LMFDB - Embedded newform 1155.3.b.a.736.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,3,Mod(736,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1155.736");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1155.b (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:	$31.4714705336$
Analytic rank:	$0$
Dimension:	$96$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			736.8
Character	$\chi$	$=$	1155.736
Dual form			1155.3.b.a.736.89

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.64908i q^{2} +1.73205 q^{3} -9.31580 q^{4} +2.23607 q^{5} -6.32039i q^{6} +2.64575i q^{7} +19.3978i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-3.64908i q^{2} +1.73205 q^{3} -9.31580 q^{4} +2.23607 q^{5} -6.32039i q^{6} +2.64575i q^{7} +19.3978i q^{8} +3.00000 q^{9} -8.15959i q^{10} +(3.25029 - 10.5088i) q^{11} -16.1354 q^{12} -7.79635i q^{13} +9.65456 q^{14} +3.87298 q^{15} +33.5209 q^{16} +10.5260i q^{17} -10.9472i q^{18} -14.0951i q^{19} -20.8308 q^{20} +4.58258i q^{21} +(-38.3476 - 11.8606i) q^{22} +33.0811 q^{23} +33.5979i q^{24} +5.00000 q^{25} -28.4495 q^{26} +5.19615 q^{27} -24.6473i q^{28} -25.1912i q^{29} -14.1328i q^{30} +54.1293 q^{31} -44.7293i q^{32} +(5.62967 - 18.2018i) q^{33} +38.4102 q^{34} +5.91608i q^{35} -27.9474 q^{36} -35.4258 q^{37} -51.4341 q^{38} -13.5037i q^{39} +43.3747i q^{40} -8.19086i q^{41} +16.7222 q^{42} -73.0340i q^{43} +(-30.2791 + 97.8982i) q^{44} +6.70820 q^{45} -120.715i q^{46} -89.2387 q^{47} +58.0599 q^{48} -7.00000 q^{49} -18.2454i q^{50} +18.2315i q^{51} +72.6292i q^{52} +41.9216 q^{53} -18.9612i q^{54} +(7.26787 - 23.4985i) q^{55} -51.3217 q^{56} -24.4134i q^{57} -91.9248 q^{58} -69.2000 q^{59} -36.0799 q^{60} -21.4734i q^{61} -197.522i q^{62} +7.93725i q^{63} -29.1375 q^{64} -17.4332i q^{65} +(-66.4200 - 20.5431i) q^{66} -104.429 q^{67} -98.0580i q^{68} +57.2981 q^{69} +21.5883 q^{70} -91.5629 q^{71} +58.1933i q^{72} -70.7615i q^{73} +129.272i q^{74} +8.66025 q^{75} +131.307i q^{76} +(27.8038 + 8.59946i) q^{77} -49.2760 q^{78} +46.3899i q^{79} +74.9550 q^{80} +9.00000 q^{81} -29.8891 q^{82} -7.21651i q^{83} -42.6903i q^{84} +23.5368i q^{85} -266.507 q^{86} -43.6325i q^{87} +(203.848 + 63.0484i) q^{88} +61.2495 q^{89} -24.4788i q^{90} +20.6272 q^{91} -308.176 q^{92} +93.7547 q^{93} +325.639i q^{94} -31.5175i q^{95} -77.4735i q^{96} +147.297 q^{97} +25.5436i q^{98} +(9.75087 - 31.5265i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 216 q^{4} + 288 q^{9}+O(q^{10}) $ 96 * q - 216 * q^4 + 288 * q^9	$ 96 q - 216 q^{4} + 288 q^{9} + 40 q^{11} - 56 q^{14} + 488 q^{16} + 56 q^{22} + 16 q^{23} + 480 q^{25} - 64 q^{26} + 192 q^{31} + 24 q^{33} + 176 q^{34} - 648 q^{36} - 112 q^{37} - 272 q^{38} - 520 q^{44} + 416 q^{47} - 192 q^{48} - 672 q^{49} + 112 q^{53} - 80 q^{55} + 280 q^{56} - 352 q^{58} + 512 q^{59} - 1112 q^{64} + 288 q^{66} - 304 q^{67} - 480 q^{71} + 224 q^{77} + 240 q^{78} + 864 q^{81} - 720 q^{82} - 432 q^{86} - 376 q^{88} - 32 q^{89} - 384 q^{92} + 384 q^{93} + 272 q^{97} + 120 q^{99}+O(q^{100}) $ 96 * q - 216 * q^4 + 288 * q^9 + 40 * q^11 - 56 * q^14 + 488 * q^16 + 56 * q^22 + 16 * q^23 + 480 * q^25 - 64 * q^26 + 192 * q^31 + 24 * q^33 + 176 * q^34 - 648 * q^36 - 112 * q^37 - 272 * q^38 - 520 * q^44 + 416 * q^47 - 192 * q^48 - 672 * q^49 + 112 * q^53 - 80 * q^55 + 280 * q^56 - 352 * q^58 + 512 * q^59 - 1112 * q^64 + 288 * q^66 - 304 * q^67 - 480 * q^71 + 224 * q^77 + 240 * q^78 + 864 * q^81 - 720 * q^82 - 432 * q^86 - 376 * q^88 - 32 * q^89 - 384 * q^92 + 384 * q^93 + 272 * q^97 + 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$-1$	$1$	$1$	$1$

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 $

$2$		−	3.64908i		−	1.82454i	−0.409588	−	0.912270i	$-0.634328\pi$
$2$		−	3.64908i		−	1.82454i	0.409588	−	0.912270i	$-0.365672\pi$
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	−9.31580			−2.32895
$5$	2.23607			0.447214
$5$	2.23607			0.447214
$6$		−	6.32039i		−	1.05340i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$			19.3978i			2.42472i
$9$	3.00000			0.333333
$10$		−	8.15959i		−	0.815959i
$11$	3.25029	−	10.5088i	0.295481	−	0.955349i
$11$	3.25029	−	10.5088i	0.295481	−	0.955349i
$12$	−16.1354			−1.34462
$13$		−	7.79635i		−	0.599719i	−0.953983	−	0.299860i	$-0.903060\pi$
$13$		−	7.79635i		−	0.599719i	0.953983	−	0.299860i	$-0.0969399\pi$
$14$	9.65456			0.689612
$15$	3.87298			0.258199
$16$	33.5209			2.09506
$17$			10.5260i			0.619176i	0.950871	+	0.309588i	$0.100191\pi$
$17$			10.5260i			0.619176i	−0.950871	+	0.309588i	$0.899809\pi$
$18$		−	10.9472i		−	0.608180i
$19$		−	14.0951i		−	0.741846i	−0.928664	−	0.370923i	$-0.879041\pi$
$19$		−	14.0951i		−	0.741846i	0.928664	−	0.370923i	$-0.120959\pi$
$20$	−20.8308			−1.04154
$21$			4.58258i			0.218218i
$22$	−38.3476	−	11.8606i	−1.74307	−	0.539117i
$23$	33.0811			1.43831			0.719153	−	0.694851i	$-0.244530\pi$
$23$	33.0811			1.43831			0.719153	+	0.694851i	$0.244530\pi$
$24$			33.5979i			1.39991i
$25$	5.00000			0.200000
$26$	−28.4495			−1.09421
$27$	5.19615			0.192450
$28$		−	24.6473i		−	0.880260i
$29$		−	25.1912i		−	0.868662i	−0.900753	−	0.434331i	$-0.856985\pi$
$29$		−	25.1912i		−	0.868662i	0.900753	−	0.434331i	$-0.143015\pi$
$30$		−	14.1328i		−	0.471094i
$31$	54.1293			1.74611			0.873054	−	0.487624i	$-0.162136\pi$
$31$	54.1293			1.74611			0.873054	+	0.487624i	$0.162136\pi$
$32$		−	44.7293i		−	1.39779i
$33$	5.62967	−	18.2018i	0.170596	−	0.551571i
$34$	38.4102			1.12971
$35$			5.91608i			0.169031i
$36$	−27.9474			−0.776316
$37$	−35.4258			−0.957453			−0.478727	−	0.877964i	$-0.658901\pi$
$37$	−35.4258			−0.957453			−0.478727	+	0.877964i	$0.658901\pi$
$38$	−51.4341			−1.35353
$39$		−	13.5037i		−	0.346248i
$40$			43.3747i			1.08437i
$41$		−	8.19086i		−	0.199777i	−0.994999	−	0.0998886i	$-0.968151\pi$
$41$		−	8.19086i		−	0.199777i	0.994999	−	0.0998886i	$-0.0318486\pi$
$42$	16.7222			0.398147
$43$		−	73.0340i		−	1.69846i	−0.528019	−	0.849232i	$-0.677065\pi$
$43$		−	73.0340i		−	1.69846i	0.528019	−	0.849232i	$-0.322935\pi$
$44$	−30.2791	+	97.8982i	−0.688160	+	2.22496i
$45$	6.70820			0.149071
$46$		−	120.715i		−	2.62425i
$47$	−89.2387			−1.89869			−0.949347	−	0.314228i	$-0.898254\pi$
$47$	−89.2387			−1.89869			−0.949347	+	0.314228i	$0.898254\pi$
$48$	58.0599			1.20958
$49$	−7.00000			−0.142857
$50$		−	18.2454i		−	0.364908i
$51$			18.2315i			0.357481i
$52$			72.6292i			1.39672i
$53$	41.9216			0.790973			0.395487	−	0.918472i	$-0.370576\pi$
$53$	41.9216			0.790973			0.395487	+	0.918472i	$0.370576\pi$
$54$		−	18.9612i		−	0.351133i
$55$	7.26787	−	23.4985i	0.132143	−	0.427245i
$56$	−51.3217			−0.916459
$57$		−	24.4134i		−	0.428305i
$58$	−91.9248			−1.58491
$59$	−69.2000			−1.17288			−0.586441	−	0.809992i	$-0.699471\pi$
$59$	−69.2000			−1.17288			−0.586441	+	0.809992i	$0.699471\pi$
$60$	−36.0799			−0.601332
$61$		−	21.4734i		−	0.352023i	−0.984388	−	0.176011i	$-0.943680\pi$
$61$		−	21.4734i		−	0.352023i	0.984388	−	0.176011i	$-0.0563195\pi$
$62$		−	197.522i		−	3.18584i
$63$			7.93725i			0.125988i
$64$	−29.1375			−0.455273
$65$		−	17.4332i		−	0.268203i
$66$	−66.4200	−	20.5431i	−1.00636	−	0.311259i
$67$	−104.429			−1.55864			−0.779321	−	0.626625i	$-0.784436\pi$
$67$	−104.429			−1.55864			−0.779321	+	0.626625i	$0.784436\pi$
$68$		−	98.0580i		−	1.44203i
$69$	57.2981			0.830407
$70$	21.5883			0.308404
$71$	−91.5629			−1.28962			−0.644809	−	0.764344i	$-0.723063\pi$
$71$	−91.5629			−1.28962			−0.644809	+	0.764344i	$0.723063\pi$
$72$			58.1933i			0.808241i
$73$		−	70.7615i		−	0.969336i	−0.874698	−	0.484668i	$-0.838940\pi$
$73$		−	70.7615i		−	0.969336i	0.874698	−	0.484668i	$-0.161060\pi$
$74$			129.272i			1.74691i
$75$	8.66025			0.115470
$76$			131.307i			1.72772i
$77$	27.8038	+	8.59946i	0.361088	+	0.111681i
$78$	−49.2760			−0.631744
$79$			46.3899i			0.587214i	0.955926	+	0.293607i	$0.0948557\pi$
$79$			46.3899i			0.587214i	−0.955926	+	0.293607i	$0.905144\pi$
$80$	74.9550			0.936937
$81$	9.00000			0.111111
$82$	−29.8891			−0.364502
$83$		−	7.21651i		−	0.0869459i	−0.999055	−	0.0434730i	$-0.986158\pi$
$83$		−	7.21651i		−	0.0869459i	0.999055	−	0.0434730i	$-0.0138422\pi$
$84$		−	42.6903i		−	0.508218i
$85$			23.5368i			0.276904i
$86$	−266.507			−3.09892
$87$		−	43.6325i		−	0.501522i
$88$	203.848	+	63.0484i	2.31645	+	0.716459i
$89$	61.2495			0.688196			0.344098	−	0.938934i	$-0.388185\pi$
$89$	61.2495			0.688196			0.344098	+	0.938934i	$0.388185\pi$
$90$		−	24.4788i		−	0.271986i
$91$	20.6272			0.226673
$92$	−308.176			−3.34974
$93$	93.7547			1.00812
$94$			325.639i			3.46425i
$95$		−	31.5175i		−	0.331763i
$96$		−	77.4735i		−	0.807015i
$97$	147.297			1.51853			0.759264	−	0.650782i	$-0.225559\pi$
$97$	147.297			1.51853			0.759264	+	0.650782i	$0.225559\pi$
$98$			25.5436i			0.260649i
$99$	9.75087	−	31.5265i	0.0984937	−	0.318450i
$100$	−46.5790			−0.465790
$101$		−	8.50866i		−	0.0842441i	−0.999112	−	0.0421221i	$-0.986588\pi$
$101$		−	8.50866i		−	0.0842441i	0.999112	−	0.0421221i	$-0.0134118\pi$
$102$	66.5284			0.652239
$103$	44.6417			0.433414			0.216707	−	0.976237i	$-0.430468\pi$
$103$	44.6417			0.433414			0.216707	+	0.976237i	$0.430468\pi$
$104$	151.232			1.45415
$105$			10.2470i			0.0975900i
$106$		−	152.975i		−	1.44316i
$107$			5.44364i			0.0508751i	0.999676	+	0.0254376i	$0.00809790\pi$
$107$			5.44364i			0.0508751i	−0.999676	+	0.0254376i	$0.991902\pi$
$108$	−48.4063			−0.448206
$109$			126.465i			1.16023i	0.814534	+	0.580115i	$0.196993\pi$
$109$			126.465i			1.16023i	−0.814534	+	0.580115i	$0.803007\pi$
$110$	−85.7478	−	26.5211i	−0.779526	−	0.241101i
$111$	−61.3592			−0.552786
$112$			88.6879i			0.791856i
$113$	−137.636			−1.21802			−0.609009	−	0.793163i	$-0.708433\pi$
$113$	−137.636			−1.21802			−0.609009	+	0.793163i	$0.708433\pi$
$114$	−89.0864			−0.781460
$115$	73.9715			0.643230
$116$			234.676i			2.02307i
$117$		−	23.3891i		−	0.199906i
$118$			252.517i			2.13997i
$119$	−27.8491			−0.234026
$120$			75.1273i			0.626061i
$121$	−99.8712	−	68.3136i	−0.825382	−	0.564575i
$122$	−78.3581			−0.642280
$123$		−	14.1870i		−	0.115341i
$124$	−504.258			−4.06660
$125$	11.1803			0.0894427
$126$	28.9637			0.229871
$127$			124.614i			0.981213i	0.871381	+	0.490606i	$0.163225\pi$
$127$			124.614i			0.981213i	−0.871381	+	0.490606i	$0.836775\pi$
$128$		−	72.5924i		−	0.567128i
$129$		−	126.499i		−	0.980609i
$130$	−63.6151			−0.489347
$131$		−	231.865i		−	1.76996i	−0.465628	−	0.884981i	$-0.654171\pi$
$131$		−	231.865i		−	1.76996i	0.465628	−	0.884981i	$-0.345829\pi$
$132$	−52.4449	+	169.565i	−0.397310	+	1.28458i
$133$	37.2920			0.280391
$134$			381.070i			2.84381i
$135$	11.6190			0.0860663
$136$	−204.181			−1.50133
$137$	219.208			1.60006			0.800028	−	0.599962i	$-0.204818\pi$
$137$	219.208			1.60006			0.800028	+	0.599962i	$0.204818\pi$
$138$		−	209.085i		−	1.51511i
$139$		−	198.943i		−	1.43124i	−0.698488	−	0.715622i	$-0.746144\pi$
$139$		−	198.943i		−	1.43124i	0.698488	−	0.715622i	$-0.253856\pi$
$140$		−	55.1130i		−	0.393664i
$141$	−154.566			−1.09621
$142$			334.120i			2.35296i
$143$	−81.9306	−	25.3404i	−0.572941	−	0.177206i
$144$	100.563			0.698352
$145$		−	56.3293i		−	0.388478i
$146$	−258.215			−1.76859
$147$	−12.1244			−0.0824786
$148$	330.019			2.22986
$149$		−	229.101i		−	1.53759i	−0.639496	−	0.768794i	$-0.720857\pi$
$149$		−	229.101i		−	1.53759i	0.639496	−	0.768794i	$-0.279143\pi$
$150$		−	31.6020i		−	0.210680i
$151$			34.1164i			0.225936i	0.993599	+	0.112968i	$0.0360358\pi$
$151$			34.1164i			0.225936i	−0.993599	+	0.112968i	$0.963964\pi$
$152$	273.413			1.79877
$153$			31.5780i			0.206392i
$154$	31.3801	−	101.458i	0.203767	−	0.658819i
$155$	121.037			0.780883
$156$			125.797i			0.806394i
$157$	−103.877			−0.661635			−0.330818	−	0.943695i	$-0.607324\pi$
$157$	−103.877			−0.661635			−0.330818	+	0.943695i	$0.607324\pi$
$158$	169.281			1.07140
$159$	72.6103			0.456669
$160$		−	100.018i		−	0.625111i
$161$			87.5242i			0.543629i
$162$		−	32.8417i		−	0.202727i
$163$	295.132			1.81063			0.905314	−	0.424743i	$-0.139635\pi$
$163$	295.132			1.81063			0.905314	+	0.424743i	$0.139635\pi$
$164$			76.3044i			0.465271i
$165$	12.5883	−	40.7005i	0.0762929	−	0.246670i
$166$	−26.3336			−0.158636
$167$		−	114.795i		−	0.687396i	−0.939080	−	0.343698i	$-0.888320\pi$
$167$		−	114.795i		−	0.687396i	0.939080	−	0.343698i	$-0.111680\pi$
$168$	−88.8918			−0.529118
$169$	108.217			0.640337
$170$	85.8878			0.505222
$171$		−	42.2852i		−	0.247282i
$172$			680.370i			3.95564i
$173$			160.479i			0.927623i	0.885934	+	0.463812i	$0.153519\pi$
$173$			160.479i			0.927623i	−0.885934	+	0.463812i	$0.846481\pi$
$174$	−159.218			−0.915048
$175$			13.2288i			0.0755929i
$176$	108.953	−	352.265i	0.619049	−	2.00151i
$177$	−119.858			−0.677164
$178$		−	223.504i		−	1.25564i
$179$	241.176			1.34735			0.673676	−	0.739027i	$-0.264714\pi$
$179$	241.176			1.34735			0.673676	+	0.739027i	$0.264714\pi$
$180$	−62.4923			−0.347179
$181$	163.413			0.902835			0.451418	−	0.892313i	$-0.350919\pi$
$181$	163.413			0.902835			0.451418	+	0.892313i	$0.350919\pi$
$182$		−	75.2704i		−	0.413573i
$183$		−	37.1930i		−	0.203240i
$184$			641.699i			3.48749i
$185$	−79.2144			−0.428186
$186$		−	342.119i		−	1.83935i
$187$	110.616	+	34.2125i	0.591529	+	0.182955i
$188$	831.329			4.42196
$189$			13.7477i			0.0727393i
$190$	−115.010			−0.605316
$191$	−38.9115			−0.203725			−0.101863	−	0.994798i	$-0.532480\pi$
$191$	−38.9115			−0.203725			−0.101863	+	0.994798i	$0.532480\pi$
$192$	−50.4676			−0.262852
$193$			123.474i			0.639761i	0.947458	+	0.319880i	$0.103643\pi$
$193$			123.474i			0.639761i	−0.947458	+	0.319880i	$0.896357\pi$
$194$		−	537.500i		−	2.77062i
$195$		−	30.1951i		−	0.154847i
$196$	65.2106			0.332707
$197$		−	301.950i		−	1.53274i	−0.642398	−	0.766371i	$-0.722060\pi$
$197$		−	301.950i		−	1.53274i	0.642398	−	0.766371i	$-0.277940\pi$
$198$	−115.043	−	35.5817i	−0.581024	−	0.179706i
$199$	−49.9118			−0.250813			−0.125407	−	0.992105i	$-0.540024\pi$
$199$	−49.9118			−0.250813			−0.125407	+	0.992105i	$0.540024\pi$
$200$			96.9889i			0.484944i
$201$	−180.876			−0.899882
$202$	−31.0488			−0.153707
$203$	66.6497			0.328324
$204$		−	169.841i		−	0.832556i
$205$		−	18.3153i		−	0.0893431i
$206$		−	162.901i		−	0.790782i
$207$	99.2432			0.479436
$208$		−	261.341i		−	1.25645i
$209$	−148.123	−	45.8131i	−0.708721	−	0.219201i
$210$	37.3920			0.178057
$211$			62.6756i			0.297041i	0.988909	+	0.148520i	$0.0474511\pi$
$211$			62.6756i			0.297041i	−0.988909	+	0.148520i	$0.952549\pi$
$212$	−390.533			−1.84214
$213$	−158.592			−0.744561
$214$	19.8643			0.0928238
$215$		−	163.309i		−	0.759577i
$216$			100.794i			0.466638i
$217$			143.213i			0.659967i
$218$	461.482			2.11689
$219$		−	122.563i		−	0.559646i
$220$	−67.7060	+	218.907i	−0.307755	+	0.995032i
$221$	82.0643			0.371332
$222$			223.905i			1.00858i
$223$	199.312			0.893776			0.446888	−	0.894590i	$-0.352532\pi$
$223$	199.312			0.893776			0.446888	+	0.894590i	$0.352532\pi$
$224$	118.343			0.528316
$225$	15.0000			0.0666667
$226$			502.245i			2.22232i
$227$			272.656i			1.20113i	0.799578	+	0.600563i	$0.205057\pi$
$227$			272.656i			1.20113i	−0.799578	+	0.600563i	$0.794943\pi$
$228$			227.430i			0.997500i
$229$	−428.264			−1.87015			−0.935075	−	0.354451i	$-0.884668\pi$
$229$	−428.264			−1.87015			−0.935075	+	0.354451i	$0.884668\pi$
$230$		−	269.928i		−	1.17360i
$231$	48.1575	+	14.8947i	0.208474	+	0.0644792i
$232$	488.653			2.10626
$233$			419.417i			1.80007i	0.435816	+	0.900036i	$0.356460\pi$
$233$			419.417i			1.80007i	−0.435816	+	0.900036i	$0.643540\pi$
$234$	−85.3486			−0.364737
$235$	−199.544			−0.849122
$236$	644.653			2.73158
$237$			80.3497i			0.339028i
$238$			101.624i			0.426991i
$239$			176.151i			0.737032i	0.929621	+	0.368516i	$0.120134\pi$
$239$			176.151i			0.737032i	−0.929621	+	0.368516i	$0.879866\pi$
$240$	129.826			0.540941
$241$			82.3692i			0.341781i	0.985290	+	0.170890i	$0.0546644\pi$
$241$			82.3692i			0.341781i	−0.985290	+	0.170890i	$0.945336\pi$
$242$	−249.282	+	364.438i	−1.03009	+	1.50594i
$243$	15.5885			0.0641500
$244$			200.042i			0.819843i
$245$	−15.6525			−0.0638877
$246$	−51.7695			−0.210445
$247$	−109.890			−0.444899
$248$			1049.99i			4.23383i
$249$		−	12.4994i		−	0.0501983i
$250$		−	40.7980i		−	0.163192i
$251$	103.664			0.413004			0.206502	−	0.978446i	$-0.433792\pi$
$251$	103.664			0.413004			0.206502	+	0.978446i	$0.433792\pi$
$252$		−	73.9418i		−	0.293420i
$253$	107.523	−	347.643i	0.424992	−	1.37408i
$254$	454.727			1.79026
$255$			40.7670i			0.159871i
$256$	−381.445			−1.49002
$257$	−69.8956			−0.271967			−0.135984	−	0.990711i	$-0.543419\pi$
$257$	−69.8956			−0.271967			−0.135984	+	0.990711i	$0.543419\pi$
$258$	−461.604			−1.78916
$259$		−	93.7278i		−	0.361883i
$260$			162.404i			0.624630i
$261$		−	75.5736i		−	0.289554i
$262$	−846.094			−3.22937
$263$			167.563i			0.637122i	0.947902	+	0.318561i	$0.103199\pi$
$263$			167.563i			0.637122i	−0.947902	+	0.318561i	$0.896801\pi$
$264$	353.075	+	109.203i	1.33741	+	0.413648i
$265$	93.7395			0.353734
$266$		−	136.082i		−	0.511585i
$267$	106.087			0.397330
$268$	972.839			3.63000
$269$	−3.89194			−0.0144682			−0.00723409	−	0.999974i	$-0.502303\pi$
$269$	−3.89194			−0.0144682			−0.00723409	+	0.999974i	$0.502303\pi$
$270$		−	42.3985i		−	0.157031i
$271$		−	58.0094i		−	0.214057i	−0.994256	−	0.107028i	$-0.965866\pi$
$271$		−	58.0094i		−	0.214057i	0.994256	−	0.107028i	$-0.0341336\pi$
$272$			352.840i			1.29721i
$273$	35.7274			0.130869
$274$		−	799.907i		−	2.91937i
$275$	16.2515	−	52.5442i	0.0590962	−	0.191070i
$276$	−533.777			−1.93397
$277$			317.880i			1.14758i	0.819002	+	0.573791i	$0.194528\pi$
$277$			317.880i			1.14758i	−0.819002	+	0.573791i	$0.805472\pi$
$278$	−725.959			−2.61136
$279$	162.388			0.582036
$280$	−114.759			−0.409853
$281$			196.457i			0.699134i	0.936911	+	0.349567i	$0.113671\pi$
$281$			196.457i			0.699134i	−0.936911	+	0.349567i	$0.886329\pi$
$282$			564.024i			2.00008i
$283$			175.497i			0.620131i	0.950715	+	0.310065i	$0.100351\pi$
$283$			175.497i			0.620131i	−0.950715	+	0.310065i	$0.899649\pi$
$284$	852.981			3.00345
$285$		−	54.5900i		−	0.191544i
$286$	−92.4692	+	298.971i	−0.323319	+	1.04535i
$287$	21.6710			0.0755087
$288$		−	134.188i		−	0.465931i
$289$	178.204			0.616621
$290$	−205.550			−0.708793
$291$	255.126			0.876723
$292$			659.200i			2.25753i
$293$		−	197.769i		−	0.674981i	−0.941329	−	0.337490i	$-0.890422\pi$
$293$		−	197.769i		−	0.674981i	0.941329	−	0.337490i	$-0.109578\pi$
$294$			44.2428i			0.150486i
$295$	−154.736			−0.524529
$296$		−	687.181i		−	2.32156i
$297$	16.8890	−	54.6055i	0.0568654	−	0.183857i
$298$	−836.007			−2.80539
$299$		−	257.911i		−	0.862580i
$300$	−80.6772			−0.268924
$301$	193.230			0.641959
$302$	124.493			0.412230
$303$		−	14.7374i		−	0.0486384i
$304$		−	472.479i		−	1.55421i
$305$		−	48.0159i		−	0.157429i
$306$	115.231			0.376571
$307$		−	355.139i		−	1.15680i	−0.815752	−	0.578402i	$-0.803676\pi$
$307$		−	355.139i		−	1.15680i	0.815752	−	0.578402i	$-0.196324\pi$
$308$	−259.014	−	80.1108i	−0.840955	−	0.260100i
$309$	77.3216			0.250232
$310$		−	441.673i		−	1.42475i
$311$	527.855			1.69728			0.848642	−	0.528968i	$-0.177421\pi$
$311$	527.855			1.69728			0.848642	+	0.528968i	$0.177421\pi$
$312$	261.941			0.839555
$313$	−210.346			−0.672032			−0.336016	−	0.941856i	$-0.609080\pi$
$313$	−210.346			−0.672032			−0.336016	+	0.941856i	$0.609080\pi$
$314$			379.055i			1.20718i
$315$			17.7482i			0.0563436i
$316$		−	432.159i		−	1.36759i
$317$	211.561			0.667383			0.333692	−	0.942682i	$-0.391706\pi$
$317$	211.561			0.667383			0.333692	+	0.942682i	$0.391706\pi$
$318$		−	264.961i		−	0.833210i
$319$	−264.730	−	81.8788i	−0.829875	−	0.256673i
$320$	−65.1533			−0.203604
$321$			9.42866i			0.0293728i
$322$	319.383			0.991873
$323$	148.365			0.459333
$324$	−83.8422			−0.258772
$325$		−	38.9818i		−	0.119944i
$326$		−	1076.96i		−	3.30357i
$327$			219.044i			0.669859i
$328$	158.885			0.484404
$329$		−	236.103i		−	0.717639i
$330$	−148.520	−	45.9358i	−0.450059	−	0.139199i
$331$	−483.843			−1.46176			−0.730881	−	0.682505i	$-0.760890\pi$
$331$	−483.843			−1.46176			−0.730881	+	0.682505i	$0.760890\pi$
$332$			67.2276i			0.202493i
$333$	−106.277			−0.319151
$334$	−418.897			−1.25418
$335$	−233.510			−0.697046
$336$			153.612i			0.457179i
$337$			79.7238i			0.236569i	0.992980	+	0.118285i	$0.0377395\pi$
$337$			79.7238i			0.236569i	−0.992980	+	0.118285i	$0.962261\pi$
$338$		−	394.892i		−	1.16832i
$339$	−238.393			−0.703223
$340$		−	219.264i		−	0.644895i
$341$	175.936	−	568.836i	0.515942	−	1.66814i
$342$	−154.302			−0.451176
$343$		−	18.5203i		−	0.0539949i
$344$	1416.70			4.11831
$345$	128.122			0.371369
$346$	585.600			1.69249
$347$		−	480.550i		−	1.38487i	−0.721480	−	0.692436i	$-0.756538\pi$
$347$		−	480.550i		−	1.38487i	0.721480	−	0.692436i	$-0.243462\pi$
$348$			406.471i			1.16802i
$349$			47.4605i			0.135990i	0.997686	+	0.0679949i	$0.0216602\pi$
$349$			47.4605i			0.135990i	−0.997686	+	0.0679949i	$0.978340\pi$
$350$	48.2728			0.137922
$351$		−	40.5110i		−	0.115416i
$352$	−470.053	−	145.383i	−1.33538	−	0.413021i
$353$	−142.178			−0.402771			−0.201385	−	0.979512i	$-0.564544\pi$
$353$	−142.178			−0.402771			−0.201385	+	0.979512i	$0.564544\pi$
$354$			437.371i			1.23551i
$355$	−204.741			−0.576735
$356$	−570.587			−1.60277
$357$	−48.2361			−0.135115
$358$		−	880.071i		−	2.45830i
$359$			128.513i			0.357976i	0.983851	+	0.178988i	$0.0572823\pi$
$359$			128.513i			0.357976i	−0.983851	+	0.178988i	$0.942718\pi$
$360$			130.124i			0.361456i
$361$	162.329			0.449665
$362$		−	596.308i		−	1.64726i
$363$	−172.982	−	118.323i	−0.476534	−	0.325957i
$364$	−192.159			−0.527909
$365$		−	158.228i		−	0.433500i
$366$	−135.720			−0.370820
$367$	350.653			0.955458			0.477729	−	0.878507i	$-0.341460\pi$
$367$	350.653			0.955458			0.477729	+	0.878507i	$0.341460\pi$
$368$	1108.91			3.01333
$369$		−	24.5726i		−	0.0665924i
$370$			289.060i			0.781243i
$371$			110.914i			0.298960i
$372$	−873.400			−2.34785
$373$		−	19.6173i		−	0.0525934i	−0.999654	−	0.0262967i	$-0.991629\pi$
$373$		−	19.6173i		−	0.0525934i	0.999654	−	0.0262967i	$-0.00837147\pi$
$374$	124.844	−	403.646i	0.333808	−	1.07927i
$375$	19.3649			0.0516398
$376$		−	1731.03i		−	4.60381i
$377$	−196.400			−0.520954
$378$	50.1666			0.132716
$379$	−132.036			−0.348379			−0.174190	−	0.984712i	$-0.555731\pi$
$379$	−132.036			−0.348379			−0.174190	+	0.984712i	$0.555731\pi$
$380$			293.611i			0.772660i
$381$			215.838i			0.566503i
$382$			141.991i			0.371705i
$383$	−56.5899			−0.147754			−0.0738772	−	0.997267i	$-0.523537\pi$
$383$	−56.5899			−0.147754			−0.0738772	+	0.997267i	$0.523537\pi$
$384$		−	125.734i		−	0.327431i
$385$	62.1711	+	19.2290i	0.161483	+	0.0499454i
$386$	450.566			1.16727
$387$		−	219.102i		−	0.566155i
$388$	−1372.19			−3.53658
$389$	−485.143			−1.24715			−0.623577	−	0.781762i	$-0.714321\pi$
$389$	−485.143			−1.24715			−0.623577	+	0.781762i	$0.714321\pi$
$390$	−110.185			−0.282524
$391$			348.211i			0.890565i
$392$		−	135.784i		−	0.346389i
$393$		−	401.602i		−	1.02189i
$394$	−1101.84			−2.79655
$395$			103.731i			0.262610i
$396$	−90.8372	+	293.695i	−0.229387	+	0.741653i
$397$	315.829			0.795539			0.397770	−	0.917485i	$-0.369784\pi$
$397$	315.829			0.795539			0.397770	+	0.917485i	$0.369784\pi$
$398$			182.132i			0.457619i
$399$	64.5917			0.161884
$400$	167.604			0.419011
$401$	−235.137			−0.586377			−0.293189	−	0.956055i	$-0.594716\pi$
$401$	−235.137			−0.586377			−0.293189	+	0.956055i	$0.594716\pi$
$402$			660.033i			1.64187i
$403$		−	422.011i		−	1.04717i
$404$			79.2649i			0.196200i
$405$	20.1246			0.0496904
$406$		−	243.210i		−	0.599040i
$407$	−115.144	+	372.284i	−0.282909	+	0.914701i
$408$	−353.651			−0.866793
$409$		−	61.6392i		−	0.150707i	−0.997157	−	0.0753536i	$-0.975991\pi$
$409$		−	61.6392i		−	0.150707i	0.997157	−	0.0753536i	$-0.0240085\pi$
$410$	−66.8341			−0.163010
$411$	379.679			0.923793
$412$	−415.873			−1.00940
$413$		−	183.086i		−	0.443308i
$414$		−	362.146i		−	0.874750i
$415$		−	16.1366i		−	0.0388834i
$416$	−348.726			−0.838283
$417$		−	344.579i		−	0.826329i
$418$	−167.176	+	540.512i	−0.399942	+	1.29309i
$419$	−16.6267			−0.0396819			−0.0198410	−	0.999803i	$-0.506316\pi$
$419$	−16.6267			−0.0396819			−0.0198410	+	0.999803i	$0.506316\pi$
$420$		−	95.4585i		−	0.227282i
$421$	343.655			0.816282			0.408141	−	0.912919i	$-0.366177\pi$
$421$	343.655			0.816282			0.408141	+	0.912919i	$0.366177\pi$
$422$	228.709			0.541963
$423$	−267.716			−0.632898
$424$			813.185i			1.91789i
$425$			52.6299i			0.123835i
$426$			578.713i			1.35848i
$427$	56.8132			0.133052
$428$		−	50.7118i		−	0.118486i
$429$	−141.908	−	43.8909i	−0.330788	−	0.102310i
$430$	−595.928			−1.38588
$431$		−	58.6155i		−	0.135999i	−0.997685	−	0.0679994i	$-0.978338\pi$
$431$		−	58.6155i		−	0.135999i	0.997685	−	0.0679994i	$-0.0216616\pi$
$432$	174.180			0.403194
$433$	321.456			0.742394			0.371197	−	0.928554i	$-0.378948\pi$
$433$	321.456			0.742394			0.371197	+	0.928554i	$0.378948\pi$
$434$	522.595			1.20414
$435$		−	97.5651i		−	0.224288i
$436$		−	1178.12i		−	2.70212i
$437$		−	466.280i		−	1.06700i
$438$	−447.241			−1.02110
$439$			774.146i			1.76343i	0.471782	+	0.881715i	$0.343611\pi$
$439$			774.146i			1.76343i	−0.471782	+	0.881715i	$0.656389\pi$
$440$	455.818	+	140.981i	1.03595	+	0.320410i
$441$	−21.0000			−0.0476190
$442$		−	299.459i		−	0.677510i
$443$	510.060			1.15138			0.575688	−	0.817669i	$-0.304734\pi$
$443$	510.060			1.15138			0.575688	+	0.817669i	$0.304734\pi$
$444$	571.610			1.28741
$445$	136.958			0.307771
$446$		−	727.306i		−	1.63073i
$447$		−	396.814i		−	0.887727i
$448$		−	77.0905i		−	0.172077i
$449$	−475.169			−1.05828			−0.529142	−	0.848534i	$-0.677486\pi$
$449$	−475.169			−1.05828			−0.529142	+	0.848534i	$0.677486\pi$
$450$		−	54.7362i		−	0.121636i
$451$	−86.0764	−	26.6227i	−0.190857	−	0.0590304i
$452$	1282.19			2.83670
$453$			59.0913i			0.130444i
$454$	994.942			2.19150
$455$	46.1238			0.101371
$456$	473.565			1.03852
$457$			253.444i			0.554582i	0.960786	+	0.277291i	$0.0894367\pi$
$457$			253.444i			0.554582i	−0.960786	+	0.277291i	$0.910563\pi$
$458$			1562.77i			3.41216i
$459$			54.6946i			0.119160i
$460$	−689.103			−1.49805
$461$		−	428.532i		−	0.929570i	−0.885424	−	0.464785i	$-0.846132\pi$
$461$		−	428.532i		−	0.929570i	0.885424	−	0.464785i	$-0.153868\pi$
$462$	54.3520	−	175.731i	0.117645	−	0.380370i
$463$	358.650			0.774622			0.387311	−	0.921949i	$-0.373404\pi$
$463$	358.650			0.774622			0.387311	+	0.921949i	$0.373404\pi$
$464$		−	844.432i		−	1.81990i
$465$	209.642			0.450843
$466$	1530.49			3.28430
$467$	−384.489			−0.823316			−0.411658	−	0.911338i	$-0.635050\pi$
$467$	−384.489			−0.823316			−0.411658	+	0.911338i	$0.635050\pi$
$468$			217.888i			0.465572i
$469$		−	276.293i		−	0.589111i
$470$			728.151i			1.54926i
$471$	−179.920			−0.381995
$472$		−	1342.33i		−	2.84391i
$473$	−767.502	−	237.382i	−1.62263	−	0.501864i
$474$	293.202			0.618571
$475$		−	70.4753i		−	0.148369i
$476$	259.437			0.545036
$477$	125.765			0.263658
$478$	642.788			1.34474
$479$		−	16.5150i		−	0.0344782i	−0.999851	−	0.0172391i	$-0.994512\pi$
$479$		−	16.5150i		−	0.0344782i	0.999851	−	0.0172391i	$-0.00548764\pi$
$480$		−	173.236i		−	0.360908i
$481$			276.192i			0.574203i
$482$	300.572			0.623593
$483$			151.596i			0.313864i
$484$	930.380	+	636.395i	1.92227	+	1.31487i
$485$	329.367			0.679107
$486$		−	56.8836i		−	0.117044i
$487$	121.715			0.249928			0.124964	−	0.992161i	$-0.460118\pi$
$487$	121.715			0.249928			0.124964	+	0.992161i	$0.460118\pi$
$488$	416.536			0.853557
$489$	511.184			1.04537
$490$			57.1172i			0.116566i
$491$			188.392i			0.383691i	0.981425	+	0.191845i	$0.0614472\pi$
$491$			188.392i			0.383691i	−0.981425	+	0.191845i	$0.938553\pi$
$492$			132.163i			0.268624i
$493$	265.162			0.537855
$494$			400.998i			0.811737i
$495$	21.8036	−	70.4954i	0.0440477	−	0.142415i
$496$	1814.46			3.65819
$497$		−	242.253i		−	0.487430i
$498$	−45.6112			−0.0915888
$499$	326.713			0.654736			0.327368	−	0.944897i	$-0.393838\pi$
$499$	326.713			0.654736			0.327368	+	0.944897i	$0.393838\pi$
$500$	−104.154			−0.208308
$501$		−	198.831i		−	0.396869i
$502$		−	378.278i		−	0.753543i
$503$			220.453i			0.438277i	0.975694	+	0.219138i	$0.0703247\pi$
$503$			220.453i			0.438277i	−0.975694	+	0.219138i	$0.929675\pi$
$504$	−153.965			−0.305486
$505$		−	19.0259i		−	0.0376751i
$506$	−1268.58	−	392.360i	−2.50707	−	0.775416i
$507$	187.437			0.369699
$508$		−	1160.88i		−	2.28519i
$509$	−329.612			−0.647567			−0.323784	−	0.946131i	$-0.604955\pi$
$509$	−329.612			−0.647567			−0.323784	+	0.946131i	$0.604955\pi$
$510$	148.762			0.291690
$511$	187.217			0.366375
$512$			1101.56i			2.15148i
$513$		−	73.2401i		−	0.142768i
$514$			255.055i			0.496215i
$515$	99.8218			0.193829
$516$			1178.44i			2.28379i
$517$	−290.052	+	937.794i	−0.561028	+	1.81392i
$518$	−342.020			−0.660271
$519$			277.957i			0.535563i
$520$	338.165			0.650317
$521$	−527.575			−1.01262			−0.506310	−	0.862351i	$-0.668991\pi$
$521$	−527.575			−1.01262			−0.506310	+	0.862351i	$0.668991\pi$
$522$	−275.774			−0.528303
$523$			460.223i			0.879968i	0.898006	+	0.439984i	$0.145016\pi$
$523$			460.223i			0.879968i	−0.898006	+	0.439984i	$0.854984\pi$
$524$			2160.01i			4.12215i
$525$			22.9129i			0.0436436i
$526$	611.451			1.16245
$527$			569.765i			1.08115i
$528$	188.712	−	610.142i	0.357408	−	1.15557i
$529$	565.356			1.06873
$530$		−	342.063i		−	0.645402i
$531$	−207.600			−0.390961
$532$	−347.405			−0.653017
$533$	−63.8588			−0.119810
$534$		−	387.121i		−	0.724945i
$535$			12.1723i			0.0227521i
$536$		−	2025.69i		−	3.77927i
$537$	417.729			0.777894
$538$			14.2020i			0.0263978i
$539$	−22.7520	+	73.5618i	−0.0422116	+	0.136478i
$540$	−108.240			−0.200444
$541$			18.3336i			0.0338883i	0.999856	+	0.0169441i	$0.00539374\pi$
$541$			18.3336i			0.0338883i	−0.999856	+	0.0169441i	$0.994606\pi$
$542$	−211.681			−0.390555
$543$	283.040			0.521252
$544$	470.820			0.865479
$545$			282.785i			0.518871i
$546$		−	130.372i		−	0.238777i
$547$			549.293i			1.00419i	0.864812	+	0.502096i	$0.167438\pi$
$547$			549.293i			1.00419i	−0.864812	+	0.502096i	$0.832562\pi$
$548$	−2042.09			−3.72645
$549$		−	64.4201i		−	0.117341i
$550$	−191.738	−	59.3029i	−0.348615	−	0.107823i
$551$	−355.072			−0.644413
$552$			1111.45i			2.01351i
$553$	−122.736			−0.221946
$554$	1159.97			2.09381
$555$	−137.203			−0.247213
$556$			1853.31i			3.33329i
$557$			313.394i			0.562647i	0.959613	+	0.281323i	$0.0907733\pi$
$557$			313.394i			0.562647i	−0.959613	+	0.281323i	$0.909227\pi$
$558$		−	592.567i		−	1.06195i
$559$	−569.399			−1.01860
$560$			198.312i			0.354129i
$561$	191.592	+	59.2578i	0.341519	+	0.105629i
$562$	716.886			1.27560
$563$		−	1009.25i		−	1.79264i	−0.443413	−	0.896318i	$-0.646232\pi$
$563$		−	1009.25i		−	1.79264i	0.443413	−	0.896318i	$-0.353768\pi$
$564$	1439.90			2.55302
$565$	−307.764			−0.544714
$566$	640.403			1.13145
$567$			23.8118i			0.0419961i
$568$		−	1776.12i		−	3.12696i
$569$		−	990.577i		−	1.74091i	−0.492250	−	0.870454i	$-0.663825\pi$
$569$		−	990.577i		−	1.74091i	0.492250	−	0.870454i	$-0.336175\pi$
$570$	−199.203			−0.349479
$571$		−	385.152i		−	0.674523i	−0.941411	−	0.337261i	$-0.890499\pi$
$571$		−	385.152i		−	0.674523i	0.941411	−	0.337261i	$-0.109501\pi$
$572$	763.248	+	236.066i	1.33435	+	0.412703i
$573$	−67.3968			−0.117621
$574$		−	79.0792i		−	0.137769i
$575$	165.405			0.287661
$576$	−87.4124			−0.151758
$577$	334.566			0.579837			0.289919	−	0.957051i	$-0.406372\pi$
$577$	334.566			0.579837			0.289919	+	0.957051i	$0.406372\pi$
$578$		−	650.279i		−	1.12505i
$579$			213.863i			0.369366i
$580$			524.752i			0.904745i
$581$	19.0931			0.0328625
$582$		−	930.977i		−	1.59962i
$583$	136.257	−	440.547i	0.233718	−	0.755655i
$584$	1372.62			2.35037
$585$		−	52.2995i		−	0.0894009i
$586$	−721.676			−1.23153
$587$	−19.6096			−0.0334065			−0.0167033	−	0.999860i	$-0.505317\pi$
$587$	−19.6096			−0.0334065			−0.0167033	+	0.999860i	$0.505317\pi$
$588$	112.948			0.192088
$589$		−	762.957i		−	1.29534i
$590$			564.644i			0.957024i
$591$		−	522.993i		−	0.884929i
$592$	−1187.50			−2.00592
$593$			1081.33i			1.82349i	0.410753	+	0.911747i	$0.365266\pi$
$593$			1081.33i			1.82349i	−0.410753	+	0.911747i	$0.634734\pi$
$594$	−199.260	−	61.6294i	−0.335454	−	0.103753i
$595$	−62.2726			−0.104660
$596$			2134.26i			3.58097i
$597$	−86.4498			−0.144807
$598$	−941.140			−1.57381
$599$	596.814			0.996351			0.498176	−	0.867076i	$-0.334003\pi$
$599$	596.814			0.996351			0.498176	+	0.867076i	$0.334003\pi$
$600$			167.990i			0.279983i
$601$			545.481i			0.907621i	0.891098	+	0.453811i	$0.149936\pi$
$601$			545.481i			0.907621i	−0.891098	+	0.453811i	$0.850064\pi$
$602$		−	705.111i		−	1.17128i
$603$	−313.287			−0.519547
$604$		−	317.821i		−	0.526194i
$605$	−223.319	−	152.754i	−0.369122	−	0.252486i
$606$	−53.7781			−0.0887427
$607$		−	417.652i		−	0.688059i	−0.938959	−	0.344030i	$-0.888208\pi$
$607$		−	417.652i		−	0.688059i	0.938959	−	0.344030i	$-0.111792\pi$
$608$	−630.463			−1.03695
$609$	115.441			0.189558
$610$	−175.214			−0.287236
$611$			695.736i			1.13868i
$612$		−	294.174i		−	0.480676i
$613$			1005.65i			1.64054i	0.571977	+	0.820270i	$0.306177\pi$
$613$			1005.65i			1.64054i	−0.571977	+	0.820270i	$0.693823\pi$
$614$	−1295.93			−2.11064
$615$		−	31.7231i		−	0.0515822i
$616$	−166.810	+	539.331i	−0.270796	+	0.875538i
$617$	−206.961			−0.335431			−0.167715	−	0.985835i	$-0.553639\pi$
$617$	−206.961			−0.335431			−0.167715	+	0.985835i	$0.553639\pi$
$618$		−	282.153i		−	0.456558i
$619$	862.827			1.39390			0.696952	−	0.717118i	$-0.254539\pi$
$619$	862.827			1.39390			0.696952	+	0.717118i	$0.254539\pi$
$620$	−1127.55			−1.81864
$621$	171.894			0.276802
$622$		−	1926.19i		−	3.09676i
$623$			162.051i			0.260114i
$624$		−	452.655i		−	0.725409i
$625$	25.0000			0.0400000
$626$			767.569i			1.22615i
$627$	−256.556	−	79.3506i	−0.409180	−	0.126556i
$628$	967.694			1.54091
$629$		−	372.891i		−	0.592832i
$630$	64.7648			0.102801
$631$	932.984			1.47858			0.739290	−	0.673388i	$-0.235161\pi$
$631$	932.984			1.47858			0.739290	+	0.673388i	$0.235161\pi$
$632$	−899.861			−1.42383
$633$			108.557i			0.171497i
$634$		−	772.002i		−	1.21767i
$635$			278.645i			0.438812i
$636$	−676.423			−1.06356
$637$			54.5745i			0.0856742i
$638$	−298.782	+	966.022i	−0.468311	+	1.51414i
$639$	−274.689			−0.429873
$640$		−	162.321i		−	0.253627i
$641$	235.086			0.366749			0.183375	−	0.983043i	$-0.441298\pi$
$641$	235.086			0.366749			0.183375	+	0.983043i	$0.441298\pi$
$642$	34.4059			0.0535918
$643$	366.560			0.570078			0.285039	−	0.958516i	$-0.407993\pi$
$643$	366.560			0.570078			0.285039	+	0.958516i	$0.407993\pi$
$644$		−	815.358i		−	1.26608i
$645$		−	282.859i		−	0.438542i
$646$		−	541.394i		−	0.838072i
$647$	92.7590			0.143368			0.0716839	−	0.997427i	$-0.477163\pi$
$647$	92.7590			0.143368			0.0716839	+	0.997427i	$0.477163\pi$
$648$			174.580i			0.269414i
$649$	−224.920	+	727.212i	−0.346564	+	1.12051i
$650$	−142.248			−0.218842
$651$			248.052i			0.381032i
$652$	−2749.39			−4.21686
$653$	−319.785			−0.489717			−0.244858	−	0.969559i	$-0.578741\pi$
$653$	−319.785			−0.489717			−0.244858	+	0.969559i	$0.578741\pi$
$654$	799.310			1.22219
$655$		−	518.466i		−	0.791551i
$656$		−	274.565i		−	0.418544i
$657$		−	212.285i		−	0.323112i
$658$	−861.560			−1.30936
$659$		−	667.087i		−	1.01227i	−0.862454	−	0.506136i	$-0.831074\pi$
$659$		−	667.087i		−	1.01227i	0.862454	−	0.506136i	$-0.168926\pi$
$660$	−117.270	+	379.158i	−0.177682	+	0.574482i
$661$	92.0625			0.139278			0.0696388	−	0.997572i	$-0.477815\pi$
$661$	92.0625			0.139278			0.0696388	+	0.997572i	$0.477815\pi$
$662$			1765.58i			2.66704i
$663$	142.140			0.214388
$664$	139.984			0.210820
$665$	83.3875			0.125395
$666$			387.815i			0.582304i
$667$		−	833.352i		−	1.24940i
$668$			1069.41i			1.60091i
$669$	345.219			0.516022
$670$			852.098i			1.27179i
$671$	−225.660	−	69.7947i	−0.336304	−	0.104016i
$672$	204.976			0.305023
$673$			716.315i			1.06436i	0.846631	+	0.532181i	$0.178627\pi$
$673$			716.315i			1.06436i	−0.846631	+	0.532181i	$0.821373\pi$
$674$	290.919			0.431630
$675$	25.9808			0.0384900
$676$	−1008.13			−1.49131
$677$			645.809i			0.953927i	0.878923	+	0.476963i	$0.158263\pi$
$677$			645.809i			0.953927i	−0.878923	+	0.476963i	$0.841737\pi$
$678$			869.914i			1.28306i
$679$			389.712i			0.573950i
$680$	−456.562			−0.671415
$681$			472.253i			0.693470i
$682$	−2075.73	−	642.005i	−3.04359	−	0.941357i
$683$	58.5049			0.0856587			0.0428294	−	0.999082i	$-0.486363\pi$
$683$	58.5049			0.0856587			0.0428294	+	0.999082i	$0.486363\pi$
$684$			393.920i			0.575907i
$685$	490.163			0.715567
$686$	−67.5819			−0.0985159
$687$	−741.775			−1.07973
$688$		−	2448.16i		−	3.55838i
$689$		−	326.835i		−	0.474362i
$690$		−	467.529i		−	0.677578i
$691$	−18.0060			−0.0260579			−0.0130289	−	0.999915i	$-0.504147\pi$
$691$	−18.0060			−0.0260579			−0.0130289	+	0.999915i	$0.504147\pi$
$692$		−	1494.99i		−	2.16039i
$693$	83.4113	+	25.7984i	0.120363	+	0.0372271i
$694$	−1753.57			−2.52675
$695$		−	444.850i		−	0.640071i
$696$	846.373			1.21605
$697$	86.2169			0.123697
$698$	173.187			0.248119
$699$			726.451i			1.03927i
$700$		−	123.236i		−	0.176052i
$701$			776.736i			1.10804i	0.832503	+	0.554020i	$0.186907\pi$
$701$			776.736i			1.10804i	−0.832503	+	0.554020i	$0.813093\pi$
$702$	−147.828			−0.210581
$703$			499.329i			0.710282i
$704$	−94.7052	+	306.201i	−0.134524	+	0.434944i
$705$	−345.620			−0.490241
$706$			518.819i			0.734872i
$707$	22.5118			0.0318413
$708$	1116.57			1.57708
$709$	−344.276			−0.485579			−0.242790	−	0.970079i	$-0.578063\pi$
$709$	−344.276			−0.485579			−0.242790	+	0.970079i	$0.578063\pi$
$710$			747.116i			1.05228i
$711$			139.170i			0.195738i
$712$			1188.10i			1.66868i
$713$	1790.66			2.51144
$714$			176.018i			0.246523i
$715$	−183.202	−	56.6629i	−0.256227	−	0.0792488i
$716$	−2246.75			−3.13791
$717$			305.102i			0.425526i
$718$	468.955			0.653141
$719$	−350.815			−0.487920			−0.243960	−	0.969785i	$-0.578447\pi$
$719$	−350.815			−0.487920			−0.243960	+	0.969785i	$0.578447\pi$
$720$	224.865			0.312312
$721$			118.111i			0.163815i
$722$		−	592.352i		−	0.820432i
$723$			142.668i			0.197327i
$724$	−1522.32			−2.10266
$725$		−	125.956i		−	0.173732i
$726$	−431.769	+	631.225i	−0.594723	+	0.869457i
$727$	1204.80			1.65722			0.828610	−	0.559826i	$-0.189132\pi$
$727$	1204.80			1.65722			0.828610	+	0.559826i	$0.189132\pi$
$728$			400.122i			0.549618i
$729$	27.0000			0.0370370
$730$	−577.385			−0.790939
$731$	768.755			1.05165
$732$			346.482i			0.473336i
$733$			1411.22i			1.92526i	0.270821	+	0.962630i	$0.412705\pi$
$733$			1411.22i			1.92526i	−0.270821	+	0.962630i	$0.587295\pi$
$734$		−	1279.56i		−	1.74327i
$735$	−27.1109			−0.0368856
$736$		−	1479.69i		−	2.01045i
$737$	−339.425	+	1097.43i	−0.460549	+	1.48905i
$738$	−89.6674			−0.121501
$739$			280.230i			0.379202i	0.981861	+	0.189601i	$0.0607194\pi$
$739$			280.230i			0.379202i	−0.981861	+	0.189601i	$0.939281\pi$
$740$	737.945			0.997224
$741$	−190.335			−0.256863
$742$	404.734			0.545464
$743$			605.629i			0.815113i	0.913180	+	0.407556i	$0.133619\pi$
$743$			605.629i			0.815113i	−0.913180	+	0.407556i	$0.866381\pi$
$744$			1818.63i			2.44440i
$745$		−	512.285i		−	0.687630i
$746$	−71.5853			−0.0959588
$747$		−	21.6495i		−	0.0289820i
$748$	−1030.48	−	318.717i	−1.37764	−	0.426092i
$749$	−14.4025			−0.0192290
$750$		−	70.6642i		−	0.0942189i
$751$	735.893			0.979884			0.489942	−	0.871755i	$-0.337018\pi$
$751$	735.893			0.979884			0.489942	+	0.871755i	$0.337018\pi$
$752$	−2991.36			−3.97787
$753$	179.551			0.238448
$754$			716.678i			0.950501i
$755$			76.2866i			0.101042i
$756$		−	128.071i		−	0.169406i
$757$	−617.979			−0.816352			−0.408176	−	0.912903i	$-0.633835\pi$
$757$	−617.979			−0.816352			−0.408176	+	0.912903i	$0.633835\pi$
$758$			481.809i			0.635632i
$759$	186.235	−	602.136i	0.245369	−	0.793328i
$760$	611.370			0.804434
$761$			458.281i			0.602209i	0.953591	+	0.301105i	$0.0973553\pi$
$761$			458.281i			0.602209i	−0.953591	+	0.301105i	$0.902645\pi$
$762$	787.610			1.03361
$763$	−334.595			−0.438526
$764$	362.492			0.474466
$765$			70.6105i			0.0923013i
$766$			206.501i			0.269584i
$767$			539.508i			0.703400i
$768$	−660.683			−0.860264
$769$			82.6332i			0.107455i	0.998556	+	0.0537277i	$0.0171103\pi$
$769$			82.6332i			0.107455i	−0.998556	+	0.0537277i	$0.982890\pi$
$770$	70.1681	−	226.867i	0.0911274	−	0.294633i
$771$	−121.063			−0.157020
$772$		−	1150.26i		−	1.48997i
$773$	−762.642			−0.986600			−0.493300	−	0.869859i	$-0.664210\pi$
$773$	−762.642			−0.986600			−0.493300	+	0.869859i	$0.664210\pi$
$774$	−799.521			−1.03297
$775$	270.647			0.349221
$776$			2857.24i			3.68201i
$777$		−	162.341i		−	0.208933i
$778$			1770.33i			2.27548i
$779$	−115.451			−0.148204
$780$			281.292i			0.360630i
$781$	−297.606	+	962.219i	−0.381058	+	1.23203i
$782$	1270.65			1.62487
$783$		−	130.897i		−	0.167174i
$784$	−234.646			−0.299294
$785$	−232.275			−0.295892
$786$	−1465.48			−1.86448
$787$		−	281.882i		−	0.358172i	−0.983833	−	0.179086i	$-0.942686\pi$
$787$		−	281.882i		−	0.358172i	0.983833	−	0.179086i	$-0.0573141\pi$
$788$			2812.91i			3.56968i
$789$			290.228i			0.367842i
$790$	378.523			0.479143
$791$		−	364.151i		−	0.460368i
$792$	611.544	+	189.145i	0.772152	+	0.238820i
$793$	−167.414			−0.211115
$794$		−	1152.49i		−	1.45149i
$795$	162.362			0.204228
$796$	464.968			0.584131
$797$	−108.121			−0.135660			−0.0678299	−	0.997697i	$-0.521608\pi$
$797$	−108.121			−0.135660			−0.0678299	+	0.997697i	$0.521608\pi$
$798$		−	235.700i		−	0.295364i
$799$		−	939.325i		−	1.17563i
$800$		−	223.647i		−	0.279558i
$801$	183.748			0.229399
$802$			858.035i			1.06987i
$803$	−743.621	−	229.996i	−0.926054	−	0.286420i
$804$	1685.01			2.09578
$805$			195.710i			0.243118i
$806$	−1539.95			−1.91061
$807$	−6.74104			−0.00835321
$808$	165.049			0.204269
$809$		−	1170.04i		−	1.44628i	−0.690703	−	0.723139i	$-0.742699\pi$
$809$		−	1170.04i		−	1.44628i	0.690703	−	0.723139i	$-0.257301\pi$
$810$		−	73.4364i		−	0.0906622i
$811$			935.348i			1.15333i	0.816982	+	0.576663i	$0.195646\pi$
$811$			935.348i			1.15333i	−0.816982	+	0.576663i	$0.804354\pi$
$812$	−620.895			−0.764649
$813$		−	100.475i		−	0.123586i
$814$	1358.49	+	420.170i	1.66891	+	0.516179i
$815$	659.936			0.809738
$816$			611.138i			0.748943i
$817$	−1029.42			−1.26000
$818$	−224.927			−0.274971
$819$	61.8816			0.0755575
$820$			170.622i			0.208075i
$821$		−	819.714i		−	0.998434i	−0.866477	−	0.499217i	$-0.833621\pi$
$821$		−	819.714i		−	0.998434i	0.866477	−	0.499217i	$-0.166379\pi$
$822$		−	1385.48i		−	1.68550i
$823$	1296.62			1.57548			0.787740	−	0.616008i	$-0.211251\pi$
$823$	1296.62			1.57548			0.787740	+	0.616008i	$0.211251\pi$
$824$			865.949i			1.05091i
$825$	28.1483	−	91.0092i	0.0341192	−	0.110314i
$826$	−668.096			−0.808833
$827$			141.618i			0.171243i	0.996328	+	0.0856216i	$0.0272876\pi$
$827$			141.618i			0.171243i	−0.996328	+	0.0856216i	$0.972712\pi$
$828$	−924.529			−1.11658
$829$	769.166			0.927823			0.463912	−	0.885881i	$-0.346446\pi$
$829$	769.166			0.927823			0.463912	+	0.885881i	$0.346446\pi$
$830$	−58.8838			−0.0709444
$831$			550.584i			0.662556i
$832$			227.166i			0.273036i
$833$		−	73.6819i		−	0.0884537i
$834$	−1257.40			−1.50767
$835$		−	256.690i		−	0.307413i
$836$	1379.88	+	426.785i	1.65058	+	0.510509i
$837$	281.264			0.336039
$838$			60.6723i			0.0724013i
$839$	−1510.12			−1.79990			−0.899952	−	0.435989i	$-0.856399\pi$
$839$	−1510.12			−1.79990			−0.899952	+	0.435989i	$0.856399\pi$
$840$	−198.768			−0.236629
$841$	206.403			0.245426
$842$		−	1254.02i		−	1.48934i
$843$			340.273i			0.403645i
$844$		−	583.874i		−	0.691793i
$845$	241.980			0.286367
$846$			976.917i			1.15475i
$847$	180.741	−	264.234i	0.213389	−	0.311965i
$848$	1405.25			1.65713
$849$			303.970i			0.358033i
$850$	192.051			0.225942
$851$	−1171.92			−1.37711
$852$	1477.41			1.73404
$853$		−	1559.24i		−	1.82795i	−0.405769	−	0.913976i	$-0.632996\pi$
$853$		−	1559.24i		−	1.82795i	0.405769	−	0.913976i	$-0.367004\pi$
$854$		−	207.316i		−	0.242759i
$855$		−	94.5526i		−	0.110588i
$856$	−105.595			−0.123358
$857$			1523.46i			1.77766i	0.458234	+	0.888832i	$0.348482\pi$
$857$			1523.46i			1.77766i	−0.458234	+	0.888832i	$0.651518\pi$
$858$	−160.161	+	517.833i	−0.186668	+	0.603536i
$859$	−611.597			−0.711987			−0.355993	−	0.934488i	$-0.615857\pi$
$859$	−611.597			−0.711987			−0.355993	+	0.934488i	$0.615857\pi$
$860$			1521.35i			1.76902i
$861$	37.5353			0.0435950
$862$	−213.893			−0.248135
$863$	839.077			0.972279			0.486139	−	0.873881i	$-0.338405\pi$
$863$	839.077			0.972279			0.486139	+	0.873881i	$0.338405\pi$
$864$		−	232.420i		−	0.269005i
$865$			358.842i			0.414846i
$866$		−	1173.02i		−	1.35453i
$867$	308.658			0.356006
$868$		−	1334.14i		−	1.53703i
$869$	487.504	+	150.781i	0.560994	+	0.173511i
$870$	−356.023			−0.409222
$871$			814.165i			0.934748i
$872$	−2453.14			−2.81324
$873$	441.892			0.506176
$874$	−1701.49			−1.94679
$875$			29.5804i			0.0338062i
$876$			1141.77i			1.30339i
$877$			81.1629i			0.0925461i	0.998929	+	0.0462731i	$0.0147344\pi$
$877$			81.1629i			0.0925461i	−0.998929	+	0.0462731i	$0.985266\pi$
$878$	2824.92			3.21745
$879$		−	342.547i		−	0.389700i
$880$	243.626	−	787.689i	0.276847	−	0.895102i
$881$	172.837			0.196183			0.0980913	−	0.995177i	$-0.468726\pi$
$881$	172.837			0.196183			0.0980913	+	0.995177i	$0.468726\pi$
$882$			76.6307i			0.0868829i
$883$	−966.115			−1.09413			−0.547064	−	0.837091i	$-0.684255\pi$
$883$	−966.115			−1.09413			−0.547064	+	0.837091i	$0.684255\pi$
$884$	−764.494			−0.864813
$885$	−268.011			−0.302837
$886$		−	1861.25i		−	2.10073i
$887$			875.409i			0.986933i	0.869765	+	0.493466i	$0.164270\pi$
$887$			875.409i			0.986933i	−0.869765	+	0.493466i	$0.835730\pi$
$888$		−	1190.23i		−	1.34035i
$889$	−329.698			−0.370863
$890$		−	499.771i		−	0.561540i
$891$	29.2526	−	94.5795i	0.0328312	−	0.106150i
$892$	−1856.75			−2.08156
$893$			1257.82i			1.40854i
$894$	−1448.01			−1.61969
$895$	539.286			0.602554
$896$	192.061			0.214354
$897$		−	446.716i		−	0.498011i
$898$			1733.93i			1.93088i
$899$		−	1363.58i		−	1.51678i
$900$	−139.737			−0.155263
$901$			441.266i			0.489751i
$902$	−97.1484	+	314.100i	−0.107703	+	0.348226i
$903$	334.684			0.370635
$904$		−	2669.83i		−	2.95336i
$905$	365.403			0.403760
$906$	215.629			0.238001
$907$	995.269			1.09732			0.548660	−	0.836046i	$-0.315138\pi$
$907$	995.269			1.09732			0.548660	+	0.836046i	$0.315138\pi$
$908$		−	2540.00i		−	2.79736i
$909$		−	25.5260i		−	0.0280814i
$910$		−	168.310i		−	0.184956i
$911$	433.509			0.475861			0.237930	−	0.971282i	$-0.423531\pi$
$911$	433.509			0.475861			0.237930	+	0.971282i	$0.423531\pi$
$912$		−	818.358i		−	0.897322i
$913$	−75.8371	−	23.4558i	−0.0830637	−	0.0256909i
$914$	924.838			1.01186
$915$		−	83.1660i		−	0.0908918i
$916$	3989.62			4.35548
$917$	613.457			0.668983
$918$	199.585			0.217413
$919$			1312.35i			1.42802i	0.700133	+	0.714012i	$0.253124\pi$
$919$			1312.35i			1.42802i	−0.700133	+	0.714012i	$0.746876\pi$
$920$			1434.88i			1.55965i
$921$		−	615.119i		−	0.667882i
$922$	−1563.75			−1.69604
$923$			713.856i			0.773409i
$924$	−448.626	−	138.756i	−0.485526	−	0.150169i
$925$	−177.129			−0.191491
$926$		−	1308.74i		−	1.41333i
$927$	133.925			0.144471
$928$	−1126.79			−1.21421
$929$	360.851			0.388429			0.194215	−	0.980959i	$-0.437784\pi$
$929$	360.851			0.388429			0.194215	+	0.980959i	$0.437784\pi$
$930$		−	765.001i		−	0.822581i
$931$			98.6655i			0.105978i
$932$		−	3907.20i		−	4.19228i
$933$	914.272			0.979927
$934$			1403.03i			1.50217i
$935$	247.345	+	76.5015i	0.264540	+	0.0818198i
$936$	453.696			0.484718
$937$			128.616i			0.137264i	0.997642	+	0.0686318i	$0.0218634\pi$
$937$			128.616i			0.137264i	−0.997642	+	0.0686318i	$0.978137\pi$
$938$	−1008.22			−1.07486
$939$	−364.330			−0.387998
$940$	1858.91			1.97756
$941$			941.556i			1.00059i	0.865855	+	0.500295i	$0.166775\pi$
$941$			941.556i			1.00059i	−0.865855	+	0.500295i	$0.833225\pi$
$942$			656.542i			0.696966i
$943$		−	270.962i		−	0.287341i
$944$	−2319.65			−2.45725
$945$			30.7409i			0.0325300i
$946$	−866.225	+	2800.68i	−0.915672	+	2.96055i
$947$	−1425.57			−1.50535			−0.752676	−	0.658391i	$-0.771238\pi$
$947$	−1425.57			−1.50535			−0.752676	+	0.658391i	$0.771238\pi$
$948$		−	748.521i		−	0.789579i
$949$	−551.682			−0.581329
$950$	−257.170			−0.270706
$951$	366.434			0.385314
$952$		−	540.212i		−	0.567449i
$953$			759.255i			0.796700i	0.917233	+	0.398350i	$0.130417\pi$
$953$			759.255i			0.796700i	−0.917233	+	0.398350i	$0.869583\pi$
$954$		−	458.926i		−	0.481054i
$955$	−87.0089			−0.0911087
$956$		−	1640.98i		−	1.71651i
$957$	−458.526	−	141.818i	−0.479129	−	0.148190i
$958$	−60.2647			−0.0629068
$959$			579.969i			0.604765i
$960$	−112.849			−0.117551
$961$	1968.98			2.04889
$962$	1007.85			1.04766
$963$			16.3309i			0.0169584i
$964$		−	767.335i		−	0.795990i
$965$			276.096i			0.286110i
$966$	553.188			0.572658
$967$			379.026i			0.391960i	0.980608	+	0.195980i	$0.0627888\pi$
$967$			379.026i			0.391960i	−0.980608	+	0.195980i	$0.937211\pi$
$968$	1325.13	−	1937.28i	1.36894	−	2.00132i
$969$	256.975			0.265196
$970$		−	1201.89i		−	1.23906i
$971$	−862.189			−0.887939			−0.443969	−	0.896042i	$-0.646430\pi$
$971$	−862.189			−0.887939			−0.443969	+	0.896042i	$0.646430\pi$
$972$	−145.219			−0.149402
$973$	526.353			0.540959
$974$		−	444.148i		−	0.456004i
$975$		−	67.5184i		−	0.0692496i
$976$		−	719.807i		−	0.737507i
$977$	−227.420			−0.232774			−0.116387	−	0.993204i	$-0.537131\pi$
$977$	−227.420			−0.232774			−0.116387	+	0.993204i	$0.537131\pi$
$978$		−	1865.35i		−	1.90731i
$979$	199.079	−	643.660i	0.203349	−	0.657467i
$980$	145.815			0.148791
$981$			379.395i			0.386744i
$982$	687.458			0.700059
$983$	1402.68			1.42694			0.713471	−	0.700685i	$-0.247122\pi$
$983$	1402.68			1.42694			0.713471	+	0.700685i	$0.247122\pi$
$984$	275.196			0.279671
$985$		−	675.181i		−	0.685463i
$986$		−	967.599i		−	0.981338i
$987$		−	408.943i		−	0.414329i
$988$	1023.71			1.03615
$989$		−	2416.04i		−	2.44291i
$990$	−257.243	−	79.5632i	−0.259842	−	0.0803669i
$991$	−538.013			−0.542899			−0.271450	−	0.962453i	$-0.587503\pi$
$991$	−538.013			−0.542899			−0.271450	+	0.962453i	$0.587503\pi$
$992$		−	2421.17i		−	2.44069i
$993$	−838.041			−0.843948
$994$	−883.999			−0.889335
$995$	−111.606			−0.112167
$996$			116.442i			0.116909i
$997$		−	1318.41i		−	1.32238i	−0.750218	−	0.661190i	$-0.770052\pi$
$997$		−	1318.41i		−	1.32238i	0.750218	−	0.661190i	$-0.229948\pi$
$998$		−	1192.20i		−	1.19459i
$999$	−184.078			−0.184262

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.3.b.a.736.8	✓	96
11.10	odd	2	inner	1155.3.b.a.736.89	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.3.b.a.736.8	✓	96	1.1	even	1	trivial
1155.3.b.a.736.89	yes	96	11.10	odd	2	inner

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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1155.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.64908i q^{2} +1.73205 q^{3} -9.31580 q^{4} +2.23607 q^{5} -6.32039i q^{6} +2.64575i q^{7} +19.3978i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-3.64908i q^{2} +1.73205 q^{3} -9.31580 q^{4} +2.23607 q^{5} -6.32039i q^{6} +2.64575i q^{7} +19.3978i q^{8} +3.00000 q^{9} -8.15959i q^{10} +(3.25029 - 10.5088i) q^{11} -16.1354 q^{12} -7.79635i q^{13} +9.65456 q^{14} +3.87298 q^{15} +33.5209 q^{16} +10.5260i q^{17} -10.9472i q^{18} -14.0951i q^{19} -20.8308 q^{20} +4.58258i q^{21} +(-38.3476 - 11.8606i) q^{22} +33.0811 q^{23} +33.5979i q^{24} +5.00000 q^{25} -28.4495 q^{26} +5.19615 q^{27} -24.6473i q^{28} -25.1912i q^{29} -14.1328i q^{30} +54.1293 q^{31} -44.7293i q^{32} +(5.62967 - 18.2018i) q^{33} +38.4102 q^{34} +5.91608i q^{35} -27.9474 q^{36} -35.4258 q^{37} -51.4341 q^{38} -13.5037i q^{39} +43.3747i q^{40} -8.19086i q^{41} +16.7222 q^{42} -73.0340i q^{43} +(-30.2791 + 97.8982i) q^{44} +6.70820 q^{45} -120.715i q^{46} -89.2387 q^{47} +58.0599 q^{48} -7.00000 q^{49} -18.2454i q^{50} +18.2315i q^{51} +72.6292i q^{52} +41.9216 q^{53} -18.9612i q^{54} +(7.26787 - 23.4985i) q^{55} -51.3217 q^{56} -24.4134i q^{57} -91.9248 q^{58} -69.2000 q^{59} -36.0799 q^{60} -21.4734i q^{61} -197.522i q^{62} +7.93725i q^{63} -29.1375 q^{64} -17.4332i q^{65} +(-66.4200 - 20.5431i) q^{66} -104.429 q^{67} -98.0580i q^{68} +57.2981 q^{69} +21.5883 q^{70} -91.5629 q^{71} +58.1933i q^{72} -70.7615i q^{73} +129.272i q^{74} +8.66025 q^{75} +131.307i q^{76} +(27.8038 + 8.59946i) q^{77} -49.2760 q^{78} +46.3899i q^{79} +74.9550 q^{80} +9.00000 q^{81} -29.8891 q^{82} -7.21651i q^{83} -42.6903i q^{84} +23.5368i q^{85} -266.507 q^{86} -43.6325i q^{87} +(203.848 + 63.0484i) q^{88} +61.2495 q^{89} -24.4788i q^{90} +20.6272 q^{91} -308.176 q^{92} +93.7547 q^{93} +325.639i q^{94} -31.5175i q^{95} -77.4735i q^{96} +147.297 q^{97} +25.5436i q^{98} +(9.75087 - 31.5265i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 216 q^{4} + 288 q^{9}+O(q^{10}) \) 96 * q - 216 * q^4 + 288 * q^9	\( 96 q - 216 q^{4} + 288 q^{9} + 40 q^{11} - 56 q^{14} + 488 q^{16} + 56 q^{22} + 16 q^{23} + 480 q^{25} - 64 q^{26} + 192 q^{31} + 24 q^{33} + 176 q^{34} - 648 q^{36} - 112 q^{37} - 272 q^{38} - 520 q^{44} + 416 q^{47} - 192 q^{48} - 672 q^{49} + 112 q^{53} - 80 q^{55} + 280 q^{56} - 352 q^{58} + 512 q^{59} - 1112 q^{64} + 288 q^{66} - 304 q^{67} - 480 q^{71} + 224 q^{77} + 240 q^{78} + 864 q^{81} - 720 q^{82} - 432 q^{86} - 376 q^{88} - 32 q^{89} - 384 q^{92} + 384 q^{93} + 272 q^{97} + 120 q^{99}+O(q^{100}) \) 96 * q - 216 * q^4 + 288 * q^9 + 40 * q^11 - 56 * q^14 + 488 * q^16 + 56 * q^22 + 16 * q^23 + 480 * q^25 - 64 * q^26 + 192 * q^31 + 24 * q^33 + 176 * q^34 - 648 * q^36 - 112 * q^37 - 272 * q^38 - 520 * q^44 + 416 * q^47 - 192 * q^48 - 672 * q^49 + 112 * q^53 - 80 * q^55 + 280 * q^56 - 352 * q^58 + 512 * q^59 - 1112 * q^64 + 288 * q^66 - 304 * q^67 - 480 * q^71 + 224 * q^77 + 240 * q^78 + 864 * q^81 - 720 * q^82 - 432 * q^86 - 376 * q^88 - 32 * q^89 - 384 * q^92 + 384 * q^93 + 272 * q^97 + 120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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