LMFDB - Embedded newform 354.4.c.a.353.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,4,Mod(353,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("354.353");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	354.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$20.8866761420$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			353.18
Character	$\chi$	$=$	354.353
Dual form			354.4.c.a.353.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} +(1.53016 + 4.96574i) q^{3} +4.00000 q^{4} +1.00990i q^{5} +(-3.06032 - 9.93149i) q^{6} +8.17095 q^{7} -8.00000 q^{8} +(-22.3172 + 15.1967i) q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +(1.53016 + 4.96574i) q^{3} +4.00000 q^{4} +1.00990i q^{5} +(-3.06032 - 9.93149i) q^{6} +8.17095 q^{7} -8.00000 q^{8} +(-22.3172 + 15.1967i) q^{9} -2.01980i q^{10} +49.9249 q^{11} +(6.12063 + 19.8630i) q^{12} -46.3361i q^{13} -16.3419 q^{14} +(-5.01489 + 1.54530i) q^{15} +16.0000 q^{16} +111.065i q^{17} +(44.6345 - 30.3935i) q^{18} +48.6148 q^{19} +4.03959i q^{20} +(12.5028 + 40.5749i) q^{21} -99.8499 q^{22} +73.0469 q^{23} +(-12.2413 - 39.7260i) q^{24} +123.980 q^{25} +92.6723i q^{26} +(-109.612 - 87.5683i) q^{27} +32.6838 q^{28} +10.9184i q^{29} +(10.0298 - 3.09061i) q^{30} +14.5096i q^{31} -32.0000 q^{32} +(76.3930 + 247.914i) q^{33} -222.129i q^{34} +8.25183i q^{35} +(-89.2689 + 60.7870i) q^{36} -2.36071i q^{37} -97.2296 q^{38} +(230.093 - 70.9016i) q^{39} -8.07918i q^{40} +127.469i q^{41} +(-25.0057 - 81.1497i) q^{42} -82.9776i q^{43} +199.700 q^{44} +(-15.3472 - 22.5381i) q^{45} -146.094 q^{46} -39.4630 q^{47} +(24.4825 + 79.4519i) q^{48} -276.236 q^{49} -247.960 q^{50} +(-551.519 + 169.947i) q^{51} -185.345i q^{52} +434.211i q^{53} +(219.224 + 175.137i) q^{54} +50.4191i q^{55} -65.3676 q^{56} +(74.3883 + 241.409i) q^{57} -21.8368i q^{58} +(-431.505 - 138.502i) q^{59} +(-20.0596 + 6.18121i) q^{60} +572.237i q^{61} -29.0192i q^{62} +(-182.353 + 124.172i) q^{63} +64.0000 q^{64} +46.7947 q^{65} +(-152.786 - 495.829i) q^{66} +265.749i q^{67} +444.259i q^{68} +(111.773 + 362.732i) q^{69} -16.5037i q^{70} +491.294i q^{71} +(178.538 - 121.574i) q^{72} +841.352i q^{73} +4.72142i q^{74} +(189.709 + 615.654i) q^{75} +194.459 q^{76} +407.934 q^{77} +(-460.187 + 141.803i) q^{78} +1303.47 q^{79} +16.1584i q^{80} +(267.118 - 678.299i) q^{81} -254.938i q^{82} -322.881 q^{83} +(50.0114 + 162.299i) q^{84} -112.164 q^{85} +165.955i q^{86} +(-54.2179 + 16.7069i) q^{87} -399.399 q^{88} +816.419 q^{89} +(30.6943 + 45.0762i) q^{90} -378.610i q^{91} +292.188 q^{92} +(-72.0511 + 22.2020i) q^{93} +78.9260 q^{94} +49.0960i q^{95} +(-48.9651 - 158.904i) q^{96} -854.008i q^{97} +552.471 q^{98} +(-1114.19 + 758.697i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 60 q^{2} + 5 q^{3} + 120 q^{4} - 10 q^{6} + 6 q^{7} - 240 q^{8} + 27 q^{9}+O(q^{10}) $ 30 * q - 60 * q^2 + 5 * q^3 + 120 * q^4 - 10 * q^6 + 6 * q^7 - 240 * q^8 + 27 * q^9	$ 30 q - 60 q^{2} + 5 q^{3} + 120 q^{4} - 10 q^{6} + 6 q^{7} - 240 q^{8} + 27 q^{9} - 60 q^{11} + 20 q^{12} - 12 q^{14} + 20 q^{15} + 480 q^{16} - 54 q^{18} + 90 q^{19} + 132 q^{21} + 120 q^{22} + 24 q^{23} - 40 q^{24} - 1080 q^{25} - 55 q^{27} + 24 q^{28} - 40 q^{30} - 960 q^{32} + 336 q^{33} + 108 q^{36} - 180 q^{38} + 652 q^{39} - 264 q^{42} - 240 q^{44} - 878 q^{45} - 48 q^{46} + 792 q^{47} + 80 q^{48} + 2016 q^{49} + 2160 q^{50} + 650 q^{51} + 110 q^{54} - 48 q^{56} + 846 q^{57} - 480 q^{59} + 80 q^{60} + 887 q^{63} + 1920 q^{64} - 1416 q^{65} - 672 q^{66} - 590 q^{69} - 216 q^{72} - 952 q^{75} + 360 q^{76} + 864 q^{77} - 1304 q^{78} + 738 q^{79} - 1217 q^{81} + 876 q^{83} + 528 q^{84} + 1176 q^{85} + 534 q^{87} + 480 q^{88} - 300 q^{89} + 1756 q^{90} + 96 q^{92} + 1684 q^{93} - 1584 q^{94} - 160 q^{96} - 4032 q^{98} + 730 q^{99}+O(q^{100}) $ 30 * q - 60 * q^2 + 5 * q^3 + 120 * q^4 - 10 * q^6 + 6 * q^7 - 240 * q^8 + 27 * q^9 - 60 * q^11 + 20 * q^12 - 12 * q^14 + 20 * q^15 + 480 * q^16 - 54 * q^18 + 90 * q^19 + 132 * q^21 + 120 * q^22 + 24 * q^23 - 40 * q^24 - 1080 * q^25 - 55 * q^27 + 24 * q^28 - 40 * q^30 - 960 * q^32 + 336 * q^33 + 108 * q^36 - 180 * q^38 + 652 * q^39 - 264 * q^42 - 240 * q^44 - 878 * q^45 - 48 * q^46 + 792 * q^47 + 80 * q^48 + 2016 * q^49 + 2160 * q^50 + 650 * q^51 + 110 * q^54 - 48 * q^56 + 846 * q^57 - 480 * q^59 + 80 * q^60 + 887 * q^63 + 1920 * q^64 - 1416 * q^65 - 672 * q^66 - 590 * q^69 - 216 * q^72 - 952 * q^75 + 360 * q^76 + 864 * q^77 - 1304 * q^78 + 738 * q^79 - 1217 * q^81 + 876 * q^83 + 528 * q^84 + 1176 * q^85 + 534 * q^87 + 480 * q^88 - 300 * q^89 + 1756 * q^90 + 96 * q^92 + 1684 * q^93 - 1584 * q^94 - 160 * q^96 - 4032 * q^98 + 730 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−2.00000			−0.707107
$2$	−2.00000			−0.707107
$3$	1.53016	+	4.96574i	0.294479	+	0.955658i
$3$	1.53016	+	4.96574i	0.294479	+	0.955658i
$4$	4.00000			0.500000
$5$			1.00990i			0.0903280i	0.998980	+	0.0451640i	$0.0143810\pi$
$5$			1.00990i			0.0903280i	−0.998980	+	0.0451640i	$0.985619\pi$
$6$	−3.06032	−	9.93149i	−0.208228	−	0.675752i
$7$	8.17095			0.441190			0.220595	−	0.975365i	$-0.429200\pi$
$7$	8.17095			0.441190			0.220595	+	0.975365i	$0.429200\pi$
$8$	−8.00000			−0.353553
$9$	−22.3172	+	15.1967i	−0.826564	+	0.562842i
$10$		−	2.01980i		−	0.0638715i
$11$	49.9249			1.36845			0.684224	−	0.729272i	$-0.260141\pi$
$11$	49.9249			1.36845			0.684224	+	0.729272i	$0.260141\pi$
$12$	6.12063	+	19.8630i	0.147240	+	0.477829i
$13$		−	46.3361i		−	0.988564i	−0.869302	−	0.494282i	$-0.835431\pi$
$13$		−	46.3361i		−	0.988564i	0.869302	−	0.494282i	$-0.164569\pi$
$14$	−16.3419			−0.311968
$15$	−5.01489	+	1.54530i	−0.0863227	+	0.0265997i
$16$	16.0000			0.250000
$17$			111.065i			1.58454i	0.610172	+	0.792269i	$0.291101\pi$
$17$			111.065i			1.58454i	−0.610172	+	0.792269i	$0.708899\pi$
$18$	44.6345	−	30.3935i	0.584469	−	0.397990i
$19$	48.6148			0.587000			0.293500	−	0.955959i	$-0.405180\pi$
$19$	48.6148			0.587000			0.293500	+	0.955959i	$0.405180\pi$
$20$			4.03959i			0.0451640i
$21$	12.5028	+	40.5749i	0.129921	+	0.421627i
$22$	−99.8499			−0.967639
$23$	73.0469			0.662232			0.331116	−	0.943590i	$-0.392575\pi$
$23$	73.0469			0.662232			0.331116	+	0.943590i	$0.392575\pi$
$24$	−12.2413	−	39.7260i	−0.104114	−	0.337876i
$25$	123.980			0.991841
$26$			92.6723i			0.699020i
$27$	−109.612	−	87.5683i	−0.781291	−	0.624167i
$28$	32.6838			0.220595
$29$			10.9184i			0.0699136i	0.999389	+	0.0349568i	$0.0111294\pi$
$29$			10.9184i			0.0699136i	−0.999389	+	0.0349568i	$0.988871\pi$
$30$	10.0298	−	3.09061i	0.0610393	−	0.0188088i
$31$			14.5096i			0.0840647i	0.999116	+	0.0420323i	$0.0133833\pi$
$31$			14.5096i			0.0840647i	−0.999116	+	0.0420323i	$0.986617\pi$
$32$	−32.0000			−0.176777
$33$	76.3930	+	247.914i	0.402979	+	1.30777i
$34$		−	222.129i		−	1.12044i
$35$			8.25183i			0.0398518i
$36$	−89.2689	+	60.7870i	−0.413282	+	0.281421i
$37$		−	2.36071i		−	0.0104891i	−0.999986	−	0.00524457i	$-0.998331\pi$
$37$		−	2.36071i		−	0.0104891i	0.999986	−	0.00524457i	$-0.00166941\pi$
$38$	−97.2296			−0.415072
$39$	230.093	−	70.9016i	0.944729	−	0.291111i
$40$		−	8.07918i		−	0.0319358i
$41$			127.469i			0.485544i	0.970083	+	0.242772i	$0.0780567\pi$
$41$			127.469i			0.485544i	−0.970083	+	0.242772i	$0.921943\pi$
$42$	−25.0057	−	81.1497i	−0.0918682	−	0.298135i
$43$		−	82.9776i		−	0.294278i	−0.989116	−	0.147139i	$-0.952993\pi$
$43$		−	82.9776i		−	0.294278i	0.989116	−	0.147139i	$-0.0470065\pi$
$44$	199.700			0.684224
$45$	−15.3472	−	22.5381i	−0.0508404	−	0.0746619i
$46$	−146.094			−0.468269
$47$	−39.4630			−0.122474			−0.0612369	−	0.998123i	$-0.519505\pi$
$47$	−39.4630			−0.122474			−0.0612369	+	0.998123i	$0.519505\pi$
$48$	24.4825	+	79.4519i	0.0736198	+	0.238914i
$49$	−276.236			−0.805351
$50$	−247.960			−0.701337
$51$	−551.519	+	169.947i	−1.51428	+	0.466613i
$52$		−	185.345i		−	0.494282i
$53$			434.211i			1.12535i	0.826678	+	0.562675i	$0.190228\pi$
$53$			434.211i			1.12535i	−0.826678	+	0.562675i	$0.809772\pi$
$54$	219.224	+	175.137i	0.552456	+	0.441353i
$55$			50.4191i			0.123609i
$56$	−65.3676			−0.155984
$57$	74.3883	+	241.409i	0.172859	+	0.560971i
$58$		−	21.8368i		−	0.0494364i
$59$	−431.505	−	138.502i	−0.952155	−	0.305616i
$59$	−431.505	−	138.502i	−0.952155	−	0.305616i
$60$	−20.0596	+	6.18121i	−0.0431613	+	0.0132998i
$61$			572.237i			1.20110i	0.799585	+	0.600552i	$0.205053\pi$
$61$			572.237i			1.20110i	−0.799585	+	0.600552i	$0.794947\pi$
$62$		−	29.0192i		−	0.0594427i
$63$	−182.353	+	124.172i	−0.364672	+	0.248320i
$64$	64.0000			0.125000
$65$	46.7947			0.0892950
$66$	−152.786	−	495.829i	−0.284949	−	0.924732i
$67$			265.749i			0.484574i	0.970205	+	0.242287i	$0.0778975\pi$
$67$			265.749i			0.484574i	−0.970205	+	0.242287i	$0.922102\pi$
$68$			444.259i			0.792269i
$69$	111.773	+	362.732i	0.195013	+	0.632867i
$70$		−	16.5037i		−	0.0281795i
$71$			491.294i			0.821210i	0.911813	+	0.410605i	$0.134682\pi$
$71$			491.294i			0.821210i	−0.911813	+	0.410605i	$0.865318\pi$
$72$	178.538	−	121.574i	0.292235	−	0.198995i
$73$			841.352i			1.34894i	0.738301	+	0.674472i	$0.235628\pi$
$73$			841.352i			1.34894i	−0.738301	+	0.674472i	$0.764372\pi$
$74$			4.72142i			0.00741694i
$75$	189.709	+	615.654i	0.292076	+	0.947861i
$76$	194.459			0.293500
$77$	407.934			0.603746
$78$	−460.187	+	141.803i	−0.668024	+	0.205847i
$79$	1303.47			1.85635			0.928176	−	0.372142i	$-0.121377\pi$
$79$	1303.47			1.85635			0.928176	+	0.372142i	$0.121377\pi$
$80$			16.1584i			0.0225820i
$81$	267.118	−	678.299i	0.366417	−	0.930451i
$82$		−	254.938i		−	0.343331i
$83$	−322.881			−0.426998			−0.213499	−	0.976943i	$-0.568486\pi$
$83$	−322.881			−0.426998			−0.213499	+	0.976943i	$0.568486\pi$
$84$	50.0114	+	162.299i	0.0649606	+	0.210813i
$85$	−112.164			−0.143128
$86$			165.955i			0.208086i
$87$	−54.2179	+	16.7069i	−0.0668135	+	0.0205881i
$88$	−399.399			−0.483820
$89$	816.419			0.972362			0.486181	−	0.873858i	$-0.338390\pi$
$89$	816.419			0.972362			0.486181	+	0.873858i	$0.338390\pi$
$90$	30.6943	+	45.0762i	0.0359496	+	0.0527939i
$91$		−	378.610i		−	0.436145i
$92$	292.188			0.331116
$93$	−72.0511	+	22.2020i	−0.0803371	+	0.0247553i
$94$	78.9260			0.0866021
$95$			49.0960i			0.0530225i
$96$	−48.9651	−	158.904i	−0.0520570	−	0.168938i
$97$		−	854.008i		−	0.893932i	−0.894551	−	0.446966i	$-0.852504\pi$
$97$		−	854.008i		−	0.893932i	0.894551	−	0.446966i	$-0.147496\pi$
$98$	552.471			0.569469
$99$	−1114.19	+	758.697i	−1.13111	+	0.770221i
$100$	495.920			0.495920
$101$	−734.438			−0.723557			−0.361779	−	0.932264i	$-0.617830\pi$
$101$	−734.438			−0.723557			−0.361779	+	0.932264i	$0.617830\pi$
$102$	1103.04	−	339.893i	1.07076	−	0.329945i
$103$			1236.25i			1.18263i	0.806440	+	0.591316i	$0.201391\pi$
$103$			1236.25i			1.18263i	−0.806440	+	0.591316i	$0.798609\pi$
$104$			370.689i			0.349510i
$105$	−40.9765	+	12.6266i	−0.0380847	+	0.0117355i
$106$		−	868.423i		−	0.795742i
$107$			463.524i			0.418790i	0.977831	+	0.209395i	$0.0671495\pi$
$107$			463.524i			0.418790i	−0.977831	+	0.209395i	$0.932851\pi$
$108$	−438.448	−	350.273i	−0.390645	−	0.312084i
$109$		−	678.710i		−	0.596409i	−0.954502	−	0.298205i	$-0.903612\pi$
$109$		−	678.710i		−	0.596409i	0.954502	−	0.298205i	$-0.0963878\pi$
$110$		−	100.838i		−	0.0874049i
$111$	11.7227	−	3.61226i	0.0100240	−	0.00308883i
$112$	130.735			0.110298
$113$	−1892.89			−1.57582			−0.787911	−	0.615789i	$-0.788838\pi$
$113$	−1892.89			−1.57582			−0.787911	+	0.615789i	$0.788838\pi$
$114$	−148.777	−	482.818i	−0.122230	−	0.396667i
$115$			73.7699i			0.0598181i
$116$			43.6736i			0.0349568i
$117$	704.158	+	1034.09i	0.556406	+	0.817112i
$118$	863.009	+	277.003i	0.673275	+	0.216103i
$119$			907.505i			0.699083i
$120$	40.1191	−	12.3624i	0.0305197	−	0.00940441i
$121$	1161.50			0.872651
$122$		−	1144.47i		−	0.849309i
$123$	−632.978	+	195.048i	−0.464014	+	0.142983i
$124$			58.0385i			0.0420323i
$125$			251.444i			0.179919i
$126$	364.706	−	248.344i	0.257862	−	0.175589i
$127$	681.227			0.475977			0.237989	−	0.971268i	$-0.423512\pi$
$127$	681.227			0.475977			0.237989	+	0.971268i	$0.423512\pi$
$128$	−128.000			−0.0883883
$129$	412.046	−	126.969i	0.281229	−	0.0866588i
$130$	−93.5895			−0.0631411
$131$	−2157.68			−1.43906			−0.719530	−	0.694461i	$-0.755643\pi$
$131$	−2157.68			−1.43906			−0.719530	+	0.694461i	$0.755643\pi$
$132$	305.572	+	991.658i	0.201490	+	0.653884i
$133$	397.229			0.258979
$134$		−	531.499i		−	0.342645i
$135$	88.4350	−	110.697i	0.0563798	−	0.0705724i
$136$		−	888.518i		−	0.560219i
$137$		−	2647.20i		−	1.65084i	−0.564516	−	0.825422i	$-0.690937\pi$
$137$		−	2647.20i		−	1.65084i	0.564516	−	0.825422i	$-0.309063\pi$
$138$	−223.547	−	725.464i	−0.137895	−	0.447505i
$139$	979.177			0.597502			0.298751	−	0.954331i	$-0.403430\pi$
$139$	979.177			0.597502			0.298751	+	0.954331i	$0.403430\pi$
$140$			33.0073i			0.0199259i
$141$	−60.3847	−	195.963i	−0.0360660	−	0.117043i
$142$		−	982.588i		−	0.580683i
$143$		−	2313.33i		−	1.35280i
$144$	−357.076	+	243.148i	−0.206641	+	0.140711i
$145$	−11.0265			−0.00631515
$146$		−	1682.70i		−	0.953847i
$147$	−422.684	−	1371.71i	−0.237159	−	0.769640i
$148$		−	9.44284i		−	0.00524457i
$149$	1375.95			0.756523			0.378261	−	0.925699i	$-0.376522\pi$
$149$	1375.95			0.756523			0.378261	+	0.925699i	$0.376522\pi$
$150$	−379.418	−	1231.31i	−0.206529	−	0.670239i
$151$		−	2429.85i		−	1.30953i	−0.755834	−	0.654763i	$-0.772768\pi$
$151$		−	2429.85i		−	1.30953i	0.755834	−	0.654763i	$-0.227232\pi$
$152$	−388.919			−0.207536
$153$	−1687.82	−	2478.66i	−0.891846	−	1.30972i
$154$	−815.869			−0.426913
$155$	−14.6532			−0.00759339
$156$	920.374	−	283.606i	0.472364	−	0.145556i
$157$		−	719.395i		−	0.365694i	−0.983141	−	0.182847i	$-0.941469\pi$
$157$		−	719.395i		−	0.365694i	0.983141	−	0.182847i	$-0.0585313\pi$
$158$	−2606.94			−1.31264
$159$	−2156.18	+	664.412i	−1.07545	+	0.331392i
$160$		−	32.3167i		−	0.0159679i
$161$	596.863			0.292170
$162$	−534.236	+	1356.60i	−0.259096	+	0.657928i
$163$	1691.64			0.812880			0.406440	−	0.913677i	$-0.366770\pi$
$163$	1691.64			0.812880			0.406440	+	0.913677i	$0.366770\pi$
$164$			509.876i			0.242772i
$165$	−250.368	+	77.1491i	−0.118128	+	0.0364003i
$166$	645.762			0.301933
$167$		−	2022.86i		−	0.937326i	−0.883377	−	0.468663i	$-0.844736\pi$
$167$		−	2022.86i		−	0.937326i	0.883377	−	0.468663i	$-0.155264\pi$
$168$	−100.023	−	324.599i	−0.0459341	−	0.149068i
$169$	49.9628			0.0227414
$170$	224.328			0.101207
$171$	−1084.95	+	738.787i	−0.485193	+	0.330389i
$172$		−	331.910i		−	0.147139i
$173$	2445.00			1.07451			0.537255	−	0.843420i	$-0.319461\pi$
$173$	2445.00			1.07451			0.537255	+	0.843420i	$0.319461\pi$
$174$	108.436	−	33.4137i	0.0472443	−	0.0145580i
$175$	1013.04			0.437590
$176$	798.799			0.342112
$177$	27.4931	−	2354.67i	0.0116752	−	0.999932i
$178$	−1632.84			−0.687564
$179$	31.5422			0.0131708			0.00658540	−	0.999978i	$-0.497904\pi$
$179$	31.5422			0.0131708			0.00658540	+	0.999978i	$0.497904\pi$
$180$	−61.3886	−	90.1525i	−0.0254202	−	0.0373309i
$181$	192.198			0.0789279			0.0394639	−	0.999221i	$-0.487435\pi$
$181$	192.198			0.0789279			0.0394639	+	0.999221i	$0.487435\pi$
$182$			757.221i			0.308401i
$183$	−2841.58	+	875.612i	−1.14785	+	0.353700i
$184$	−584.375			−0.234134
$185$	2.38407			0.000947463
$186$	144.102	−	44.4040i	0.0568069	−	0.0175046i
$187$			5544.90i			2.16836i
$188$	−157.852			−0.0612369
$189$	−895.635	−	715.516i	−0.344698	−	0.275376i
$190$		−	98.1920i		−	0.0374926i
$191$	3192.12			1.20929			0.604643	−	0.796497i	$-0.293316\pi$
$191$	3192.12			1.20929			0.604643	+	0.796497i	$0.293316\pi$
$192$	97.9301	+	317.808i	0.0368099	+	0.119457i
$193$	1611.77			0.601129			0.300565	−	0.953761i	$-0.402825\pi$
$193$	1611.77			0.601129			0.300565	+	0.953761i	$0.402825\pi$
$194$			1708.02i			0.632105i
$195$	71.6033	+	232.371i	0.0262955	+	0.0853355i
$196$	−1104.94			−0.402676
$197$		−	2262.65i		−	0.818309i	−0.912465	−	0.409155i	$-0.865824\pi$
$197$		−	2262.65i		−	0.818309i	0.912465	−	0.409155i	$-0.134176\pi$
$198$	2228.37	−	1517.39i	0.799816	−	0.544628i
$199$	−656.038			−0.233695			−0.116848	−	0.993150i	$-0.537279\pi$
$199$	−656.038			−0.233695			−0.116848	+	0.993150i	$0.537279\pi$
$200$	−991.841			−0.350669
$201$	−1319.64	+	406.638i	−0.463087	+	0.142697i
$202$	1468.88			0.511632
$203$			89.2137i			0.0308452i
$204$	−2206.08	+	679.786i	−0.757138	+	0.233307i
$205$	−128.731			−0.0438582
$206$		−	2472.50i		−	0.836247i
$207$	−1630.20	+	1110.08i	−0.547377	+	0.372732i
$208$		−	741.378i		−	0.247141i
$209$	2427.09			0.803280
$210$	81.9529	−	25.2532i	0.0269299	−	0.00829827i
$211$		−	1583.57i		−	0.516669i	−0.966056	−	0.258334i	$-0.916826\pi$
$211$		−	1583.57i		−	0.516669i	0.966056	−	0.258334i	$-0.0831737\pi$
$212$			1736.85i			0.562675i
$213$	−2439.64	+	751.758i	−0.784795	+	0.241829i
$214$		−	927.048i		−	0.296129i
$215$	83.7989			0.0265816
$216$	876.896	+	700.546i	0.276228	+	0.220676i
$217$			118.557i			0.0370885i
$218$			1357.42i			0.421725i
$219$	−4177.94	+	1287.40i	−1.28913	+	0.397235i
$220$			201.676i			0.0618046i
$221$	5146.31			1.56642
$222$	−23.4454	+	7.22451i	−0.00708806	+	0.00218413i
$223$	765.803			0.229964			0.114982	−	0.993368i	$-0.463319\pi$
$223$	765.803			0.229964			0.114982	+	0.993368i	$0.463319\pi$
$224$	−261.471			−0.0779921
$225$	−2766.89	+	1884.09i	−0.819820	+	0.558250i
$226$	3785.78			1.11428
$227$	−3759.41			−1.09921			−0.549606	−	0.835424i	$-0.685222\pi$
$227$	−3759.41			−1.09921			−0.549606	+	0.835424i	$0.685222\pi$
$228$	297.553	+	965.635i	0.0864296	+	0.280486i
$229$		−	2981.53i		−	0.860370i	−0.902741	−	0.430185i	$-0.858448\pi$
$229$		−	2981.53i		−	0.860370i	0.902741	−	0.430185i	$-0.141552\pi$
$230$		−	147.540i		−	0.0422978i
$231$	624.204	+	2025.70i	0.177790	+	0.576975i
$232$		−	87.3471i		−	0.0247182i
$233$	−1898.32			−0.533748			−0.266874	−	0.963731i	$-0.585991\pi$
$233$	−1898.32			−0.533748			−0.266874	+	0.963731i	$0.585991\pi$
$234$	−1408.32	−	2068.19i	−0.393438	−	0.577785i
$235$		−	39.8536i		−	0.0110628i
$236$	−1726.02	−	554.006i	−0.476077	−	0.152808i
$237$	1994.51	+	6472.70i	0.546657	+	1.77404i
$238$		−	1815.01i		−	0.494326i
$239$		−	3245.30i		−	0.878332i	−0.898406	−	0.439166i	$-0.855274\pi$
$239$		−	3245.30i		−	0.878332i	0.898406	−	0.439166i	$-0.144726\pi$
$240$	−80.2383	+	24.7248i	−0.0215807	+	0.00664992i
$241$	5486.60			1.46648			0.733242	−	0.679967i	$-0.238006\pi$
$241$	5486.60			1.46648			0.733242	+	0.679967i	$0.238006\pi$
$242$	−2323.00			−0.617058
$243$	3776.99	+	288.535i	0.997095	+	0.0761709i
$244$			2288.95i			0.600552i
$245$		−	278.970i		−	0.0727458i
$246$	1265.96	−	390.095i	0.328107	−	0.101104i
$247$		−	2252.62i		−	0.580287i
$248$		−	116.077i		−	0.0297214i
$249$	−494.059	−	1603.35i	−0.125742	−	0.408064i
$250$		−	502.889i		−	0.127222i
$251$		−	1453.51i		−	0.365516i	−0.983158	−	0.182758i	$-0.941497\pi$
$251$		−	1453.51i		−	0.365516i	0.983158	−	0.182758i	$-0.0585025\pi$
$252$	−729.412	+	496.688i	−0.182336	+	0.124160i
$253$	3646.86			0.906230
$254$	−1362.45			−0.336567
$255$	−171.629	−	556.978i	−0.0421482	−	0.136782i
$256$	256.000			0.0625000
$257$		−	2145.38i		−	0.520721i	−0.965511	−	0.260361i	$-0.916159\pi$
$257$		−	2145.38i		−	0.520721i	0.965511	−	0.260361i	$-0.0838415\pi$
$258$	−824.091	+	253.938i	−0.198859	+	0.0612770i
$259$		−	19.2892i		−	0.00462770i
$260$	187.179			0.0446475
$261$	−165.924	−	243.668i	−0.0393503	−	0.0577881i
$262$	4315.35			1.01757
$263$			7984.68i			1.87208i	0.351896	+	0.936039i	$0.385537\pi$
$263$			7984.68i			1.87208i	−0.351896	+	0.936039i	$0.614463\pi$
$264$	−611.144	−	1983.32i	−0.142475	−	0.462366i
$265$	−438.509			−0.101651
$266$	−794.459			−0.183126
$267$	1249.25	+	4054.13i	0.286340	+	0.929245i
$268$			1063.00i			0.242287i
$269$	6546.15			1.48374			0.741869	−	0.670545i	$-0.233940\pi$
$269$	6546.15			1.48374			0.741869	+	0.670545i	$0.233940\pi$
$270$	−176.870	+	221.394i	−0.0398665	+	0.0499022i
$271$	4079.53			0.914442			0.457221	−	0.889353i	$-0.348845\pi$
$271$	4079.53			0.914442			0.457221	+	0.889353i	$0.348845\pi$
$272$			1777.04i			0.396135i
$273$	1880.08	−	579.334i	0.416805	−	0.128435i
$274$			5294.40i			1.16732i
$275$	6189.70			1.35728
$276$	447.093	+	1450.93i	0.0975067	+	0.316434i
$277$	−7476.74			−1.62178			−0.810892	−	0.585196i	$-0.801017\pi$
$277$	−7476.74			−1.62178			−0.810892	+	0.585196i	$0.801017\pi$
$278$	−1958.35			−0.422498
$279$	−220.499	−	323.815i	−0.0473152	−	0.0694849i
$280$		−	66.0146i		−	0.0140897i
$281$			8532.42i			1.81139i	0.423927	+	0.905696i	$0.360651\pi$
$281$			8532.42i			1.81139i	−0.423927	+	0.905696i	$0.639349\pi$
$282$	120.769	+	391.927i	0.0255025	+	0.0827620i
$283$			342.546i			0.0719514i	0.999353	+	0.0359757i	$0.0114539\pi$
$283$			342.546i			0.0719514i	−0.999353	+	0.0359757i	$0.988546\pi$
$284$			1965.18i			0.410605i
$285$	−243.798	+	75.1246i	−0.0506714	+	0.0156140i
$286$			4626.66i			0.956573i
$287$			1041.54i			0.214217i
$288$	714.151	−	486.296i	0.146117	−	0.0994974i
$289$	−7422.38			−1.51076
$290$	22.0529			0.00446549
$291$	4240.79	−	1306.77i	0.854293	−	0.263244i
$292$			3365.41i			0.674472i
$293$			1840.74i			0.367021i	0.983018	+	0.183511i	$0.0587462\pi$
$293$			1840.74i			0.367021i	−0.983018	+	0.183511i	$0.941254\pi$
$294$	845.368	+	2743.43i	0.167697	+	0.544218i
$295$	139.872	−	435.776i	0.0276057	−	0.0860062i
$296$			18.8857i			0.00370847i
$297$	−5472.37	−	4371.84i	−1.06916	−	0.854141i
$298$	−2751.89			−0.534943
$299$		−	3384.71i		−	0.654658i
$300$	758.837	+	2462.61i	0.146038	+	0.473930i
$301$		−	678.006i		−	0.129833i
$302$			4859.70i			0.925975i
$303$	−1123.81	−	3647.03i	−0.213072	−	0.691473i
$304$	777.837			0.146750
$305$	−577.900			−0.108493
$306$	3375.65	+	4957.32i	0.630630	+	0.926114i
$307$	−9423.43			−1.75187			−0.875935	−	0.482430i	$-0.839754\pi$
$307$	−9423.43			−1.75187			−0.875935	+	0.482430i	$0.839754\pi$
$308$	1631.74			0.301873
$309$	−6138.89	+	1891.65i	−1.13019	+	0.348260i
$310$	29.3065			0.00536934
$311$			4008.28i			0.730832i	0.930844	+	0.365416i	$0.119073\pi$
$311$			4008.28i			0.730832i	−0.930844	+	0.365416i	$0.880927\pi$
$312$	−1840.75	+	567.213i	−0.334012	+	0.102923i
$313$			3968.02i			0.716567i	0.933613	+	0.358284i	$0.116638\pi$
$313$			3968.02i			0.716567i	−0.933613	+	0.358284i	$0.883362\pi$
$314$			1438.79i			0.258585i
$315$	−125.401	−	184.158i	−0.0224303	−	0.0329401i
$316$	5213.88			0.928176
$317$		−	6870.97i		−	1.21739i	−0.793405	−	0.608695i	$-0.791694\pi$
$317$		−	6870.97i		−	1.21739i	0.793405	−	0.608695i	$-0.208306\pi$
$318$	4312.37	−	1328.82i	0.760457	−	0.234329i
$319$			545.100i			0.0956731i
$320$			64.6334i			0.0112910i
$321$	−2301.74	+	709.265i	−0.400220	+	0.123325i
$322$	−1193.73			−0.206595
$323$			5399.39i			0.930125i
$324$	1068.47	−	2713.19i	0.183208	−	0.465225i
$325$		−	5744.76i		−	0.980498i
$326$	−3383.28			−0.574793
$327$	3370.30	−	1038.53i	0.569963	−	0.175630i
$328$		−	1019.75i		−	0.171666i
$329$	−322.451			−0.0540343
$330$	500.736	−	154.298i	0.0835292	−	0.0257389i
$331$	3429.14			0.569434			0.284717	−	0.958612i	$-0.408100\pi$
$331$	3429.14			0.569434			0.284717	+	0.958612i	$0.408100\pi$
$332$	−1291.52			−0.213499
$333$	35.8751	+	52.6845i	0.00590373	+	0.00866995i
$334$			4045.72i			0.662790i
$335$	−268.380			−0.0437706
$336$	200.046	+	649.198i	0.0324803	+	0.105407i
$337$		−	5002.00i		−	0.808535i	−0.914641	−	0.404267i	$-0.867526\pi$
$337$		−	5002.00i		−	0.808535i	0.914641	−	0.404267i	$-0.132474\pi$
$338$	−99.9256			−0.0160806
$339$	−2896.42	−	9399.60i	−0.464047	−	1.50595i
$340$	−448.656			−0.0715641
$341$			724.392i			0.115038i
$342$	2169.90	−	1477.57i	0.343084	−	0.233620i
$343$	−5059.74			−0.796503
$344$			663.821i			0.104043i
$345$	−366.322	+	112.880i	−0.0571656	+	0.0176152i
$346$	−4890.01			−0.759793
$347$	11413.1			1.76567			0.882837	−	0.469680i	$-0.155631\pi$
$347$	11413.1			1.76567			0.882837	+	0.469680i	$0.155631\pi$
$348$	−216.872	+	66.8274i	−0.0334067	+	0.0102940i
$349$		−	12221.6i		−	1.87452i	−0.348627	−	0.937262i	$-0.613352\pi$
$349$		−	12221.6i		−	1.87452i	0.348627	−	0.937262i	$-0.386648\pi$
$350$	−2026.07			−0.309423
$351$	−4057.57	+	5079.00i	−0.617029	+	0.772356i
$352$	−1597.60			−0.241910
$353$	−2712.45			−0.408978			−0.204489	−	0.978869i	$-0.565553\pi$
$353$	−2712.45			−0.408978			−0.204489	+	0.978869i	$0.565553\pi$
$354$	−54.9862	+	4709.34i	−0.00825560	+	0.707059i
$355$	−496.157			−0.0741782
$356$	3265.67			0.486181
$357$	−4506.44	+	1388.63i	−0.668084	+	0.205865i
$358$	−63.0843			−0.00931316
$359$			4226.20i			0.621310i	0.950523	+	0.310655i	$0.100548\pi$
$359$			4226.20i			0.621310i	−0.950523	+	0.310655i	$0.899452\pi$
$360$	122.777	+	180.305i	0.0179748	+	0.0263970i
$361$	−4495.60			−0.655431
$362$	−384.395			−0.0558104
$363$	1777.28	+	5767.71i	0.256978	+	0.833956i
$364$		−	1514.44i		−	0.218072i
$365$	−849.680			−0.121847
$366$	5683.16	−	1751.22i	0.811649	−	0.250104i
$367$			9551.33i			1.35852i	0.733900	+	0.679258i	$0.237698\pi$
$367$			9551.33i			1.35852i	−0.733900	+	0.679258i	$0.762302\pi$
$368$	1168.75			0.165558
$369$	−1937.11	−	2844.75i	−0.273285	−	0.401333i
$370$	−4.76815			−0.000669957
$371$			3547.92i			0.496493i
$372$	−288.204	+	88.8080i	−0.0401685	+	0.0123776i
$373$	−2028.24			−0.281550			−0.140775	−	0.990042i	$-0.544959\pi$
$373$	−2028.24			−0.281550			−0.140775	+	0.990042i	$0.544959\pi$
$374$		−	11089.8i		−	1.53326i
$375$	−1248.61	+	384.750i	−0.171941	+	0.0529824i
$376$	315.704			0.0433011
$377$	505.916			0.0691141
$378$	1791.27	+	1431.03i	0.243738	+	0.194721i
$379$	−4565.62			−0.618786			−0.309393	−	0.950934i	$-0.600126\pi$
$379$	−4565.62			−0.618786			−0.309393	+	0.950934i	$0.600126\pi$
$380$			196.384i			0.0265113i
$381$	1042.38	+	3382.80i	0.140165	+	0.454871i
$382$	−6384.24			−0.855094
$383$		−	7930.24i		−	1.05801i	−0.848620	−	0.529003i	$-0.822566\pi$
$383$		−	7930.24i		−	1.05801i	0.848620	−	0.529003i	$-0.177434\pi$
$384$	−195.860	−	635.615i	−0.0260285	−	0.0844690i
$385$			411.972i			0.0545351i
$386$	−3223.55			−0.425063
$387$	1260.99	+	1851.83i	0.165632	+	0.243240i
$388$		−	3416.03i		−	0.446966i
$389$		−	9952.59i		−	1.29721i	−0.761123	−	0.648607i	$-0.775352\pi$
$389$		−	9952.59i		−	1.29721i	0.761123	−	0.648607i	$-0.224648\pi$
$390$	−143.207	−	464.741i	−0.0185937	−	0.0603413i
$391$			8112.93i			1.04933i
$392$	2209.88			0.284735
$393$	−3301.58	−	10714.5i	−0.423773	−	1.37525i
$394$			4525.30i			0.578632i
$395$			1316.37i			0.167680i
$396$	−4456.75	+	3034.79i	−0.565555	+	0.385110i
$397$			641.024i			0.0810380i	0.999179	+	0.0405190i	$0.0129011\pi$
$397$			641.024i			0.0810380i	−0.999179	+	0.0405190i	$0.987099\pi$
$398$	1312.08			0.165247
$399$	607.824	+	1972.54i	0.0762638	+	0.247495i
$400$	1983.68			0.247960
$401$	3368.23			0.419455			0.209727	−	0.977760i	$-0.432742\pi$
$401$	3368.23			0.419455			0.209727	+	0.977760i	$0.432742\pi$
$402$	2639.29	−	813.277i	0.327452	−	0.100902i
$403$	672.320			0.0831033
$404$	−2937.75			−0.361779
$405$	685.012	+	269.762i	0.0840457	+	0.0330977i
$406$		−	178.427i		−	0.0218108i
$407$		−	117.858i		−	0.0143538i
$408$	4412.15	−	1359.57i	0.535378	−	0.164973i
$409$		−	14529.1i		−	1.75652i	−0.478184	−	0.878260i	$-0.658705\pi$
$409$		−	14529.1i		−	1.75652i	0.478184	−	0.878260i	$-0.341295\pi$
$410$	257.461			0.0310124
$411$	13145.3	−	4050.64i	1.57764	−	0.486139i
$412$			4944.99i			0.591316i
$413$	−3525.81	−	1131.69i	−0.420081	−	0.134835i
$414$	3260.41	−	2220.15i	0.387054	−	0.263561i
$415$		−	326.077i		−	0.0385698i
$416$			1482.76i			0.174755i
$417$	1498.30	+	4862.34i	0.175952	+	0.571007i
$418$	−4854.18			−0.568004
$419$	10438.4			1.21707			0.608533	−	0.793528i	$-0.291758\pi$
$419$	10438.4			1.21707			0.608533	+	0.793528i	$0.291758\pi$
$420$	−163.906	+	50.5064i	−0.0190423	+	0.00586776i
$421$		−	8948.57i		−	1.03593i	−0.855402	−	0.517965i	$-0.826690\pi$
$421$		−	8948.57i		−	1.03593i	0.855402	−	0.517965i	$-0.173310\pi$
$422$			3167.13i			0.365340i
$423$	880.705	−	599.709i	0.101233	−	0.0689335i
$424$		−	3473.69i		−	0.397871i
$425$			13769.8i			1.57161i
$426$	4879.28	−	1503.52i	0.554934	−	0.170999i
$427$			4675.72i			0.529915i
$428$			1854.10i			0.209395i
$429$	11487.4	−	3539.76i	1.29281	−	0.398371i
$430$	−167.598			−0.0187960
$431$	−13882.1			−1.55146			−0.775728	−	0.631067i	$-0.782617\pi$
$431$	−13882.1			−1.55146			−0.775728	+	0.631067i	$0.782617\pi$
$432$	−1753.79	−	1401.09i	−0.195323	−	0.156042i
$433$	−3935.14			−0.436745			−0.218373	−	0.975865i	$-0.570075\pi$
$433$	−3935.14			−0.436745			−0.218373	+	0.975865i	$0.570075\pi$
$434$		−	237.115i		−	0.0262255i
$435$	−16.8722	−	54.7546i	−0.00185968	−	0.00603513i
$436$		−	2714.84i		−	0.298205i
$437$	3551.16			0.388730
$438$	8355.88	−	2574.80i	0.911551	−	0.280888i
$439$	−7424.31			−0.807159			−0.403579	−	0.914945i	$-0.632234\pi$
$439$	−7424.31			−0.807159			−0.403579	+	0.914945i	$0.632234\pi$
$440$		−	403.353i		−	0.0437024i
$441$	6164.81	−	4197.88i	0.665675	−	0.453286i
$442$	−10292.6			−1.10762
$443$	−9083.07			−0.974152			−0.487076	−	0.873359i	$-0.661937\pi$
$443$	−9083.07			−0.974152			−0.487076	+	0.873359i	$0.661937\pi$
$444$	46.8907	−	14.4490i	0.00501201	−	0.00154442i
$445$			824.499i			0.0878315i
$446$	−1531.61			−0.162609
$447$	2105.42	+	6832.60i	0.222780	+	0.722977i
$448$	522.941			0.0551488
$449$		−	795.044i		−	0.0835645i	−0.999127	−	0.0417822i	$-0.986696\pi$
$449$		−	795.044i		−	0.0835645i	0.999127	−	0.0417822i	$-0.0133036\pi$
$450$	5533.79	−	3768.19i	0.579700	−	0.394742i
$451$			6363.88i			0.664442i
$452$	−7571.55			−0.787911
$453$	12066.0	−	3718.06i	1.25146	−	0.385628i
$454$	7518.83			0.777260
$455$	382.358			0.0393961
$456$	−595.107	−	1931.27i	−0.0611150	−	0.198333i
$457$		−	7955.52i		−	0.814318i	−0.913357	−	0.407159i	$-0.866519\pi$
$457$		−	7955.52i		−	0.814318i	0.913357	−	0.407159i	$-0.133481\pi$
$458$			5963.05i			0.608374i
$459$	9725.75	−	12174.0i	0.989017	−	1.23799i
$460$			295.079i			0.0299090i
$461$		−	10451.3i		−	1.05589i	−0.849280	−	0.527943i	$-0.822963\pi$
$461$		−	10451.3i		−	1.05589i	0.849280	−	0.527943i	$-0.177037\pi$
$462$	−1248.41	−	4051.40i	−0.125717	−	0.407983i
$463$			18362.0i			1.84310i	0.388257	+	0.921551i	$0.373077\pi$
$463$			18362.0i			1.84310i	−0.388257	+	0.921551i	$0.626923\pi$
$464$			174.694i			0.0174784i
$465$	−22.4218	−	72.7642i	−0.00223609	−	0.00725669i
$466$	3796.64			0.377417
$467$	−750.555			−0.0743716			−0.0371858	−	0.999308i	$-0.511839\pi$
$467$	−750.555			−0.0743716			−0.0371858	+	0.999308i	$0.511839\pi$
$468$	2816.63	+	4136.38i	0.278203	+	0.408556i
$469$			2171.43i			0.213789i
$470$			79.7072i			0.00782259i
$471$	3572.33	−	1100.79i	0.349478	−	0.107689i
$472$	3452.04	+	1108.01i	0.336638	+	0.108052i
$473$		−	4142.65i		−	0.402705i
$474$	−3989.03	−	12945.4i	−0.386545	−	1.25443i
$475$	6027.27			0.582211
$476$			3630.02i			0.349541i
$477$	−6598.60	−	9690.40i	−0.633395	−	0.930174i
$478$			6490.61i			0.621074i
$479$		−	10590.9i		−	1.01025i	−0.863046	−	0.505125i	$-0.831446\pi$
$479$		−	10590.9i		−	1.01025i	0.863046	−	0.505125i	$-0.168554\pi$
$480$	160.477	−	49.4497i	0.0152598	−	0.00470221i
$481$	−109.386			−0.0103692
$482$	−10973.2			−1.03696
$483$	913.294	+	2963.87i	0.0860380	+	0.279215i
$484$	4646.00			0.436326
$485$	862.461			0.0807471
$486$	−7553.98	−	577.070i	−0.705052	−	0.0538609i
$487$	14827.5			1.37967			0.689833	−	0.723969i	$-0.257684\pi$
$487$	14827.5			1.37967			0.689833	+	0.723969i	$0.257684\pi$
$488$		−	4577.89i		−	0.424655i
$489$	2588.48	+	8400.25i	0.239376	+	0.776836i
$490$			557.939i			0.0514390i
$491$		−	12596.2i		−	1.15776i	−0.815414	−	0.578879i	$-0.803490\pi$
$491$		−	12596.2i		−	1.15776i	0.815414	−	0.578879i	$-0.196510\pi$
$492$	−2531.91	+	780.190i	−0.232007	+	0.0714913i
$493$	−1212.65			−0.110781
$494$			4505.25i			0.410325i
$495$	−766.206	−	1125.21i	−0.0695725	−	0.102171i
$496$			232.154i			0.0210162i
$497$			4014.34i			0.362309i
$498$	988.118	+	3206.69i	0.0889129	+	0.288545i
$499$	7423.54			0.665978			0.332989	−	0.942931i	$-0.391943\pi$
$499$	7423.54			0.665978			0.332989	+	0.942931i	$0.391943\pi$
$500$			1005.78i			0.0899595i
$501$	10045.0	−	3095.29i	0.895763	−	0.276023i
$502$			2907.01i			0.258459i
$503$	−18636.7			−1.65203			−0.826015	−	0.563648i	$-0.809397\pi$
$503$	−18636.7			−1.65203			−0.826015	+	0.563648i	$0.809397\pi$
$504$	1458.82	−	993.375i	0.128931	−	0.0877945i
$505$		−	741.707i		−	0.0653575i
$506$	−7293.72			−0.640801
$507$	76.4509	+	248.102i	0.00669686	+	0.0217330i
$508$	2724.91			0.237989
$509$	9055.94			0.788600			0.394300	−	0.918982i	$-0.370987\pi$
$509$	9055.94			0.788600			0.394300	+	0.918982i	$0.370987\pi$
$510$	343.257	+	1113.96i	0.0298033	+	0.0967192i
$511$			6874.65i			0.595140i
$512$	−512.000			−0.0441942
$513$	−5328.77	−	4257.11i	−0.458618	−	0.366386i
$514$			4290.77i			0.368206i
$515$	−1248.48			−0.106825
$516$	1648.18	−	507.875i	0.140615	−	0.0433294i
$517$	−1970.19			−0.167599
$518$			38.5785i			0.00327228i
$519$	3741.24	+	12141.3i	0.316421	+	1.02686i
$520$	−374.358			−0.0315705
$521$		−	2116.30i		−	0.177959i	−0.996033	−	0.0889796i	$-0.971639\pi$
$521$		−	2116.30i		−	0.177959i	0.996033	−	0.0889796i	$-0.0283606\pi$
$522$	331.848	+	487.336i	0.0278249	+	0.0408623i
$523$	−12547.2			−1.04905			−0.524524	−	0.851396i	$-0.675757\pi$
$523$	−12547.2			−1.04905			−0.524524	+	0.851396i	$0.675757\pi$
$524$	−8630.70			−0.719530
$525$	1550.10	+	5030.48i	0.128861	+	0.418187i
$526$		−	15969.4i		−	1.32376i
$527$	−1611.51			−0.133204
$528$	1222.29	+	3966.63i	0.100745	+	0.326942i
$529$	−6831.15			−0.561449
$530$	877.018			0.0718778
$531$	11734.8	−	3466.50i	0.959031	−	0.283301i
$532$	1588.92			0.129489
$533$	5906.42			0.479991
$534$	−2498.50	−	8108.25i	−0.202473	−	0.657076i
$535$	−468.112			−0.0378285
$536$		−	2125.99i		−	0.171323i
$537$	48.2645	+	156.630i	0.00387852	+	0.0125868i
$538$	−13092.3			−1.04916
$539$	−13791.0			−1.10208
$540$	353.740	−	442.788i	0.0281899	−	0.0352862i
$541$			22240.7i			1.76747i	0.467985	+	0.883736i	$0.344980\pi$
$541$			22240.7i			1.76747i	−0.467985	+	0.883736i	$0.655020\pi$
$542$	−8159.06			−0.646608
$543$	294.093	+	954.405i	0.0232426	+	0.0754280i
$544$		−	3554.07i		−	0.280109i
$545$	685.427			0.0538724
$546$	−3760.17	+	1158.67i	−0.294726	+	0.0908176i
$547$	−7506.72			−0.586772			−0.293386	−	0.955994i	$-0.594782\pi$
$547$	−7506.72			−0.586772			−0.293386	+	0.955994i	$0.594782\pi$
$548$		−	10588.8i		−	0.825422i
$549$	−8696.13	−	12770.7i	−0.676033	−	0.992790i
$550$	−12379.4			−0.959744
$551$			530.796i			0.0410393i
$552$	−894.186	−	2901.86i	−0.0689476	−	0.223752i
$553$	10650.6			0.819004
$554$	14953.5			1.14677
$555$	3.64801	+	11.8387i	0.000279008	+	0.000905450i
$556$	3916.71			0.298751
$557$		−	10739.4i		−	0.816954i	−0.912769	−	0.408477i	$-0.866060\pi$
$557$		−	10739.4i		−	0.816954i	0.912769	−	0.408477i	$-0.133940\pi$
$558$	440.998	+	647.629i	0.0334569	+	0.0491332i
$559$	−3844.86			−0.290913
$560$			132.029i			0.00996295i
$561$	−27534.6	+	8484.57i	−2.07221	+	0.638536i
$562$		−	17064.8i		−	1.28085i
$563$	−6687.65			−0.500623			−0.250312	−	0.968165i	$-0.580533\pi$
$563$	−6687.65			−0.500623			−0.250312	+	0.968165i	$0.580533\pi$
$564$	−241.539	−	783.853i	−0.0180330	−	0.0585216i
$565$		−	1911.62i		−	0.142341i
$566$		−	685.092i		−	0.0508774i
$567$	2182.61	−	5542.35i	0.161659	−	0.410506i
$568$		−	3930.35i		−	0.290341i
$569$	−2966.72			−0.218579			−0.109290	−	0.994010i	$-0.534858\pi$
$569$	−2966.72			−0.218579			−0.109290	+	0.994010i	$0.534858\pi$
$570$	487.596	−	150.249i	0.0358301	−	0.0110408i
$571$			6474.79i			0.474538i	0.971444	+	0.237269i	$0.0762524\pi$
$571$			6474.79i			0.474538i	−0.971444	+	0.237269i	$0.923748\pi$
$572$		−	9253.31i		−	0.676399i
$573$	4884.45	+	15851.2i	0.356109	+	1.15566i
$574$		−	2083.09i		−	0.151474i
$575$	9056.36			0.656828
$576$	−1428.30	+	972.592i	−0.103321	+	0.0703553i
$577$	−23956.5			−1.72846			−0.864232	−	0.503094i	$-0.832195\pi$
$577$	−23956.5			−1.72846			−0.864232	+	0.503094i	$0.832195\pi$
$578$	14844.8			1.06827
$579$	2466.27	+	8003.65i	0.177020	+	0.574474i
$580$	−44.1058			−0.00315758
$581$	−2638.25			−0.188387
$582$	−8481.57	+	2613.54i	−0.604077	+	0.186142i
$583$			21678.0i			1.53998i
$584$		−	6730.82i		−	0.476923i
$585$	−1044.33	+	711.128i	−0.0738080	+	0.0502590i
$586$		−	3681.48i		−	0.259523i
$587$	12951.6			0.910683			0.455342	−	0.890317i	$-0.349517\pi$
$587$	12951.6			0.910683			0.455342	+	0.890317i	$0.349517\pi$
$588$	−1690.74	−	5486.86i	−0.118580	−	0.384820i
$589$			705.383i			0.0493460i
$590$	−279.745	+	871.551i	−0.0195202	+	0.0608156i
$591$	11235.7	−	3462.21i	0.782024	−	0.240975i
$592$		−	37.7713i		−	0.00262228i
$593$			17844.9i			1.23576i	0.786274	+	0.617879i	$0.212008\pi$
$593$			17844.9i			1.23576i	−0.786274	+	0.617879i	$0.787992\pi$
$594$	10944.7	+	8743.68i	0.756008	+	0.603969i
$595$	−916.487			−0.0631467
$596$	5503.79			0.378261
$597$	−1003.84	−	3257.72i	−0.0688183	−	0.223333i
$598$			6769.42i			0.462913i
$599$		−	14323.7i		−	0.977046i	−0.872551	−	0.488523i	$-0.837536\pi$
$599$		−	14323.7i		−	0.977046i	0.872551	−	0.488523i	$-0.162464\pi$
$600$	−1517.67	−	4925.23i	−0.103265	−	0.335119i
$601$		−	22720.9i		−	1.54210i	−0.636773	−	0.771052i	$-0.719731\pi$
$601$		−	22720.9i		−	1.54210i	0.636773	−	0.771052i	$-0.280269\pi$
$602$			1356.01i			0.0918055i
$603$	−4038.52	−	5930.79i	−0.272739	−	0.400531i
$604$		−	9719.41i		−	0.654763i
$605$			1172.99i			0.0788248i
$606$	2247.61	+	7294.06i	0.150665	+	0.488945i
$607$	16617.8			1.11119			0.555597	−	0.831452i	$-0.312490\pi$
$607$	16617.8			1.11119			0.555597	+	0.831452i	$0.312490\pi$
$608$	−1555.67			−0.103768
$609$	−443.012	+	136.511i	−0.0294774	+	0.00908326i
$610$	1155.80			0.0767164
$611$			1828.56i			0.121073i
$612$	−6751.29	−	9914.63i	−0.445923	−	0.654861i
$613$			16136.1i			1.06318i	0.847002	+	0.531590i	$0.178405\pi$
$613$			16136.1i			1.06318i	−0.847002	+	0.531590i	$0.821595\pi$
$614$	18846.9			1.23876
$615$	−196.978	−	639.243i	−0.0129153	−	0.0419134i
$616$	−3263.47			−0.213456
$617$			34.7700i			0.00226870i	0.999999	+	0.00113435i	$0.000361075\pi$
$617$			34.7700i			0.00226870i	−0.999999	+	0.00113435i	$0.999639\pi$
$618$	12277.8	−	3783.31i	0.799166	−	0.246257i
$619$	−8493.40			−0.551500			−0.275750	−	0.961229i	$-0.588926\pi$
$619$	−8493.40			−0.551500			−0.275750	+	0.961229i	$0.588926\pi$
$620$	−58.6129			−0.00379670
$621$	−8006.82	−	6396.59i	−0.517395	−	0.413343i
$622$		−	8016.56i		−	0.516776i
$623$	6670.92			0.428996
$624$	3681.49	−	1134.43i	0.236182	−	0.0727778i
$625$	15243.6			0.975589
$626$		−	7936.03i		−	0.506689i
$627$	3713.83	+	12052.3i	0.236549	+	0.767661i
$628$		−	2877.58i		−	0.182847i
$629$	262.192			0.0166204
$630$	250.802	+	368.316i	0.0158606	+	0.0232922i
$631$	18884.0			1.19138			0.595690	−	0.803214i	$-0.296879\pi$
$631$	18884.0			1.19138			0.595690	+	0.803214i	$0.296879\pi$
$632$	−10427.8			−0.656319
$633$	7863.58	−	2423.11i	0.493759	−	0.152148i
$634$			13741.9i			0.860824i
$635$			687.969i			0.0429941i
$636$	−8624.73	+	2657.65i	−0.537725	+	0.165696i
$637$			12799.7i			0.796141i
$638$		−	1090.20i		−	0.0676511i
$639$	−7466.07	−	10964.3i	−0.462212	−	0.678782i
$640$		−	129.267i		−	0.00798394i
$641$		−	17284.6i		−	1.06506i	−0.846412	−	0.532529i	$-0.821242\pi$
$641$		−	17284.6i		−	1.06506i	0.846412	−	0.532529i	$-0.178758\pi$
$642$	4603.48	−	1418.53i	0.282998	−	0.0872039i
$643$	−2903.86			−0.178098			−0.0890491	−	0.996027i	$-0.528383\pi$
$643$	−2903.86			−0.178098			−0.0890491	+	0.996027i	$0.528383\pi$
$644$	2387.45			0.146085
$645$	128.226	+	416.124i	0.00782771	+	0.0254029i
$646$		−	10798.8i		−	0.657697i
$647$			3386.22i			0.205759i	0.994694	+	0.102879i	$0.0328056\pi$
$647$			3386.22i			0.205759i	−0.994694	+	0.102879i	$0.967194\pi$
$648$	−2136.94	+	5426.39i	−0.129548	+	0.328964i
$649$	−21542.8	−	6914.68i	−1.30297	−	0.418220i
$650$			11489.5i			0.693317i
$651$	−588.726	+	181.412i	−0.0354439	+	0.0109218i
$652$	6766.56			0.406440
$653$			20860.8i			1.25015i	0.780566	+	0.625073i	$0.214931\pi$
$653$			20860.8i			1.25015i	−0.780566	+	0.625073i	$0.785069\pi$
$654$	−6740.60	+	2077.07i	−0.403025	+	0.124189i
$655$		−	2179.03i		−	0.129987i
$656$			2039.50i			0.121386i
$657$	−12785.8	−	18776.7i	−0.759242	−	1.11499i
$658$	644.901			0.0382080
$659$	−18698.3			−1.10529			−0.552643	−	0.833418i	$-0.686381\pi$
$659$	−18698.3			−1.10529			−0.552643	+	0.833418i	$0.686381\pi$
$660$	−1001.47	+	308.597i	−0.0590641	+	0.0182002i
$661$	5288.74			0.311207			0.155604	−	0.987820i	$-0.450268\pi$
$661$	5288.74			0.311207			0.155604	+	0.987820i	$0.450268\pi$
$662$	−6858.28			−0.402651
$663$	7874.67	+	25555.3i	0.461277	+	1.49696i
$664$	2583.05			0.150966
$665$			401.161i			0.0233930i
$666$	−71.7502	−	105.369i	−0.00417457	−	0.00613058i
$667$			797.554i			0.0462990i
$668$		−	8091.43i		−	0.468663i
$669$	1171.80	+	3802.78i	0.0677196	+	0.219767i
$670$	536.759			0.0309505
$671$			28568.9i			1.64365i
$672$	−400.091	−	1298.40i	−0.0229670	−	0.0745338i
$673$		−	8135.62i		−	0.465981i	−0.972479	−	0.232991i	$-0.925149\pi$
$673$		−	8135.62i		−	0.465981i	0.972479	−	0.232991i	$-0.0748511\pi$
$674$			10004.0i			0.571721i
$675$	−13589.7	−	10856.7i	−0.774916	−	0.619075i
$676$	199.851			0.0113707
$677$		−	3656.45i		−	0.207576i	−0.994599	−	0.103788i	$-0.966904\pi$
$677$		−	3656.45i		−	0.207576i	0.994599	−	0.103788i	$-0.0330963\pi$
$678$	5792.84	+	18799.2i	0.328131	+	1.06487i
$679$		−	6978.06i		−	0.394394i
$680$	897.312			0.0506035
$681$	−5752.50	−	18668.3i	−0.323695	−	1.05047i
$682$		−	1448.78i		−	0.0813443i
$683$	−4111.81			−0.230357			−0.115179	−	0.993345i	$-0.536744\pi$
$683$	−4111.81			−0.230357			−0.115179	+	0.993345i	$0.536744\pi$
$684$	−4339.79	+	2955.15i	−0.242597	+	0.165194i
$685$	2673.40			0.149117
$686$	10119.5			0.563213
$687$	14805.5	−	4562.21i	0.822220	−	0.253361i
$688$		−	1327.64i		−	0.0735696i
$689$	20119.7			1.11248
$690$	732.645	−	225.759i	0.0404222	−	0.0124558i
$691$		−	21229.5i		−	1.16875i	−0.811482	−	0.584377i	$-0.801339\pi$
$691$		−	21229.5i		−	1.16875i	0.811482	−	0.584377i	$-0.198661\pi$
$692$	9780.02			0.537255
$693$	−9103.97	+	6199.27i	−0.499035	+	0.339814i
$694$	−22826.2			−1.24852
$695$			988.869i			0.0539711i
$696$	433.743	−	133.655i	0.0236221	−	0.00727899i
$697$	−14157.3			−0.769363
$698$			24443.2i			1.32549i
$699$	−2904.73	−	9426.58i	−0.157177	−	0.510080i
$700$	4052.14			0.218795
$701$	11278.6			0.607683			0.303841	−	0.952723i	$-0.401731\pi$
$701$	11278.6			0.607683			0.303841	+	0.952723i	$0.401731\pi$
$702$	8115.15	−	10158.0i	0.436306	−	0.546138i
$703$		−	114.765i		−	0.00615713i
$704$	3195.20			0.171056
$705$	197.903	−	60.9823i	0.0105723	−	0.00325777i
$706$	5424.90			0.289191
$707$	−6001.06			−0.319226
$708$	109.972	−	9418.69i	0.00583759	−	0.499966i
$709$	1658.17			0.0878334			0.0439167	−	0.999035i	$-0.486016\pi$
$709$	1658.17			0.0878334			0.0439167	+	0.999035i	$0.486016\pi$
$710$	992.313			0.0524519
$711$	−29089.8	+	19808.5i	−1.53439	+	1.04483i
$712$	−6531.35			−0.343782
$713$			1059.88i			0.0556703i
$714$	9012.87	−	2777.25i	0.472407	−	0.145569i
$715$	2336.22			0.122196
$716$	126.169			0.00658540
$717$	16115.4	−	4965.83i	0.839385	−	0.258650i
$718$		−	8452.40i		−	0.439332i
$719$	−25343.1			−1.31452			−0.657258	−	0.753666i	$-0.728284\pi$
$719$	−25343.1			−1.31452			−0.657258	+	0.753666i	$0.728284\pi$
$720$	−245.554	−	360.610i	−0.0127101	−	0.0186655i
$721$			10101.3i			0.521765i
$722$	8991.20			0.463460
$723$	8395.36	+	27245.0i	0.431849	+	1.40146i
$724$	768.791			0.0394639
$725$			1353.66i			0.0693432i
$726$	−3554.55	−	11535.4i	−0.181711	−	0.589696i
$727$	20731.8			1.05763			0.528817	−	0.848736i	$-0.322636\pi$
$727$	20731.8			1.05763			0.528817	+	0.848736i	$0.322636\pi$
$728$			3028.88i			0.154200i
$729$	4346.60	+	19197.1i	0.220830	+	0.975312i
$730$	1699.36			0.0861591
$731$	9215.89			0.466295
$732$	−11366.3	+	3502.45i	−0.573923	+	0.176850i
$733$	−9104.57			−0.458779			−0.229390	−	0.973335i	$-0.573673\pi$
$733$	−9104.57			−0.458779			−0.229390	+	0.973335i	$0.573673\pi$
$734$		−	19102.7i		−	0.960616i
$735$	1385.29	−	426.867i	0.0695201	−	0.0214221i
$736$	−2337.50			−0.117067
$737$			13267.5i			0.663114i
$738$	3874.23	+	5689.51i	0.193242	+	0.283785i
$739$		−	20947.3i		−	1.04270i	−0.853342	−	0.521352i	$-0.825428\pi$
$739$		−	20947.3i		−	1.04270i	0.853342	−	0.521352i	$-0.174572\pi$
$740$	9.53630			0.000473731
$741$	11185.9	−	3446.87i	0.554556	−	0.170882i
$742$		−	7095.84i		−	0.351074i
$743$			31792.4i			1.56978i	0.619632	+	0.784892i	$0.287282\pi$
$743$			31792.4i			1.56978i	−0.619632	+	0.784892i	$0.712718\pi$
$744$	576.409	−	177.616i	0.0284034	−	0.00875231i
$745$			1389.56i			0.0683352i
$746$	4056.48			0.199086
$747$	7205.81	−	4906.74i	0.352941	−	0.240332i
$748$			22179.6i			1.08418i
$749$			3787.43i			0.184766i
$750$	2497.22	−	769.499i	0.121581	−	0.0374642i
$751$		−	16149.0i		−	0.784669i	−0.919823	−	0.392335i	$-0.871668\pi$
$751$		−	16149.0i		−	0.784669i	0.919823	−	0.392335i	$-0.128332\pi$
$752$	−631.408			−0.0306185
$753$	7217.75	−	2224.10i	0.349308	−	0.107637i
$754$	−1011.83			−0.0488710
$755$	2453.90			0.118287
$756$	−3582.54	−	2862.06i	−0.172349	−	0.137688i
$757$	11404.8			0.547573			0.273787	−	0.961790i	$-0.411724\pi$
$757$	11404.8			0.547573			0.273787	+	0.961790i	$0.411724\pi$
$758$	9131.23			0.437548
$759$	5580.27	+	18109.4i	0.266866	+	0.866046i
$760$		−	392.768i		−	0.0187463i
$761$		−	18057.8i		−	0.860177i	−0.902787	−	0.430089i	$-0.858482\pi$
$761$		−	18057.8i		−	0.860177i	0.902787	−	0.430089i	$-0.141518\pi$
$762$	−2084.77	−	6765.60i	−0.0991119	−	0.321643i
$763$		−	5545.71i		−	0.263130i
$764$	12768.5			0.604643
$765$	2503.19	−	1704.53i	0.118305	−	0.0805586i
$766$			15860.5i			0.748123i
$767$	−6417.63	+	19994.3i	−0.302121	+	0.941266i
$768$	391.720	+	1271.23i	0.0184049	+	0.0597286i
$769$			22776.2i			1.06805i	0.845469	+	0.534025i	$0.179321\pi$
$769$			22776.2i			1.06805i	−0.845469	+	0.534025i	$0.820679\pi$
$770$		−	823.944i		−	0.0385622i
$771$	10653.4	−	3282.78i	0.497632	−	0.153342i
$772$	6447.09			0.300565
$773$	34122.2			1.58770			0.793849	−	0.608115i	$-0.208074\pi$
$773$	34122.2			1.58770			0.793849	+	0.608115i	$0.208074\pi$
$774$	−2521.98	−	3703.66i	−0.117120	−	0.171997i
$775$			1798.90i			0.0833788i
$776$			6832.07i			0.316053i
$777$	95.7854	−	29.5156i	0.00442250	−	0.00136276i
$778$			19905.2i			0.917269i
$779$			6196.88i			0.285014i
$780$	286.413	+	929.483i	0.0131477	+	0.0426677i
$781$			24527.8i			1.12378i
$782$		−	16225.9i		−	0.741990i
$783$	956.104	−	1196.79i	0.0436378	−	0.0546228i
$784$	−4419.77			−0.201338
$785$	726.515			0.0330324
$786$	6603.17	+	21428.9i	0.299653	+	0.972449i
$787$	−39898.2			−1.80714			−0.903569	−	0.428443i	$-0.859062\pi$
$787$	−39898.2			−1.80714			−0.903569	+	0.428443i	$0.859062\pi$
$788$		−	9050.59i		−	0.409155i
$789$	−39649.9	+	12217.8i	−1.78907	+	0.551288i
$790$		−	2632.74i		−	0.118568i
$791$	−15466.7			−0.695237
$792$	8913.49	−	6069.57i	0.399908	−	0.272314i
$793$	26515.2			1.18737
$794$		−	1282.05i		−	0.0573025i
$795$	−670.988	−	2177.52i	−0.0299340	−	0.0971432i
$796$	−2624.15			−0.116848
$797$	17348.5			0.771036			0.385518	−	0.922700i	$-0.374023\pi$
$797$	17348.5			0.771036			0.385518	+	0.922700i	$0.374023\pi$
$798$	−1215.65	−	3945.08i	−0.0539266	−	0.175005i
$799$		−	4382.95i		−	0.194065i
$800$	−3967.36			−0.175334
$801$	−18220.2	+	12406.9i	−0.803719	+	0.547286i
$802$	−6736.46			−0.296599
$803$			42004.5i			1.84596i
$804$	−5278.57	+	1626.55i	−0.231543	+	0.0713484i
$805$			602.770i			0.0263911i
$806$	−1344.64			−0.0587629
$807$	10016.6	+	32506.5i	0.436930	+	1.41795i
$808$	5875.50			0.255816
$809$	−3866.13			−0.168017			−0.0840085	−	0.996465i	$-0.526772\pi$
$809$	−3866.13			−0.168017			−0.0840085	+	0.996465i	$0.526772\pi$
$810$	−1370.02	−	539.523i	−0.0594293	−	0.0234036i
$811$			4702.65i			0.203616i	0.994804	+	0.101808i	$0.0324627\pi$
$811$			4702.65i			0.203616i	−0.994804	+	0.101808i	$0.967537\pi$
$812$			356.855i			0.0154226i
$813$	6242.33	+	20257.9i	0.269284	+	0.873894i
$814$			235.716i			0.0101497i
$815$			1708.38i			0.0734258i
$816$	−8824.31	+	2719.15i	−0.378569	+	0.116653i
$817$		−	4033.94i		−	0.172741i
$818$			29058.1i			1.24205i
$819$	5753.65	+	8449.54i	0.245481	+	0.360501i
$820$	−514.922			−0.0219291
$821$	−22245.1			−0.945627			−0.472813	−	0.881163i	$-0.656762\pi$
$821$	−22245.1			−0.945627			−0.472813	+	0.881163i	$0.656762\pi$
$822$	−26290.6	+	8101.27i	−1.11556	+	0.343752i
$823$			8210.19i			0.347739i	0.984769	+	0.173869i	$0.0556271\pi$
$823$			8210.19i			0.347739i	−0.984769	+	0.173869i	$0.944373\pi$
$824$		−	9889.98i		−	0.418124i
$825$	9471.22	+	30736.5i	0.399691	+	1.29710i
$826$	7051.61	+	2263.38i	0.297042	+	0.0953427i
$827$		−	43731.6i		−	1.83881i	−0.393311	−	0.919405i	$-0.628671\pi$
$827$		−	43731.6i		−	1.83881i	0.393311	−	0.919405i	$-0.371329\pi$
$828$	−6520.82	+	4440.30i	−0.273689	+	0.186366i
$829$	−25521.4			−1.06923			−0.534616	−	0.845095i	$-0.679544\pi$
$829$	−25521.4			−1.06923			−0.534616	+	0.845095i	$0.679544\pi$
$830$			652.154i			0.0272730i
$831$	−11440.6	−	37127.6i	−0.477581	−	1.54987i
$832$		−	2965.51i		−	0.123570i
$833$		−	30680.0i		−	1.27611i
$834$	−2996.59	−	9724.69i	−0.124417	−	0.403763i
$835$	2042.88			0.0846668
$836$	9708.37			0.401640
$837$	1270.58	−	1590.43i	0.0524704	−	0.0656789i
$838$	−20876.9			−0.860596
$839$	−35062.2			−1.44277			−0.721384	−	0.692535i	$-0.756494\pi$
$839$	−35062.2			−1.44277			−0.721384	+	0.692535i	$0.756494\pi$
$840$	327.812	−	101.013i	0.0134650	−	0.00414913i
$841$	24269.8			0.995112
$842$			17897.1i			0.732513i
$843$	−42369.8	+	13055.9i	−1.73107	+	0.533417i
$844$		−	6334.26i		−	0.258334i
$845$			50.4573i			0.00205418i
$846$	−1761.41	+	1199.42i	−0.0715822	+	0.0487433i
$847$	9490.56			0.385005
$848$			6947.38i			0.281337i
$849$	−1701.00	+	524.150i	−0.0687610	+	0.0211882i
$850$		−	27539.6i		−	1.11130i
$851$		−	172.442i		−	0.00694624i
$852$	−9758.56	+	3007.03i	−0.392398	+	0.120914i
$853$	30925.2			1.24134			0.620668	−	0.784074i	$-0.286862\pi$
$853$	30925.2			1.24134			0.620668	+	0.784074i	$0.286862\pi$
$854$		−	9351.44i		−	0.374707i
$855$	−746.099	−	1095.69i	−0.0298433	−	0.0438265i
$856$		−	3708.19i		−	0.148065i
$857$	24736.5			0.985979			0.492989	−	0.870035i	$-0.335904\pi$
$857$	24736.5			0.985979			0.492989	+	0.870035i	$0.335904\pi$
$858$	−22974.8	+	7079.52i	−0.914157	+	0.281691i
$859$		−	3832.38i		−	0.152223i	−0.997099	−	0.0761113i	$-0.975750\pi$
$859$		−	3832.38i		−	0.152223i	0.997099	−	0.0761113i	$-0.0242504\pi$
$860$	335.195			0.0132908
$861$	−5172.04	+	1593.73i	−0.204718	+	0.0630825i
$862$	27764.2			1.09705
$863$	22189.6			0.875251			0.437626	−	0.899157i	$-0.355819\pi$
$863$	22189.6			0.875251			0.437626	+	0.899157i	$0.355819\pi$
$864$	3507.59	+	2802.18i	0.138114	+	0.110338i
$865$			2469.20i			0.0970583i
$866$	7870.27			0.308825
$867$	−11357.4	−	36857.6i	−0.444888	−	1.44377i
$868$			474.230i			0.0185442i
$869$	65075.6			2.54032
$870$	33.7444	+	109.509i	0.00131499	+	0.00426748i
$871$	12313.8			0.479032
$872$			5429.68i			0.210862i
$873$	12978.1	+	19059.1i	0.503143	+	0.738892i
$874$	−7102.32			−0.274874
$875$			2054.54i			0.0793785i
$876$	−16711.8	+	5149.61i	−0.644564	+	0.198618i
$877$	28130.4			1.08312			0.541560	−	0.840662i	$-0.317834\pi$
$877$	28130.4			1.08312			0.541560	+	0.840662i	$0.317834\pi$
$878$	14848.6			0.570748
$879$	−9140.65	+	2816.62i	−0.350747	+	0.108080i
$880$			806.705i			0.0309023i
$881$	−25813.2			−0.987137			−0.493569	−	0.869707i	$-0.664308\pi$
$881$	−25813.2			−0.987137			−0.493569	+	0.869707i	$0.664308\pi$
$882$	−12329.6	+	8395.76i	−0.470703	+	0.320522i
$883$	−20038.4			−0.763699			−0.381850	−	0.924224i	$-0.624713\pi$
$883$	−20038.4			−0.763699			−0.381850	+	0.924224i	$0.624713\pi$
$884$	20585.2			0.783209
$885$	2377.98	+	27.7652i	0.0903218	+	0.00105460i
$886$	18166.1			0.688830
$887$	−50337.3			−1.90548			−0.952741	−	0.303783i	$-0.901750\pi$
$887$	−50337.3			−1.90548			−0.952741	+	0.303783i	$0.901750\pi$
$888$	−93.7814	+	28.8981i	−0.00354403	+	0.00109207i
$889$	5566.27			0.209996
$890$		−	1649.00i		−	0.0621062i
$891$	13335.8	−	33864.0i	0.501423	−	1.27327i
$892$	3063.21			0.114982
$893$	−1918.49			−0.0718922
$894$	−4210.83	−	13665.2i	−0.157529	−	0.511222i
$895$			31.8544i			0.00118969i
$896$	−1045.88			−0.0389961
$897$	16807.6	−	5179.14i	0.625629	−	0.192783i
$898$			1590.09i			0.0590890i
$899$	−158.422			−0.00587726
$900$	−11067.6	+	7536.38i	−0.409910	+	0.279125i
$901$	−48225.6			−1.78316
$902$		−	12727.8i		−	0.469831i
$903$	3366.81	−	1037.46i	0.124076	−	0.0382330i
$904$	15143.1			0.557138
$905$			194.100i			0.00712939i
$906$	−24132.0	+	7436.11i	−0.884916	+	0.272680i
$907$	18265.9			0.668697			0.334349	−	0.942449i	$-0.391484\pi$
$907$	18265.9			0.668697			0.334349	+	0.942449i	$0.391484\pi$
$908$	−15037.7			−0.549606
$909$	16390.6	−	11161.1i	0.598067	−	0.407249i
$910$	−764.715			−0.0278572
$911$		−	17760.3i		−	0.645910i	−0.946414	−	0.322955i	$-0.895324\pi$
$911$		−	17760.3i		−	0.645910i	0.946414	−	0.322955i	$-0.104676\pi$
$912$	1190.21	+	3862.54i	0.0432148	+	0.140243i
$913$	−16119.8			−0.584324
$914$			15911.0i			0.575810i
$915$	−884.279	−	2869.71i	−0.0319490	−	0.103683i
$916$		−	11926.1i		−	0.430185i
$917$	−17630.3			−0.634899
$918$	−19451.5	+	24348.1i	−0.699341	+	0.875388i
$919$		−	28224.9i		−	1.01312i	−0.862206	−	0.506558i	$-0.830917\pi$
$919$		−	28224.9i		−	1.01312i	0.862206	−	0.506558i	$-0.169083\pi$
$920$		−	590.159i		−	0.0211489i
$921$	−14419.3	−	46794.4i	−0.515889	−	1.67419i
$922$			20902.5i			0.746624i
$923$	22764.7			0.811818
$924$	2496.82	+	8102.79i	0.0888952	+	0.288487i
$925$		−	292.681i		−	0.0104036i
$926$		−	36724.1i		−	1.30327i
$927$	−18786.9	−	27589.6i	−0.665635	−	0.977521i
$928$		−	349.388i		−	0.0123591i
$929$	−23341.7			−0.824343			−0.412172	−	0.911106i	$-0.635230\pi$
$929$	−23341.7			−0.824343			−0.412172	+	0.911106i	$0.635230\pi$
$930$	44.8435	+	145.528i	0.00158116	+	0.00513125i
$931$	−13429.1			−0.472741
$932$	−7593.29			−0.266874
$933$	−19904.1	+	6133.30i	−0.698425	+	0.215215i
$934$	1501.11			0.0525887
$935$	−5599.78			−0.195864
$936$	−5633.27	−	8272.75i	−0.196719	−	0.288893i
$937$			1668.62i			0.0581766i	0.999577	+	0.0290883i	$0.00926041\pi$
$937$			1668.62i			0.0581766i	−0.999577	+	0.0290883i	$0.990740\pi$
$938$		−	4342.85i		−	0.151172i
$939$	−19704.2	+	6071.69i	−0.684793	+	0.211014i
$940$		−	159.414i		−	0.00553141i
$941$	−16750.9			−0.580303			−0.290152	−	0.956981i	$-0.593706\pi$
$941$	−16750.9			−0.580303			−0.290152	+	0.956981i	$0.593706\pi$
$942$	−7144.66	+	2201.57i	−0.247118	+	0.0761477i
$943$			9311.21i			0.321543i
$944$	−6904.08	−	2216.03i	−0.238039	−	0.0764041i
$945$	722.598	−	904.500i	0.0248742	−	0.0311358i
$946$			8285.30i			0.284755i
$947$			3310.46i			0.113596i	0.998386	+	0.0567981i	$0.0180891\pi$
$947$			3310.46i			0.113596i	−0.998386	+	0.0567981i	$0.981911\pi$
$948$	7978.06	+	25890.8i	0.273328	+	0.887019i
$949$	38985.0			1.33352
$950$	−12054.5			−0.411685
$951$	34119.5	−	10513.7i	1.16341	−	0.358496i
$952$		−	7260.04i		−	0.247163i
$953$		−	21992.9i		−	0.747557i	−0.927518	−	0.373778i	$-0.878062\pi$
$953$		−	21992.9i		−	0.747557i	0.927518	−	0.373778i	$-0.121938\pi$
$954$	13197.2	+	19380.8i	0.447878	+	0.657732i
$955$			3223.71i			0.109232i
$956$		−	12981.2i		−	0.439166i
$957$	−2706.83	+	834.089i	−0.0914308	+	0.0281737i
$958$			21181.8i			0.714355i
$959$		−	21630.2i		−	0.728336i
$960$	−320.953	+	98.8994i	−0.0107903	+	0.00332496i
$961$	29580.5			0.992933
$962$	218.772			0.00733212
$963$	−7044.05	−	10344.6i	−0.235713	−	0.346157i
$964$	21946.4			0.733242
$965$			1627.73i			0.0542988i
$966$	−1826.59	−	5927.74i	−0.0608380	−	0.197435i
$967$			6570.37i			0.218499i	0.994014	+	0.109250i	$0.0348448\pi$
$967$			6570.37i			0.218499i	−0.994014	+	0.109250i	$0.965155\pi$
$968$	−9291.99			−0.308529
$969$	−26812.0	+	8261.92i	−0.888881	+	0.273902i
$970$	−1724.92			−0.0570968
$971$		−	20689.0i		−	0.683772i	−0.939741	−	0.341886i	$-0.888934\pi$
$971$		−	20689.0i		−	0.683772i	0.939741	−	0.341886i	$-0.111066\pi$
$972$	15108.0	+	1154.14i	0.498547	+	0.0380854i
$973$	8000.81			0.263612
$974$	−29654.9			−0.975571
$975$	28527.0	−	8790.39i	0.937021	−	0.288736i
$976$			9155.79i			0.300276i
$977$	−17471.1			−0.572110			−0.286055	−	0.958213i	$-0.592344\pi$
$977$	−17471.1			−0.572110			−0.286055	+	0.958213i	$0.592344\pi$
$978$	−5176.95	−	16800.5i	−0.169265	−	0.549306i
$979$	40759.6			1.33063
$980$		−	1115.88i		−	0.0363729i
$981$	10314.2	+	15146.9i	0.335684	+	0.492970i
$982$			25192.4i			0.818658i
$983$	−15314.9			−0.496918			−0.248459	−	0.968642i	$-0.579924\pi$
$983$	−15314.9			−0.496918			−0.248459	+	0.968642i	$0.579924\pi$
$984$	5063.83	−	1560.38i	0.164054	−	0.0505520i
$985$	2285.04			0.0739162
$986$	2425.30			0.0783338
$987$	−493.400	−	1601.21i	−0.0159120	−	0.0516383i
$988$		−	9010.49i		−	0.290144i
$989$		−	6061.26i		−	0.194880i
$990$	1532.41	+	2250.43i	0.0491952	+	0.0722458i
$991$			31292.6i			1.00307i	0.865137	+	0.501536i	$0.167231\pi$
$991$			31292.6i			1.00307i	−0.865137	+	0.501536i	$0.832769\pi$
$992$		−	464.308i		−	0.0148607i
$993$	5247.13	+	17028.2i	0.167686	+	0.544184i
$994$		−	8028.68i		−	0.256192i
$995$		−	662.531i		−	0.0211092i
$996$	−1976.24	−	6413.38i	−0.0628709	−	0.204032i
$997$	50.9131			0.00161728			0.000808642	−	1.00000i	$-0.499743\pi$
$997$	50.9131			0.00161728			0.000808642		1.00000i	$0.499743\pi$
$998$	−14847.1			−0.470918
$999$	−206.723	+	258.762i	−0.00654698	+	0.00819507i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.4.c.a.353.18	yes	30
3.2	odd	2		354.4.c.b.353.17	yes	30
59.58	odd	2		354.4.c.b.353.18	yes	30
177.176	even	2	inner	354.4.c.a.353.17	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.4.c.a.353.17	✓	30	177.176	even	2	inner
354.4.c.a.353.18	yes	30	1.1	even	1	trivial
354.4.c.b.353.17	yes	30	3.2	odd	2
354.4.c.b.353.18	yes	30	59.58	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	354.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +(1.53016 + 4.96574i) q^{3} +4.00000 q^{4} +1.00990i q^{5} +(-3.06032 - 9.93149i) q^{6} +8.17095 q^{7} -8.00000 q^{8} +(-22.3172 + 15.1967i) q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +(1.53016 + 4.96574i) q^{3} +4.00000 q^{4} +1.00990i q^{5} +(-3.06032 - 9.93149i) q^{6} +8.17095 q^{7} -8.00000 q^{8} +(-22.3172 + 15.1967i) q^{9} -2.01980i q^{10} +49.9249 q^{11} +(6.12063 + 19.8630i) q^{12} -46.3361i q^{13} -16.3419 q^{14} +(-5.01489 + 1.54530i) q^{15} +16.0000 q^{16} +111.065i q^{17} +(44.6345 - 30.3935i) q^{18} +48.6148 q^{19} +4.03959i q^{20} +(12.5028 + 40.5749i) q^{21} -99.8499 q^{22} +73.0469 q^{23} +(-12.2413 - 39.7260i) q^{24} +123.980 q^{25} +92.6723i q^{26} +(-109.612 - 87.5683i) q^{27} +32.6838 q^{28} +10.9184i q^{29} +(10.0298 - 3.09061i) q^{30} +14.5096i q^{31} -32.0000 q^{32} +(76.3930 + 247.914i) q^{33} -222.129i q^{34} +8.25183i q^{35} +(-89.2689 + 60.7870i) q^{36} -2.36071i q^{37} -97.2296 q^{38} +(230.093 - 70.9016i) q^{39} -8.07918i q^{40} +127.469i q^{41} +(-25.0057 - 81.1497i) q^{42} -82.9776i q^{43} +199.700 q^{44} +(-15.3472 - 22.5381i) q^{45} -146.094 q^{46} -39.4630 q^{47} +(24.4825 + 79.4519i) q^{48} -276.236 q^{49} -247.960 q^{50} +(-551.519 + 169.947i) q^{51} -185.345i q^{52} +434.211i q^{53} +(219.224 + 175.137i) q^{54} +50.4191i q^{55} -65.3676 q^{56} +(74.3883 + 241.409i) q^{57} -21.8368i q^{58} +(-431.505 - 138.502i) q^{59} +(-20.0596 + 6.18121i) q^{60} +572.237i q^{61} -29.0192i q^{62} +(-182.353 + 124.172i) q^{63} +64.0000 q^{64} +46.7947 q^{65} +(-152.786 - 495.829i) q^{66} +265.749i q^{67} +444.259i q^{68} +(111.773 + 362.732i) q^{69} -16.5037i q^{70} +491.294i q^{71} +(178.538 - 121.574i) q^{72} +841.352i q^{73} +4.72142i q^{74} +(189.709 + 615.654i) q^{75} +194.459 q^{76} +407.934 q^{77} +(-460.187 + 141.803i) q^{78} +1303.47 q^{79} +16.1584i q^{80} +(267.118 - 678.299i) q^{81} -254.938i q^{82} -322.881 q^{83} +(50.0114 + 162.299i) q^{84} -112.164 q^{85} +165.955i q^{86} +(-54.2179 + 16.7069i) q^{87} -399.399 q^{88} +816.419 q^{89} +(30.6943 + 45.0762i) q^{90} -378.610i q^{91} +292.188 q^{92} +(-72.0511 + 22.2020i) q^{93} +78.9260 q^{94} +49.0960i q^{95} +(-48.9651 - 158.904i) q^{96} -854.008i q^{97} +552.471 q^{98} +(-1114.19 + 758.697i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 60 q^{2} + 5 q^{3} + 120 q^{4} - 10 q^{6} + 6 q^{7} - 240 q^{8} + 27 q^{9}+O(q^{10}) \) 30 * q - 60 * q^2 + 5 * q^3 + 120 * q^4 - 10 * q^6 + 6 * q^7 - 240 * q^8 + 27 * q^9	\( 30 q - 60 q^{2} + 5 q^{3} + 120 q^{4} - 10 q^{6} + 6 q^{7} - 240 q^{8} + 27 q^{9} - 60 q^{11} + 20 q^{12} - 12 q^{14} + 20 q^{15} + 480 q^{16} - 54 q^{18} + 90 q^{19} + 132 q^{21} + 120 q^{22} + 24 q^{23} - 40 q^{24} - 1080 q^{25} - 55 q^{27} + 24 q^{28} - 40 q^{30} - 960 q^{32} + 336 q^{33} + 108 q^{36} - 180 q^{38} + 652 q^{39} - 264 q^{42} - 240 q^{44} - 878 q^{45} - 48 q^{46} + 792 q^{47} + 80 q^{48} + 2016 q^{49} + 2160 q^{50} + 650 q^{51} + 110 q^{54} - 48 q^{56} + 846 q^{57} - 480 q^{59} + 80 q^{60} + 887 q^{63} + 1920 q^{64} - 1416 q^{65} - 672 q^{66} - 590 q^{69} - 216 q^{72} - 952 q^{75} + 360 q^{76} + 864 q^{77} - 1304 q^{78} + 738 q^{79} - 1217 q^{81} + 876 q^{83} + 528 q^{84} + 1176 q^{85} + 534 q^{87} + 480 q^{88} - 300 q^{89} + 1756 q^{90} + 96 q^{92} + 1684 q^{93} - 1584 q^{94} - 160 q^{96} - 4032 q^{98} + 730 q^{99}+O(q^{100}) \) 30 * q - 60 * q^2 + 5 * q^3 + 120 * q^4 - 10 * q^6 + 6 * q^7 - 240 * q^8 + 27 * q^9 - 60 * q^11 + 20 * q^12 - 12 * q^14 + 20 * q^15 + 480 * q^16 - 54 * q^18 + 90 * q^19 + 132 * q^21 + 120 * q^22 + 24 * q^23 - 40 * q^24 - 1080 * q^25 - 55 * q^27 + 24 * q^28 - 40 * q^30 - 960 * q^32 + 336 * q^33 + 108 * q^36 - 180 * q^38 + 652 * q^39 - 264 * q^42 - 240 * q^44 - 878 * q^45 - 48 * q^46 + 792 * q^47 + 80 * q^48 + 2016 * q^49 + 2160 * q^50 + 650 * q^51 + 110 * q^54 - 48 * q^56 + 846 * q^57 - 480 * q^59 + 80 * q^60 + 887 * q^63 + 1920 * q^64 - 1416 * q^65 - 672 * q^66 - 590 * q^69 - 216 * q^72 - 952 * q^75 + 360 * q^76 + 864 * q^77 - 1304 * q^78 + 738 * q^79 - 1217 * q^81 + 876 * q^83 + 528 * q^84 + 1176 * q^85 + 534 * q^87 + 480 * q^88 - 300 * q^89 + 1756 * q^90 + 96 * q^92 + 1684 * q^93 - 1584 * q^94 - 160 * q^96 - 4032 * q^98 + 730 * q^99

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