LMFDB - Embedded newform 525.3.c.a.176.1

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

$q$-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	$-0.659885\pi$
$2$		−	3.50592i		−	1.75296i	0.481436	−	0.876481i	$-0.340115\pi$
$3$	−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	$0.103253\pi$
$11$			7.01185i			0.637441i	−0.947849	+	0.318720i	$0.896747\pi$
$12$	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	$0.0425169\pi$
$17$			4.52791i			0.266348i	−0.991093	+	0.133174i	$0.957483\pi$
$18$	−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	$-0.812440\pi$
$23$		−	25.5635i		−	1.11145i	0.831365	−	0.555727i	$-0.187560\pi$
$24$	−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	$-0.947650\pi$
$29$		−	9.49579i		−	0.327441i	0.986507	−	0.163720i	$-0.0523495\pi$
$30$		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	$-0.694281\pi$
$41$		−	67.1946i		−	1.63889i	0.573156	−	0.819446i	$-0.305719\pi$
$42$	−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	$-0.885765\pi$
$47$		−	33.0153i		−	0.702452i	0.936291	−	0.351226i	$-0.114235\pi$
$48$	−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	$-0.954235\pi$
$53$		−	15.1877i		−	0.286561i	0.989682	−	0.143281i	$-0.0457651\pi$
$54$	−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	$-0.713680\pi$
$59$		−	92.3960i		−	1.56603i	0.622000	−	0.783017i	$-0.286320\pi$
$60$		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	$0.165525\pi$
$71$			70.5584i			0.993781i	−0.867813	+	0.496890i	$0.834475\pi$
$72$	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	$0.147684\pi$
$83$			74.2844i			0.894992i	−0.894286	+	0.447496i	$0.852316\pi$
$84$	−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	$0.253848\pi$
$89$			127.377i			1.43121i	−0.698507	+	0.715603i	$0.746152\pi$
$90$		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	$0.232788\pi$
$101$			134.907i			1.33571i	−0.744290	+	0.667857i	$0.767212\pi$
$102$	−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	$-0.881477\pi$
$107$		−	77.8544i		−	0.727611i	0.931475	−	0.363806i	$-0.118523\pi$
$108$	−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	$0.0306949\pi$
$113$			21.7596i			0.192563i	−0.995354	+	0.0962815i	$0.969305\pi$
$114$	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	$-0.753676\pi$
$131$		−	183.110i		−	1.39779i	0.715226	−	0.698893i	$-0.246324\pi$
$132$	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	$0.0384477\pi$
$137$			33.0153i			0.240987i	−0.992714	+	0.120494i	$0.961552\pi$
$138$	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	$-0.771896\pi$
$149$		−	195.736i		−	1.31366i	0.754037	−	0.656832i	$-0.228104\pi$
$150$		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	$-0.787240\pi$
$167$		−	206.992i		−	1.23947i	0.784811	−	0.619735i	$-0.212760\pi$
$168$	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	$0.101494\pi$
$173$			108.464i			0.626958i	−0.949595	+	0.313479i	$0.898506\pi$
$174$	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	$-0.853157\pi$
$179$		−	159.357i		−	0.890261i	0.895466	−	0.445131i	$-0.146843\pi$
$180$		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	$0.272109\pi$
$191$			288.210i			1.50895i	−0.656328	+	0.754476i	$0.727891\pi$
$192$	−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	$-0.887446\pi$
$197$		−	136.433i		−	0.692554i	0.938132	−	0.346277i	$-0.112554\pi$
$198$	−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	$-0.872084\pi$
$227$		−	177.574i		−	0.782264i	0.920335	−	0.391132i	$-0.127916\pi$
$228$	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	$0.312784\pi$
$233$			387.696i			1.66393i	−0.554828	+	0.831965i	$0.687216\pi$
$234$	−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	$0.0330376\pi$
$239$			49.5229i			0.207209i	−0.994619	+	0.103604i	$0.966962\pi$
$240$		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	$0.176071\pi$
$251$			263.732i			1.05073i	−0.850878	+	0.525364i	$0.823929\pi$
$252$	−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	$-0.904971\pi$
$257$		−	151.181i		−	0.588252i	0.955767	−	0.294126i	$-0.0950286\pi$
$258$	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	$0.0697805\pi$
$263$			114.389i			0.434941i	−0.976067	+	0.217470i	$0.930219\pi$
$264$	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	$-0.997183\pi$
$269$		−	4.76170i		−	0.0177015i	0.999961	−	0.00885074i	$-0.00281731\pi$
$270$		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	$-0.742000\pi$
$281$		−	407.255i		−	1.44931i	0.689113	−	0.724654i	$-0.258000\pi$
$282$	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	$0.00137659\pi$
$293$			2.53426i			0.00864935i	−0.999991	+	0.00432468i	$0.998623\pi$
$294$	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	$-0.921536\pi$
$311$		−	151.777i		−	0.488028i	0.969772	−	0.244014i	$-0.0784643\pi$
$312$	−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	$0.194673\pi$
$317$			364.020i			1.14833i	−0.818740	+	0.574164i	$0.805327\pi$
$318$	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	$-0.762404\pi$
$347$		−	471.242i		−	1.35805i	0.734117	−	0.679023i	$-0.237596\pi$
$348$	−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	$-0.960974\pi$
$353$		−	86.3420i		−	0.244595i	0.992493	−	0.122297i	$-0.0390262\pi$
$354$	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	$-0.826602\pi$
$359$		−	372.068i		−	1.03640i	0.855259	−	0.518200i	$-0.173398\pi$
$360$		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	$0.0472891\pi$
$383$			113.381i			0.296034i	−0.988985	+	0.148017i	$0.952711\pi$
$384$	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	$0.382490\pi$
$389$			725.584i			1.86526i	−0.360841	+	0.932628i	$0.617510\pi$
$390$		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	$0.320381\pi$
$401$			677.665i			1.68994i	−0.534815	+	0.844969i	$0.679619\pi$
$402$	−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	$-0.948084\pi$
$419$		−	136.071i		−	0.324752i	0.986729	−	0.162376i	$-0.0519157\pi$
$420$		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	$-0.870843\pi$
$431$		−	340.244i		−	0.789430i	0.918804	−	0.394715i	$-0.129157\pi$
$432$	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	$-0.928503\pi$
$443$		−	197.340i		−	0.445463i	0.974880	−	0.222731i	$-0.0714973\pi$
$444$	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	$-0.947262\pi$
$449$		−	148.101i		−	0.329847i	0.986306	−	0.164923i	$-0.0527377\pi$
$450$		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	$-0.773500\pi$
$461$		−	602.089i		−	1.30605i	0.757337	−	0.653025i	$-0.226500\pi$
$462$	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	$-0.692884\pi$
$467$		−	767.706i		−	1.64391i	0.569553	−	0.821955i	$-0.307116\pi$
$468$	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	$-0.865137\pi$
$479$		−	393.855i		−	0.822245i	0.911580	−	0.411122i	$-0.134863\pi$
$480$		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	$0.0556455\pi$
$491$			170.796i			0.347853i	−0.984759	+	0.173927i	$0.944354\pi$
$492$	−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	$0.0629398\pi$
$503$			197.624i			0.392891i	−0.980515	+	0.196445i	$0.937060\pi$
$504$	−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	$-0.839635\pi$
$509$		−	491.448i		−	0.965516i	0.875754	−	0.482758i	$-0.160365\pi$
$510$		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	$-0.685501\pi$
$521$		−	870.010i		−	1.66988i	0.550338	−	0.834942i	$-0.314499\pi$
$522$	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	$0.302465\pi$
$557$			906.288i			1.62709i	−0.581503	+	0.813544i	$0.697535\pi$
$558$	−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	$-0.866471\pi$
$563$		−	458.616i		−	0.814593i	0.913296	−	0.407297i	$-0.133529\pi$
$564$	−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	$0.169395\pi$
$569$			577.428i			1.01481i	−0.861707	+	0.507406i	$0.830605\pi$
$570$		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	$0.0431563\pi$
$587$			158.683i			0.270329i	−0.990823	+	0.135164i	$0.956844\pi$
$588$	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	$-0.710766\pi$
$593$		−	935.371i		−	1.57735i	0.614807	−	0.788677i	$-0.289234\pi$
$594$	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	$-0.980388\pi$
$599$		−	73.7665i		−	0.123149i	0.998102	−	0.0615747i	$-0.0196122\pi$
$600$		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	$0.396780\pi$
$617$			1169.69i			1.89576i	−0.318622	+	0.947882i	$0.603220\pi$
$618$	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	$-0.864709\pi$
$641$		−	528.629i		−	0.824694i	0.911027	−	0.412347i	$-0.135291\pi$
$642$	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	$-0.792110\pi$
$647$		−	786.308i		−	1.21531i	0.794200	−	0.607657i	$-0.207890\pi$
$648$	−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	$-0.904543\pi$
$653$		−	385.807i		−	0.590823i	0.955370	−	0.295412i	$-0.0954568\pi$
$654$	−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	$0.0235102\pi$
$659$			97.2583i			0.147585i	−0.997274	+	0.0737924i	$0.976490\pi$
$660$		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	$0.376003\pi$
$677$			1252.56i			1.85016i	−0.379771	+	0.925080i	$0.623997\pi$
$678$	−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	$0.0803335\pi$
$683$			341.097i			0.499409i	−0.968322	+	0.249705i	$0.919666\pi$
$684$	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	$0.398813\pi$
$701$			1331.76i			1.89979i	−0.312562	+	0.949897i	$0.601187\pi$
$702$	−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	$0.142806\pi$
$719$			623.715i			0.867476i	−0.901039	+	0.433738i	$0.857194\pi$
$720$		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	$0.0830776\pi$
$743$			383.452i			0.516086i	−0.966133	+	0.258043i	$0.916922\pi$
$744$	−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	$-0.981228\pi$
$761$		−	89.7059i		−	0.117879i	0.998262	−	0.0589395i	$-0.0187719\pi$
$762$	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	$-0.911542\pi$
$773$		−	424.125i		−	0.548674i	0.961634	−	0.274337i	$-0.0884584\pi$
$774$	−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	$0.148999\pi$
$797$			719.191i			0.902373i	−0.892430	+	0.451186i	$0.851001\pi$
$798$	−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	$-0.958125\pi$
$809$		−	212.244i		−	0.262353i	0.991359	−	0.131176i	$-0.0418755\pi$
$810$		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	$0.166123\pi$
$821$			818.571i			0.997042i	−0.866878	+	0.498521i	$0.833877\pi$
$822$	−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	$0.0854376\pi$
$827$			438.639i			0.530398i	−0.964194	+	0.265199i	$0.914562\pi$
$828$	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	$0.00967049\pi$
$839$			50.9710i			0.0607521i	−0.999539	+	0.0303761i	$0.990330\pi$
$840$		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	$0.105260\pi$
$857$			556.521i			0.649382i	−0.945820	+	0.324691i	$0.894740\pi$
$858$	−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	$0.0378757\pi$
$863$			204.892i			0.237419i	−0.992929	+	0.118709i	$0.962124\pi$
$864$	−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	$0.289740\pi$
$881$			1391.37i			1.57931i	−0.613552	+	0.789654i	$0.710260\pi$
$882$	−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	$0.0268475\pi$
$887$			149.449i			0.168488i	−0.996445	+	0.0842439i	$0.973153\pi$
$888$	−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	$-0.786217\pi$
$911$		−	1133.75i		−	1.24451i	0.782815	−	0.622254i	$-0.213783\pi$
$912$	−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	$0.0330066\pi$
$929$			192.317i			0.207015i	−0.994629	+	0.103507i	$0.966993\pi$
$930$		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	$-0.973423\pi$
$941$		−	156.951i		−	0.166791i	0.996517	−	0.0833957i	$-0.0265766\pi$
$942$	−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	$0.153801\pi$
$947$			879.945i			0.929193i	−0.885523	+	0.464596i	$0.846199\pi$
$948$	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	$0.0954955\pi$
$953$			563.276i			0.591056i	−0.955334	+	0.295528i	$0.904505\pi$
$954$	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	$0.245808\pi$
$971$			1355.00i			1.39546i	−0.716359	+	0.697732i	$0.754192\pi$
$972$	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	$-0.918690\pi$
$977$		−	493.726i		−	0.505349i	0.967551	−	0.252674i	$-0.0813101\pi$
$978$	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	$-0.714034\pi$
$983$		−	1538.05i		−	1.56465i	0.622870	−	0.782325i	$-0.285966\pi$
$984$	−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.176.1		4
3.2	odd	2	inner	525.3.c.a.176.4		4
5.2	odd	4		525.3.f.a.449.8		8
5.3	odd	4		525.3.f.a.449.1		8
5.4	even	2		21.3.b.a.8.4	yes	4
15.2	even	4		525.3.f.a.449.2		8
15.8	even	4		525.3.f.a.449.7		8
15.14	odd	2		21.3.b.a.8.1	✓	4
20.19	odd	2		336.3.d.c.113.2		4
35.4	even	6		147.3.h.e.128.1		8
35.9	even	6		147.3.h.e.116.4		8
35.19	odd	6		147.3.h.c.116.4		8
35.24	odd	6		147.3.h.c.128.1		8
35.34	odd	2		147.3.b.f.50.4		4
40.19	odd	2		1344.3.d.b.449.3		4
40.29	even	2		1344.3.d.f.449.2		4
45.4	even	6		567.3.r.c.512.1		8
45.14	odd	6		567.3.r.c.512.4		8
45.29	odd	6		567.3.r.c.134.1		8
45.34	even	6		567.3.r.c.134.4		8
60.59	even	2		336.3.d.c.113.1		4
105.44	odd	6		147.3.h.e.116.1		8
105.59	even	6		147.3.h.c.128.4		8
105.74	odd	6		147.3.h.e.128.4		8
105.89	even	6		147.3.h.c.116.1		8
105.104	even	2		147.3.b.f.50.1		4
120.29	odd	2		1344.3.d.f.449.1		4
120.59	even	2		1344.3.d.b.449.4		4

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

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