LMFDB - Embedded newform 690.3.g.a.461.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(461,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("690.461");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.g (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:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			461.18
Character	$\chi$	$=$	690.461
Dual form			690.3.g.a.461.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +(-1.05752 - 2.80743i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(3.97030 - 1.49556i) q^{6} +11.9645 q^{7} -2.82843i q^{8} +(-6.76329 + 5.93784i) q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +(-1.05752 - 2.80743i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(3.97030 - 1.49556i) q^{6} +11.9645 q^{7} -2.82843i q^{8} +(-6.76329 + 5.93784i) q^{9} +3.16228 q^{10} +12.8979i q^{11} +(2.11505 + 5.61485i) q^{12} +20.2679 q^{13} +16.9204i q^{14} +(-6.27760 + 2.36470i) q^{15} +4.00000 q^{16} +2.71211i q^{17} +(-8.39738 - 9.56473i) q^{18} -31.6020 q^{19} +4.47214i q^{20} +(-12.6528 - 33.5896i) q^{21} -18.2404 q^{22} -4.79583i q^{23} +(-7.94060 + 2.99113i) q^{24} -5.00000 q^{25} +28.6632i q^{26} +(23.8224 + 12.7080i) q^{27} -23.9291 q^{28} +32.1682i q^{29} +(-3.34418 - 8.87786i) q^{30} +30.5608 q^{31} +5.65685i q^{32} +(36.2099 - 13.6399i) q^{33} -3.83551 q^{34} -26.7535i q^{35} +(13.5266 - 11.8757i) q^{36} +26.7311 q^{37} -44.6920i q^{38} +(-21.4338 - 56.9008i) q^{39} -6.32456 q^{40} +17.8221i q^{41} +(47.5028 - 17.8937i) q^{42} +63.9371 q^{43} -25.7958i q^{44} +(13.2774 + 15.1232i) q^{45} +6.78233 q^{46} +2.85097i q^{47} +(-4.23010 - 11.2297i) q^{48} +94.1502 q^{49} -7.07107i q^{50} +(7.61406 - 2.86812i) q^{51} -40.5359 q^{52} -61.3108i q^{53} +(-17.9719 + 33.6899i) q^{54} +28.8406 q^{55} -33.8408i q^{56} +(33.4199 + 88.7203i) q^{57} -45.4927 q^{58} +63.3148i q^{59} +(12.5552 - 4.72939i) q^{60} -48.8150 q^{61} +43.2195i q^{62} +(-80.9196 + 71.0435i) q^{63} -8.00000 q^{64} -45.3205i q^{65} +(19.2897 + 51.2086i) q^{66} +84.5799 q^{67} -5.42423i q^{68} +(-13.4639 + 5.07171i) q^{69} +37.8352 q^{70} -56.5778i q^{71} +(16.7948 + 19.1295i) q^{72} +79.0816 q^{73} +37.8034i q^{74} +(5.28762 + 14.0371i) q^{75} +63.2040 q^{76} +154.318i q^{77} +(80.4698 - 30.3120i) q^{78} +74.6226 q^{79} -8.94427i q^{80} +(10.4841 - 80.3186i) q^{81} -25.2042 q^{82} -102.897i q^{83} +(25.3056 + 67.1791i) q^{84} +6.06447 q^{85} +90.4207i q^{86} +(90.3099 - 34.0186i) q^{87} +36.4808 q^{88} -127.899i q^{89} +(-21.3874 + 18.7771i) q^{90} +242.497 q^{91} +9.59166i q^{92} +(-32.3188 - 85.7973i) q^{93} -4.03188 q^{94} +70.6643i q^{95} +(15.8812 - 5.98226i) q^{96} -148.644 q^{97} +133.149i q^{98} +(-76.5858 - 87.2323i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{3} - 112 q^{4} + 16 q^{6} - 16 q^{7}+O(q^{10}) $ 56 * q - 8 * q^3 - 112 * q^4 + 16 * q^6 - 16 * q^7	$ 56 q - 8 q^{3} - 112 q^{4} + 16 q^{6} - 16 q^{7} + 16 q^{12} + 80 q^{13} - 40 q^{15} + 224 q^{16} - 32 q^{18} - 64 q^{19} + 56 q^{21} - 96 q^{22} - 32 q^{24} - 280 q^{25} + 40 q^{27} + 32 q^{28} - 80 q^{31} + 32 q^{33} + 192 q^{34} + 240 q^{37} - 56 q^{39} - 144 q^{43} - 32 q^{48} + 72 q^{49} - 24 q^{51} - 160 q^{52} + 16 q^{54} - 16 q^{57} + 80 q^{60} + 112 q^{61} - 64 q^{63} - 448 q^{64} + 160 q^{66} + 832 q^{67} + 64 q^{72} - 608 q^{73} + 40 q^{75} + 128 q^{76} - 320 q^{78} + 48 q^{79} - 32 q^{81} - 448 q^{82} - 112 q^{84} + 240 q^{85} + 200 q^{87} + 192 q^{88} + 80 q^{91} - 232 q^{93} + 160 q^{94} + 64 q^{96} - 448 q^{97} + 464 q^{99}+O(q^{100}) $ 56 * q - 8 * q^3 - 112 * q^4 + 16 * q^6 - 16 * q^7 + 16 * q^12 + 80 * q^13 - 40 * q^15 + 224 * q^16 - 32 * q^18 - 64 * q^19 + 56 * q^21 - 96 * q^22 - 32 * q^24 - 280 * q^25 + 40 * q^27 + 32 * q^28 - 80 * q^31 + 32 * q^33 + 192 * q^34 + 240 * q^37 - 56 * q^39 - 144 * q^43 - 32 * q^48 + 72 * q^49 - 24 * q^51 - 160 * q^52 + 16 * q^54 - 16 * q^57 + 80 * q^60 + 112 * q^61 - 64 * q^63 - 448 * q^64 + 160 * q^66 + 832 * q^67 + 64 * q^72 - 608 * q^73 + 40 * q^75 + 128 * q^76 - 320 * q^78 + 48 * q^79 - 32 * q^81 - 448 * q^82 - 112 * q^84 + 240 * q^85 + 200 * q^87 + 192 * q^88 + 80 * q^91 - 232 * q^93 + 160 * q^94 + 64 * q^96 - 448 * q^97 + 464 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$	−1.05752	−	2.80743i	−0.352508	−	0.935809i
$3$	−1.05752	−	2.80743i	−0.352508	−	0.935809i
$4$	−2.00000			−0.500000
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$	3.97030	−	1.49556i	0.661717	−	0.249261i
$7$	11.9645			1.70922			0.854610	−	0.519270i	$-0.173796\pi$
$7$	11.9645			1.70922			0.854610	+	0.519270i	$0.173796\pi$
$8$		−	2.82843i		−	0.353553i
$9$	−6.76329	+	5.93784i	−0.751476	+	0.659760i
$10$	3.16228			0.316228
$11$			12.8979i			1.17254i	0.810117	+	0.586269i	$0.199404\pi$
$11$			12.8979i			1.17254i	−0.810117	+	0.586269i	$0.800596\pi$
$12$	2.11505	+	5.61485i	0.176254	+	0.467904i
$13$	20.2679			1.55907			0.779536	−	0.626357i	$-0.215455\pi$
$13$	20.2679			1.55907			0.779536	+	0.626357i	$0.215455\pi$
$14$			16.9204i			1.20860i
$15$	−6.27760	+	2.36470i	−0.418506	+	0.157646i
$16$	4.00000			0.250000
$17$			2.71211i			0.159536i	0.996813	+	0.0797680i	$0.0254180\pi$
$17$			2.71211i			0.159536i	−0.996813	+	0.0797680i	$0.974582\pi$
$18$	−8.39738	−	9.56473i	−0.466521	−	0.531374i
$19$	−31.6020			−1.66326			−0.831632	−	0.555327i	$-0.812593\pi$
$19$	−31.6020			−1.66326			−0.831632	+	0.555327i	$0.812593\pi$
$20$			4.47214i			0.223607i
$21$	−12.6528	−	33.5896i	−0.602514	−	1.59950i
$22$	−18.2404			−0.829109
$23$		−	4.79583i		−	0.208514i
$23$		−	4.79583i		−	0.208514i
$24$	−7.94060	+	2.99113i	−0.330858	+	0.124630i
$25$	−5.00000			−0.200000
$26$			28.6632i			1.10243i
$27$	23.8224	+	12.7080i	0.882311	+	0.470667i
$28$	−23.9291			−0.854610
$29$			32.1682i			1.10925i	0.832101	+	0.554624i	$0.187138\pi$
$29$			32.1682i			1.10925i	−0.832101	+	0.554624i	$0.812862\pi$
$30$	−3.34418	−	8.87786i	−0.111473	−	0.295929i
$31$	30.5608			0.985833			0.492917	−	0.870077i	$-0.335931\pi$
$31$	30.5608			0.985833			0.492917	+	0.870077i	$0.335931\pi$
$32$			5.65685i			0.176777i
$33$	36.2099	−	13.6399i	1.09727	−	0.413329i
$34$	−3.83551			−0.112809
$35$		−	26.7535i		−	0.764386i
$36$	13.5266	−	11.8757i	0.375738	−	0.329880i
$37$	26.7311			0.722461			0.361230	−	0.932477i	$-0.382357\pi$
$37$	26.7311			0.722461			0.361230	+	0.932477i	$0.382357\pi$
$38$		−	44.6920i		−	1.17611i
$39$	−21.4338	−	56.9008i	−0.549586	−	1.45899i
$40$	−6.32456			−0.158114
$41$			17.8221i			0.434685i	0.976095	+	0.217343i	$0.0697389\pi$
$41$			17.8221i			0.434685i	−0.976095	+	0.217343i	$0.930261\pi$
$42$	47.5028	−	17.8937i	1.13102	−	0.426042i
$43$	63.9371			1.48691			0.743454	−	0.668787i	$-0.233186\pi$
$43$	63.9371			1.48691			0.743454	+	0.668787i	$0.233186\pi$
$44$		−	25.7958i		−	0.586269i
$45$	13.2774	+	15.1232i	0.295054	+	0.336070i
$46$	6.78233			0.147442
$47$			2.85097i			0.0606589i	0.999540	+	0.0303294i	$0.00965564\pi$
$47$			2.85097i			0.0606589i	−0.999540	+	0.0303294i	$0.990344\pi$
$48$	−4.23010	−	11.2297i	−0.0881270	−	0.233952i
$49$	94.1502			1.92143
$50$		−	7.07107i		−	0.141421i
$51$	7.61406	−	2.86812i	0.149295	−	0.0562377i
$52$	−40.5359			−0.779536
$53$		−	61.3108i		−	1.15681i	−0.815750	−	0.578404i	$-0.803676\pi$
$53$		−	61.3108i		−	1.15681i	0.815750	−	0.578404i	$-0.196324\pi$
$54$	−17.9719	+	33.6899i	−0.332812	+	0.623888i
$55$	28.8406			0.524375
$56$		−	33.8408i		−	0.604301i
$57$	33.4199	+	88.7203i	0.586314	+	1.55650i
$58$	−45.4927			−0.784357
$59$			63.3148i			1.07313i	0.843858	+	0.536566i	$0.180279\pi$
$59$			63.3148i			1.07313i	−0.843858	+	0.536566i	$0.819721\pi$
$60$	12.5552	−	4.72939i	0.209253	−	0.0788232i
$61$	−48.8150			−0.800247			−0.400123	−	0.916461i	$-0.631033\pi$
$61$	−48.8150			−0.800247			−0.400123	+	0.916461i	$0.631033\pi$
$62$			43.2195i			0.697089i
$63$	−80.9196	+	71.0435i	−1.28444	+	1.12768i
$64$	−8.00000			−0.125000
$65$		−	45.3205i		−	0.697239i
$66$	19.2897	+	51.2086i	0.292268	+	0.775888i
$67$	84.5799			1.26239			0.631194	−	0.775625i	$-0.282565\pi$
$67$	84.5799			1.26239			0.631194	+	0.775625i	$0.282565\pi$
$68$		−	5.42423i		−	0.0797680i
$69$	−13.4639	+	5.07171i	−0.195130	+	0.0735030i
$70$	37.8352			0.540503
$71$		−	56.5778i		−	0.796871i	−0.917196	−	0.398435i	$-0.869553\pi$
$71$		−	56.5778i		−	0.796871i	0.917196	−	0.398435i	$-0.130447\pi$
$72$	16.7948	+	19.1295i	0.233260	+	0.265687i
$73$	79.0816			1.08331			0.541655	−	0.840601i	$-0.317798\pi$
$73$	79.0816			1.08331			0.541655	+	0.840601i	$0.317798\pi$
$74$			37.8034i			0.510857i
$75$	5.28762	+	14.0371i	0.0705016	+	0.187162i
$76$	63.2040			0.831632
$77$			154.318i			2.00412i
$78$	80.4698	−	30.3120i	1.03166	−	0.388616i
$79$	74.6226			0.944590			0.472295	−	0.881441i	$-0.343426\pi$
$79$	74.6226			0.944590			0.472295	+	0.881441i	$0.343426\pi$
$80$		−	8.94427i		−	0.111803i
$81$	10.4841	−	80.3186i	0.129433	−	0.991588i
$82$	−25.2042			−0.307369
$83$		−	102.897i		−	1.23972i	−0.784711	−	0.619862i	$-0.787189\pi$
$83$		−	102.897i		−	1.23972i	0.784711	−	0.619862i	$-0.212811\pi$
$84$	25.3056	+	67.1791i	0.301257	+	0.799752i
$85$	6.06447			0.0713467
$86$			90.4207i			1.05140i
$87$	90.3099	−	34.0186i	1.03804	−	0.391019i
$88$	36.4808			0.414555
$89$		−	127.899i		−	1.43707i	−0.695489	−	0.718536i	$-0.744812\pi$
$89$		−	127.899i		−	1.43707i	0.695489	−	0.718536i	$-0.255188\pi$
$90$	−21.3874	+	18.7771i	−0.237638	+	0.208634i
$91$	242.497			2.66480
$92$			9.59166i			0.104257i
$93$	−32.3188	−	85.7973i	−0.347514	−	0.922551i
$94$	−4.03188			−0.0428923
$95$			70.6643i			0.743834i
$96$	15.8812	−	5.98226i	0.165429	−	0.0623152i
$97$	−148.644			−1.53241			−0.766204	−	0.642597i	$-0.777857\pi$
$97$	−148.644			−1.53241			−0.766204	+	0.642597i	$0.777857\pi$
$98$			133.149i			1.35866i
$99$	−76.5858	−	87.2323i	−0.773594	−	0.881134i
$100$	10.0000			0.100000
$101$			80.7538i			0.799542i	0.916615	+	0.399771i	$0.130910\pi$
$101$			80.7538i			0.799542i	−0.916615	+	0.399771i	$0.869090\pi$
$102$	4.05614	+	10.7679i	0.0397661	+	0.105568i
$103$	−136.026			−1.32064			−0.660319	−	0.750985i	$-0.729579\pi$
$103$	−136.026			−1.32064			−0.660319	+	0.750985i	$0.729579\pi$
$104$		−	57.3264i		−	0.551215i
$105$	−75.1085	+	28.2925i	−0.715320	+	0.269452i
$106$	86.7066			0.817987
$107$			125.903i			1.17666i	0.808621	+	0.588330i	$0.200214\pi$
$107$			125.903i			1.17666i	−0.808621	+	0.588330i	$0.799786\pi$
$108$	−47.6448	−	25.4160i	−0.441155	−	0.235334i
$109$	89.7028			0.822961			0.411481	−	0.911419i	$-0.365012\pi$
$109$	89.7028			0.822961			0.411481	+	0.911419i	$0.365012\pi$
$110$			40.7868i			0.370789i
$111$	−28.2687	−	75.0455i	−0.254673	−	0.676085i
$112$	47.8582			0.427305
$113$			74.8993i			0.662825i	0.943486	+	0.331413i	$0.107525\pi$
$113$			74.8993i			0.662825i	−0.943486	+	0.331413i	$0.892475\pi$
$114$	−125.469	+	47.2629i	−1.10061	+	0.414586i
$115$	−10.7238			−0.0932505
$116$		−	64.3364i		−	0.554624i
$117$	−137.078	+	120.348i	−1.17161	+	1.02861i
$118$	−89.5407			−0.758820
$119$			32.4492i			0.272682i
$120$	6.68837	+	17.7557i	0.0557364	+	0.147964i
$121$	−45.3562			−0.374844
$122$		−	69.0349i		−	0.565860i
$123$	50.0342	−	18.8473i	0.406782	−	0.153230i
$124$	−61.1217			−0.492917
$125$			11.1803i			0.0894427i
$126$	−100.471	−	114.438i	−0.797387	−	0.908235i
$127$	12.5296			0.0986580			0.0493290	−	0.998783i	$-0.484292\pi$
$127$	12.5296			0.0986580			0.0493290	+	0.998783i	$0.484292\pi$
$128$		−	11.3137i		−	0.0883883i
$129$	−67.6150	−	179.499i	−0.524147	−	1.39146i
$130$	64.0929			0.493022
$131$		−	173.928i		−	1.32770i	−0.747867	−	0.663849i	$-0.768922\pi$
$131$		−	173.928i		−	1.32770i	0.747867	−	0.663849i	$-0.231078\pi$
$132$	−72.4199	+	27.2797i	−0.548636	+	0.206664i
$133$	−378.104			−2.84288
$134$			119.614i			0.892643i
$135$	28.4160	−	53.2685i	0.210489	−	0.394581i
$136$	7.67101			0.0564045
$137$		−	120.287i		−	0.878006i	−0.898486	−	0.439003i	$-0.855332\pi$
$137$		−	120.287i		−	0.878006i	0.898486	−	0.439003i	$-0.144668\pi$
$138$	−7.17248	−	19.0409i	−0.0519745	−	0.137977i
$139$	75.7495			0.544960			0.272480	−	0.962161i	$-0.412156\pi$
$139$	75.7495			0.544960			0.272480	+	0.962161i	$0.412156\pi$
$140$			53.5070i			0.382193i
$141$	8.00388	−	3.01497i	0.0567651	−	0.0213827i
$142$	80.0131			0.563473
$143$			261.414i			1.82807i
$144$	−27.0531	+	23.7514i	−0.187869	+	0.164940i
$145$	71.9303			0.496071
$146$			111.838i			0.766016i
$147$	−99.5661	−	264.320i	−0.677320	−	1.79809i
$148$	−53.4621			−0.361230
$149$			145.429i			0.976032i	0.872835	+	0.488016i	$0.162279\pi$
$149$			145.429i			0.976032i	−0.872835	+	0.488016i	$0.837721\pi$
$150$	−19.8515	+	7.47782i	−0.132343	+	0.0498522i
$151$	−88.0585			−0.583169			−0.291584	−	0.956545i	$-0.594182\pi$
$151$	−88.0585			−0.583169			−0.291584	+	0.956545i	$0.594182\pi$
$152$			89.3840i			0.588053i
$153$	−16.1041	−	18.3428i	−0.105256	−	0.119888i
$154$	−218.238			−1.41713
$155$		−	68.3361i		−	0.440878i
$156$	42.8677	+	113.802i	0.274793	+	0.729497i
$157$	221.115			1.40837			0.704187	−	0.710014i	$-0.251312\pi$
$157$	221.115			1.40837			0.704187	+	0.710014i	$0.251312\pi$
$158$			105.532i			0.667926i
$159$	−172.126	+	64.8377i	−1.08255	+	0.407784i
$160$	12.6491			0.0790569
$161$		−	57.3799i		−	0.356397i
$162$	113.588	+	14.8267i	0.701159	+	0.0915230i
$163$	−101.135			−0.620463			−0.310232	−	0.950661i	$-0.600407\pi$
$163$	−101.135			−0.620463			−0.310232	+	0.950661i	$0.600407\pi$
$164$		−	35.6442i		−	0.217343i
$165$	−30.4996	−	80.9679i	−0.184846	−	0.490715i
$166$	145.518			0.876617
$167$			113.469i			0.679456i	0.940524	+	0.339728i	$0.110335\pi$
$167$			113.469i			0.679456i	−0.940524	+	0.339728i	$0.889665\pi$
$168$	−95.0056	+	35.7875i	−0.565510	+	0.213021i
$169$	241.790			1.43071
$170$			8.57645i			0.0504497i
$171$	213.733	−	187.648i	1.24990	−	1.09736i
$172$	−127.874			−0.743454
$173$		−	269.411i		−	1.55729i	−0.627467	−	0.778643i	$-0.715908\pi$
$173$		−	269.411i		−	1.55729i	0.627467	−	0.778643i	$-0.284092\pi$
$174$	48.1096	+	127.717i	0.276492	+	0.734008i
$175$	−59.8227			−0.341844
$176$			51.5917i			0.293134i
$177$	177.752	−	66.9570i	1.00425	−	0.378288i
$178$	180.877			1.01616
$179$			179.383i			1.00214i	0.865407	+	0.501069i	$0.167060\pi$
$179$			179.383i			1.00214i	−0.865407	+	0.501069i	$0.832940\pi$
$180$	−26.5548	−	30.2463i	−0.147527	−	0.168035i
$181$	−221.212			−1.22217			−0.611083	−	0.791567i	$-0.709266\pi$
$181$	−221.212			−1.22217			−0.611083	+	0.791567i	$0.709266\pi$
$182$			342.942i			1.88430i
$183$	51.6231	+	137.045i	0.282093	+	0.748878i
$184$	−13.5647			−0.0737210
$185$		−	59.7724i		−	0.323094i
$186$	121.336	−	45.7057i	0.652342	−	0.245730i
$187$	−34.9806			−0.187062
$188$		−	5.70193i		−	0.0303294i
$189$	285.024	+	152.046i	1.50806	+	0.804474i
$190$	−99.9343			−0.525970
$191$			42.3868i			0.221920i	0.993825	+	0.110960i	$0.0353926\pi$
$191$			42.3868i			0.221920i	−0.993825	+	0.110960i	$0.964607\pi$
$192$	8.46019	+	22.4594i	0.0440635	+	0.116976i
$193$	−56.1826			−0.291102			−0.145551	−	0.989351i	$-0.546495\pi$
$193$	−56.1826			−0.291102			−0.145551	+	0.989351i	$0.546495\pi$
$194$		−	210.214i		−	1.08358i
$195$	−127.234	+	47.9275i	−0.652482	+	0.245782i
$196$	−188.300			−0.960716
$197$		−	114.289i		−	0.580149i	−0.957004	−	0.290075i	$-0.906320\pi$
$197$		−	114.289i		−	0.580149i	0.957004	−	0.290075i	$-0.0936801\pi$
$198$	123.365	−	108.309i	0.623056	−	0.547013i
$199$	−185.324			−0.931275			−0.465638	−	0.884975i	$-0.654175\pi$
$199$	−185.324			−0.931275			−0.465638	+	0.884975i	$0.654175\pi$
$200$			14.1421i			0.0707107i
$201$	−89.4453	−	237.452i	−0.445002	−	1.18135i
$202$	−114.203			−0.565362
$203$			384.878i			1.89595i
$204$	−15.2281	+	5.73625i	−0.0746476	+	0.0281189i
$205$	39.8514			0.194397
$206$		−	192.369i		−	0.933832i
$207$	28.4769	+	32.4356i	0.137570	+	0.156694i
$208$	81.0718			0.389768
$209$		−	407.600i		−	1.95024i
$210$	−40.0116	−	106.220i	−0.190532	−	0.505807i
$211$	196.309			0.930374			0.465187	−	0.885212i	$-0.345987\pi$
$211$	196.309			0.930374			0.465187	+	0.885212i	$0.345987\pi$
$212$			122.622i			0.578404i
$213$	−158.838	+	59.8324i	−0.745719	+	0.280903i
$214$	−178.053			−0.832025
$215$		−	142.968i		−	0.664966i
$216$	35.9437	−	67.3799i	0.166406	−	0.311944i
$217$	365.646			1.68501
$218$			126.859i			0.581921i
$219$	−83.6307	−	222.016i	−0.381875	−	1.01377i
$220$	−57.6812			−0.262187
$221$			54.9690i			0.248728i
$222$	106.130	−	39.9780i	0.478064	−	0.180081i
$223$	−128.398			−0.575774			−0.287887	−	0.957664i	$-0.592953\pi$
$223$	−128.398			−0.575774			−0.287887	+	0.957664i	$0.592953\pi$
$224$			67.6817i			0.302150i
$225$	33.8164	−	29.6892i	0.150295	−	0.131952i
$226$	−105.924			−0.468688
$227$			272.176i			1.19901i	0.800370	+	0.599507i	$0.204637\pi$
$227$			272.176i			1.19901i	−0.800370	+	0.599507i	$0.795363\pi$
$228$	−66.8398	−	177.441i	−0.293157	−	0.778248i
$229$	107.101			0.467692			0.233846	−	0.972274i	$-0.424869\pi$
$229$	107.101			0.467692			0.233846	+	0.972274i	$0.424869\pi$
$230$		−	15.1658i		−	0.0659380i
$231$	433.235	−	163.195i	1.87548	−	0.706470i
$232$	90.9854			0.392179
$233$		−	80.1887i		−	0.344158i	−0.985083	−	0.172079i	$-0.944952\pi$
$233$		−	80.1887i		−	0.344158i	0.985083	−	0.172079i	$-0.0550484\pi$
$234$	−170.198	−	193.857i	−0.727340	−	0.828451i
$235$	6.37496			0.0271275
$236$		−	126.630i		−	0.536566i
$237$	−78.9152	−	209.497i	−0.332976	−	0.883956i
$238$	−45.8901			−0.192815
$239$			171.517i			0.717643i	0.933406	+	0.358821i	$0.116821\pi$
$239$			171.517i			0.717643i	−0.933406	+	0.358821i	$0.883179\pi$
$240$	−25.1104	+	9.45878i	−0.104627	+	0.0394116i
$241$	−429.769			−1.78327			−0.891637	−	0.452751i	$-0.850443\pi$
$241$	−429.769			−1.78327			−0.891637	+	0.452751i	$0.850443\pi$
$242$		−	64.1433i		−	0.265055i
$243$	−236.576	+	55.5056i	−0.973563	+	0.228418i
$244$	97.6301			0.400123
$245$		−	210.526i		−	0.859291i
$246$	26.6541	+	70.7590i	0.108350	+	0.287638i
$247$	−640.508			−2.59315
$248$		−	86.4391i		−	0.348545i
$249$	−288.876	+	108.816i	−1.16014	+	0.437013i
$250$	−15.8114			−0.0632456
$251$			475.569i			1.89470i	0.320206	+	0.947348i	$0.396248\pi$
$251$			475.569i			1.89470i	−0.320206	+	0.947348i	$0.603752\pi$
$252$	161.839	−	142.087i	0.642219	−	0.563838i
$253$	61.8562			0.244491
$254$			17.7195i			0.0697618i
$255$	−6.41332	−	17.0255i	−0.0251503	−	0.0667669i
$256$	16.0000			0.0625000
$257$		−	321.762i		−	1.25199i	−0.779827	−	0.625996i	$-0.784693\pi$
$257$		−	321.762i		−	1.25199i	0.779827	−	0.625996i	$-0.215307\pi$
$258$	253.849	−	95.6220i	0.983912	−	0.370628i
$259$	319.825			1.23484
$260$			90.6410i			0.348619i
$261$	−191.010	−	217.563i	−0.731838	−	0.833574i
$262$	245.972			0.938824
$263$			360.215i			1.36964i	0.728713	+	0.684819i	$0.240119\pi$
$263$			360.215i			1.36964i	−0.728713	+	0.684819i	$0.759881\pi$
$264$	−38.5793	−	102.417i	−0.146134	−	0.387944i
$265$	−137.095			−0.517340
$266$		−	534.719i		−	2.01022i
$267$	−359.068	+	135.257i	−1.34483	+	0.506580i
$268$	−169.160			−0.631194
$269$		−	23.2136i		−	0.0862960i	−0.999069	−	0.0431480i	$-0.986261\pi$
$269$		−	23.2136i		−	0.0862960i	0.999069	−	0.0431480i	$-0.0137387\pi$
$270$	75.3330	+	40.1863i	0.279011	+	0.148838i
$271$	−339.304			−1.25204			−0.626022	−	0.779806i	$-0.715318\pi$
$271$	−339.304			−1.25204			−0.626022	+	0.779806i	$0.715318\pi$
$272$			10.8485i			0.0398840i
$273$	−256.446	−	680.791i	−0.939363	−	2.49374i
$274$	170.111			0.620844
$275$		−	64.4896i		−	0.234508i
$276$	26.9279	−	10.1434i	0.0975648	−	0.0367515i
$277$	−330.334			−1.19254			−0.596271	−	0.802784i	$-0.703351\pi$
$277$	−330.334			−1.19254			−0.596271	+	0.802784i	$0.703351\pi$
$278$			107.126i			0.385345i
$279$	−206.692	+	181.465i	−0.740830	+	0.650414i
$280$	−75.6704			−0.270251
$281$		−	263.092i		−	0.936272i	−0.883657	−	0.468136i	$-0.844926\pi$
$281$		−	263.092i		−	0.936272i	0.883657	−	0.468136i	$-0.155074\pi$
$282$	4.26381	+	11.3192i	0.0151199	+	0.0401390i
$283$	292.248			1.03268			0.516339	−	0.856384i	$-0.327294\pi$
$283$	292.248			1.03268			0.516339	+	0.856384i	$0.327294\pi$
$284$			113.156i			0.398435i
$285$	198.385	−	74.7291i	0.696087	−	0.262208i
$286$	−369.696			−1.29264
$287$			213.233i			0.742972i
$288$	−33.5895	−	38.2589i	−0.116630	−	0.132843i
$289$	281.644			0.974548
$290$			101.725i			0.350775i
$291$	157.194	+	417.306i	0.540186	+	1.43404i
$292$	−158.163			−0.541655
$293$		−	541.886i		−	1.84944i	−0.380650	−	0.924719i	$-0.624300\pi$
$293$		−	541.886i		−	1.84944i	0.380650	−	0.924719i	$-0.375700\pi$
$294$	373.805	−	140.808i	1.27144	−	0.478938i
$295$	141.576			0.479920
$296$		−	75.6068i		−	0.255428i
$297$	−163.907	+	307.259i	−0.551875	+	1.03454i
$298$	−205.667			−0.690159
$299$		−	97.2017i		−	0.325089i
$300$	−10.5752	−	28.0743i	−0.0352508	−	0.0935809i
$301$	764.978			2.54145
$302$		−	124.534i		−	0.412363i
$303$	226.710	−	85.3990i	0.748219	−	0.281845i
$304$	−126.408			−0.415816
$305$			109.154i			0.357881i
$306$	25.9406	−	22.7746i	0.0847733	−	0.0744269i
$307$	−166.121			−0.541109			−0.270555	−	0.962705i	$-0.587207\pi$
$307$	−166.121			−0.541109			−0.270555	+	0.962705i	$0.587207\pi$
$308$		−	308.635i		−	1.00206i
$309$	143.850	+	381.882i	0.465535	+	1.23586i
$310$	96.6418			0.311748
$311$		−	181.875i		−	0.584807i	−0.956295	−	0.292403i	$-0.905545\pi$
$311$		−	181.875i		−	0.584807i	0.956295	−	0.292403i	$-0.0944550\pi$
$312$	−160.940	+	60.6241i	−0.515832	+	0.194308i
$313$	377.507			1.20609			0.603047	−	0.797706i	$-0.293953\pi$
$313$	377.507			1.20609			0.603047	+	0.797706i	$0.293953\pi$
$314$			312.704i			0.995871i
$315$	158.858	+	180.942i	0.504312	+	0.574418i
$316$	−149.245			−0.472295
$317$			153.129i			0.483058i	0.970394	+	0.241529i	$0.0776488\pi$
$317$			153.129i			0.483058i	−0.970394	+	0.241529i	$0.922351\pi$
$318$	−91.6943	−	243.422i	−0.288347	−	0.765480i
$319$	−414.903			−1.30064
$320$			17.8885i			0.0559017i
$321$	353.462	−	133.145i	1.10113	−	0.414782i
$322$	81.1475			0.252011
$323$		−	85.7082i		−	0.265351i
$324$	−20.9681	+	160.637i	−0.0647165	+	0.495794i
$325$	−101.340			−0.311815
$326$		−	143.027i		−	0.438734i
$327$	−94.8628	−	251.834i	−0.290100	−	0.770134i
$328$	50.4085			0.153684
$329$			34.1105i			0.103679i
$330$	114.506	−	43.1330i	0.346988	−	0.130706i
$331$	−159.551			−0.482028			−0.241014	−	0.970522i	$-0.577480\pi$
$331$	−159.551			−0.482028			−0.241014	+	0.970522i	$0.577480\pi$
$332$			205.794i			0.619862i
$333$	−180.790	+	158.725i	−0.542912	+	0.476651i
$334$	−160.470			−0.480448
$335$		−	189.127i		−	0.564557i
$336$	−50.6112	−	134.358i	−0.150628	−	0.399876i
$337$	−110.341			−0.327422			−0.163711	−	0.986508i	$-0.552347\pi$
$337$	−110.341			−0.327422			−0.163711	+	0.986508i	$0.552347\pi$
$338$			341.942i			1.01166i
$339$	210.274	−	79.2078i	0.620278	−	0.233651i
$340$	−12.1289			−0.0356733
$341$			394.171i			1.15593i
$342$	265.374	+	302.265i	0.775947	+	0.883815i
$343$	540.201			1.57493
$344$		−	180.841i		−	0.525702i
$345$	11.3407	+	30.1063i	0.0328715	+	0.0872646i
$346$	381.004			1.10117
$347$			345.104i			0.994537i	0.867597	+	0.497269i	$0.165664\pi$
$347$			345.104i			0.994537i	−0.867597	+	0.497269i	$0.834336\pi$
$348$	−180.620	+	68.0373i	−0.519022	+	0.195509i
$349$	−414.181			−1.18677			−0.593383	−	0.804920i	$-0.702208\pi$
$349$	−414.181			−1.18677			−0.593383	+	0.804920i	$0.702208\pi$
$350$		−	84.6021i		−	0.241720i
$351$	482.831	+	257.565i	1.37559	+	0.733805i
$352$	−72.9616			−0.207277
$353$			151.503i			0.429187i	0.976703	+	0.214594i	$0.0688427\pi$
$353$			151.503i			0.429187i	−0.976703	+	0.214594i	$0.931157\pi$
$354$	94.6915	+	251.379i	0.267490	+	0.710110i
$355$	−126.512			−0.356371
$356$			255.799i			0.718536i
$357$	91.0987	−	34.3158i	0.255178	−	0.0961227i
$358$	−253.686			−0.708619
$359$		−	307.489i		−	0.856517i	−0.903656	−	0.428258i	$-0.859127\pi$
$359$		−	307.489i		−	0.856517i	0.903656	−	0.428258i	$-0.140873\pi$
$360$	42.7748	−	37.5542i	0.118819	−	0.104317i
$361$	637.687			1.76645
$362$		−	312.841i		−	0.864202i
$363$	47.9652	+	127.334i	0.132136	+	0.350783i
$364$	−484.993			−1.33240
$365$		−	176.832i		−	0.484471i
$366$	−193.810	+	73.0061i	−0.529537	+	0.199470i
$367$	−599.959			−1.63476			−0.817382	−	0.576095i	$-0.804576\pi$
$367$	−599.959			−1.63476			−0.817382	+	0.576095i	$0.804576\pi$
$368$		−	19.1833i		−	0.0521286i
$369$	−105.825	−	120.536i	−0.286788	−	0.326655i
$370$	84.5310			0.228462
$371$		−	733.556i		−	1.97724i
$372$	64.6376	+	171.595i	0.173757	+	0.461276i
$373$	361.365			0.968807			0.484404	−	0.874845i	$-0.339037\pi$
$373$	361.365			0.968807			0.484404	+	0.874845i	$0.339037\pi$
$374$		−	49.4700i		−	0.132273i
$375$	31.3880	−	11.8235i	0.0837013	−	0.0315293i
$376$	8.06375			0.0214461
$377$			651.983i			1.72940i
$378$	−215.025	+	403.085i	−0.568849	+	1.06636i
$379$	520.151			1.37243			0.686215	−	0.727399i	$-0.259271\pi$
$379$	520.151			1.37243			0.686215	+	0.727399i	$0.259271\pi$
$380$		−	141.329i		−	0.371917i
$381$	−13.2503	−	35.1758i	−0.0347777	−	0.0923250i
$382$	−59.9440			−0.156921
$383$			133.204i			0.347791i	0.984764	+	0.173895i	$0.0556354\pi$
$383$			133.204i			0.347791i	−0.984764	+	0.173895i	$0.944365\pi$
$384$	−31.7624	+	11.9645i	−0.0827146	+	0.0311576i
$385$	345.065			0.896272
$386$		−	79.4542i		−	0.205840i
$387$	−432.425	+	379.648i	−1.11738	+	0.981003i
$388$	297.287			0.766204
$389$		−	8.66553i		−	0.0222764i	−0.999938	−	0.0111382i	$-0.996455\pi$
$389$		−	8.66553i		−	0.0222764i	0.999938	−	0.0111382i	$-0.00354548\pi$
$390$	−67.7798	−	179.936i	−0.173794	−	0.461374i
$391$	13.0068			0.0332656
$392$		−	266.297i		−	0.679329i
$393$	−488.291	+	183.933i	−1.24247	+	0.468024i
$394$	161.630			0.410228
$395$		−	166.861i		−	0.422433i
$396$	153.172	+	174.465i	0.386797	+	0.440567i
$397$	−551.873			−1.39011			−0.695054	−	0.718957i	$-0.744620\pi$
$397$	−551.873			−1.39011			−0.695054	+	0.718957i	$0.744620\pi$
$398$		−	262.087i		−	0.658511i
$399$	399.854	+	1061.50i	1.00214	+	2.66040i
$400$	−20.0000			−0.0500000
$401$		−	554.382i		−	1.38250i	−0.722616	−	0.691249i	$-0.757061\pi$
$401$		−	554.382i		−	1.38250i	0.722616	−	0.691249i	$-0.242939\pi$
$402$	335.808	−	126.495i	0.835343	−	0.314664i
$403$	619.405			1.53699
$404$		−	161.508i		−	0.399771i
$405$	−179.598	−	23.4431i	−0.443452	−	0.0578842i
$406$	−544.299			−1.34064
$407$			344.775i			0.847112i
$408$	−8.11228	−	21.5358i	−0.0198830	−	0.0527838i
$409$	−43.0172			−0.105176			−0.0525882	−	0.998616i	$-0.516747\pi$
$409$	−43.0172			−0.105176			−0.0525882	+	0.998616i	$0.516747\pi$
$410$			56.3584i			0.137459i
$411$	−337.697	+	127.206i	−0.821646	+	0.309504i
$412$	272.051			0.660319
$413$			757.533i			1.83422i
$414$	−45.8708	+	40.2724i	−0.110799	+	0.0972763i
$415$	−230.085			−0.554422
$416$			114.653i			0.275608i
$417$	−80.1069	−	212.661i	−0.192103	−	0.509978i
$418$	576.434			1.37903
$419$			115.812i			0.276402i	0.990404	+	0.138201i	$0.0441319\pi$
$419$			115.812i			0.276402i	−0.990404	+	0.138201i	$0.955868\pi$
$420$	150.217	−	56.5850i	0.357660	−	0.134726i
$421$	67.9898			0.161496			0.0807480	−	0.996735i	$-0.474269\pi$
$421$	67.9898			0.161496			0.0807480	+	0.996735i	$0.474269\pi$
$422$			277.623i			0.657874i
$423$	−16.9286	−	19.2819i	−0.0400203	−	0.0455837i
$424$	−173.413			−0.408994
$425$		−	13.5606i		−	0.0319072i
$426$	−84.6158	−	224.631i	−0.198629	−	0.527303i
$427$	−584.050			−1.36780
$428$		−	251.805i		−	0.588330i
$429$	733.901	−	276.452i	1.71073	−	0.644410i
$430$	202.187			0.470202
$431$			299.480i			0.694849i	0.937708	+	0.347424i	$0.112944\pi$
$431$			299.480i			0.694849i	−0.937708	+	0.347424i	$0.887056\pi$
$432$	95.2896	+	50.8321i	0.220578	+	0.117667i
$433$	−75.7013			−0.174830			−0.0874149	−	0.996172i	$-0.527861\pi$
$433$	−75.7013			−0.174830			−0.0874149	+	0.996172i	$0.527861\pi$
$434$			517.102i			1.19148i
$435$	−76.0680	−	201.939i	−0.174869	−	0.464228i
$436$	−179.406			−0.411481
$437$			151.558i			0.346814i
$438$	313.978	−	118.272i	0.716844	−	0.270027i
$439$	−348.819			−0.794575			−0.397288	−	0.917694i	$-0.630049\pi$
$439$	−348.819			−0.794575			−0.397288	+	0.917694i	$0.630049\pi$
$440$		−	81.5736i		−	0.185394i
$441$	−636.765	+	559.049i	−1.44391	+	1.26768i
$442$	−77.7378			−0.175877
$443$			199.180i			0.449616i	0.974403	+	0.224808i	$0.0721755\pi$
$443$			199.180i			0.449616i	−0.974403	+	0.224808i	$0.927825\pi$
$444$	56.5375	+	150.091i	0.127337	+	0.338043i
$445$	−285.992			−0.642678
$446$		−	181.582i		−	0.407134i
$447$	408.281	−	153.794i	0.913379	−	0.344059i
$448$	−95.7163			−0.213652
$449$			246.727i			0.549503i	0.961515	+	0.274752i	$0.0885957\pi$
$449$			246.727i			0.549503i	−0.961515	+	0.274752i	$0.911404\pi$
$450$	41.9869	+	47.8237i	0.0933042	+	0.106275i
$451$	−229.868			−0.509685
$452$		−	149.799i		−	0.331413i
$453$	93.1240	+	247.218i	0.205572	+	0.545735i
$454$	−384.915			−0.847830
$455$		−	542.239i		−	1.19173i
$456$	250.939	−	94.5257i	0.550305	−	0.207293i
$457$	−825.255			−1.80581			−0.902905	−	0.429841i	$-0.858570\pi$
$457$	−825.255			−1.80581			−0.902905	+	0.429841i	$0.858570\pi$
$458$			151.464i			0.330708i
$459$	−34.4656	+	64.6090i	−0.0750884	+	0.140760i
$460$	21.4476			0.0466252
$461$			811.399i			1.76009i	0.474895	+	0.880043i	$0.342486\pi$
$461$			811.399i			1.76009i	−0.474895	+	0.880043i	$0.657514\pi$
$462$	230.792	+	612.687i	0.499550	+	1.32616i
$463$	177.948			0.384338			0.192169	−	0.981362i	$-0.438448\pi$
$463$	177.948			0.384338			0.192169	+	0.981362i	$0.438448\pi$
$464$			128.673i			0.277312i
$465$	−191.849	+	72.2671i	−0.412578	+	0.155413i
$466$	113.404			0.243356
$467$			168.607i			0.361042i	0.983571	+	0.180521i	$0.0577784\pi$
$467$			168.607i			0.361042i	−0.983571	+	0.180521i	$0.942222\pi$
$468$	274.156	−	240.696i	0.585803	−	0.514307i
$469$	1011.96			2.15770
$470$			9.01555i			0.0191820i
$471$	−233.834	−	620.764i	−0.496463	−	1.31797i
$472$	179.081			0.379410
$473$			824.655i			1.74346i
$474$	296.274	−	111.603i	0.625051	−	0.235449i
$475$	158.010			0.332653
$476$		−	64.8984i		−	0.136341i
$477$	364.054	+	414.663i	0.763216	+	0.869314i
$478$	−242.561			−0.507450
$479$		−	77.6858i		−	0.162183i	−0.996707	−	0.0810917i	$-0.974159\pi$
$479$		−	77.6858i		−	0.162183i	0.996707	−	0.0810917i	$-0.0258407\pi$
$480$	−13.3767	−	35.5114i	−0.0278682	−	0.0739822i
$481$	541.783			1.12637
$482$		−	607.785i		−	1.26096i
$483$	−161.090	+	60.6806i	−0.333519	+	0.125633i
$484$	90.7124			0.187422
$485$			332.377i			0.685314i
$486$	−78.4968	−	334.569i	−0.161516	−	0.688413i
$487$	890.670			1.82889			0.914446	−	0.404708i	$-0.132627\pi$
$487$	890.670			1.82889			0.914446	+	0.404708i	$0.132627\pi$
$488$			138.070i			0.282930i
$489$	106.953	+	283.930i	0.218718	+	0.580635i
$490$	297.729			0.607610
$491$			383.262i			0.780574i	0.920693	+	0.390287i	$0.127624\pi$
$491$			383.262i			0.780574i	−0.920693	+	0.390287i	$0.872376\pi$
$492$	−100.068	+	37.6946i	−0.203391	+	0.0766150i
$493$	−87.2438			−0.176965
$494$		−	905.815i		−	1.83363i
$495$	−195.057	+	171.251i	−0.394055	+	0.345962i
$496$	122.243			0.246458
$497$		−	676.928i		−	1.36203i
$498$	−153.889	−	408.532i	−0.309015	−	0.820346i
$499$	−658.924			−1.32049			−0.660245	−	0.751050i	$-0.729547\pi$
$499$	−658.924			−1.32049			−0.660245	+	0.751050i	$0.729547\pi$
$500$		−	22.3607i		−	0.0447214i
$501$	318.556	−	119.996i	0.635841	−	0.239514i
$502$	−672.556			−1.33975
$503$			131.526i			0.261484i	0.991416	+	0.130742i	$0.0417359\pi$
$503$			131.526i			0.261484i	−0.991416	+	0.130742i	$0.958264\pi$
$504$	200.941	+	228.875i	0.398693	+	0.454117i
$505$	180.571			0.357566
$506$			87.4779i			0.172881i
$507$	−255.698	−	678.807i	−0.504336	−	1.33887i
$508$	−25.0591			−0.0493290
$509$			440.534i			0.865489i	0.901517	+	0.432744i	$0.142455\pi$
$509$			440.534i			0.865489i	−0.901517	+	0.432744i	$0.857545\pi$
$510$	24.0778	−	9.06981i	0.0472113	−	0.0177839i
$511$	946.175			1.85161
$512$			22.6274i			0.0441942i
$513$	−752.836	−	401.599i	−1.46752	−	0.782844i
$514$	455.040			0.885292
$515$			304.163i			0.590607i
$516$	135.230	+	358.997i	0.262074	+	0.695731i
$517$	−36.7715			−0.0711248
$518$			452.300i			0.873167i
$519$	−756.350	+	284.908i	−1.45732	+	0.548956i
$520$	−128.186			−0.246511
$521$		−	843.155i		−	1.61834i	−0.587575	−	0.809170i	$-0.699917\pi$
$521$		−	843.155i		−	1.61834i	0.587575	−	0.809170i	$-0.300083\pi$
$522$	307.680	−	270.129i	0.589426	−	0.517488i
$523$	233.277			0.446037			0.223018	−	0.974814i	$-0.428409\pi$
$523$	233.277			0.446037			0.223018	+	0.974814i	$0.428409\pi$
$524$			347.857i			0.663849i
$525$	63.2639	+	167.948i	0.120503	+	0.319901i
$526$	−509.421			−0.968480
$527$			82.8844i			0.157276i
$528$	144.840	−	54.5594i	0.274318	−	0.103332i
$529$	−23.0000			−0.0434783
$530$		−	193.882i		−	0.365815i
$531$	−375.954	−	428.216i	−0.708010	−	0.806434i
$532$	756.207			1.42144
$533$			361.217i			0.677706i
$534$	−191.282	−	507.799i	−0.358206	−	0.950935i
$535$	281.527			0.526219
$536$		−	239.228i		−	0.446321i
$537$	503.604	−	189.702i	0.937810	−	0.353262i
$538$	32.8290			0.0610205
$539$			1214.34i			2.25295i
$540$	−56.8320	+	106.537i	−0.105244	+	0.197291i
$541$	−432.754			−0.799916			−0.399958	−	0.916534i	$-0.630975\pi$
$541$	−432.754			−0.799916			−0.399958	+	0.916534i	$0.630975\pi$
$542$		−	479.848i		−	0.885328i
$543$	233.937	+	621.037i	0.430823	+	1.14371i
$544$	−15.3420			−0.0282023
$545$		−	200.582i		−	0.368039i
$546$	962.785	−	362.669i	1.76334	−	0.664230i
$547$	−287.768			−0.526084			−0.263042	−	0.964784i	$-0.584726\pi$
$547$	−287.768			−0.526084			−0.263042	+	0.964784i	$0.584726\pi$
$548$			240.574i			0.439003i
$549$	330.150	−	289.856i	0.601366	−	0.527971i
$550$	91.2020			0.165822
$551$		−	1016.58i		−	1.84497i
$552$	14.3450	+	38.0818i	0.0259872	+	0.0689887i
$553$	892.825			1.61451
$554$		−	467.163i		−	0.843254i
$555$	−167.807	+	63.2108i	−0.302354	+	0.113893i
$556$	−151.499			−0.272480
$557$		−	285.062i		−	0.511780i	−0.966706	−	0.255890i	$-0.917631\pi$
$557$		−	285.062i		−	0.511780i	0.966706	−	0.255890i	$-0.0823685\pi$
$558$	−256.631	−	292.306i	−0.459912	−	0.523846i
$559$	1295.87			2.31820
$560$		−	107.014i		−	0.191097i
$561$	36.9928	+	98.2054i	0.0659409	+	0.175054i
$562$	372.069			0.662044
$563$			142.443i			0.253007i	0.991966	+	0.126504i	$0.0403756\pi$
$563$			142.443i			0.253007i	−0.991966	+	0.126504i	$0.959624\pi$
$564$	−16.0078	+	6.02993i	−0.0283826	+	0.0106914i
$565$	167.480			0.296424
$566$			413.301i			0.730214i
$567$	125.437	−	960.976i	0.221229	−	1.69484i
$568$	−160.026			−0.281736
$569$		−	262.892i		−	0.462025i	−0.972951	−	0.231013i	$-0.925796\pi$
$569$		−	262.892i		−	0.462025i	0.972951	−	0.231013i	$-0.0742039\pi$
$570$	105.683	+	280.558i	0.185409	+	0.492208i
$571$	120.906			0.211744			0.105872	−	0.994380i	$-0.466237\pi$
$571$	120.906			0.211744			0.105872	+	0.994380i	$0.466237\pi$
$572$		−	522.828i		−	0.914036i
$573$	118.998	−	44.8250i	0.207675	−	0.0782287i
$574$	−301.557			−0.525361
$575$			23.9792i			0.0417029i
$576$	54.1063	−	47.5027i	0.0939345	−	0.0824700i
$577$	−223.738			−0.387762			−0.193881	−	0.981025i	$-0.562107\pi$
$577$	−223.738			−0.387762			−0.193881	+	0.981025i	$0.562107\pi$
$578$			398.305i			0.689110i
$579$	59.4145	+	157.729i	0.102616	+	0.272416i
$580$	−143.861			−0.248035
$581$		−	1231.12i		−	2.11896i
$582$	−590.160	+	222.306i	−1.01402	+	0.381969i
$583$	790.782			1.35640
$584$		−	223.677i		−	0.383008i
$585$	269.106	+	306.516i	0.460010	+	0.523958i
$586$	766.342			1.30775
$587$			593.776i			1.01154i	0.862667	+	0.505772i	$0.168792\pi$
$587$			593.776i			1.01154i	−0.862667	+	0.505772i	$0.831208\pi$
$588$	199.132	+	528.640i	0.338660	+	0.899047i
$589$	−965.784			−1.63970
$590$			200.219i			0.339354i
$591$	−320.859	+	120.864i	−0.542909	+	0.204507i
$592$	106.924			0.180615
$593$		−	707.402i		−	1.19292i	−0.802643	−	0.596460i	$-0.796573\pi$
$593$		−	707.402i		−	1.19292i	0.802643	−	0.596460i	$-0.203427\pi$
$594$	−434.530	−	231.799i	−0.731532	−	0.390235i
$595$	72.5586			0.121947
$596$		−	290.858i		−	0.488016i
$597$	195.984	+	520.283i	0.328282	+	0.871496i
$598$	137.464			0.229873
$599$		−	89.8222i		−	0.149954i	−0.997185	−	0.0749768i	$-0.976112\pi$
$599$		−	89.8222i		−	0.149954i	0.997185	−	0.0749768i	$-0.0238883\pi$
$600$	39.7030	−	14.9556i	0.0661717	−	0.0249261i
$601$	−1122.70			−1.86806			−0.934029	−	0.357197i	$-0.883732\pi$
$601$	−1122.70			−1.86806			−0.934029	+	0.357197i	$0.883732\pi$
$602$			1081.84i			1.79708i
$603$	−572.038	+	502.222i	−0.948654	+	0.832873i
$604$	176.117			0.291584
$605$			101.419i			0.167636i
$606$	120.772	+	320.617i	0.199295	+	0.529070i
$607$	−335.109			−0.552074			−0.276037	−	0.961147i	$-0.589021\pi$
$607$	−335.109			−0.552074			−0.276037	+	0.961147i	$0.589021\pi$
$608$		−	178.768i		−	0.294026i
$609$	1080.52	−	407.017i	1.77425	−	0.668337i
$610$	−154.367			−0.253060
$611$			57.7832i			0.0945716i
$612$	32.2082	+	36.6856i	0.0526278	+	0.0599438i
$613$	927.809			1.51356			0.756778	−	0.653672i	$-0.226773\pi$
$613$	927.809			1.51356			0.756778	+	0.653672i	$0.226773\pi$
$614$		−	234.930i		−	0.382622i
$615$	−42.1438	−	111.880i	−0.0685265	−	0.181918i
$616$	436.476			0.708565
$617$		−	823.595i		−	1.33484i	−0.744682	−	0.667419i	$-0.767399\pi$
$617$		−	823.595i		−	1.33484i	0.744682	−	0.667419i	$-0.232601\pi$
$618$	−540.063	+	203.435i	−0.873888	+	0.329183i
$619$	610.174			0.985742			0.492871	−	0.870103i	$-0.335948\pi$
$619$	610.174			0.985742			0.492871	+	0.870103i	$0.335948\pi$
$620$			136.672i			0.220439i
$621$	60.9455	−	114.248i	0.0981409	−	0.183975i
$622$	257.210			0.413521
$623$		−	1530.26i		−	2.45627i
$624$	−85.7354	−	227.603i	−0.137396	−	0.364749i
$625$	25.0000			0.0400000
$626$			533.876i			0.852837i
$627$	−1144.31	+	431.047i	−1.82505	+	0.687475i
$628$	−442.230			−0.704187
$629$			72.4976i			0.115259i
$630$	−255.890	+	224.659i	−0.406175	+	0.356602i
$631$	−564.071			−0.893932			−0.446966	−	0.894551i	$-0.647495\pi$
$631$	−564.071			−0.893932			−0.446966	+	0.894551i	$0.647495\pi$
$632$		−	211.065i		−	0.333963i
$633$	−207.601	−	551.123i	−0.327964	−	0.870653i
$634$	−216.557			−0.341573
$635$		−	28.0170i		−	0.0441212i
$636$	344.251	−	129.675i	0.541276	−	0.203892i
$637$	1908.23			2.99565
$638$		−	586.761i		−	0.919688i
$639$	335.950	+	382.652i	0.525744	+	0.598829i
$640$	−25.2982			−0.0395285
$641$			711.513i			1.11001i	0.831849	+	0.555003i	$0.187283\pi$
$641$			711.513i			1.11001i	−0.831849	+	0.555003i	$0.812717\pi$
$642$	188.296	+	499.871i	0.293295	+	0.778616i
$643$	1104.71			1.71805			0.859027	−	0.511930i	$-0.171069\pi$
$643$	1104.71			1.71805			0.859027	+	0.511930i	$0.171069\pi$
$644$			114.760i			0.178198i
$645$	−401.371	+	151.192i	−0.622281	+	0.234406i
$646$	121.210			0.187631
$647$		−	1047.39i		−	1.61884i	−0.587228	−	0.809422i	$-0.699781\pi$
$647$		−	1047.39i		−	1.61884i	0.587228	−	0.809422i	$-0.300219\pi$
$648$	−227.175	−	29.6534i	−0.350579	−	0.0457615i
$649$	−816.629			−1.25829
$650$		−	143.316i		−	0.220486i
$651$	−386.680	−	1026.53i	−0.593978	−	1.57684i
$652$	202.271			0.310232
$653$			400.037i			0.612615i	0.951933	+	0.306307i	$0.0990935\pi$
$653$			400.037i			0.612615i	−0.951933	+	0.306307i	$0.900906\pi$
$654$	356.147	−	134.156i	0.544567	−	0.205132i
$655$	−388.916			−0.593765
$656$			71.2884i			0.108671i
$657$	−534.852	+	469.574i	−0.814081	+	0.714725i
$658$	−48.2395			−0.0733124
$659$		−	53.4238i		−	0.0810680i	−0.999178	−	0.0405340i	$-0.987094\pi$
$659$		−	53.4238i		−	0.0810680i	0.999178	−	0.0405340i	$-0.0129059\pi$
$660$	60.9993	+	161.936i	0.0924231	+	0.245357i
$661$	−748.518			−1.13240			−0.566201	−	0.824267i	$-0.691588\pi$
$661$	−748.518			−1.13240			−0.566201	+	0.824267i	$0.691588\pi$
$662$		−	225.640i		−	0.340845i
$663$	154.321	−	58.1310i	0.232762	−	0.0876787i
$664$	−291.037			−0.438309
$665$			845.465i			1.27138i
$666$	−224.471	−	255.675i	−0.337043	−	0.383897i
$667$	154.273			0.231294
$668$		−	226.938i		−	0.339728i
$669$	135.783	+	360.467i	0.202965	+	0.538814i
$670$	267.465			0.399202
$671$		−	629.612i		−	0.938319i
$672$	190.011	−	71.5750i	0.282755	−	0.106510i
$673$	−59.5933			−0.0885487			−0.0442743	−	0.999019i	$-0.514098\pi$
$673$	−59.5933			−0.0885487			−0.0442743	+	0.999019i	$0.514098\pi$
$674$		−	156.046i		−	0.231523i
$675$	−119.112	−	63.5401i	−0.176462	−	0.0941335i
$676$	−483.579			−0.715354
$677$		−	991.775i		−	1.46496i	−0.680791	−	0.732478i	$-0.738364\pi$
$677$		−	991.775i		−	1.46496i	0.680791	−	0.732478i	$-0.261636\pi$
$678$	112.017	+	297.373i	0.165216	+	0.438603i
$679$	−1778.45			−2.61922
$680$		−	17.1529i		−	0.0252249i
$681$	764.114	−	287.833i	1.12205	−	0.422662i
$682$	−557.442			−0.817364
$683$		−	514.441i		−	0.753208i	−0.926374	−	0.376604i	$-0.877092\pi$
$683$		−	514.441i		−	0.753208i	0.926374	−	0.376604i	$-0.122908\pi$
$684$	−427.467	+	375.296i	−0.624952	+	0.548678i
$685$	−268.970			−0.392656
$686$			763.960i			1.11364i
$687$	−113.262	−	300.679i	−0.164865	−	0.437670i
$688$	255.748			0.371727
$689$		−	1242.64i		−	1.80355i
$690$	−42.5767	+	16.0381i	−0.0617054	+	0.0232437i
$691$	−85.8481			−0.124238			−0.0621188	−	0.998069i	$-0.519786\pi$
$691$	−85.8481			−0.124238			−0.0621188	+	0.998069i	$0.519786\pi$
$692$			538.821i			0.778643i
$693$	−916.313	−	1043.69i	−1.32224	−	1.50605i
$694$	−488.051			−0.703244
$695$		−	169.381i		−	0.243714i
$696$	−96.2193	−	255.435i	−0.138246	−	0.367004i
$697$	−48.3355			−0.0693479
$698$		−	585.741i		−	0.839170i
$699$	−225.124	+	84.8015i	−0.322066	+	0.121318i
$700$	119.645			0.170922
$701$		−	847.483i		−	1.20896i	−0.796619	−	0.604481i	$-0.793380\pi$
$701$		−	847.483i		−	1.20896i	0.796619	−	0.604481i	$-0.206620\pi$
$702$	−364.252	+	682.826i	−0.518878	+	0.972687i
$703$	−844.755			−1.20164
$704$		−	103.183i		−	0.146567i
$705$	−6.74167	−	17.8972i	−0.00956265	−	0.0253861i
$706$	−214.258			−0.303481
$707$			966.182i			1.36659i
$708$	−355.504	+	133.914i	−0.502124	+	0.189144i
$709$	−434.828			−0.613297			−0.306649	−	0.951823i	$-0.599208\pi$
$709$	−434.828			−0.613297			−0.306649	+	0.951823i	$0.599208\pi$
$710$		−	178.915i		−	0.251993i
$711$	−504.694	+	443.097i	−0.709837	+	0.623203i
$712$	−361.754			−0.508082
$713$		−	146.565i		−	0.205560i
$714$	48.5299	+	128.833i	0.0679690	+	0.180438i
$715$	584.540			0.817538
$716$		−	358.766i		−	0.501069i
$717$	481.520	−	181.383i	0.671576	−	0.252975i
$718$	434.856			0.605649
$719$		−	1036.78i		−	1.44198i	−0.692947	−	0.720988i	$-0.743688\pi$
$719$		−	1036.78i		−	1.44198i	0.692947	−	0.720988i	$-0.256312\pi$
$720$	53.1097	+	60.4927i	0.0737634	+	0.0840176i
$721$	−1627.48			−2.25726
$722$			901.826i			1.24907i
$723$	454.491	+	1206.54i	0.628618	+	1.66880i
$724$	442.424			0.611083
$725$		−	160.841i		−	0.221850i
$726$	−180.078	+	67.8331i	−0.248041	+	0.0934340i
$727$	−371.369			−0.510823			−0.255412	−	0.966832i	$-0.582211\pi$
$727$	−371.369			−0.510823			−0.255412	+	0.966832i	$0.582211\pi$
$728$		−	685.884i		−	0.942148i
$729$	406.013	+	605.471i	0.556945	+	0.830550i
$730$	250.078			0.342573
$731$			173.405i			0.237215i
$732$	−103.246	−	274.089i	−0.141047	−	0.374439i
$733$	−524.689			−0.715810			−0.357905	−	0.933758i	$-0.616509\pi$
$733$	−524.689			−0.715810			−0.357905	+	0.933758i	$0.616509\pi$
$734$		−	848.470i		−	1.15595i
$735$	−591.037	+	222.637i	−0.804132	+	0.302907i
$736$	27.1293			0.0368605
$737$			1090.90i			1.48020i
$738$	170.463	−	149.659i	0.230980	−	0.202790i
$739$	439.493			0.594713			0.297357	−	0.954766i	$-0.403895\pi$
$739$	439.493			0.594713			0.297357	+	0.954766i	$0.403895\pi$
$740$			119.545i			0.161547i
$741$	677.352	+	1798.18i	0.914106	+	2.42669i
$742$	1037.40			1.39812
$743$		−	1233.57i		−	1.66025i	−0.557577	−	0.830125i	$-0.688269\pi$
$743$		−	1233.57i		−	1.66025i	0.557577	−	0.830125i	$-0.311731\pi$
$744$	−242.671	+	91.4114i	−0.326171	+	0.122865i
$745$	325.189			0.436495
$746$			511.047i			0.685050i
$747$	610.987	+	695.923i	0.817921	+	0.931623i
$748$	69.9612			0.0935310
$749$			1506.37i			2.01117i
$750$	16.7209	+	44.3893i	0.0222946	+	0.0591857i
$751$	−80.5428			−0.107247			−0.0536237	−	0.998561i	$-0.517077\pi$
$751$	−80.5428			−0.107247			−0.0536237	+	0.998561i	$0.517077\pi$
$752$			11.4039i			0.0151647i
$753$	1335.12	−	502.925i	1.77307	−	0.667895i
$754$	−922.044			−1.22287
$755$			196.905i			0.260801i
$756$	−570.048	−	304.091i	−0.754032	−	0.402237i
$757$	1135.47			1.49996			0.749982	−	0.661459i	$-0.230062\pi$
$757$	1135.47			1.49996			0.749982	+	0.661459i	$0.230062\pi$
$758$			735.605i			0.970455i
$759$	−65.4144	−	173.657i	−0.0861850	−	0.228797i
$760$	199.869			0.262985
$761$			398.257i			0.523334i	0.965158	+	0.261667i	$0.0842722\pi$
$761$			398.257i			0.523334i	−0.965158	+	0.261667i	$0.915728\pi$
$762$	49.7462	−	18.7388i	0.0652837	−	0.0245916i
$763$	1073.25			1.40662
$764$		−	84.7736i		−	0.110960i
$765$	−41.0157	+	36.0099i	−0.0536153	+	0.0470717i
$766$	−188.379			−0.245925
$767$			1283.26i			1.67309i
$768$	−16.9204	−	44.9188i	−0.0220318	−	0.0584880i
$769$	52.7698			0.0686213			0.0343107	−	0.999411i	$-0.489076\pi$
$769$	52.7698			0.0686213			0.0343107	+	0.999411i	$0.489076\pi$
$770$			487.995i			0.633760i
$771$	−903.322	+	340.271i	−1.17162	+	0.441337i
$772$	112.365			0.145551
$773$			267.888i			0.346556i	0.984873	+	0.173278i	$0.0554359\pi$
$773$			267.888i			0.346556i	−0.984873	+	0.173278i	$0.944564\pi$
$774$	−536.904	−	611.541i	−0.693674	−	0.790104i
$775$	−152.804			−0.197167
$776$			420.428i			0.541788i
$777$	−338.222	−	897.884i	−0.435293	−	1.15558i
$778$	12.2549			0.0157518
$779$		−	563.214i		−	0.722996i
$780$	254.468	−	95.8550i	0.326241	−	0.122891i
$781$	729.736			0.934361
$782$			18.3944i			0.0235223i
$783$	−408.794	+	766.324i	−0.522087	+	0.978702i
$784$	376.601			0.480358
$785$		−	494.428i		−	0.629844i
$786$	−260.121	−	690.548i	−0.330943	−	0.878560i
$787$	−66.6819			−0.0847292			−0.0423646	−	0.999102i	$-0.513489\pi$
$787$	−66.6819			−0.0847292			−0.0423646	+	0.999102i	$0.513489\pi$
$788$			228.579i			0.290075i
$789$	1011.28	−	380.936i	1.28172	−	0.482808i
$790$	235.977			0.298706
$791$			896.135i			1.13291i
$792$	−246.730	+	216.617i	−0.311528	+	0.273507i
$793$	−989.381			−1.24764
$794$		−	780.466i		−	0.982955i
$795$	144.981	+	384.885i	0.182367	+	0.484132i
$796$	370.648			0.465638
$797$		−	1390.20i		−	1.74429i	−0.489249	−	0.872144i	$-0.662729\pi$
$797$		−	1390.20i		−	1.74429i	0.489249	−	0.872144i	$-0.337271\pi$
$798$	−1501.18	+	565.478i	−1.88118	+	0.708620i
$799$	−7.73214			−0.00967728
$800$		−	28.2843i		−	0.0353553i
$801$	759.447	+	865.021i	0.948123	+	1.07993i
$802$	784.015			0.977574
$803$			1019.99i			1.27022i
$804$	178.891	+	474.904i	0.222501	+	0.590677i
$805$	−128.305			−0.159386
$806$			875.971i			1.08681i
$807$	−65.1706	+	24.5490i	−0.0807566	+	0.0304200i
$808$	228.406			0.282681
$809$		−	939.878i		−	1.16178i	−0.813983	−	0.580889i	$-0.802705\pi$
$809$		−	939.878i		−	1.16178i	0.813983	−	0.580889i	$-0.197295\pi$
$810$	33.1535	−	253.990i	0.0409303	−	0.313568i
$811$	−814.703			−1.00457			−0.502283	−	0.864703i	$-0.667506\pi$
$811$	−814.703			−1.00457			−0.502283	+	0.864703i	$0.667506\pi$
$812$		−	769.755i		−	0.947975i
$813$	358.822	+	952.570i	0.441355	+	1.17167i
$814$	−487.585			−0.598999
$815$			226.146i			0.277480i
$816$	30.4562	−	11.4725i	0.0373238	−	0.0140594i
$817$	−2020.54			−2.47312
$818$		−	60.8354i		−	0.0743710i
$819$	−1640.07	+	1439.91i	−2.00253	+	1.75813i
$820$	−79.7028			−0.0971985
$821$		−	860.745i		−	1.04841i	−0.851592	−	0.524205i	$-0.824362\pi$
$821$		−	860.745i		−	1.04841i	0.851592	−	0.524205i	$-0.175638\pi$
$822$	−179.897	−	477.575i	−0.218853	−	0.580992i
$823$	448.624			0.545108			0.272554	−	0.962141i	$-0.412132\pi$
$823$	448.624			0.545108			0.272554	+	0.962141i	$0.412132\pi$
$824$			384.739i			0.466916i
$825$	−181.050	+	68.1993i	−0.219454	+	0.0826658i
$826$	−1071.31			−1.29699
$827$		−	275.902i		−	0.333618i	−0.985989	−	0.166809i	$-0.946654\pi$
$827$		−	275.902i		−	0.333618i	0.985989	−	0.166809i	$-0.0533464\pi$
$828$	−56.9538	−	64.8712i	−0.0687848	−	0.0783468i
$829$	−269.278			−0.324823			−0.162412	−	0.986723i	$-0.551927\pi$
$829$	−269.278			−0.324823			−0.162412	+	0.986723i	$0.551927\pi$
$830$		−	325.389i		−	0.392035i
$831$	349.336	+	927.388i	0.420380	+	1.11599i
$832$	−162.144			−0.194884
$833$			255.346i			0.306538i
$834$	300.748	−	113.288i	0.360609	−	0.135837i
$835$	253.725			0.303862
$836$			815.200i			0.975120i
$837$	728.032	+	388.368i	0.869811	+	0.464000i
$838$	−163.783			−0.195446
$839$		−	865.772i		−	1.03191i	−0.856616	−	0.515954i	$-0.827437\pi$
$839$		−	865.772i		−	1.03191i	0.856616	−	0.515954i	$-0.172563\pi$
$840$	80.0233	+	212.439i	0.0952658	+	0.252904i
$841$	−193.793			−0.230432
$842$			96.1521i			0.114195i
$843$	−738.612	+	278.226i	−0.876171	+	0.330043i
$844$	−392.618			−0.465187
$845$		−	540.658i		−	0.639832i
$846$	27.2687	−	23.9406i	0.0322325	−	0.0282986i
$847$	−542.666			−0.640692
$848$		−	245.243i		−	0.289202i
$849$	−309.059	−	820.465i	−0.364028	−	0.966390i
$850$	19.1775			0.0225618
$851$		−	128.198i		−	0.150643i
$852$	317.676	−	119.665i	0.372859	−	0.140452i
$853$	−427.675			−0.501377			−0.250689	−	0.968068i	$-0.580657\pi$
$853$	−427.675			−0.501377			−0.250689	+	0.968068i	$0.580657\pi$
$854$		−	825.971i		−	0.967179i
$855$	−419.593	−	477.923i	−0.490752	−	0.558974i
$856$	356.107			0.416012
$857$		−	899.536i		−	1.04963i	−0.851215	−	0.524817i	$-0.824134\pi$
$857$		−	899.536i		−	1.04963i	0.851215	−	0.524817i	$-0.175866\pi$
$858$	390.962	+	1037.89i	0.455667	+	1.20967i
$859$	255.234			0.297129			0.148564	−	0.988903i	$-0.452535\pi$
$859$	255.234			0.297129			0.148564	+	0.988903i	$0.452535\pi$
$860$			285.935i			0.332483i
$861$	598.636	−	225.499i	0.695280	−	0.261904i
$862$	−423.528			−0.491332
$863$		−	268.195i		−	0.310770i	−0.987854	−	0.155385i	$-0.950338\pi$
$863$		−	268.195i		−	0.310770i	0.987854	−	0.155385i	$-0.0496619\pi$
$864$	−71.8874	+	134.760i	−0.0832030	+	0.155972i
$865$	−602.420			−0.696440
$866$		−	107.058i		−	0.123623i
$867$	−297.846	−	790.696i	−0.343536	−	0.911991i
$868$	−731.293			−0.842503
$869$			962.476i			1.10757i
$870$	285.585	−	107.576i	0.328258	−	0.123651i
$871$	1714.26			1.96815
$872$		−	253.718i		−	0.290961i
$873$	1005.32	−	882.623i	1.15157	−	1.01102i
$874$	−214.335			−0.245235
$875$			133.768i			0.152877i
$876$	167.261	+	444.032i	0.190938	+	0.506885i
$877$	804.277			0.917077			0.458539	−	0.888675i	$-0.348373\pi$
$877$	804.277			0.917077			0.458539	+	0.888675i	$0.348373\pi$
$878$		−	493.304i		−	0.561850i
$879$	−1521.30	+	573.057i	−1.73072	+	0.651942i
$880$	115.362			0.131094
$881$			825.080i			0.936526i	0.883589	+	0.468263i	$0.155120\pi$
$881$			825.080i			0.936526i	−0.883589	+	0.468263i	$0.844880\pi$
$882$	−790.615	−	900.521i	−0.896389	−	1.02100i
$883$	−1650.19			−1.86884			−0.934422	−	0.356168i	$-0.884083\pi$
$883$	−1650.19			−1.86884			−0.934422	+	0.356168i	$0.884083\pi$
$884$		−	109.938i		−	0.124364i
$885$	−149.720	−	397.465i	−0.169176	−	0.449113i
$886$	−281.683			−0.317927
$887$			527.251i			0.594421i	0.954812	+	0.297210i	$0.0960563\pi$
$887$			527.251i			0.594421i	−0.954812	+	0.297210i	$0.903944\pi$
$888$	−212.261	+	79.9560i	−0.239032	+	0.0900406i
$889$	149.911			0.168628
$890$		−	404.454i		−	0.454442i
$891$	1035.94	+	135.223i	1.16267	+	0.151765i
$892$	256.795			0.287887
$893$		−	90.0963i		−	0.100892i
$894$	217.498	+	577.396i	0.243287	+	0.645857i
$895$	401.112			0.448170
$896$		−	135.363i		−	0.151075i
$897$	−272.886	+	102.793i	−0.304221	+	0.114597i
$898$	−348.925			−0.388558
$899$			983.087i			1.09353i
$900$	−67.6329	+	59.3784i	−0.0751476	+	0.0659760i
$901$	166.282			0.184553
$902$		−	325.082i		−	0.360401i
$903$	−808.982	−	2147.62i	−0.895883	−	2.37831i
$904$	211.847			0.234344
$905$			494.645i			0.546569i
$906$	−349.619	+	131.697i	−0.385893	+	0.145361i
$907$	−1181.95			−1.30315			−0.651573	−	0.758586i	$-0.725890\pi$
$907$	−1181.95			−1.30315			−0.651573	+	0.758586i	$0.725890\pi$
$908$		−	544.352i		−	0.599507i
$909$	−479.503	−	546.161i	−0.527506	−	0.600837i
$910$	766.842			0.842683
$911$			951.060i			1.04397i	0.852953	+	0.521987i	$0.174809\pi$
$911$			951.060i			1.04397i	−0.852953	+	0.521987i	$0.825191\pi$
$912$	133.680	+	354.881i	0.146578	+	0.389124i
$913$	1327.16			1.45362
$914$		−	1167.09i		−	1.27690i
$915$	306.441	−	115.433i	0.334908	−	0.126156i
$916$	−214.203			−0.233846
$917$		−	2080.97i		−	2.26933i
$918$	−91.3709	−	48.7417i	−0.0995326	−	0.0530955i
$919$	−1492.05			−1.62356			−0.811778	−	0.583966i	$-0.801500\pi$
$919$	−1492.05			−1.62356			−0.811778	+	0.583966i	$0.801500\pi$
$920$			30.3315i			0.0329690i
$921$	175.676	+	466.371i	0.190745	+	0.506375i
$922$	−1147.49			−1.24457
$923$		−	1146.72i		−	1.24238i
$924$	−866.471	+	326.389i	−0.937739	+	0.353235i
$925$	−133.655			−0.144492
$926$			251.657i			0.271768i
$927$	919.980	−	807.699i	0.992428	−	0.871304i
$928$	−181.971			−0.196089
$929$			473.690i			0.509893i	0.966955	+	0.254946i	$0.0820578\pi$
$929$			473.690i			0.509893i	−0.966955	+	0.254946i	$0.917942\pi$
$930$	−102.201	−	271.315i	−0.109894	−	0.291736i
$931$	−2975.34			−3.19585
$932$			160.377i			0.172079i
$933$	−510.600	+	192.337i	−0.547267	+	0.206149i
$934$	−238.446			−0.255295
$935$			78.2190i			0.0836567i
$936$	340.395	+	387.715i	0.363670	+	0.414225i
$937$	−137.344			−0.146579			−0.0732893	−	0.997311i	$-0.523350\pi$
$937$	−137.344			−0.146579			−0.0732893	+	0.997311i	$0.523350\pi$
$938$			1431.13i			1.52572i
$939$	−399.223	−	1059.82i	−0.425158	−	1.12867i
$940$	−12.7499			−0.0135637
$941$		−	54.6018i		−	0.0580253i	−0.999579	−	0.0290127i	$-0.990764\pi$
$941$		−	54.6018i		−	0.0580253i	0.999579	−	0.0290127i	$-0.00923631\pi$
$942$	877.892	−	330.692i	0.931945	−	0.351053i
$943$	85.4717			0.0906381
$944$			253.259i			0.268283i
$945$	339.984	−	637.333i	0.359772	−	0.674426i
$946$	−1166.24			−1.23281
$947$			1340.61i			1.41564i	0.706391	+	0.707822i	$0.250322\pi$
$947$			1340.61i			1.41564i	−0.706391	+	0.707822i	$0.749678\pi$
$948$	157.830	+	418.995i	0.166488	+	0.441978i
$949$	1602.82			1.68896
$950$			223.460i			0.235221i
$951$	429.899	−	161.938i	0.452049	−	0.170282i
$952$	91.7801			0.0964077
$953$		−	1393.97i		−	1.46272i	−0.681991	−	0.731361i	$-0.738886\pi$
$953$		−	1393.97i		−	1.46272i	0.681991	−	0.731361i	$-0.261114\pi$
$954$	−586.422	+	514.850i	−0.614698	+	0.539675i
$955$	94.7797			0.0992458
$956$		−	343.033i		−	0.358821i
$957$	438.770	+	1164.81i	0.458484	+	1.21715i
$958$	109.864			0.114681
$959$		−	1439.18i		−	1.50071i
$960$	50.2208	−	18.9176i	0.0523133	−	0.0197058i
$961$	−27.0355			−0.0281327
$962$			766.198i			0.796463i
$963$	−747.590	−	851.516i	−0.776314	−	0.884232i
$964$	859.538			0.891637
$965$			125.628i			0.130185i
$966$	−85.8154	−	227.816i	−0.0888358	−	0.235834i
$967$	1762.49			1.82263			0.911317	−	0.411705i	$-0.135067\pi$
$967$	1762.49			1.82263			0.911317	+	0.411705i	$0.135067\pi$
$968$			128.287i			0.132528i
$969$	−240.620	+	90.6385i	−0.248317	+	0.0935382i
$970$	−470.053			−0.484590
$971$		−	46.4332i		−	0.0478200i	−0.999714	−	0.0239100i	$-0.992388\pi$
$971$		−	46.4332i		−	0.0478200i	0.999714	−	0.0239100i	$-0.00761151\pi$
$972$	473.152	−	111.011i	0.486782	−	0.114209i
$973$	906.307			0.931457
$974$			1259.60i			1.29322i
$975$	107.169	+	284.504i	0.109917	+	0.291799i
$976$	−195.260			−0.200062
$977$		−	1706.37i		−	1.74654i	−0.487235	−	0.873271i	$-0.661994\pi$
$977$		−	1706.37i		−	1.74654i	0.487235	−	0.873271i	$-0.338006\pi$
$978$	−401.538	+	151.255i	−0.410571	+	0.154657i
$979$	1649.64			1.68502
$980$			421.053i			0.429645i
$981$	−606.686	+	532.641i	−0.618436	+	0.542957i
$982$	−542.014			−0.551949
$983$			465.368i			0.473416i	0.971581	+	0.236708i	$0.0760685\pi$
$983$			465.368i			0.473416i	−0.971581	+	0.236708i	$0.923932\pi$
$984$	−53.3082	−	141.518i	−0.0541750	−	0.143819i
$985$	−255.559			−0.259451
$986$		−	123.381i		−	0.125133i
$987$	95.7627	−	36.0727i	0.0970240	−	0.0365478i
$988$	1281.02			1.29657
$989$		−	306.631i		−	0.310042i
$990$	−242.185	−	275.853i	−0.244632	−	0.278639i
$991$	−228.581			−0.230657			−0.115329	−	0.993327i	$-0.536792\pi$
$991$	−228.581			−0.230657			−0.115329	+	0.993327i	$0.536792\pi$
$992$			172.878i			0.174272i
$993$	168.729	+	447.928i	0.169919	+	0.451086i
$994$	957.320			0.963099
$995$			414.397i			0.416479i
$996$	577.752	−	217.632i	0.580072	−	0.218506i
$997$	−428.726			−0.430016			−0.215008	−	0.976612i	$-0.568978\pi$
$997$	−428.726			−0.430016			−0.215008	+	0.976612i	$0.568978\pi$
$998$		−	931.860i		−	0.933727i
$999$	636.798	+	339.699i	0.637435	+	0.340039i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.g.a.461.18	yes	56
3.2	odd	2	inner	690.3.g.a.461.17	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.g.a.461.17	✓	56	3.2	odd	2	inner
690.3.g.a.461.18	yes	56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +(-1.05752 - 2.80743i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(3.97030 - 1.49556i) q^{6} +11.9645 q^{7} -2.82843i q^{8} +(-6.76329 + 5.93784i) q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +(-1.05752 - 2.80743i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(3.97030 - 1.49556i) q^{6} +11.9645 q^{7} -2.82843i q^{8} +(-6.76329 + 5.93784i) q^{9} +3.16228 q^{10} +12.8979i q^{11} +(2.11505 + 5.61485i) q^{12} +20.2679 q^{13} +16.9204i q^{14} +(-6.27760 + 2.36470i) q^{15} +4.00000 q^{16} +2.71211i q^{17} +(-8.39738 - 9.56473i) q^{18} -31.6020 q^{19} +4.47214i q^{20} +(-12.6528 - 33.5896i) q^{21} -18.2404 q^{22} -4.79583i q^{23} +(-7.94060 + 2.99113i) q^{24} -5.00000 q^{25} +28.6632i q^{26} +(23.8224 + 12.7080i) q^{27} -23.9291 q^{28} +32.1682i q^{29} +(-3.34418 - 8.87786i) q^{30} +30.5608 q^{31} +5.65685i q^{32} +(36.2099 - 13.6399i) q^{33} -3.83551 q^{34} -26.7535i q^{35} +(13.5266 - 11.8757i) q^{36} +26.7311 q^{37} -44.6920i q^{38} +(-21.4338 - 56.9008i) q^{39} -6.32456 q^{40} +17.8221i q^{41} +(47.5028 - 17.8937i) q^{42} +63.9371 q^{43} -25.7958i q^{44} +(13.2774 + 15.1232i) q^{45} +6.78233 q^{46} +2.85097i q^{47} +(-4.23010 - 11.2297i) q^{48} +94.1502 q^{49} -7.07107i q^{50} +(7.61406 - 2.86812i) q^{51} -40.5359 q^{52} -61.3108i q^{53} +(-17.9719 + 33.6899i) q^{54} +28.8406 q^{55} -33.8408i q^{56} +(33.4199 + 88.7203i) q^{57} -45.4927 q^{58} +63.3148i q^{59} +(12.5552 - 4.72939i) q^{60} -48.8150 q^{61} +43.2195i q^{62} +(-80.9196 + 71.0435i) q^{63} -8.00000 q^{64} -45.3205i q^{65} +(19.2897 + 51.2086i) q^{66} +84.5799 q^{67} -5.42423i q^{68} +(-13.4639 + 5.07171i) q^{69} +37.8352 q^{70} -56.5778i q^{71} +(16.7948 + 19.1295i) q^{72} +79.0816 q^{73} +37.8034i q^{74} +(5.28762 + 14.0371i) q^{75} +63.2040 q^{76} +154.318i q^{77} +(80.4698 - 30.3120i) q^{78} +74.6226 q^{79} -8.94427i q^{80} +(10.4841 - 80.3186i) q^{81} -25.2042 q^{82} -102.897i q^{83} +(25.3056 + 67.1791i) q^{84} +6.06447 q^{85} +90.4207i q^{86} +(90.3099 - 34.0186i) q^{87} +36.4808 q^{88} -127.899i q^{89} +(-21.3874 + 18.7771i) q^{90} +242.497 q^{91} +9.59166i q^{92} +(-32.3188 - 85.7973i) q^{93} -4.03188 q^{94} +70.6643i q^{95} +(15.8812 - 5.98226i) q^{96} -148.644 q^{97} +133.149i q^{98} +(-76.5858 - 87.2323i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{3} - 112 q^{4} + 16 q^{6} - 16 q^{7}+O(q^{10}) \) 56 * q - 8 * q^3 - 112 * q^4 + 16 * q^6 - 16 * q^7	\( 56 q - 8 q^{3} - 112 q^{4} + 16 q^{6} - 16 q^{7} + 16 q^{12} + 80 q^{13} - 40 q^{15} + 224 q^{16} - 32 q^{18} - 64 q^{19} + 56 q^{21} - 96 q^{22} - 32 q^{24} - 280 q^{25} + 40 q^{27} + 32 q^{28} - 80 q^{31} + 32 q^{33} + 192 q^{34} + 240 q^{37} - 56 q^{39} - 144 q^{43} - 32 q^{48} + 72 q^{49} - 24 q^{51} - 160 q^{52} + 16 q^{54} - 16 q^{57} + 80 q^{60} + 112 q^{61} - 64 q^{63} - 448 q^{64} + 160 q^{66} + 832 q^{67} + 64 q^{72} - 608 q^{73} + 40 q^{75} + 128 q^{76} - 320 q^{78} + 48 q^{79} - 32 q^{81} - 448 q^{82} - 112 q^{84} + 240 q^{85} + 200 q^{87} + 192 q^{88} + 80 q^{91} - 232 q^{93} + 160 q^{94} + 64 q^{96} - 448 q^{97} + 464 q^{99}+O(q^{100}) \) 56 * q - 8 * q^3 - 112 * q^4 + 16 * q^6 - 16 * q^7 + 16 * q^12 + 80 * q^13 - 40 * q^15 + 224 * q^16 - 32 * q^18 - 64 * q^19 + 56 * q^21 - 96 * q^22 - 32 * q^24 - 280 * q^25 + 40 * q^27 + 32 * q^28 - 80 * q^31 + 32 * q^33 + 192 * q^34 + 240 * q^37 - 56 * q^39 - 144 * q^43 - 32 * q^48 + 72 * q^49 - 24 * q^51 - 160 * q^52 + 16 * q^54 - 16 * q^57 + 80 * q^60 + 112 * q^61 - 64 * q^63 - 448 * q^64 + 160 * q^66 + 832 * q^67 + 64 * q^72 - 608 * q^73 + 40 * q^75 + 128 * q^76 - 320 * q^78 + 48 * q^79 - 32 * q^81 - 448 * q^82 - 112 * q^84 + 240 * q^85 + 200 * q^87 + 192 * q^88 + 80 * q^91 - 232 * q^93 + 160 * q^94 + 64 * q^96 - 448 * q^97 + 464 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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