0607521i	−0.999539	−	0.0303761i	$-0.990330\pi$
$839$		−	50.9710i		−	0.0607521i	0.999539	−	0.0303761i	$-0.00967049\pi$
$840$		0			0
$841$	750.830			0.892782
$842$			1486.48i			1.76542i
$843$	1174.91	−	335.121i	1.39372	−	0.397533i
$844$	−160.996			−0.190754
$845$		0			0
$846$	884.988	−	549.564i	1.04609	−	0.649603i
$847$	−190.055			−0.224386
$848$			297.422i			0.350733i
$849$	−328.026	−	1150.03i	−0.386368	−	1.35458i
$850$		0			0
$851$			844.630i			0.992514i
$852$	1687.79	−	481.411i	1.98098	−	0.565037i
$853$	883.941			1.03627			0.518137	−	0.855298i	$-0.326626\pi$
$853$	883.941			1.03627			0.518137	+	0.855298i	$0.326626\pi$
$854$			533.547i			0.624762i
$855$		0			0
$856$	1171.37			1.36843
$857$		−	556.521i		−	0.649382i	−0.945820	−	0.324691i	$-0.894740\pi$
$857$		−	556.521i		−	0.649382i	0.945820	−	0.324691i	$-0.105260\pi$
$858$	−235.579	−	825.922i	−0.274568	−	0.962613i
$859$	−643.078			−0.748636			−0.374318	−	0.927300i	$-0.622123\pi$
$859$	−643.078			−0.748636			−0.374318	+	0.927300i	$0.622123\pi$
$860$		0			0
$861$	−512.885	+	146.291i	−0.595685	+	0.169908i
$862$	−1192.87			−1.38384
$863$		−	204.892i		−	0.237419i	−0.992929	−	0.118709i	$-0.962124\pi$
$863$		−	204.892i		−	0.237419i	0.992929	−	0.118709i	$-0.0378757\pi$
$864$	−153.805	+	169.382i	−0.178015	+	0.196044i
$865$		0			0
$866$		−	558.024i		−	0.644369i
$867$	−220.940	−	774.601i	−0.254833	−	0.893426i
$868$	629.786			0.725559
$869$		−	892.237i		−	1.02674i
$870$		0			0
$871$	−176.620			−0.202778
$872$			549.747i			0.630444i
$873$	−177.122	+	109.990i	−0.202888	+	0.125991i
$874$	−1454.48			−1.66416
$875$		0			0
$876$	523.925	+	1836.84i	0.598088	+	2.09685i
$877$	207.210			0.236272			0.118136	−	0.992997i	$-0.462308\pi$
$877$	207.210			0.236272			0.118136	+	0.992997i	$0.462308\pi$
$878$			449.015i			0.511406i
$879$	−7.31119	+	2.08538i	−0.00831762	+	0.00237245i
$880$		0			0
$881$		−	1391.37i		−	1.57931i	−0.613552	−	0.789654i	$-0.710260\pi$
$881$		−	1391.37i		−	1.57931i	0.613552	−	0.789654i	$-0.289740\pi$
$882$	−116.520	−	187.638i	−0.132109	−	0.212741i
$883$	1091.99			1.23668			0.618342	−	0.785909i	$-0.287805\pi$
$883$	1091.99			1.23668			0.618342	+	0.785909i	$0.287805\pi$
$884$			437.219i			0.494591i
$885$		0			0
$886$	−691.859			−0.780879
$887$		−	149.449i		−	0.168488i	−0.996445	−	0.0842439i	$-0.973153\pi$
$887$		−	149.449i		−	0.168488i	0.996445	−	0.0842439i	$-0.0268475\pi$
$888$	−1434.15	+	409.066i	−1.61504	+	0.460659i
$889$	−40.7895			−0.0458825
$890$		0			0
$891$	−509.077	−	251.831i	−0.571355	−	0.282638i
$892$	1451.35			1.62707
$893$			535.797i			0.599996i
$894$	564.686	+	1979.75i	0.631640	+	2.21448i
$895$		0			0
$896$		−	540.700i		−	0.603460i
$897$	858.863	−	244.975i	0.957483	−	0.273104i
$898$	−519.231			−0.578209
$899$			272.610i			0.303237i
$900$		0			0
$901$	68.7687			0.0763249
$902$			1651.84i			1.83131i
$903$	52.5242	+	184.146i	0.0581663	+	0.203927i
$904$	−327.388			−0.362155
$905$		0			0
$906$	1034.21	−	294.988i	1.14151	−	0.325594i
$907$	−593.718			−0.654595			−0.327297	−	0.944921i	$-0.606138\pi$
$907$	−593.718			−0.654595			−0.327297	+	0.944921i	$0.606138\pi$
$908$		−	1472.35i		−	1.62154i
$909$	640.524	+	1031.47i	0.704647	+	1.13473i
$910$		0			0
$911$			1133.75i			1.24451i	0.782815	+	0.622254i	$0.213783\pi$
$911$			1133.75i			1.24451i	−0.782815	+	0.622254i	$0.786217\pi$
$912$	−261.516	−	916.856i	−0.286750	−	1.00532i
$913$	−520.871			−0.570504
$914$			428.474i			0.468790i
$915$		0			0
$916$	−338.391			−0.369422
$917$		−	484.464i		−	0.528314i
$918$	317.314	+	288.132i	0.345658	+	0.313869i
$919$	−684.988			−0.745363			−0.372681	−	0.927959i	$-0.621562\pi$
$919$	−684.988			−0.745363			−0.372681	+	0.927959i	$0.621562\pi$
$920$		0			0
$921$	70.9620	+	248.787i	0.0770489	+	0.270128i
$922$	−2110.88			−2.28945
$923$		−	821.706i		−	0.890256i
$924$	−443.763	+	126.575i	−0.480263	+	0.136986i
$925$		0			0
$926$			2233.49i			2.41197i
$927$	−915.571	+	568.556i	−0.987671	+	0.613328i
$928$	−80.4654			−0.0867084
$929$		−	192.317i		−	0.207015i	−0.994629	−	0.103507i	$-0.966993\pi$
$929$		−	192.317i		−	0.207015i	0.994629	−	0.103507i	$-0.0330066\pi$
$930$		0			0
$931$	113.601			0.122021
$932$			3214.58i			3.44912i
$933$	437.867	−	124.893i	0.469310	−	0.133862i
$934$	−2691.52			−2.88171
$935$		0			0
$936$	831.918	+	1339.68i	0.888801	+	1.43128i
$937$	1270.28			1.35569			0.677844	−	0.735206i	$-0.262914\pi$
$937$	1270.28			1.35569			0.677844	+	0.735206i	$0.262914\pi$
$938$			140.677i			0.149975i
$939$	261.771	+	917.750i	0.278777	+	0.977370i
$940$		0			0
$941$			156.951i			0.166791i	0.996517	+	0.0833957i	$0.0265766\pi$
$941$			156.951i			0.166791i	−0.996517	+	0.0833957i	$0.973423\pi$
$942$	−1059.21	+	302.119i	−1.12442	+	0.320721i
$943$	−1717.73			−1.82155
$944$			1809.39i			1.91673i
$945$		0			0
$946$	593.077			0.626931
$947$		−	879.945i		−	0.929193i	−0.885523	−	0.464596i	$-0.846199\pi$
$947$		−	879.945i		−	0.929193i	0.885523	−	0.464596i	$-0.153801\pi$
$948$	868.191	+	3043.81i	0.915813	+	3.21077i
$949$	894.272			0.942331
$950$		0			0
$951$	−1050.18	+	299.543i	−1.10429	+	0.314977i
$952$	180.243			0.189331
$953$		−	563.276i		−	0.591056i	−0.955334	−	0.295528i	$-0.904505\pi$
$953$		−	563.276i		−	0.591056i	0.955334	−	0.295528i	$-0.0954955\pi$
$954$	407.114	−	252.811i	0.426744	−	0.265001i
$955$		0			0
$956$			410.619i			0.429518i
$957$	−54.7895	−	192.088i	−0.0572513	−	0.200719i
$958$	−1380.83			−1.44136
$959$			87.3502i			0.0910847i
$960$		0			0
$961$	−136.822			−0.142375
$962$			1349.02i			1.40230i
$963$	−369.644	−	595.255i	−0.383847	−	0.618126i
$964$	−2696.79			−2.79750
$965$		0			0
$966$	−195.122	−	684.081i	−0.201989	−	0.708159i
$967$	−237.676			−0.245787			−0.122893	−	0.992420i	$-0.539217\pi$
$967$	−237.676			−0.245787			−0.122893	+	0.992420i	$0.539217\pi$
$968$		−	1080.79i		−	1.11652i
$969$	−211.992	+	60.4668i	−0.218774	+	0.0624013i
$970$		0			0
$971$		−	1355.00i		−	1.39546i	−0.716359	−	0.697732i	$-0.754192\pi$
$971$		−	1355.00i		−	1.39546i	0.716359	−	0.697732i	$-0.245808\pi$
$972$	1981.73	+	363.748i	2.03882	+	0.374226i
$973$	−171.026			−0.175772
$974$		−	2010.33i		−	2.06399i
$975$		0			0
$976$	−1126.42			−1.15412
$977$			493.726i			0.505349i	0.967551	+	0.252674i	$0.0813101\pi$
$977$			493.726i			0.505349i	−0.967551	+	0.252674i	$0.918690\pi$
$978$	717.711	−	204.714i	0.733856	−	0.209319i
$979$	−893.150			−0.912309
$980$		0			0
$981$	279.365	−	173.481i	0.284775	−	0.176841i
$982$	598.797			0.609773
$983$			1538.05i			1.56465i	0.622870	+	0.782325i	$0.285966\pi$
$983$			1538.05i			1.56465i	−0.622870	+	0.782325i	$0.714034\pi$
$984$	−831.918	−	2916.64i	−0.845445	−	2.96406i
$985$		0			0
$986$			150.741i			0.152881i
$987$	−252.000	+	71.8783i	−0.255319	+	0.0728251i
$988$	−1567.06			−1.58609
$989$			616.731i			0.623590i
$990$		0			0
$991$	1514.73			1.52849			0.764243	−	0.644929i	$-0.223113\pi$
$991$	1514.73			1.52849			0.764243	+	0.644929i	$0.223113\pi$
$992$			243.270i			0.245232i
$993$	−127.026	−	445.344i	−0.127922	−	0.448483i
$994$	−654.486			−0.658437
$995$		0			0
$996$	1776.92	−	506.833i	1.78405	−	0.508868i
$997$	−1826.43			−1.83193			−0.915964	−	0.401260i	$-0.868572\pi$
$997$	−1826.43			−1.83193			−0.915964	+	0.401260i	$0.868572\pi$
$998$		−	2972.37i		−	2.97833i
$999$	660.443	+	599.705i	0.661104	+	0.600306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.c.a.176.4		4
3.2	odd	2	inner	525.3.c.a.176.1		4
5.2	odd	4		525.3.f.a.449.2		8
5.3	odd	4		525.3.f.a.449.7		8
5.4	even	2		21.3.b.a.8.1	✓	4
15.2	even	4		525.3.f.a.449.8		8
15.8	even	4		525.3.f.a.449.1		8
15.14	odd	2		21.3.b.a.8.4	yes	4
20.19	odd	2		336.3.d.c.113.1		4
35.4	even	6		147.3.h.e.128.4		8
35.9	even	6		147.3.h.e.116.1		8
35.19	odd	6		147.3.h.c.116.1		8
35.24	odd	6		147.3.h.c.128.4		8
35.34	odd	2		147.3.b.f.50.1		4
40.19	odd	2		1344.3.d.b.449.4		4
40.29	even	2		1344.3.d.f.449.1		4
45.4	even	6		567.3.r.c.512.4		8
45.14	odd	6		567.3.r.c.512.1		8
45.29	odd	6		567.3.r.c.134.4		8
45.34	even	6		567.3.r.c.134.1		8
60.59	even	2		336.3.d.c.113.2		4
105.44	odd	6		147.3.h.e.116.4		8
105.59	even	6		147.3.h.c.128.1		8
105.74	odd	6		147.3.h.e.128.1		8
105.89	even	6		147.3.h.c.116.4		8
105.104	even	2		147.3.b.f.50.4		4
120.29	odd	2		1344.3.d.f.449.2		4
120.59	even	2		1344.3.d.b.449.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.b.a.8.1	✓	4	5.4	even	2
21.3.b.a.8.4	yes	4	15.14	odd	2
147.3.b.f.50.1		4	35.34	odd	2
147.3.b.f.50.4		4	105.104	even	2
147.3.h.c.116.1		8	35.19	odd	6
147.3.h.c.116.4		8	105.89	even	6
147.3.h.c.128.1		8	105.59	even	6
147.3.h.c.128.4		8	35.24	odd	6
147.3.h.e.116.1		8	35.9	even	6
147.3.h.e.116.4		8	105.44	odd	6
147.3.h.e.128.1		8	105.74	odd	6
147.3.h.e.128.4		8	35.4	even	6
336.3.d.c.113.1		4	20.19	odd	2
336.3.d.c.113.2		4	60.59	even	2
525.3.c.a.176.1		4	3.2	odd	2	inner
525.3.c.a.176.4		4	1.1	even	1	trivial
525.3.f.a.449.1		8	15.8	even	4
525.3.f.a.449.2		8	5.2	odd	4
525.3.f.a.449.7		8	5.3	odd	4
525.3.f.a.449.8		8	15.2	even	4
567.3.r.c.134.1		8	45.34	even	6
567.3.r.c.134.4		8	45.29	odd	6
567.3.r.c.512.1		8	45.14	odd	6
567.3.r.c.512.4		8	45.4	even	6
1344.3.d.b.449.3		4	120.59	even	2
1344.3.d.b.449.4		4	40.19	odd	2
1344.3.d.f.449.1		4	40.29	even	2
1344.3.d.f.449.2		4	120.29	odd	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)

\(f(q)\)	\(=\)	\(q+3.50592i q^{2} +(-0.822876 - 2.88494i) q^{3} -8.29150 q^{4} +(10.1144 - 2.88494i) q^{6} -2.64575 q^{7} -15.0457i q^{8} +(-7.64575 + 4.74789i) q^{9} +O(q^{10})\)	\(q+3.50592i q^{2} +(-0.822876 - 2.88494i) q^{3} -8.29150 q^{4} +(10.1144 - 2.88494i) q^{6} -2.64575 q^{7} -15.0457i q^{8} +(-7.64575 + 4.74789i) q^{9} -7.01185i q^{11} +(6.82288 + 23.9205i) q^{12} +11.6458 q^{13} -9.27580i q^{14} +19.5830 q^{16} -4.52791i q^{17} +(-16.6458 - 26.8054i) q^{18} +16.2288 q^{19} +(2.17712 + 7.63283i) q^{21} +24.5830 q^{22} +25.5635i q^{23} +(-43.4059 + 12.3807i) q^{24} +40.8291i q^{26} +(19.9889 + 18.1506i) q^{27} +21.9373 q^{28} +9.49579i q^{29} +28.7085 q^{31} +8.47380i q^{32} +(-20.2288 + 5.76988i) q^{33} +15.8745 q^{34} +(63.3948 - 39.3672i) q^{36} +33.0405 q^{37} +56.8968i q^{38} +(-9.58301 - 33.5973i) q^{39} +67.1946i q^{41} +(-26.7601 + 7.63283i) q^{42} +24.1255 q^{43} +58.1388i q^{44} -89.6235 q^{46} +33.0153i q^{47} +(-16.1144 - 56.4958i) q^{48} +7.00000 q^{49} +(-13.0627 + 3.72591i) q^{51} -96.5608 q^{52} +15.1877i q^{53} +(-63.6346 + 70.0795i) q^{54} +39.8071i q^{56} +(-13.3542 - 46.8190i) q^{57} -33.2915 q^{58} +92.3960i q^{59} -57.5203 q^{61} +100.650i q^{62} +(20.2288 - 12.5617i) q^{63} +48.6235 q^{64} +(-20.2288 - 70.9205i) q^{66} -15.1660 q^{67} +37.5432i q^{68} +(73.7490 - 21.0355i) q^{69} -70.5584i q^{71} +(71.4353 + 115.036i) q^{72} +76.7895 q^{73} +115.838i q^{74} -134.561 q^{76} +18.5516i q^{77} +(117.790 - 33.5973i) q^{78} +127.247 q^{79} +(35.9150 - 72.6024i) q^{81} -235.579 q^{82} -74.2844i q^{83} +(-18.0516 - 63.2876i) q^{84} +84.5821i q^{86} +(27.3948 - 7.81385i) q^{87} -105.498 q^{88} -127.377i q^{89} -30.8118 q^{91} -211.959i q^{92} +(-23.6235 - 82.8223i) q^{93} -115.749 q^{94} +(24.4464 - 6.97288i) q^{96} +23.1660 q^{97} +24.5415i q^{98} +(33.2915 + 53.6108i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 12 q^{4} + 14 q^{6} - 20 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 12 * q^4 + 14 * q^6 - 20 * q^9	\( 4 q + 2 q^{3} - 12 q^{4} + 14 q^{6} - 20 q^{9} + 22 q^{12} + 36 q^{13} + 36 q^{16} - 56 q^{18} + 12 q^{19} + 14 q^{21} + 56 q^{22} - 126 q^{24} - 10 q^{27} + 56 q^{28} + 136 q^{31} - 28 q^{33} + 116 q^{36} - 16 q^{37} + 4 q^{39} - 70 q^{42} + 160 q^{43} - 168 q^{46} - 38 q^{48} + 28 q^{49} - 84 q^{51} - 164 q^{52} - 154 q^{54} - 64 q^{57} - 112 q^{58} - 156 q^{61} + 28 q^{63} + 4 q^{64} - 28 q^{66} + 24 q^{67} + 168 q^{69} + 32 q^{73} - 316 q^{76} + 196 q^{78} + 128 q^{79} - 68 q^{81} - 392 q^{82} - 14 q^{84} - 28 q^{87} - 168 q^{88} - 28 q^{91} + 96 q^{93} - 336 q^{94} - 98 q^{96} + 8 q^{97} + 112 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 12 * q^4 + 14 * q^6 - 20 * q^9 + 22 * q^12 + 36 * q^13 + 36 * q^16 - 56 * q^18 + 12 * q^19 + 14 * q^21 + 56 * q^22 - 126 * q^24 - 10 * q^27 + 56 * q^28 + 136 * q^31 - 28 * q^33 + 116 * q^36 - 16 * q^37 + 4 * q^39 - 70 * q^42 + 160 * q^43 - 168 * q^46 - 38 * q^48 + 28 * q^49 - 84 * q^51 - 164 * q^52 - 154 * q^54 - 64 * q^57 - 112 * q^58 - 156 * q^61 + 28 * q^63 + 4 * q^64 - 28 * q^66 + 24 * q^67 + 168 * q^69 + 32 * q^73 - 316 * q^76 + 196 * q^78 + 128 * q^79 - 68 * q^81 - 392 * q^82 - 14 * q^84 - 28 * q^87 - 168 * q^88 - 28 * q^91 + 96 * q^93 - 336 * q^94 - 98 * q^96 + 8 * q^97 + 112 * q^99

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