LMFDB - Embedded newform 1155.3.b.a.736.1

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			736.1
Character	$\chi$	$=$	1155.736
Dual form			1155.3.b.a.736.96

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.97461i q^{2} -1.73205 q^{3} -11.7975 q^{4} -2.23607 q^{5} +6.88422i q^{6} +2.64575i q^{7} +30.9920i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-3.97461i q^{2} -1.73205 q^{3} -11.7975 q^{4} -2.23607 q^{5} +6.88422i q^{6} +2.64575i q^{7} +30.9920i q^{8} +3.00000 q^{9} +8.88749i q^{10} +(9.07106 - 6.22220i) q^{11} +20.4339 q^{12} -18.7431i q^{13} +10.5158 q^{14} +3.87298 q^{15} +75.9911 q^{16} -8.65110i q^{17} -11.9238i q^{18} +27.0268i q^{19} +26.3800 q^{20} -4.58258i q^{21} +(-24.7308 - 36.0539i) q^{22} +10.9340 q^{23} -53.6798i q^{24} +5.00000 q^{25} -74.4963 q^{26} -5.19615 q^{27} -31.2133i q^{28} -47.3487i q^{29} -15.3936i q^{30} +47.7649 q^{31} -178.067i q^{32} +(-15.7115 + 10.7772i) q^{33} -34.3847 q^{34} -5.91608i q^{35} -35.3925 q^{36} -8.36469 q^{37} +107.421 q^{38} +32.4639i q^{39} -69.3003i q^{40} -10.9442i q^{41} -18.2139 q^{42} +68.7495i q^{43} +(-107.016 + 73.4065i) q^{44} -6.70820 q^{45} -43.4584i q^{46} -10.1759 q^{47} -131.620 q^{48} -7.00000 q^{49} -19.8730i q^{50} +14.9841i q^{51} +221.121i q^{52} -36.1125 q^{53} +20.6527i q^{54} +(-20.2835 + 13.9133i) q^{55} -81.9972 q^{56} -46.8119i q^{57} -188.192 q^{58} +6.29969 q^{59} -45.6915 q^{60} -87.1660i q^{61} -189.847i q^{62} +7.93725i q^{63} -403.781 q^{64} +41.9108i q^{65} +(42.8350 + 62.4472i) q^{66} +88.0521 q^{67} +102.061i q^{68} -18.9383 q^{69} -23.5141 q^{70} +18.5649 q^{71} +92.9761i q^{72} +52.7532i q^{73} +33.2464i q^{74} -8.66025 q^{75} -318.849i q^{76} +(16.4624 + 23.9998i) q^{77} +129.031 q^{78} -3.75487i q^{79} -169.921 q^{80} +9.00000 q^{81} -43.4988 q^{82} -4.28580i q^{83} +54.0630i q^{84} +19.3444i q^{85} +273.252 q^{86} +82.0103i q^{87} +(192.839 + 281.131i) q^{88} -12.6330 q^{89} +26.6625i q^{90} +49.5895 q^{91} -128.994 q^{92} -82.7312 q^{93} +40.4453i q^{94} -60.4339i q^{95} +308.421i q^{96} -124.058 q^{97} +27.8223i q^{98} +(27.2132 - 18.6666i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	3.97461i		−	1.98730i	−0.112499	−	0.993652i	$-0.535885\pi$
$2$		−	3.97461i		−	1.98730i	0.112499	−	0.993652i	$-0.464115\pi$
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−11.7975			−2.94938
$5$	−2.23607			−0.447214
$5$	−2.23607			−0.447214
$6$			6.88422i			1.14737i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$			30.9920i			3.87400i
$9$	3.00000			0.333333
$10$			8.88749i			0.888749i
$11$	9.07106	−	6.22220i	0.824642	−	0.565655i
$11$	9.07106	−	6.22220i	0.824642	−	0.565655i
$12$	20.4339			1.70282
$13$		−	18.7431i		−	1.44177i	−0.693053	−	0.720887i	$-0.743735\pi$
$13$		−	18.7431i		−	1.44177i	0.693053	−	0.720887i	$-0.256265\pi$
$14$	10.5158			0.751130
$15$	3.87298			0.258199
$16$	75.9911			4.74944
$17$		−	8.65110i		−	0.508888i	−0.967088	−	0.254444i	$-0.918108\pi$
$17$		−	8.65110i		−	0.508888i	0.967088	−	0.254444i	$-0.0818925\pi$
$18$		−	11.9238i		−	0.662435i
$19$			27.0268i			1.42247i	0.702957	+	0.711233i	$0.251863\pi$
$19$			27.0268i			1.42247i	−0.702957	+	0.711233i	$0.748137\pi$
$20$	26.3800			1.31900
$21$		−	4.58258i		−	0.218218i
$22$	−24.7308	−	36.0539i	−1.12413	−	1.63881i
$23$	10.9340			0.475392			0.237696	−	0.971340i	$-0.423608\pi$
$23$	10.9340			0.475392			0.237696	+	0.971340i	$0.423608\pi$
$24$		−	53.6798i		−	2.23666i
$25$	5.00000			0.200000
$26$	−74.4963			−2.86524
$27$	−5.19615			−0.192450
$28$		−	31.2133i		−	1.11476i
$29$		−	47.3487i		−	1.63271i	−0.577549	−	0.816356i	$-0.695991\pi$
$29$		−	47.3487i		−	1.63271i	0.577549	−	0.816356i	$-0.304009\pi$
$30$		−	15.3936i		−	0.513120i
$31$	47.7649			1.54080			0.770401	−	0.637559i	$-0.220056\pi$
$31$	47.7649			1.54080			0.770401	+	0.637559i	$0.220056\pi$
$32$		−	178.067i		−	5.56458i
$33$	−15.7115	+	10.7772i	−0.476107	+	0.326581i
$34$	−34.3847			−1.01132
$35$		−	5.91608i		−	0.169031i
$36$	−35.3925			−0.983125
$37$	−8.36469			−0.226073			−0.113036	−	0.993591i	$-0.536058\pi$
$37$	−8.36469			−0.226073			−0.113036	+	0.993591i	$0.536058\pi$
$38$	107.421			2.82687
$39$			32.4639i			0.832408i
$40$		−	69.3003i		−	1.73251i
$41$		−	10.9442i		−	0.266931i	−0.991053	−	0.133466i	$-0.957389\pi$
$41$		−	10.9442i		−	0.266931i	0.991053	−	0.133466i	$-0.0426105\pi$
$42$	−18.2139			−0.433665
$43$			68.7495i			1.59883i	0.600782	+	0.799413i	$0.294856\pi$
$43$			68.7495i			1.59883i	−0.600782	+	0.799413i	$0.705144\pi$
$44$	−107.016	+	73.4065i	−2.43218	+	1.66833i
$45$	−6.70820			−0.149071
$46$		−	43.4584i		−	0.944748i
$47$	−10.1759			−0.216509			−0.108254	−	0.994123i	$-0.534526\pi$
$47$	−10.1759			−0.216509			−0.108254	+	0.994123i	$0.534526\pi$
$48$	−131.620			−2.74209
$49$	−7.00000			−0.142857
$50$		−	19.8730i		−	0.397461i
$51$			14.9841i			0.293807i
$52$			221.121i			4.25233i
$53$	−36.1125			−0.681368			−0.340684	−	0.940178i	$-0.610659\pi$
$53$	−36.1125			−0.681368			−0.340684	+	0.940178i	$0.610659\pi$
$54$			20.6527i			0.382457i
$55$	−20.2835	+	13.9133i	−0.368791	+	0.252969i
$56$	−81.9972			−1.46424
$57$		−	46.8119i		−	0.821261i
$58$	−188.192			−3.24470
$59$	6.29969			0.106774			0.0533872	−	0.998574i	$-0.482998\pi$
$59$	6.29969			0.106774			0.0533872	+	0.998574i	$0.482998\pi$
$60$	−45.6915			−0.761526
$61$		−	87.1660i		−	1.42895i	−0.699660	−	0.714476i	$-0.746665\pi$
$61$		−	87.1660i		−	1.42895i	0.699660	−	0.714476i	$-0.253335\pi$
$62$		−	189.847i		−	3.06204i
$63$			7.93725i			0.125988i
$64$	−403.781			−6.30908
$65$			41.9108i			0.644781i
$66$	42.8350	+	62.4472i	0.649016	+	0.946170i
$67$	88.0521			1.31421			0.657105	−	0.753799i	$-0.271781\pi$
$67$	88.0521			1.31421			0.657105	+	0.753799i	$0.271781\pi$
$68$			102.061i			1.50090i
$69$	−18.9383			−0.274468
$70$	−23.5141			−0.335916
$71$	18.5649			0.261477			0.130738	−	0.991417i	$-0.458265\pi$
$71$	18.5649			0.261477			0.130738	+	0.991417i	$0.458265\pi$
$72$			92.9761i			1.29133i
$73$			52.7532i			0.722646i	0.932441	+	0.361323i	$0.117675\pi$
$73$			52.7532i			0.722646i	−0.932441	+	0.361323i	$0.882325\pi$
$74$			33.2464i			0.449275i
$75$	−8.66025			−0.115470
$76$		−	318.849i		−	4.19539i
$77$	16.4624	+	23.9998i	0.213797	+	0.311685i
$78$	129.031			1.65425
$79$		−	3.75487i		−	0.0475300i	−0.999718	−	0.0237650i	$-0.992435\pi$
$79$		−	3.75487i		−	0.0475300i	0.999718	−	0.0237650i	$-0.00756534\pi$
$80$	−169.921			−2.12402
$81$	9.00000			0.111111
$82$	−43.4988			−0.530473
$83$		−	4.28580i		−	0.0516361i	−0.999667	−	0.0258181i	$-0.991781\pi$
$83$		−	4.28580i		−	0.0516361i	0.999667	−	0.0258181i	$-0.00821906\pi$
$84$			54.0630i			0.643607i
$85$			19.3444i			0.227582i
$86$	273.252			3.17735
$87$			82.0103i			0.942647i
$88$	192.839	+	281.131i	2.19135	+	3.19467i
$89$	−12.6330			−0.141944			−0.0709718	−	0.997478i	$-0.522610\pi$
$89$	−12.6330			−0.141944			−0.0709718	+	0.997478i	$0.522610\pi$
$90$			26.6625i			0.296250i
$91$	49.5895			0.544939
$92$	−128.994			−1.40211
$93$	−82.7312			−0.889583
$94$			40.4453i			0.430269i
$95$		−	60.4339i		−	0.636146i
$96$			308.421i			3.21271i
$97$	−124.058			−1.27895			−0.639477	−	0.768810i	$-0.720849\pi$
$97$	−124.058			−1.27895			−0.639477	+	0.768810i	$0.720849\pi$
$98$			27.8223i			0.283901i
$99$	27.2132	−	18.6666i	0.274881	−	0.188552i
$100$	−58.9875			−0.589875
$101$		−	71.5170i		−	0.708089i	−0.935229	−	0.354044i	$-0.884806\pi$
$101$		−	71.5170i		−	0.708089i	0.935229	−	0.354044i	$-0.115194\pi$
$102$	59.5561			0.583883
$103$	−107.028			−1.03911			−0.519555	−	0.854437i	$-0.673902\pi$
$103$	−107.028			−1.03911			−0.519555	+	0.854437i	$0.673902\pi$
$104$	580.885			5.58543
$105$			10.2470i			0.0975900i
$106$			143.533i			1.35409i
$107$		−	13.3339i		−	0.124616i	−0.998057	−	0.0623079i	$-0.980154\pi$
$107$		−	13.3339i		−	0.124616i	0.998057	−	0.0623079i	$-0.0198461\pi$
$108$	61.3016			0.567608
$109$		−	71.4601i		−	0.655597i	−0.944748	−	0.327798i	$-0.893693\pi$
$109$		−	71.4601i		−	0.655597i	0.944748	−	0.327798i	$-0.106307\pi$
$110$	55.2998	+	80.6190i	0.502725	+	0.732900i
$111$	14.4881			0.130523
$112$			201.054i			1.79512i
$113$	30.8420			0.272938			0.136469	−	0.990644i	$-0.456425\pi$
$113$	30.8420			0.272938			0.136469	+	0.990644i	$0.456425\pi$
$114$	−186.059			−1.63209
$115$	−24.4492			−0.212602
$116$			558.596i			4.81548i
$117$		−	56.2292i		−	0.480591i
$118$		−	25.0388i		−	0.212193i
$119$	22.8887			0.192342
$120$			120.032i			1.00026i
$121$	43.5683	−	112.884i	0.360069	−	0.932926i
$122$	−346.451			−2.83976
$123$			18.9559i			0.154113i
$124$	−563.506			−4.54441
$125$	−11.1803			−0.0894427
$126$	31.5475			0.250377
$127$		−	90.3071i		−	0.711080i	−0.934661	−	0.355540i	$-0.884297\pi$
$127$		−	90.3071i		−	0.711080i	0.934661	−	0.355540i	$-0.115703\pi$
$128$			892.604i			6.97347i
$129$		−	119.078i		−	0.923082i
$130$	166.579			1.28138
$131$		−	22.8479i		−	0.174412i	−0.996190	−	0.0872059i	$-0.972206\pi$
$131$		−	22.8479i		−	0.174412i	0.996190	−	0.0872059i	$-0.0277938\pi$
$132$	185.357	−	127.144i	1.40422	−	0.963210i
$133$	−71.5063			−0.537641
$134$		−	349.973i		−	2.61174i
$135$	11.6190			0.0860663
$136$	268.115			1.97143
$137$	226.821			1.65562			0.827812	−	0.561005i	$-0.189585\pi$
$137$	226.821			1.65562			0.827812	+	0.561005i	$0.189585\pi$
$138$			75.2722i			0.545451i
$139$		−	87.9487i		−	0.632725i	−0.948638	−	0.316362i	$-0.897538\pi$
$139$		−	87.9487i		−	0.632725i	0.948638	−	0.316362i	$-0.102462\pi$
$140$			69.7950i			0.498536i
$141$	17.6252			0.125001
$142$		−	73.7880i		−	0.519634i
$143$	−116.623	−	170.019i	−0.815546	−	1.18895i
$144$	227.973			1.58315
$145$			105.875i			0.730171i
$146$	209.673			1.43612
$147$	12.1244			0.0824786
$148$	98.6825			0.666773
$149$			48.3186i			0.324286i	0.986767	+	0.162143i	$0.0518406\pi$
$149$			48.3186i			0.324286i	−0.986767	+	0.162143i	$0.948159\pi$
$150$			34.4211i			0.229474i
$151$		−	221.905i		−	1.46957i	−0.678301	−	0.734784i	$-0.737284\pi$
$151$		−	221.905i		−	1.46957i	0.678301	−	0.734784i	$-0.262716\pi$
$152$	−837.616			−5.51063
$153$		−	25.9533i		−	0.169629i
$154$	95.3897	−	65.4316i	0.619414	−	0.424881i
$155$	−106.806			−0.689068
$156$		−	382.993i		−	2.45509i
$157$	−218.728			−1.39317			−0.696585	−	0.717474i	$-0.745298\pi$
$157$	−218.728			−1.39317			−0.696585	+	0.717474i	$0.745298\pi$
$158$	−14.9241			−0.0944565
$159$	62.5487			0.393388
$160$			398.169i			2.48856i
$161$			28.9287i			0.179681i
$162$		−	35.7715i		−	0.220812i
$163$	−234.386			−1.43795			−0.718977	−	0.695034i	$-0.755389\pi$
$163$	−234.386			−1.43795			−0.718977	+	0.695034i	$0.755389\pi$
$164$			129.114i			0.787280i
$165$	35.1321	−	24.0985i	0.212922	−	0.146051i
$166$	−17.0344			−0.102617
$167$			161.179i			0.965144i	0.875856	+	0.482572i	$0.160297\pi$
$167$			161.179i			0.965144i	−0.875856	+	0.482572i	$0.839703\pi$
$168$	142.023			0.845377
$169$	−182.302			−1.07871
$170$	76.8866			0.452274
$171$			81.0805i			0.474155i
$172$		−	811.073i		−	4.71554i
$173$		−	152.777i		−	0.883105i	−0.897236	−	0.441552i	$-0.854428\pi$
$173$		−	152.777i		−	0.883105i	0.897236	−	0.441552i	$-0.145572\pi$
$174$	325.959			1.87333
$175$			13.2288i			0.0755929i
$176$	689.320	−	472.832i	3.91659	−	2.68655i
$177$	−10.9114			−0.0616462
$178$			50.2111i			0.282085i
$179$	68.5505			0.382964			0.191482	−	0.981496i	$-0.438671\pi$
$179$	68.5505			0.382964			0.191482	+	0.981496i	$0.438671\pi$
$180$	79.1401			0.439667
$181$	−265.782			−1.46841			−0.734205	−	0.678927i	$-0.762445\pi$
$181$	−265.782			−1.46841			−0.734205	+	0.678927i	$0.762445\pi$
$182$		−	197.099i		−	1.08296i
$183$			150.976i			0.825006i
$184$			338.867i			1.84167i
$185$	18.7040			0.101103
$186$			328.824i			1.76787i
$187$	−53.8289	−	78.4746i	−0.287855	−	0.419650i
$188$	120.050			0.638566
$189$		−	13.7477i		−	0.0727393i
$190$	−240.201			−1.26422
$191$	−179.463			−0.939596			−0.469798	−	0.882774i	$-0.655673\pi$
$191$	−179.463			−0.939596			−0.469798	+	0.882774i	$0.655673\pi$
$192$	699.369			3.64255
$193$		−	368.759i		−	1.91067i	−0.295529	−	0.955334i	$-0.595496\pi$
$193$		−	368.759i		−	1.91067i	0.295529	−	0.955334i	$-0.404504\pi$
$194$			493.084i			2.54167i
$195$		−	72.5915i		−	0.372264i
$196$	82.5825			0.421339
$197$		−	67.9213i		−	0.344778i	−0.985029	−	0.172389i	$-0.944851\pi$
$197$		−	67.9213i		−	0.344778i	0.985029	−	0.172389i	$-0.0551486\pi$
$198$	−74.1925	−	108.162i	−0.374709	−	0.546271i
$199$	−19.0786			−0.0958724			−0.0479362	−	0.998850i	$-0.515264\pi$
$199$	−19.0786			−0.0958724			−0.0479362	+	0.998850i	$0.515264\pi$
$200$			154.960i			0.774801i
$201$	−152.511			−0.758760
$202$	−284.252			−1.40719
$203$	125.273			0.617107
$204$		−	176.775i		−	0.866546i
$205$			24.4719i			0.119375i
$206$			425.395i			2.06503i
$207$	32.8020			0.158464
$208$		−	1424.31i		−	6.84762i
$209$	168.167	+	245.162i	0.804625	+	1.17302i
$210$	40.7276			0.193941
$211$			41.1907i			0.195217i	0.995225	+	0.0976083i	$0.0311192\pi$
$211$			41.1907i			0.195217i	−0.995225	+	0.0976083i	$0.968881\pi$
$212$	426.037			2.00961
$213$	−32.1553			−0.150964
$214$	−52.9970			−0.247649
$215$		−	153.729i		−	0.715016i
$216$		−	161.039i		−	0.745552i
$217$			126.374i			0.582369i
$218$	−284.026			−1.30287
$219$		−	91.3712i		−	0.417220i
$220$	239.295	−	164.142i	1.08770	−	0.746100i
$221$	−162.148			−0.733701
$222$		−	57.5844i		−	0.259389i
$223$	−419.034			−1.87908			−0.939539	−	0.342443i	$-0.888746\pi$
$223$	−419.034			−1.87908			−0.939539	+	0.342443i	$0.888746\pi$
$224$	471.120			2.10322
$225$	15.0000			0.0666667
$226$		−	122.585i		−	0.542410i
$227$		−	401.922i		−	1.77058i	−0.465039	−	0.885290i	$-0.653960\pi$
$227$		−	401.922i		−	1.77058i	0.465039	−	0.885290i	$-0.346040\pi$
$228$			552.263i			2.42221i
$229$	187.008			0.816627			0.408314	−	0.912842i	$-0.366117\pi$
$229$	187.008			0.816627			0.408314	+	0.912842i	$0.366117\pi$
$230$			97.1760i			0.422504i
$231$	−28.5137	−	41.5688i	−0.123436	−	0.179952i
$232$	1467.43			6.32513
$233$			300.124i			1.28809i	0.764989	+	0.644043i	$0.222744\pi$
$233$			300.124i			1.28809i	−0.764989	+	0.644043i	$0.777256\pi$
$234$	−223.489			−0.955081
$235$	22.7540			0.0968257
$236$	−74.3206			−0.314918
$237$			6.50362i			0.0274414i
$238$		−	90.9734i		−	0.382241i
$239$			403.442i			1.68804i	0.536311	+	0.844021i	$0.319818\pi$
$239$			403.442i			1.68804i	−0.536311	+	0.844021i	$0.680182\pi$
$240$	294.312			1.22630
$241$			305.251i			1.26660i	0.773906	+	0.633301i	$0.218300\pi$
$241$			305.251i			1.26660i	−0.773906	+	0.633301i	$0.781700\pi$
$242$	−448.670	−	173.167i	−1.85401	−	0.715566i
$243$	−15.5885			−0.0641500
$244$			1028.34i			4.21452i
$245$	15.6525			0.0638877
$246$	75.3421			0.306269
$247$	506.566			2.05087
$248$			1480.33i			5.96907i
$249$			7.42322i			0.0298121i
$250$			44.4375i			0.177750i
$251$	132.492			0.527857			0.263929	−	0.964542i	$-0.414982\pi$
$251$	132.492			0.527857			0.263929	+	0.964542i	$0.414982\pi$
$252$		−	93.6398i		−	0.371586i
$253$	99.1831	−	68.0337i	0.392028	−	0.268908i
$254$	−358.935			−1.41313
$255$		−	33.5056i		−	0.131394i
$256$	1932.63			7.54932
$257$	106.182			0.413161			0.206581	−	0.978430i	$-0.433766\pi$
$257$	106.182			0.413161			0.206581	+	0.978430i	$0.433766\pi$
$258$	−473.287			−1.83444
$259$		−	22.1309i		−	0.0854475i
$260$		−	494.442i		−	1.90170i
$261$		−	142.046i		−	0.544237i
$262$	−90.8116			−0.346609
$263$		−	447.934i		−	1.70317i	−0.524215	−	0.851586i	$-0.675641\pi$
$263$		−	447.934i		−	1.70317i	0.524215	−	0.851586i	$-0.324359\pi$
$264$	−334.006	−	486.932i	−1.26518	−	1.84444i
$265$	80.7500			0.304717
$266$			284.209i			1.06846i
$267$	21.8810			0.0819512
$268$	−1038.80			−3.87610
$269$	−41.9097			−0.155798			−0.0778991	−	0.996961i	$-0.524821\pi$
$269$	−41.9097			−0.155798			−0.0778991	+	0.996961i	$0.524821\pi$
$270$		−	46.1808i		−	0.171040i
$271$			390.292i			1.44019i	0.693875	+	0.720095i	$0.255902\pi$
$271$			390.292i			1.44019i	−0.693875	+	0.720095i	$0.744098\pi$
$272$		−	657.406i		−	2.41694i
$273$	−85.8915			−0.314621
$274$		−	901.523i		−	3.29023i
$275$	45.3553	−	31.1110i	0.164928	−	0.113131i
$276$	223.424			0.809509
$277$			288.196i			1.04042i	0.854039	+	0.520210i	$0.174146\pi$
$277$			288.196i			1.04042i	−0.854039	+	0.520210i	$0.825854\pi$
$278$	−349.562			−1.25742
$279$	143.295			0.513601
$280$	183.351			0.654826
$281$		−	433.691i		−	1.54338i	−0.635996	−	0.771692i	$-0.719411\pi$
$281$		−	433.691i		−	1.54338i	0.635996	−	0.771692i	$-0.280589\pi$
$282$		−	70.0533i		−	0.248416i
$283$		−	189.004i		−	0.667858i	−0.942598	−	0.333929i	$-0.891625\pi$
$283$		−	189.004i		−	0.667858i	0.942598	−	0.333929i	$-0.108375\pi$
$284$	−219.019			−0.771193
$285$			104.675i			0.367279i
$286$	−675.761	+	463.531i	−2.36280	+	1.62074i
$287$	28.9556			0.100890
$288$		−	534.200i		−	1.85486i
$289$	214.159			0.741033
$290$	420.811			1.45107
$291$	214.876			0.738404
$292$		−	622.356i		−	2.13136i
$293$		−	316.947i		−	1.08173i	−0.841109	−	0.540866i	$-0.818097\pi$
$293$		−	316.947i		−	1.08173i	0.841109	−	0.540866i	$-0.181903\pi$
$294$		−	48.1896i		−	0.163910i
$295$	−14.0865			−0.0477509
$296$		−	259.239i		−	0.875806i
$297$	−47.1346	+	32.3315i	−0.158702	+	0.108860i
$298$	192.047			0.644455
$299$		−	204.937i		−	0.685408i
$300$	102.169			0.340565
$301$	−181.894			−0.604299
$302$	−881.984			−2.92048
$303$			123.871i			0.408815i
$304$			2053.80i			6.75592i
$305$			194.909i			0.639047i
$306$	−103.154			−0.337105
$307$		−	165.027i		−	0.537546i	−0.963204	−	0.268773i	$-0.913382\pi$
$307$		−	165.027i		−	0.537546i	0.963204	−	0.268773i	$-0.0866182\pi$
$308$	−194.215	−	283.137i	−0.630569	−	0.919277i
$309$	185.378			0.599930
$310$			424.510i			1.36939i
$311$	−94.0852			−0.302525			−0.151262	−	0.988494i	$-0.548334\pi$
$311$	−94.0852			−0.302525			−0.151262	+	0.988494i	$0.548334\pi$
$312$	−1006.12			−3.22475
$313$	−154.070			−0.492237			−0.246119	−	0.969240i	$-0.579155\pi$
$313$	−154.070			−0.492237			−0.246119	+	0.969240i	$0.579155\pi$
$314$			869.357i			2.76865i
$315$		−	17.7482i		−	0.0563436i
$316$			44.2981i			0.140184i
$317$	−277.938			−0.876775			−0.438387	−	0.898786i	$-0.644450\pi$
$317$	−277.938			−0.876775			−0.438387	+	0.898786i	$0.644450\pi$
$318$		−	248.607i		−	0.781781i
$319$	−294.613	−	429.503i	−0.923552	−	1.34640i
$320$	902.882			2.82150
$321$			23.0950i			0.0719470i
$322$	114.980			0.357081
$323$	233.812			0.723876
$324$	−106.178			−0.327708
$325$		−	93.7153i		−	0.288355i
$326$			931.594i			2.85765i
$327$			123.772i			0.378509i
$328$	339.182			1.03409
$329$		−	26.9230i		−	0.0818327i
$330$	−95.7821	−	139.636i	−0.290249	−	0.423140i
$331$	557.264			1.68358			0.841789	−	0.539807i	$-0.181503\pi$
$331$	557.264			1.68358			0.841789	+	0.539807i	$0.181503\pi$
$332$			50.5617i			0.152294i
$333$	−25.0941			−0.0753576
$334$	640.623			1.91803
$335$	−196.890			−0.587733
$336$		−	348.235i		−	1.03641i
$337$		−	141.561i		−	0.420063i	−0.977695	−	0.210032i	$-0.932643\pi$
$337$		−	141.561i		−	0.420063i	0.977695	−	0.210032i	$-0.0673567\pi$
$338$			724.580i			2.14373i
$339$	−53.4198			−0.157581
$340$		−	228.216i		−	0.671224i
$341$	433.278	−	297.203i	1.27061	−	0.871563i
$342$	322.263			0.942290
$343$		−	18.5203i		−	0.0539949i
$344$	−2130.69			−6.19385
$345$	42.3473			0.122746
$346$	−607.229			−1.75500
$347$			331.618i			0.955672i	0.878449	+	0.477836i	$0.158579\pi$
$347$			331.618i			0.955672i	−0.878449	+	0.477836i	$0.841421\pi$
$348$		−	967.517i		−	2.78022i
$349$		−	160.807i		−	0.460764i	−0.973100	−	0.230382i	$-0.926002\pi$
$349$		−	160.807i		−	0.460764i	0.973100	−	0.230382i	$-0.0739976\pi$
$350$	52.5791			0.150226
$351$			97.3918i			0.277469i
$352$	−1107.97	−	1615.25i	−3.14763	−	4.58879i
$353$	491.173			1.39142			0.695712	−	0.718321i	$-0.255089\pi$
$353$	491.173			1.39142			0.695712	+	0.718321i	$0.255089\pi$
$354$			43.3684i			0.122510i
$355$	−41.5123			−0.116936
$356$	149.038			0.418645
$357$	−39.6443			−0.111048
$358$		−	272.461i		−	0.761065i
$359$		−	427.076i		−	1.18963i	−0.803863	−	0.594814i	$-0.797226\pi$
$359$		−	427.076i		−	1.18963i	0.803863	−	0.594814i	$-0.202774\pi$
$360$		−	207.901i		−	0.577502i
$361$	−369.450			−1.02341
$362$			1056.38i			2.91818i
$363$	−75.4626	+	195.521i	−0.207886	+	0.538625i
$364$	−585.032			−1.60723
$365$		−	117.960i		−	0.323177i
$366$	600.070			1.63954
$367$	−181.395			−0.494264			−0.247132	−	0.968982i	$-0.579488\pi$
$367$	−181.395			−0.494264			−0.247132	+	0.968982i	$0.579488\pi$
$368$	830.888			2.25785
$369$		−	32.8325i		−	0.0889770i
$370$		−	74.3411i		−	0.200922i
$371$		−	95.5447i		−	0.257533i
$372$	976.022			2.62371
$373$		−	202.027i		−	0.541627i	−0.962632	−	0.270813i	$-0.912707\pi$
$373$		−	202.027i		−	0.541627i	0.962632	−	0.270813i	$-0.0872926\pi$
$374$	−311.906	+	213.949i	−0.833973	+	0.572055i
$375$	19.3649			0.0516398
$376$		−	315.372i		−	0.838756i
$377$	−887.459			−2.35400
$378$	−54.6418			−0.144555
$379$	−344.155			−0.908060			−0.454030	−	0.890986i	$-0.650014\pi$
$379$	−344.155			−0.908060			−0.454030	+	0.890986i	$0.650014\pi$
$380$			712.969i			1.87623i
$381$			156.416i			0.410542i
$382$			713.294i			1.86726i
$383$	−751.774			−1.96286			−0.981428	−	0.191829i	$-0.938558\pi$
$383$	−751.774			−1.96286			−0.981428	+	0.191829i	$0.938558\pi$
$384$		−	1546.03i		−	4.02613i
$385$	−36.8111	−	53.6651i	−0.0956131	−	0.139390i
$386$	−1465.67			−3.79708
$387$			206.248i			0.532942i
$388$	1463.58			3.77211
$389$	423.149			1.08779			0.543894	−	0.839154i	$-0.316949\pi$
$389$	423.149			1.08779			0.543894	+	0.839154i	$0.316949\pi$
$390$	−288.523			−0.739802
$391$		−	94.5912i		−	0.241921i
$392$		−	216.944i		−	0.553429i
$393$			39.5738i			0.100697i
$394$	−269.961			−0.685179
$395$			8.39614i			0.0212560i
$396$	−321.048	+	220.219i	−0.810727	+	0.556110i
$397$	−510.679			−1.28635			−0.643173	−	0.765721i	$-0.722382\pi$
$397$	−510.679			−1.28635			−0.643173	+	0.765721i	$0.722382\pi$
$398$			75.8300i			0.190528i
$399$	123.853			0.310407
$400$	379.955			0.949889
$401$	489.648			1.22107			0.610534	−	0.791990i	$-0.290955\pi$
$401$	489.648			1.22107			0.610534	+	0.791990i	$0.290955\pi$
$402$			606.170i			1.50789i
$403$		−	895.260i		−	2.22149i
$404$			843.722i			2.08842i
$405$	−20.1246			−0.0496904
$406$		−	497.910i		−	1.22638i
$407$	−75.8766	+	52.0468i	−0.186429	+	0.127879i
$408$	−464.389			−1.13821
$409$			2.28615i			0.00558960i	0.999996	+	0.00279480i	$0.000889614\pi$
$409$			2.28615i			0.00558960i	−0.999996	+	0.00279480i	$0.999110\pi$
$410$	97.2663			0.237235
$411$	−392.865			−0.955875
$412$	1262.67			3.06473
$413$			16.6674i			0.0403569i
$414$		−	130.375i		−	0.314916i
$415$			9.58333i			0.0230924i
$416$	−3337.51			−8.02287
$417$			152.332i			0.365304i
$418$	974.423	−	668.396i	2.33116	−	1.59903i
$419$	−12.8084			−0.0305689			−0.0152844	−	0.999883i	$-0.504865\pi$
$419$	−12.8084			−0.0305689			−0.0152844	+	0.999883i	$0.504865\pi$
$420$		−	120.888i		−	0.287830i
$421$	166.015			0.394335			0.197168	−	0.980370i	$-0.436826\pi$
$421$	166.015			0.394335			0.197168	+	0.980370i	$0.436826\pi$
$422$	163.717			0.387955
$423$	−30.5278			−0.0721696
$424$		−	1119.20i		−	2.63962i
$425$		−	43.2555i		−	0.101778i
$426$			127.805i			0.300011i
$427$	230.620			0.540093
$428$			157.307i			0.367539i
$429$	201.997	+	294.482i	0.470856	+	0.686439i
$430$	−611.011			−1.42095
$431$		−	607.166i		−	1.40874i	−0.709834	−	0.704369i	$-0.751230\pi$
$431$		−	607.166i		−	1.40874i	0.709834	−	0.704369i	$-0.248770\pi$
$432$	−394.861			−0.914031
$433$	−255.954			−0.591117			−0.295558	−	0.955325i	$-0.595506\pi$
$433$	−255.954			−0.591117			−0.295558	+	0.955325i	$0.595506\pi$
$434$	502.287			1.15734
$435$		−	183.381i		−	0.421564i
$436$			843.051i			1.93360i
$437$			295.512i			0.676229i
$438$	−363.165			−0.829143
$439$		−	193.090i		−	0.439841i	−0.975518	−	0.219921i	$-0.929420\pi$
$439$		−	193.090i		−	0.439841i	0.975518	−	0.219921i	$-0.0705799\pi$
$440$	−431.200	−	628.627i	−0.980001	−	1.42870i
$441$	−21.0000			−0.0476190
$442$			644.475i			1.45809i
$443$	90.1255			0.203444			0.101722	−	0.994813i	$-0.467565\pi$
$443$	90.1255			0.203444			0.101722	+	0.994813i	$0.467565\pi$
$444$	−170.923			−0.384962
$445$	28.2482			0.0634791
$446$			1665.50i			3.73430i
$447$		−	83.6903i		−	0.187227i
$448$		−	1068.30i		−	2.38461i
$449$	565.871			1.26029			0.630146	−	0.776477i	$-0.282995\pi$
$449$	565.871			1.26029			0.630146	+	0.776477i	$0.282995\pi$
$450$		−	59.6191i		−	0.132487i
$451$	−68.0969	−	99.2753i	−0.150991	−	0.220123i
$452$	−363.858			−0.804996
$453$			384.350i			0.848455i
$454$	−1597.48			−3.51868
$455$	−110.885			−0.243704
$456$	1450.79			3.18157
$457$			275.380i			0.602582i	0.953532	+	0.301291i	$0.0974175\pi$
$457$			275.380i			0.602582i	−0.953532	+	0.301291i	$0.902582\pi$
$458$		−	743.282i		−	1.62289i
$459$			44.9524i			0.0979355i
$460$	288.440			0.627043
$461$		−	316.861i		−	0.687334i	−0.939092	−	0.343667i	$-0.888331\pi$
$461$		−	316.861i		−	0.687334i	0.939092	−	0.343667i	$-0.111669\pi$
$462$	−165.220	+	113.331i	−0.357619	+	0.245305i
$463$	208.468			0.450255			0.225127	−	0.974329i	$-0.427720\pi$
$463$	208.468			0.450255			0.225127	+	0.974329i	$0.427720\pi$
$464$		−	3598.08i		−	7.75447i
$465$	184.993			0.397834
$466$	1192.88			2.55982
$467$	−462.845			−0.991103			−0.495551	−	0.868579i	$-0.665034\pi$
$467$	−462.845			−0.991103			−0.495551	+	0.868579i	$0.665034\pi$
$468$			663.364i			1.41744i
$469$			232.964i			0.496725i
$470$		−	90.4384i		−	0.192422i
$471$	378.848			0.804348
$472$			195.240i			0.413644i
$473$	427.773	+	623.631i	0.904384	+	1.31846i
$474$	25.8493			0.0545345
$475$			135.134i			0.284493i
$476$	−270.029			−0.567288
$477$	−108.338			−0.227123
$478$	1603.52			3.35465
$479$		−	68.1238i		−	0.142221i	−0.997468	−	0.0711104i	$-0.977346\pi$
$479$		−	68.1238i		−	0.142221i	0.997468	−	0.0711104i	$-0.0226543\pi$
$480$		−	689.649i		−	1.43677i
$481$			156.780i			0.325946i
$482$	1213.25			2.51712
$483$		−	50.1060i		−	0.103739i
$484$	−513.998	+	1331.75i	−1.06198	+	2.75155i
$485$	277.403			0.571965
$486$			61.9580i			0.127486i
$487$	182.868			0.375500			0.187750	−	0.982217i	$-0.439881\pi$
$487$	182.868			0.375500			0.187750	+	0.982217i	$0.439881\pi$
$488$	2701.45			5.53576
$489$	405.969			0.830203
$490$		−	62.2124i		−	0.126964i
$491$		−	470.423i		−	0.958092i	−0.877790	−	0.479046i	$-0.840983\pi$
$491$		−	470.423i		−	0.958092i	0.877790	−	0.479046i	$-0.159017\pi$
$492$		−	223.632i		−	0.454536i
$493$	−409.618			−0.830868
$494$		−	2013.40i		−	4.07571i
$495$	−60.8505	+	41.7398i	−0.122930	+	0.0843229i
$496$	3629.71			7.31795
$497$			49.1180i			0.0988289i
$498$	29.5044			0.0592457
$499$	109.988			0.220417			0.110209	−	0.993908i	$-0.464848\pi$
$499$	109.988			0.220417			0.110209	+	0.993908i	$0.464848\pi$
$500$	131.900			0.263800
$501$		−	279.170i		−	0.557226i
$502$		−	526.605i		−	1.04901i
$503$			721.607i			1.43461i	0.696761	+	0.717303i	$0.254624\pi$
$503$			721.607i			1.43461i	−0.696761	+	0.717303i	$0.745376\pi$
$504$	−245.992			−0.488078
$505$			159.917i			0.316667i
$506$	−270.407	−	394.214i	−0.534402	−	0.779079i
$507$	315.757			0.622794
$508$			1065.40i			2.09724i
$509$	−9.84946			−0.0193506			−0.00967530	−	0.999953i	$-0.503080\pi$
$509$	−9.84946			−0.0193506			−0.00967530	+	0.999953i	$0.503080\pi$
$510$	−133.171			−0.261120
$511$	−139.572			−0.273135
$512$		−	4111.01i		−	8.02932i
$513$		−	140.436i		−	0.273754i
$514$		−	422.034i		−	0.821077i
$515$	239.323			0.464704
$516$			1404.82i			2.72252i
$517$	−92.3064	+	63.3167i	−0.178542	+	0.122469i
$518$	−87.9616			−0.169810
$519$			264.618i			0.509861i
$520$	−1298.90			−2.49788
$521$	−59.7963			−0.114772			−0.0573861	−	0.998352i	$-0.518277\pi$
$521$	−59.7963			−0.114772			−0.0573861	+	0.998352i	$0.518277\pi$
$522$	−564.577			−1.08157
$523$		−	341.539i		−	0.653038i	−0.945191	−	0.326519i	$-0.894124\pi$
$523$		−	341.539i		−	0.653038i	0.945191	−	0.326519i	$-0.105876\pi$
$524$			269.549i			0.514406i
$525$		−	22.9129i		−	0.0436436i
$526$	−1780.36			−3.38472
$527$		−	413.219i		−	0.784096i
$528$	−1193.94	+	818.969i	−2.26124	+	1.55108i
$529$	−409.447			−0.774002
$530$		−	320.950i		−	0.605565i
$531$	18.8991			0.0355914
$532$	843.596			1.58571
$533$	−205.127			−0.384854
$534$		−	86.9682i		−	0.162862i
$535$			29.8155i			0.0557299i
$536$			2728.91i			5.09125i
$537$	−118.733			−0.221104
$538$			166.575i			0.309618i
$539$	−63.4974	+	43.5554i	−0.117806	+	0.0808078i
$540$	−137.075			−0.253842
$541$		−	516.584i		−	0.954869i	−0.878667	−	0.477435i	$-0.841567\pi$
$541$		−	516.584i		−	0.954869i	0.878667	−	0.477435i	$-0.158433\pi$
$542$	1551.26			2.86210
$543$	460.349			0.847787
$544$	−1540.47			−2.83175
$545$			159.790i			0.293192i
$546$			341.385i			0.625247i
$547$			630.019i			1.15177i	0.817530	+	0.575886i	$0.195343\pi$
$547$			630.019i			1.15177i	−0.817530	+	0.575886i	$0.804657\pi$
$548$	−2675.92			−4.88306
$549$		−	261.498i		−	0.476317i
$550$	−123.654	−	180.270i	−0.224826	−	0.327763i
$551$	1279.68			2.32248
$552$		−	586.935i		−	1.06329i
$553$	9.93445			0.0179646
$554$	1145.47			2.06763
$555$	−32.3963			−0.0583717
$556$			1037.58i			1.86614i
$557$		−	389.255i		−	0.698842i	−0.936966	−	0.349421i	$-0.886378\pi$
$557$		−	389.255i		−	0.698842i	0.936966	−	0.349421i	$-0.113622\pi$
$558$		−	569.540i		−	1.02068i
$559$	1288.58			2.30514
$560$		−	449.569i		−	0.802803i
$561$	93.2344	+	135.922i	0.166193	+	0.242285i
$562$	−1723.75			−3.06717
$563$		−	782.370i		−	1.38965i	−0.719181	−	0.694823i	$-0.755483\pi$
$563$		−	782.370i		−	1.38965i	0.719181	−	0.694823i	$-0.244517\pi$
$564$	−207.933			−0.368676
$565$	−68.9647			−0.122061
$566$	−751.216			−1.32724
$567$			23.8118i			0.0419961i
$568$			575.362i			1.01296i
$569$		−	534.270i		−	0.938963i	−0.882942	−	0.469481i	$-0.844441\pi$
$569$		−	534.270i		−	0.938963i	0.882942	−	0.469481i	$-0.155559\pi$
$570$	416.040			0.729895
$571$			416.674i			0.729726i	0.931061	+	0.364863i	$0.118884\pi$
$571$			416.674i			0.729726i	−0.931061	+	0.364863i	$0.881116\pi$
$572$	1375.86	+	2005.81i	2.40535	+	3.50665i
$573$	310.839			0.542476
$574$		−	115.087i		−	0.200500i
$575$	54.6701			0.0950784
$576$	−1211.34			−2.10303
$577$	−975.624			−1.69086			−0.845428	−	0.534089i	$-0.820655\pi$
$577$	−975.624			−1.69086			−0.845428	+	0.534089i	$0.820655\pi$
$578$		−	851.196i		−	1.47266i
$579$			638.709i			1.10312i
$580$		−	1249.06i		−	2.15355i
$581$	11.3392			0.0195166
$582$		−	854.046i		−	1.46743i
$583$	−327.579	+	224.699i	−0.561885	+	0.385419i
$584$	−1634.93			−2.79953
$585$			125.732i			0.214927i
$586$	−1259.74			−2.14973
$587$	569.546			0.970265			0.485133	−	0.874441i	$-0.338771\pi$
$587$	569.546			0.970265			0.485133	+	0.874441i	$0.338771\pi$
$588$	−143.037			−0.243260
$589$			1290.93i			2.19174i
$590$			55.9884i			0.0948956i
$591$			117.643i			0.199058i
$592$	−635.642			−1.07372
$593$		−	214.849i		−	0.362309i	−0.983455	−	0.181154i	$-0.942017\pi$
$593$		−	214.849i		−	0.362309i	0.983455	−	0.181154i	$-0.0579834\pi$
$594$	128.505	+	187.342i	0.216339	+	0.315390i
$595$	−51.1806			−0.0860178
$596$		−	570.039i		−	0.956441i
$597$	33.0451			0.0553520
$598$	−814.544			−1.36211
$599$	79.4656			0.132664			0.0663319	−	0.997798i	$-0.478870\pi$
$599$	79.4656			0.132664			0.0663319	+	0.997798i	$0.478870\pi$
$600$		−	268.399i		−	0.447331i
$601$			260.900i			0.434110i	0.976159	+	0.217055i	$0.0696451\pi$
$601$			260.900i			0.434110i	−0.976159	+	0.217055i	$0.930355\pi$
$602$			722.958i			1.20093i
$603$	264.156			0.438070
$604$			2617.92i			4.33431i
$605$	−97.4218	+	252.416i	−0.161028	+	0.417217i
$606$	492.339			0.812440
$607$		−	524.877i		−	0.864707i	−0.901704	−	0.432353i	$-0.857683\pi$
$607$		−	524.877i		−	0.864707i	0.901704	−	0.432353i	$-0.142317\pi$
$608$	4812.58			7.91543
$609$	−216.979			−0.356287
$610$	774.688			1.26998
$611$			190.728i			0.312157i
$612$			306.184i			0.500301i
$613$		−	1092.68i		−	1.78251i	−0.453506	−	0.891253i	$-0.649827\pi$
$613$		−	1092.68i		−	1.78251i	0.453506	−	0.891253i	$-0.350173\pi$
$614$	−655.916			−1.06827
$615$		−	42.3866i		−	0.0689213i
$616$	−743.802	+	510.203i	−1.20747	+	0.828252i
$617$	1089.36			1.76558			0.882790	−	0.469768i	$-0.155662\pi$
$617$	1089.36			1.76558			0.882790	+	0.469768i	$0.155662\pi$
$618$		−	736.807i		−	1.19224i
$619$	339.482			0.548435			0.274218	−	0.961668i	$-0.411581\pi$
$619$	339.482			0.548435			0.274218	+	0.961668i	$0.411581\pi$
$620$	1260.04			2.03232
$621$	−56.8148			−0.0914892
$622$			373.952i			0.601208i
$623$		−	33.4237i		−	0.0536496i
$624$			2466.97i			3.95348i
$625$	25.0000			0.0400000
$626$			612.369i			0.978225i
$627$	−291.273	−	424.633i	−0.464550	−	0.677246i
$628$	2580.44			4.10899
$629$			72.3637i			0.115046i
$630$	−70.5423			−0.111972
$631$	521.872			0.827055			0.413528	−	0.910492i	$-0.364296\pi$
$631$	521.872			0.827055			0.413528	+	0.910492i	$0.364296\pi$
$632$	116.371			0.184131
$633$		−	71.3444i		−	0.112708i
$634$			1104.69i			1.74242i
$635$			201.933i			0.318004i
$636$	−737.919			−1.16025
$637$			131.201i			0.205968i
$638$	−1707.10	+	1170.97i	−2.67571	+	1.83538i
$639$	55.6946			0.0871589
$640$		−	1995.92i		−	3.11863i
$641$	180.849			0.282136			0.141068	−	0.990000i	$-0.454946\pi$
$641$	180.849			0.282136			0.141068	+	0.990000i	$0.454946\pi$
$642$	91.7935			0.142980
$643$	−975.268			−1.51675			−0.758373	−	0.651821i	$-0.774006\pi$
$643$	−975.268			−1.51675			−0.758373	+	0.651821i	$0.774006\pi$
$644$		−	341.286i		−	0.529948i
$645$			266.266i			0.412815i
$646$		−	929.310i		−	1.43856i
$647$	1029.33			1.59092			0.795462	−	0.606003i	$-0.207228\pi$
$647$	1029.33			1.59092			0.795462	+	0.606003i	$0.207228\pi$
$648$			278.928i			0.430445i
$649$	57.1448	−	39.1979i	0.0880506	−	0.0603974i
$650$	−372.481			−0.573048
$651$		−	218.886i		−	0.336231i
$652$	2765.18			4.24107
$653$	−605.527			−0.927301			−0.463650	−	0.886018i	$-0.653461\pi$
$653$	−605.527			−0.927301			−0.463650	+	0.886018i	$0.653461\pi$
$654$	491.947			0.752213
$655$			51.0895i			0.0779993i
$656$		−	831.660i		−	1.26777i
$657$			158.260i			0.240882i
$658$	−107.008			−0.162626
$659$			633.202i			0.960853i	0.877035	+	0.480427i	$0.159518\pi$
$659$			633.202i			0.960853i	−0.877035	+	0.480427i	$0.840482\pi$
$660$	−414.471	+	284.302i	−0.627986	+	0.430761i
$661$	12.3898			0.0187440			0.00937200	−	0.999956i	$-0.497017\pi$
$661$	12.3898			0.0187440			0.00937200	+	0.999956i	$0.497017\pi$
$662$		−	2214.91i		−	3.34578i
$663$	280.849			0.423603
$664$	132.826			0.200038
$665$	159.893			0.240441
$666$			99.7391i			0.149758i
$667$		−	517.711i		−	0.776178i
$668$		−	1901.51i		−	2.84657i
$669$	725.789			1.08489
$670$			782.562i			1.16800i
$671$	−542.365	−	790.689i	−0.808293	−	1.17837i
$672$	−816.004			−1.21429
$673$			660.098i			0.980829i	0.871489	+	0.490415i	$0.163155\pi$
$673$			660.098i			0.980829i	−0.871489	+	0.490415i	$0.836845\pi$
$674$	−562.651			−0.834794
$675$	−25.9808			−0.0384900
$676$	2150.71			3.18153
$677$			373.015i			0.550982i	0.961304	+	0.275491i	$0.0888404\pi$
$677$			373.015i			0.550982i	−0.961304	+	0.275491i	$0.911160\pi$
$678$			212.323i			0.313161i
$679$		−	328.228i		−	0.483399i
$680$	−599.523			−0.881652
$681$			696.149i			1.02224i
$682$	−1181.26	−	1722.11i	−1.73206	−	2.52509i
$683$	−739.847			−1.08323			−0.541616	−	0.840626i	$-0.682187\pi$
$683$	−739.847			−1.08323			−0.541616	+	0.840626i	$0.682187\pi$
$684$		−	956.548i		−	1.39846i
$685$	−507.186			−0.740418
$686$	−73.6108			−0.107304
$687$	−323.907			−0.471480
$688$			5224.35i			7.59353i
$689$			676.859i			0.982378i
$690$		−	168.314i		−	0.243933i
$691$	626.478			0.906625			0.453312	−	0.891352i	$-0.350242\pi$
$691$	626.478			0.906625			0.453312	+	0.891352i	$0.350242\pi$
$692$			1802.39i			2.60461i
$693$	49.3872	+	71.9993i	0.0712658	+	0.103895i
$694$	1318.05			1.89921
$695$			196.659i			0.282963i
$696$	−2541.66			−3.65182
$697$	−94.6791			−0.135838
$698$	−639.144			−0.915679
$699$		−	519.830i		−	0.743677i
$700$		−	156.066i		−	0.222952i
$701$			728.562i			1.03932i	0.854374	+	0.519659i	$0.173941\pi$
$701$			728.562i			1.03932i	−0.854374	+	0.519659i	$0.826059\pi$
$702$	387.094			0.551416
$703$		−	226.071i		−	0.321581i
$704$	−3662.72	+	2512.41i	−5.20273	+	3.56876i
$705$	−39.4112			−0.0559024
$706$		−	1952.22i		−	2.76518i
$707$	189.216			0.267632
$708$	128.727			0.181818
$709$	343.342			0.484262			0.242131	−	0.970244i	$-0.422154\pi$
$709$	343.342			0.484262			0.242131	+	0.970244i	$0.422154\pi$
$710$			164.995i			0.232387i
$711$		−	11.2646i		−	0.0158433i
$712$		−	391.522i		−	0.549890i
$713$	522.262			0.732485
$714$			157.571i			0.220687i
$715$	260.777	+	380.175i	0.364723	+	0.531713i
$716$	−808.725			−1.12950
$717$		−	698.782i		−	0.974591i
$718$	−1697.46			−2.36415
$719$	1402.21			1.95023			0.975113	−	0.221707i	$-0.0711627\pi$
$719$	1402.21			1.95023			0.975113	+	0.221707i	$0.0711627\pi$
$720$	−509.764			−0.708005
$721$		−	283.170i		−	0.392747i
$722$			1468.42i			2.03382i
$723$		−	528.710i		−	0.731273i
$724$	3135.57			4.33090
$725$		−	236.743i		−	0.326542i
$726$	777.119	+	299.934i	1.07041	+	0.413132i
$727$	734.602			1.01046			0.505228	−	0.862986i	$-0.331408\pi$
$727$	734.602			1.01046			0.505228	+	0.862986i	$0.331408\pi$
$728$			1536.88i			2.11110i
$729$	27.0000			0.0370370
$730$	−468.843			−0.642251
$731$	594.759			0.813623
$732$		−	1781.14i		−	2.43325i
$733$			1234.04i			1.68354i	0.539836	+	0.841771i	$0.318486\pi$
$733$			1234.04i			1.68354i	−0.539836	+	0.841771i	$0.681514\pi$
$734$			720.973i			0.982252i
$735$	−27.1109			−0.0368856
$736$		−	1946.98i		−	2.64536i
$737$	798.726	−	547.878i	1.08375	−	0.743390i
$738$	−130.496			−0.176824
$739$			579.867i			0.784665i	0.919824	+	0.392332i	$0.128332\pi$
$739$			579.867i			0.784665i	−0.919824	+	0.392332i	$0.871668\pi$
$740$	−220.661			−0.298190
$741$	−877.397			−1.18407
$742$	−379.753			−0.511796
$743$		−	463.909i		−	0.624373i	−0.950021	−	0.312187i	$-0.898939\pi$
$743$		−	463.909i		−	0.624373i	0.950021	−	0.312187i	$-0.101061\pi$
$744$		−	2564.01i		−	3.44625i
$745$		−	108.044i		−	0.145025i
$746$	−802.977			−1.07638
$747$		−	12.8574i		−	0.0172120i
$748$	635.047	+	925.805i	0.848993	+	1.23771i
$749$	35.2782			0.0471003
$750$		−	76.9679i		−	0.102624i
$751$	−407.668			−0.542833			−0.271417	−	0.962462i	$-0.587492\pi$
$751$	−407.668			−0.542833			−0.271417	+	0.962462i	$0.587492\pi$
$752$	−773.279			−1.02830
$753$	−229.483			−0.304759
$754$			3527.30i			4.67812i
$755$			496.194i			0.657211i
$756$			162.189i			0.214536i
$757$	−350.404			−0.462885			−0.231442	−	0.972849i	$-0.574344\pi$
$757$	−350.404			−0.462885			−0.231442	+	0.972849i	$0.574344\pi$
$758$			1367.88i			1.80459i
$759$	−171.790	+	117.838i	−0.226338	+	0.155254i
$760$	1872.97			2.46443
$761$			1042.09i			1.36937i	0.728841	+	0.684683i	$0.240059\pi$
$761$			1042.09i			1.36937i	−0.728841	+	0.684683i	$0.759941\pi$
$762$	621.694			0.815872
$763$	189.066			0.247792
$764$	2117.21			2.77122
$765$			58.0333i			0.0758606i
$766$			2988.01i			3.90079i
$767$		−	118.075i		−	0.153944i
$768$	−3347.41			−4.35860
$769$		−	114.681i		−	0.149130i	−0.997216	−	0.0745651i	$-0.976243\pi$
$769$		−	114.681i		−	0.149130i	0.997216	−	0.0745651i	$-0.0237569\pi$
$770$	−213.298	+	146.310i	−0.277010	+	0.190012i
$771$	−183.913			−0.238539
$772$			4350.43i			5.63528i
$773$	−463.240			−0.599276			−0.299638	−	0.954053i	$-0.596866\pi$
$773$	−463.240			−0.599276			−0.299638	+	0.954053i	$0.596866\pi$
$774$	819.757			1.05912
$775$	238.824			0.308161
$776$		−	3844.82i		−	4.95467i
$777$			38.3318i			0.0493331i
$778$		−	1681.85i		−	2.16176i
$779$	295.786			0.379700
$780$			856.399i			1.09795i
$781$	168.403	−	115.514i	0.215625	−	0.147906i
$782$	−375.963			−0.480771
$783$			246.031i			0.314216i
$784$	−531.938			−0.678492
$785$	489.090			0.623045
$786$	157.290			0.200115
$787$		−	114.743i		−	0.145799i	−0.997339	−	0.0728993i	$-0.976775\pi$
$787$		−	114.743i		−	0.145799i	0.997339	−	0.0728993i	$-0.0232252\pi$
$788$			801.302i			1.01688i
$789$			775.845i			0.983327i
$790$	33.3714			0.0422422
$791$			81.6002i			0.103161i
$792$	578.516	+	843.392i	0.730450	+	1.06489i
$793$	−1633.76			−2.06022
$794$			2029.75i			2.55636i
$795$	−139.863			−0.175928
$796$	225.080			0.282764
$797$	1094.53			1.37331			0.686655	−	0.726983i	$-0.259078\pi$
$797$	1094.53			1.37331			0.686655	+	0.726983i	$0.259078\pi$
$798$		−	492.265i		−	0.616874i
$799$			88.0329i			0.110179i
$800$		−	890.334i		−	1.11292i
$801$	−37.8989			−0.0473145
$802$		−	1946.16i		−	2.42663i
$803$	328.241	+	478.527i	0.408768	+	0.595924i
$804$	1799.25			2.23787
$805$		−	64.6865i		−	0.0803559i
$806$	−3558.31			−4.41477
$807$	72.5898			0.0899501
$808$	2216.46			2.74314
$809$		−	740.081i		−	0.914809i	−0.889259	−	0.457405i	$-0.848779\pi$
$809$		−	740.081i		−	0.914809i	0.889259	−	0.457405i	$-0.151221\pi$
$810$			79.9874i			0.0987499i
$811$		−	799.348i		−	0.985632i	−0.870134	−	0.492816i	$-0.835968\pi$
$811$		−	799.348i		−	0.985632i	0.870134	−	0.492816i	$-0.164032\pi$
$812$	−1477.91			−1.82008
$813$		−	676.005i		−	0.831495i
$814$	206.866	+	301.580i	0.254135	+	0.370491i
$815$	524.104			0.643072
$816$			1138.66i			1.39542i
$817$	−1858.08			−2.27427
$818$	9.08654			0.0111082
$819$	148.768			0.181646
$820$		−	288.708i		−	0.352082i
$821$		−	443.767i		−	0.540520i	−0.962787	−	0.270260i	$-0.912890\pi$
$821$		−	443.767i		−	0.540520i	0.962787	−	0.270260i	$-0.0871097\pi$
$822$			1561.48i			1.89961i
$823$	804.979			0.978103			0.489051	−	0.872255i	$-0.337343\pi$
$823$	804.979			0.978103			0.489051	+	0.872255i	$0.337343\pi$
$824$		−	3317.02i		−	4.02551i
$825$	−78.5577	+	53.8859i	−0.0952215	+	0.0653162i
$826$	66.2464			0.0802014
$827$			1045.09i			1.26371i	0.775085	+	0.631857i	$0.217707\pi$
$827$			1045.09i			1.26371i	−0.775085	+	0.631857i	$0.782293\pi$
$828$	−386.982			−0.467370
$829$	1606.93			1.93840			0.969200	−	0.246274i	$-0.0792063\pi$
$829$	1606.93			1.93840			0.969200	+	0.246274i	$0.0792063\pi$
$830$	38.0900			0.0458916
$831$		−	499.170i		−	0.600686i
$832$			7568.09i			9.09626i
$833$			60.5577i			0.0726983i
$834$	605.459			0.725970
$835$		−	360.407i		−	0.431625i
$836$	−1983.95	−	2892.30i	−2.37314	−	3.45969i
$837$	−248.194			−0.296528
$838$			50.9082i			0.0607496i
$839$	−390.909			−0.465923			−0.232962	−	0.972486i	$-0.574842\pi$
$839$	−390.909			−0.465923			−0.232962	+	0.972486i	$0.574842\pi$
$840$	−317.574			−0.378064
$841$	−1400.90			−1.66575
$842$		−	659.845i		−	0.783663i
$843$			751.175i			0.891073i
$844$		−	485.947i		−	0.575767i
$845$	407.640			0.482414
$846$			121.336i			0.143423i
$847$	298.663	+	115.271i	0.352613	+	0.136093i
$848$	−2744.23			−3.23612
$849$			327.364i			0.385588i
$850$	−171.924			−0.202263
$851$	−91.4597			−0.107473
$852$	379.352			0.445249
$853$		−	818.334i		−	0.959360i	−0.877444	−	0.479680i	$-0.840753\pi$
$853$		−	818.334i		−	0.959360i	0.877444	−	0.479680i	$-0.159247\pi$
$854$		−	916.623i		−	1.07333i
$855$		−	181.302i		−	0.212049i
$856$	413.244			0.482762
$857$			1457.00i			1.70012i	0.526688	+	0.850059i	$0.323434\pi$
$857$			1457.00i			1.70012i	−0.526688	+	0.850059i	$0.676566\pi$
$858$	1170.45	−	802.860i	1.36416	−	0.935734i
$859$	−1314.89			−1.53073			−0.765363	−	0.643598i	$-0.777441\pi$
$859$	−1314.89			−1.53073			−0.765363	+	0.643598i	$0.777441\pi$
$860$			1813.61i			2.10885i
$861$	−50.1525			−0.0582491
$862$	−2413.25			−2.79959
$863$	1073.97			1.24446			0.622232	−	0.782833i	$-0.286226\pi$
$863$	1073.97			1.24446			0.622232	+	0.782833i	$0.286226\pi$
$864$			925.262i			1.07090i
$865$			341.620i			0.394936i
$866$			1017.31i			1.17473i
$867$	−370.933			−0.427836
$868$		−	1490.90i		−	1.71762i
$869$	−23.3636	−	34.0606i	−0.0268856	−	0.0391952i
$870$	−728.866			−0.837777
$871$		−	1650.37i		−	1.89479i
$872$	2214.69			2.53978
$873$	−372.175			−0.426318
$874$	1174.54			1.34387
$875$		−	29.5804i		−	0.0338062i
$876$			1077.95i			1.23054i
$877$		−	1750.76i		−	1.99630i	−0.0607628	−	0.998152i	$-0.519353\pi$
$877$		−	1750.76i		−	1.99630i	0.0607628	−	0.998152i	$-0.480647\pi$
$878$	−767.458			−0.874098
$879$			548.969i			0.624538i
$880$	−1541.37	+	1057.28i	−1.75155	+	1.20146i
$881$	941.743			1.06895			0.534474	−	0.845185i	$-0.320510\pi$
$881$	941.743			1.06895			0.534474	+	0.845185i	$0.320510\pi$
$882$			83.4668i			0.0946335i
$883$	921.842			1.04399			0.521994	−	0.852949i	$-0.325188\pi$
$883$	921.842			1.04399			0.521994	+	0.852949i	$0.325188\pi$
$884$	1912.94			2.16396
$885$	24.3986			0.0275690
$886$		−	358.214i		−	0.404304i
$887$			1081.94i			1.21977i	0.792489	+	0.609887i	$0.208785\pi$
$887$			1081.94i			1.21977i	−0.792489	+	0.609887i	$0.791215\pi$
$888$			449.015i			0.505647i
$889$	238.930			0.268763
$890$		−	112.276i		−	0.126152i
$891$	81.6396	−	55.9998i	0.0916269	−	0.0628505i
$892$	4943.56			5.54211
$893$		−	275.023i		−	0.307976i
$894$	−332.636			−0.372076
$895$	−153.284			−0.171267
$896$	−2361.61			−2.63572
$897$			354.961i			0.395720i
$898$		−	2249.12i		−	2.50458i
$899$		−	2261.60i		−	2.51569i
$900$	−176.963			−0.196625
$901$			312.413i			0.346740i
$902$	−394.580	+	270.658i	−0.437450	+	0.300065i
$903$	315.050			0.348892
$904$			955.855i			1.05736i
$905$	594.307			0.656693
$906$	1527.64			1.68614
$907$	1194.73			1.31724			0.658619	−	0.752477i	$-0.271141\pi$
$907$	1194.73			1.31724			0.658619	+	0.752477i	$0.271141\pi$
$908$			4741.67i			5.22211i
$909$		−	214.551i		−	0.236030i
$910$			440.726i			0.484314i
$911$	−1392.50			−1.52854			−0.764268	−	0.644899i	$-0.776900\pi$
$911$	−1392.50			−1.52854			−0.764268	+	0.644899i	$0.776900\pi$
$912$		−	3557.29i		−	3.90053i
$913$	−26.6671	−	38.8767i	−0.0292082	−	0.0425813i
$914$	1094.53			1.19751
$915$		−	337.593i		−	0.368954i
$916$	−2206.22			−2.40854
$917$	60.4500			0.0659214
$918$	178.668			0.194628
$919$			58.5275i			0.0636861i	0.999493	+	0.0318431i	$0.0101377\pi$
$919$			58.5275i			0.0636861i	−0.999493	+	0.0318431i	$0.989862\pi$
$920$		−	757.730i		−	0.823620i
$921$			285.835i			0.310352i
$922$	−1259.40			−1.36594
$923$		−	347.962i		−	0.376990i
$924$	336.391	+	490.408i	0.364059	+	0.530745i
$925$	−41.8235			−0.0452145
$926$		−	828.578i		−	0.894793i
$927$	−321.085			−0.346370
$928$	−8431.22			−9.08537
$929$	−759.189			−0.817210			−0.408605	−	0.912711i	$-0.633985\pi$
$929$	−759.189			−0.817210			−0.408605	+	0.912711i	$0.633985\pi$
$930$		−	735.273i		−	0.790616i
$931$		−	189.188i		−	0.203209i
$932$		−	3540.72i		−	3.79905i
$933$	162.960			0.174663
$934$			1839.63i			1.96962i
$935$	120.365	+	175.475i	0.128733	+	0.187673i
$936$	1742.66			1.86181
$937$			423.862i			0.452361i	0.974085	+	0.226181i	$0.0726239\pi$
$937$			423.862i			0.452361i	−0.974085	+	0.226181i	$0.927376\pi$
$938$	925.940			0.987143
$939$	266.857			0.284193
$940$	−268.441			−0.285576
$941$		−	23.7809i		−	0.0252720i	−0.999920	−	0.0126360i	$-0.995978\pi$
$941$		−	23.7809i		−	0.0252720i	0.999920	−	0.0126360i	$-0.00402227\pi$
$942$		−	1505.77i		−	1.59848i
$943$		−	119.664i		−	0.126897i
$944$	478.720			0.507119
$945$			30.7409i			0.0325300i
$946$	2478.69	−	1700.23i	2.62018	−	1.79728i
$947$	−716.267			−0.756353			−0.378177	−	0.925733i	$-0.623449\pi$
$947$	−716.267			−0.756353			−0.378177	+	0.925733i	$0.623449\pi$
$948$		−	76.7265i		−	0.0809351i
$949$	988.756			1.04189
$950$	537.105			0.565374
$951$	481.402			0.506206
$952$			709.366i			0.745132i
$953$		−	1049.75i		−	1.10153i	−0.834662	−	0.550763i	$-0.814337\pi$
$953$		−	1049.75i		−	1.10153i	0.834662	−	0.550763i	$-0.185663\pi$
$954$			430.599i			0.451362i
$955$	401.291			0.420200
$956$		−	4759.61i		−	4.97867i
$957$	510.285	+	743.920i	0.533213	+	0.777346i
$958$	−270.765			−0.282636
$959$			600.111i			0.625767i
$960$	−1563.84			−1.62900
$961$	1320.48			1.37407
$962$	623.138			0.647753
$963$		−	40.0017i		−	0.0415386i
$964$		−	3601.20i		−	3.73568i
$965$			824.570i			0.854476i
$966$	−199.152			−0.206161
$967$		−	365.087i		−	0.377546i	−0.982021	−	0.188773i	$-0.939549\pi$
$967$		−	365.087i		−	0.377546i	0.982021	−	0.188773i	$-0.0604510\pi$
$968$	3498.50	+	1350.27i	3.61416	+	1.39491i
$969$	−404.974			−0.417930
$970$		−	1102.57i		−	1.13667i
$971$	−88.9404			−0.0915967			−0.0457983	−	0.998951i	$-0.514583\pi$
$971$	−88.9404			−0.0915967			−0.0457983	+	0.998951i	$0.514583\pi$
$972$	183.905			0.189203
$973$	232.691			0.239147
$974$		−	726.830i		−	0.746232i
$975$			162.320i			0.166482i
$976$		−	6623.84i		−	6.78672i
$977$	−726.835			−0.743946			−0.371973	−	0.928244i	$-0.621319\pi$
$977$	−726.835			−0.743946			−0.371973	+	0.928244i	$0.621319\pi$
$978$		−	1613.57i		−	1.64987i
$979$	−114.595	+	78.6050i	−0.117053	+	0.0802911i
$980$	−184.660			−0.188429
$981$		−	214.380i		−	0.218532i
$982$	−1869.75			−1.90402
$983$	486.949			0.495371			0.247685	−	0.968841i	$-0.420330\pi$
$983$	486.949			0.495371			0.247685	+	0.968841i	$0.420330\pi$
$984$	−587.481			−0.597033
$985$			151.877i			0.154189i
$986$			1628.07i			1.65119i
$987$			46.6319i			0.0472461i
$988$	−5976.21			−6.04880
$989$			751.708i			0.760069i
$990$	165.899	+	241.857i	0.167575	+	0.244300i
$991$	−1274.01			−1.28558			−0.642788	−	0.766044i	$-0.722222\pi$
$991$	−1274.01			−1.28558			−0.642788	+	0.766044i	$0.722222\pi$
$992$		−	8505.33i		−	8.57393i
$993$	−965.210			−0.972014
$994$	195.225			0.196403
$995$	42.6611			0.0428755
$996$		−	87.5755i		−	0.0879272i
$997$			69.7005i			0.0699102i	0.999389	+	0.0349551i	$0.0111288\pi$
$997$			69.7005i			0.0699102i	−0.999389	+	0.0349551i	$0.988871\pi$
$998$		−	437.160i		−	0.438036i
$999$	43.4642			0.0435077

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.3.b.a.736.1	✓	96
11.10	odd	2	inner	1155.3.b.a.736.96	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.3.b.a.736.1	✓	96	1.1	even	1	trivial
1155.3.b.a.736.96	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)

\(f(q)\)	\(=\)	\(q-3.97461i q^{2} -1.73205 q^{3} -11.7975 q^{4} -2.23607 q^{5} +6.88422i q^{6} +2.64575i q^{7} +30.9920i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-3.97461i q^{2} -1.73205 q^{3} -11.7975 q^{4} -2.23607 q^{5} +6.88422i q^{6} +2.64575i q^{7} +30.9920i q^{8} +3.00000 q^{9} +8.88749i q^{10} +(9.07106 - 6.22220i) q^{11} +20.4339 q^{12} -18.7431i q^{13} +10.5158 q^{14} +3.87298 q^{15} +75.9911 q^{16} -8.65110i q^{17} -11.9238i q^{18} +27.0268i q^{19} +26.3800 q^{20} -4.58258i q^{21} +(-24.7308 - 36.0539i) q^{22} +10.9340 q^{23} -53.6798i q^{24} +5.00000 q^{25} -74.4963 q^{26} -5.19615 q^{27} -31.2133i q^{28} -47.3487i q^{29} -15.3936i q^{30} +47.7649 q^{31} -178.067i q^{32} +(-15.7115 + 10.7772i) q^{33} -34.3847 q^{34} -5.91608i q^{35} -35.3925 q^{36} -8.36469 q^{37} +107.421 q^{38} +32.4639i q^{39} -69.3003i q^{40} -10.9442i q^{41} -18.2139 q^{42} +68.7495i q^{43} +(-107.016 + 73.4065i) q^{44} -6.70820 q^{45} -43.4584i q^{46} -10.1759 q^{47} -131.620 q^{48} -7.00000 q^{49} -19.8730i q^{50} +14.9841i q^{51} +221.121i q^{52} -36.1125 q^{53} +20.6527i q^{54} +(-20.2835 + 13.9133i) q^{55} -81.9972 q^{56} -46.8119i q^{57} -188.192 q^{58} +6.29969 q^{59} -45.6915 q^{60} -87.1660i q^{61} -189.847i q^{62} +7.93725i q^{63} -403.781 q^{64} +41.9108i q^{65} +(42.8350 + 62.4472i) q^{66} +88.0521 q^{67} +102.061i q^{68} -18.9383 q^{69} -23.5141 q^{70} +18.5649 q^{71} +92.9761i q^{72} +52.7532i q^{73} +33.2464i q^{74} -8.66025 q^{75} -318.849i q^{76} +(16.4624 + 23.9998i) q^{77} +129.031 q^{78} -3.75487i q^{79} -169.921 q^{80} +9.00000 q^{81} -43.4988 q^{82} -4.28580i q^{83} +54.0630i q^{84} +19.3444i q^{85} +273.252 q^{86} +82.0103i q^{87} +(192.839 + 281.131i) q^{88} -12.6330 q^{89} +26.6625i q^{90} +49.5895 q^{91} -128.994 q^{92} -82.7312 q^{93} +40.4453i q^{94} -60.4339i q^{95} +308.421i q^{96} -124.058 q^{97} +27.8223i q^{98} +(27.2132 - 18.6666i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 216 q^{4} + 288 q^{9}+O(q^{10}) \) 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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