LMFDB - Embedded newform 48.6.j.a.13.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,6,Mod(13,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("48.13");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	48.j (of order $4$, degree $2$, 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:	$7.69842335102$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.19
Character	$\chi$	$=$	48.13
Dual form			48.6.j.a.37.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.58787 - 0.880730i) q^{2} +(-6.36396 - 6.36396i) q^{3} +(30.4486 - 9.84281i) q^{4} +(3.64660 - 3.64660i) q^{5} +(-41.1659 - 29.9561i) q^{6} -162.720i q^{7} +(161.474 - 81.8174i) q^{8} +81.0000i q^{9} +O(q^{10})$	\(q+(5.58787 - 0.880730i) q^{2} +(-6.36396 - 6.36396i) q^{3} +(30.4486 - 9.84281i) q^{4} +(3.64660 - 3.64660i) q^{5} +(-41.1659 - 29.9561i) q^{6} -162.720i q^{7} +(161.474 - 81.8174i) q^{8} +81.0000i q^{9} +(17.1651 - 23.5884i) q^{10} +(195.997 - 195.997i) q^{11} +(-256.413 - 131.135i) q^{12} +(-264.994 - 264.994i) q^{13} +(-143.313 - 909.260i) q^{14} -46.4137 q^{15} +(830.238 - 599.400i) q^{16} -55.8881 q^{17} +(71.3391 + 452.618i) q^{18} +(693.638 + 693.638i) q^{19} +(75.1412 - 146.927i) q^{20} +(-1035.55 + 1035.55i) q^{21} +(922.588 - 1267.83i) q^{22} +2420.75i q^{23} +(-1548.30 - 506.933i) q^{24} +3098.40i q^{25} +(-1714.14 - 1247.36i) q^{26} +(515.481 - 515.481i) q^{27} +(-1601.63 - 4954.61i) q^{28} +(958.152 + 958.152i) q^{29} +(-259.354 + 40.8779i) q^{30} +5307.87 q^{31} +(4111.35 - 4080.59i) q^{32} -2494.64 q^{33} +(-312.295 + 49.2223i) q^{34} +(-593.376 - 593.376i) q^{35} +(797.268 + 2466.34i) q^{36} +(-9955.63 + 9955.63i) q^{37} +(4486.87 + 3265.05i) q^{38} +3372.82i q^{39} +(290.477 - 887.187i) q^{40} -2150.37i q^{41} +(-4874.46 + 6698.53i) q^{42} +(-12944.1 + 12944.1i) q^{43} +(4038.69 - 7897.02i) q^{44} +(295.375 + 295.375i) q^{45} +(2132.03 + 13526.9i) q^{46} +25084.5 q^{47} +(-9098.16 - 1469.04i) q^{48} -9670.91 q^{49} +(2728.86 + 17313.5i) q^{50} +(355.670 + 355.670i) q^{51} +(-10677.0 - 5460.42i) q^{52} +(5460.54 - 5460.54i) q^{53} +(2426.44 - 3334.44i) q^{54} -1429.45i q^{55} +(-13313.4 - 26275.1i) q^{56} -8828.57i q^{57} +(6197.90 + 4510.16i) q^{58} +(27193.7 - 27193.7i) q^{59} +(-1413.23 + 456.841i) q^{60} +(-40112.6 - 40112.6i) q^{61} +(29659.7 - 4674.80i) q^{62} +13180.3 q^{63} +(19379.8 - 26422.8i) q^{64} -1932.65 q^{65} +(-13939.7 + 2197.10i) q^{66} +(-559.172 - 559.172i) q^{67} +(-1701.72 + 550.096i) q^{68} +(15405.6 - 15405.6i) q^{69} +(-3838.31 - 2793.11i) q^{70} -52249.6i q^{71} +(6627.21 + 13079.4i) q^{72} +47518.6i q^{73} +(-46862.6 + 64399.0i) q^{74} +(19718.1 - 19718.1i) q^{75} +(27947.7 + 14293.0i) q^{76} +(-31892.8 - 31892.8i) q^{77} +(2970.54 + 18846.9i) q^{78} +61006.2 q^{79} +(841.774 - 5213.32i) q^{80} -6561.00 q^{81} +(-1893.90 - 12016.0i) q^{82} +(-18005.2 - 18005.2i) q^{83} +(-21338.3 + 41723.6i) q^{84} +(-203.802 + 203.802i) q^{85} +(-60929.7 + 83730.3i) q^{86} -12195.3i q^{87} +(15612.5 - 47684.5i) q^{88} +97236.7i q^{89} +(1910.66 + 1390.37i) q^{90} +(-43119.9 + 43119.9i) q^{91} +(23827.0 + 73708.7i) q^{92} +(-33779.1 - 33779.1i) q^{93} +(140169. - 22092.7i) q^{94} +5058.84 q^{95} +(-52133.2 - 195.799i) q^{96} -100552. q^{97} +(-54039.8 + 8517.46i) q^{98} +(15875.8 + 15875.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 44 q^{4} - 492 q^{8}+O(q^{10}) $ 40 * q + 44 * q^4 - 492 * q^8	\( 40 q + 44 q^{4} - 492 q^{8} + 968 q^{10} + 1208 q^{11} - 792 q^{12} + 324 q^{14} - 1800 q^{15} - 384 q^{16} - 324 q^{18} + 2360 q^{19} - 7600 q^{20} - 1024 q^{22} + 5220 q^{24} - 12980 q^{26} + 10472 q^{28} - 8144 q^{29} - 1368 q^{30} + 23064 q^{31} + 44160 q^{32} + 4864 q^{34} - 4776 q^{35} - 1620 q^{36} + 21296 q^{37} - 72088 q^{38} - 90864 q^{40} - 14220 q^{42} + 31416 q^{43} + 43768 q^{44} + 90664 q^{46} + 44784 q^{48} - 96040 q^{49} + 106212 q^{50} + 10440 q^{51} - 116432 q^{52} - 49456 q^{53} - 14580 q^{54} - 158592 q^{56} - 111472 q^{58} + 28960 q^{59} + 49464 q^{60} + 48080 q^{61} + 191100 q^{62} + 31752 q^{63} + 369032 q^{64} - 55376 q^{65} + 63720 q^{66} + 101488 q^{67} - 122336 q^{68} - 22320 q^{69} - 460192 q^{70} - 28836 q^{72} - 94996 q^{74} - 96624 q^{75} + 211304 q^{76} - 14896 q^{77} + 200124 q^{78} - 71960 q^{79} + 623368 q^{80} - 262440 q^{81} + 33880 q^{82} - 126440 q^{83} - 116856 q^{84} + 132400 q^{85} - 581168 q^{86} - 466400 q^{88} - 46008 q^{90} + 429496 q^{91} - 12752 q^{92} + 524120 q^{94} - 76848 q^{95} + 51840 q^{96} + 477736 q^{98} + 97848 q^{99}+O(q^{100}) \) 40 * q + 44 * q^4 - 492 * q^8 + 968 * q^10 + 1208 * q^11 - 792 * q^12 + 324 * q^14 - 1800 * q^15 - 384 * q^16 - 324 * q^18 + 2360 * q^19 - 7600 * q^20 - 1024 * q^22 + 5220 * q^24 - 12980 * q^26 + 10472 * q^28 - 8144 * q^29 - 1368 * q^30 + 23064 * q^31 + 44160 * q^32 + 4864 * q^34 - 4776 * q^35 - 1620 * q^36 + 21296 * q^37 - 72088 * q^38 - 90864 * q^40 - 14220 * q^42 + 31416 * q^43 + 43768 * q^44 + 90664 * q^46 + 44784 * q^48 - 96040 * q^49 + 106212 * q^50 + 10440 * q^51 - 116432 * q^52 - 49456 * q^53 - 14580 * q^54 - 158592 * q^56 - 111472 * q^58 + 28960 * q^59 + 49464 * q^60 + 48080 * q^61 + 191100 * q^62 + 31752 * q^63 + 369032 * q^64 - 55376 * q^65 + 63720 * q^66 + 101488 * q^67 - 122336 * q^68 - 22320 * q^69 - 460192 * q^70 - 28836 * q^72 - 94996 * q^74 - 96624 * q^75 + 211304 * q^76 - 14896 * q^77 + 200124 * q^78 - 71960 * q^79 + 623368 * q^80 - 262440 * q^81 + 33880 * q^82 - 126440 * q^83 - 116856 * q^84 + 132400 * q^85 - 581168 * q^86 - 466400 * q^88 - 46008 * q^90 + 429496 * q^91 - 12752 * q^92 + 524120 * q^94 - 76848 * q^95 + 51840 * q^96 + 477736 * q^98 + 97848 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	5.58787	−	0.880730i	0.987806	−	0.155693i
$2$	5.58787	−	0.880730i	0.987806	−	0.155693i
$3$	−6.36396	−	6.36396i	−0.408248	−	0.408248i
$3$	−6.36396	−	6.36396i	−0.408248	−	0.408248i
$4$	30.4486	−	9.84281i	0.951520	−	0.307588i
$5$	3.64660	−	3.64660i	0.0652324	−	0.0652324i	−0.673738	−	0.738970i	$-0.735312\pi$
$5$	3.64660	−	3.64660i	0.0652324	−	0.0652324i	0.738970	+	0.673738i	$0.235312\pi$
$6$	−41.1659	−	29.9561i	−0.466831	−	0.339709i
$7$		−	162.720i		−	1.25515i	−0.778555	−	0.627577i	$-0.784047\pi$
$7$		−	162.720i		−	1.25515i	0.778555	−	0.627577i	$-0.215953\pi$
$8$	161.474	−	81.8174i	0.892027	−	0.451982i
$9$			81.0000i			0.333333i
$10$	17.1651	−	23.5884i	0.0542807	−	0.0745931i
$11$	195.997	−	195.997i	0.488392	−	0.488392i	−0.419407	−	0.907799i	$-0.637762\pi$
$11$	195.997	−	195.997i	0.488392	−	0.488392i	0.907799	+	0.419407i	$0.137762\pi$
$12$	−256.413	−	131.135i	−0.514029	−	0.262884i
$13$	−264.994	−	264.994i	−0.434888	−	0.434888i	0.455399	−	0.890287i	$-0.349497\pi$
$13$	−264.994	−	264.994i	−0.434888	−	0.434888i	−0.890287	+	0.455399i	$0.849497\pi$
$14$	−143.313	−	909.260i	−0.195418	−	1.23985i
$15$	−46.4137			−0.0532620
$16$	830.238	−	599.400i	0.810779	−	0.585352i
$17$	−55.8881			−0.0469026			−0.0234513	−	0.999725i	$-0.507465\pi$
$17$	−55.8881			−0.0469026			−0.0234513	+	0.999725i	$0.507465\pi$
$18$	71.3391	+	452.618i	0.0518975	+	0.329269i
$19$	693.638	+	693.638i	0.440807	+	0.440807i	0.892283	−	0.451476i	$-0.149102\pi$
$19$	693.638	+	693.638i	0.440807	+	0.440807i	−0.451476	+	0.892283i	$0.649102\pi$
$20$	75.1412	−	146.927i	0.0420052	−	0.0821346i
$21$	−1035.55	+	1035.55i	−0.512414	+	0.512414i
$22$	922.588	−	1267.83i	0.406397	−	0.558475i
$23$			2420.75i			0.954182i	0.878854	+	0.477091i	$0.158309\pi$
$23$			2420.75i			0.954182i	−0.878854	+	0.477091i	$0.841691\pi$
$24$	−1548.30	−	506.933i	−0.548689	−	0.179648i
$25$			3098.40i			0.991489i
$26$	−1714.14	−	1247.36i	−0.497294	−	0.361876i
$27$	515.481	−	515.481i	0.136083	−	0.136083i
$28$	−1601.63	−	4954.61i	−0.386070	−	1.19430i
$29$	958.152	+	958.152i	0.211563	+	0.211563i	0.804931	−	0.593368i	$-0.202202\pi$
$29$	958.152	+	958.152i	0.211563	+	0.211563i	−0.593368	+	0.804931i	$0.702202\pi$
$30$	−259.354	+	40.8779i	−0.0526125	+	0.00829250i
$31$	5307.87			0.992010			0.496005	−	0.868320i	$-0.334800\pi$
$31$	5307.87			0.992010			0.496005	+	0.868320i	$0.334800\pi$
$32$	4111.35	−	4080.59i	0.709757	−	0.704446i
$33$	−2494.64			−0.398770
$34$	−312.295	+	49.2223i	−0.0463306	+	0.00730238i
$35$	−593.376	−	593.376i	−0.0818766	−	0.0818766i
$36$	797.268	+	2466.34i	0.102529	+	0.317173i
$37$	−9955.63	+	9955.63i	−1.19554	+	1.19554i	−0.220054	+	0.975488i	$0.570623\pi$
$37$	−9955.63	+	9955.63i	−1.19554	+	1.19554i	−0.975488	+	0.220054i	$0.929377\pi$
$38$	4486.87	+	3265.05i	0.504062	+	0.366802i
$39$			3372.82i			0.355085i
$40$	290.477	−	887.187i	0.0287052	−	0.0876729i
$41$		−	2150.37i		−	0.199781i	−0.994998	−	0.0998904i	$-0.968151\pi$
$41$		−	2150.37i		−	0.199781i	0.994998	−	0.0998904i	$-0.0318492\pi$
$42$	−4874.46	+	6698.53i	−0.426386	+	0.585945i
$43$	−12944.1	+	12944.1i	−1.06758	+	1.06758i	−0.0700366	+	0.997544i	$0.522312\pi$
$43$	−12944.1	+	12944.1i	−1.06758	+	1.06758i	−0.997544	+	0.0700366i	$0.977688\pi$
$44$	4038.69	−	7897.02i	0.314491	−	0.614938i
$45$	295.375	+	295.375i	0.0217441	+	0.0217441i
$46$	2132.03	+	13526.9i	0.148559	+	0.942546i
$47$	25084.5			1.65638			0.828191	−	0.560446i	$-0.189370\pi$
$47$	25084.5			1.65638			0.828191	+	0.560446i	$0.189370\pi$
$48$	−9098.16	−	1469.04i	−0.569968	−	0.0920304i
$49$	−9670.91			−0.575409
$50$	2728.86	+	17313.5i	0.154367	+	0.979399i
$51$	355.670	+	355.670i	0.0191479	+	0.0191479i
$52$	−10677.0	−	5460.42i	−0.547571	−	0.280038i
$53$	5460.54	−	5460.54i	0.267021	−	0.267021i	−0.560878	−	0.827899i	$-0.689536\pi$
$53$	5460.54	−	5460.54i	0.267021	−	0.267021i	0.827899	+	0.560878i	$0.189536\pi$
$54$	2426.44	−	3334.44i	0.113236	−	0.155610i
$55$		−	1429.45i		−	0.0637180i
$56$	−13313.4	−	26275.1i	−0.567306	−	1.11963i
$57$		−	8828.57i		−	0.359918i
$58$	6197.90	+	4510.16i	0.241922	+	0.176044i
$59$	27193.7	−	27193.7i	1.01704	−	1.01704i	0.0171867	−	0.999852i	$-0.494529\pi$
$59$	27193.7	−	27193.7i	1.01704	−	1.01704i	0.999852	−	0.0171867i	$-0.00547097\pi$
$60$	−1413.23	+	456.841i	−0.0506799	+	0.0163828i
$61$	−40112.6	−	40112.6i	−1.38024	−	1.38024i	−0.844173	−	0.536070i	$-0.819908\pi$
$61$	−40112.6	−	40112.6i	−1.38024	−	1.38024i	−0.536070	−	0.844173i	$-0.680092\pi$
$62$	29659.7	−	4674.80i	0.979913	−	0.154449i
$63$	13180.3			0.418384
$64$	19379.8	−	26422.8i	0.591425	−	0.806360i
$65$	−1932.65			−0.0567376
$66$	−13939.7	+	2197.10i	−0.393908	+	0.0620856i
$67$	−559.172	−	559.172i	−0.0152180	−	0.0152180i	0.699457	−	0.714675i	$-0.253425\pi$
$67$	−559.172	−	559.172i	−0.0152180	−	0.0152180i	−0.714675	+	0.699457i	$0.753425\pi$
$68$	−1701.72	+	550.096i	−0.0446287	+	0.0144267i
$69$	15405.6	−	15405.6i	0.389543	−	0.389543i
$70$	−3838.31	−	2793.11i	−0.0936258	−	0.0681306i
$71$		−	52249.6i		−	1.23009i	−0.788491	−	0.615046i	$-0.789138\pi$
$71$		−	52249.6i		−	1.23009i	0.788491	−	0.615046i	$-0.210862\pi$
$72$	6627.21	+	13079.4i	0.150661	+	0.297342i
$73$			47518.6i			1.04365i	0.853052	+	0.521827i	$0.174749\pi$
$73$			47518.6i			1.04365i	−0.853052	+	0.521827i	$0.825251\pi$
$74$	−46862.6	+	64399.0i	−0.994826	+	1.36710i
$75$	19718.1	−	19718.1i	0.404774	−	0.404774i
$76$	27947.7	+	14293.0i	0.555024	+	0.283850i
$77$	−31892.8	−	31892.8i	−0.613007	−	0.613007i
$78$	2970.54	+	18846.9i	0.0552840	+	0.350755i
$79$	61006.2			1.09978			0.549890	−	0.835237i	$-0.314670\pi$
$79$	61006.2			1.09978			0.549890	+	0.835237i	$0.314670\pi$
$80$	841.774	−	5213.32i	0.0147052	−	0.0910730i
$81$	−6561.00			−0.111111
$82$	−1893.90	−	12016.0i	−0.0311044	−	0.197345i
$83$	−18005.2	−	18005.2i	−0.286882	−	0.286882i	0.548964	−	0.835846i	$-0.315022\pi$
$83$	−18005.2	−	18005.2i	−0.286882	−	0.286882i	−0.835846	+	0.548964i	$0.815022\pi$
$84$	−21338.3	+	41723.6i	−0.329960	+	0.645184i
$85$	−203.802	+	203.802i	−0.00305957	+	0.00305957i
$86$	−60929.7	+	83730.3i	−0.888348	+	1.22078i
$87$		−	12195.3i		−	0.172740i
$88$	15612.5	−	47684.5i	0.214915	−	0.656403i
$89$			97236.7i			1.30123i	0.759406	+	0.650617i	$0.225490\pi$
$89$			97236.7i			1.30123i	−0.759406	+	0.650617i	$0.774510\pi$
$90$	1910.66	+	1390.37i	0.0248644	+	0.0180936i
$91$	−43119.9	+	43119.9i	−0.545851	+	0.545851i
$92$	23827.0	+	73708.7i	0.293495	+	0.907923i
$93$	−33779.1	−	33779.1i	−0.404986	−	0.404986i
$94$	140169.	−	22092.7i	1.63618	−	0.257886i
$95$	5058.84			0.0575098
$96$	−52133.2	−	195.799i	−0.577346	−	0.00216837i
$97$	−100552.			−1.08508			−0.542540	−	0.840030i	$-0.682537\pi$
$97$	−100552.			−1.08508			−0.542540	+	0.840030i	$0.682537\pi$
$98$	−54039.8	+	8517.46i	−0.568393	+	0.0895869i
$99$	15875.8	+	15875.8i	0.162797	+	0.162797i
$100$	30497.0	+	94342.2i	0.304970	+	0.943422i
$101$	43192.6	−	43192.6i	0.421314	−	0.421314i	−0.464342	−	0.885656i	$-0.653709\pi$
$101$	43192.6	−	43192.6i	0.421314	−	0.421314i	0.885656	+	0.464342i	$0.153709\pi$
$102$	2300.68	+	1674.19i	0.0218956	+	0.0159332i
$103$			17488.6i			0.162429i	0.996697	+	0.0812143i	$0.0258798\pi$
$103$			17488.6i			0.162429i	−0.996697	+	0.0812143i	$0.974120\pi$
$104$	−64470.8	−	21108.6i	−0.584493	−	0.191371i
$105$			7552.45i			0.0668520i
$106$	25703.5	−	35322.1i	0.222192	−	0.305338i
$107$	−163419.	+	163419.i	−1.37989	+	1.37989i	−0.535101	+	0.844788i	$0.679727\pi$
$107$	−163419.	+	163419.i	−1.37989	+	1.37989i	−0.844788	+	0.535101i	$0.820273\pi$
$108$	10621.9	−	20769.5i	0.0876280	−	0.171343i
$109$	24988.6	+	24988.6i	0.201454	+	0.201454i	0.800623	−	0.599169i	$-0.204502\pi$
$109$	24988.6	+	24988.6i	0.201454	+	0.201454i	−0.599169	+	0.800623i	$0.704502\pi$
$110$	−1258.96	−	7987.58i	−0.00992041	−	0.0629410i
$111$	126715.			0.976156
$112$	−97534.6	−	135097.i	−0.734706	−	1.01765i
$113$	189680.			1.39742			0.698709	−	0.715406i	$-0.253758\pi$
$113$	189680.			1.39742			0.698709	+	0.715406i	$0.253758\pi$
$114$	−7775.59	−	49332.9i	−0.0560365	−	0.355529i
$115$	8827.53	+	8827.53i	0.0622436	+	0.0622436i
$116$	38605.3	+	19743.5i	0.266380	+	0.136232i
$117$	21464.5	−	21464.5i	0.144963	−	0.144963i
$118$	128004.	−	175905.i	0.846291	−	1.16298i
$119$			9094.13i			0.0588699i
$120$	−7494.61	+	3797.44i	−0.0475112	+	0.0240735i
$121$			84221.1i			0.522946i
$122$	−259472.	−	188816.i	−1.57831	−	1.14852i
$123$	−13684.9	+	13684.9i	−0.0815602	+	0.0815602i
$124$	161617.	−	52244.4i	0.943917	−	0.305130i
$125$	22694.3	+	22694.3i	0.129910	+	0.129910i
$126$	73650.1	−	11608.3i	0.413282	−	0.0651393i
$127$	−18420.6			−0.101343			−0.0506717	−	0.998715i	$-0.516136\pi$
$127$	−18420.6			−0.101343			−0.0506717	+	0.998715i	$0.516136\pi$
$128$	85020.7	−	164716.i	0.458669	−	0.888607i
$129$	164752.			0.871676
$130$	−10799.4	+	1702.15i	−0.0560457	+	0.00883362i
$131$	−237604.	−	237604.i	−1.20969	−	1.20969i	−0.971126	−	0.238567i	$-0.923322\pi$
$131$	−237604.	−	237604.i	−1.20969	−	1.20969i	−0.238567	−	0.971126i	$-0.576678\pi$
$132$	−75958.4	+	24554.3i	−0.379438	+	0.122657i
$133$	112869.	−	112869.i	0.553281	−	0.553281i
$134$	−3617.06	−	2632.10i	−0.0174018	−	0.0126631i
$135$		−	3759.51i		−	0.0177540i
$136$	−9024.48	+	4572.62i	−0.0418384	+	0.0211991i
$137$			339273.i			1.54436i	0.635404	+	0.772180i	$0.280834\pi$
$137$			339273.i			1.54436i	−0.635404	+	0.772180i	$0.719166\pi$
$138$	72516.3	−	99652.6i	0.324144	−	0.445442i
$139$	−243084.	+	243084.i	−1.06714	+	1.06714i	−0.0695585	+	0.997578i	$0.522159\pi$
$139$	−243084.	+	243084.i	−1.06714	+	1.06714i	−0.997578	+	0.0695585i	$0.977841\pi$
$140$	−23908.0	−	12227.0i	−0.103092	−	0.0527230i
$141$	−159637.	−	159637.i	−0.676215	−	0.676215i
$142$	−46017.8	−	291964.i	−0.191516	−	1.21509i
$143$	−103876.			−0.424792
$144$	48551.4	+	67249.3i	0.195117	+	0.270260i
$145$	6988.00			0.0276015
$146$	41851.0	+	265528.i	0.162489	+	1.03093i
$147$	61545.3	+	61545.3i	0.234910	+	0.234910i
$148$	−205144.	+	401127.i	−0.769847	+	1.50532i
$149$	138953.	−	138953.i	0.512747	−	0.512747i	−0.402620	−	0.915367i	$-0.631900\pi$
$149$	138953.	−	138953.i	0.512747	−	0.512747i	0.915367	+	0.402620i	$0.131900\pi$
$150$	92816.0	−	127549.i	0.336818	−	0.462858i
$151$			156102.i			0.557143i	0.960416	+	0.278571i	$0.0898609\pi$
$151$			156102.i			0.557143i	−0.960416	+	0.278571i	$0.910139\pi$
$152$	168756.	+	55253.0i	0.592449	+	0.193975i
$153$		−	4526.93i		−	0.0156342i
$154$	−206302.	−	150124.i	−0.700972	−	0.510091i
$155$	19355.7	−	19355.7i	0.0647112	−	0.0647112i
$156$	33198.0	+	102698.i	0.109220	+	0.337870i
$157$	−63450.4	−	63450.4i	−0.205440	−	0.205440i	0.596886	−	0.802326i	$-0.296404\pi$
$157$	−63450.4	−	63450.4i	−0.205440	−	0.205440i	−0.802326	+	0.596886i	$0.796404\pi$
$158$	340895.	−	53730.0i	1.08637	−	0.171228i
$159$	−69501.3			−0.218022
$160$	112.195	−	29872.8i	0.000346475	−	0.0922519i
$161$	393906.			1.19764
$162$	−36662.0	+	5778.47i	−0.109756	+	0.0172992i
$163$	−110707.	−	110707.i	−0.326367	−	0.326367i	0.524836	−	0.851203i	$-0.324126\pi$
$163$	−110707.	−	110707.i	−0.326367	−	0.326367i	−0.851203	+	0.524836i	$0.824126\pi$
$164$	−21165.7	−	65475.9i	−0.0614502	−	0.190095i
$165$	−9096.96	+	9096.96i	−0.0260127	+	0.0260127i
$166$	−116469.	−	84753.2i	−0.328049	−	0.238718i
$167$		−	307312.i		−	0.852686i	−0.904562	−	0.426343i	$-0.859802\pi$
$167$		−	307312.i		−	0.852686i	0.904562	−	0.426343i	$-0.140198\pi$
$168$	−82488.3	+	251940.i	−0.225486	+	0.688689i
$169$		−	230849.i		−	0.621745i
$170$	−959.323	+	1318.31i	−0.00254591	+	0.00349861i
$171$	−56184.7	+	56184.7i	−0.146936	+	0.146936i
$172$	−266724.	+	521537.i	−0.687449	+	1.34420i
$173$	198632.	+	198632.i	0.504584	+	0.504584i	0.912859	−	0.408275i	$-0.133870\pi$
$173$	198632.	+	198632.i	0.504584	+	0.504584i	−0.408275	+	0.912859i	$0.633870\pi$
$174$	−10740.8	−	68145.7i	−0.0268944	−	0.170634i
$175$	504173.			1.24447
$176$	45243.6	−	280205.i	0.110097	−	0.681859i
$177$	−346119.			−0.830409
$178$	85639.3	+	543346.i	0.202592	+	1.28537i
$179$	−331460.	−	331460.i	−0.773211	−	0.773211i	0.205455	−	0.978666i	$-0.434132\pi$
$179$	−331460.	−	331460.i	−0.773211	−	0.773211i	−0.978666	+	0.205455i	$0.934132\pi$
$180$	11901.1	+	6086.44i	0.0273782	+	0.0140017i
$181$	43751.6	−	43751.6i	0.0992654	−	0.0992654i	−0.655730	−	0.754995i	$-0.727639\pi$
$181$	43751.6	−	43751.6i	0.0992654	−	0.0992654i	0.754995	+	0.655730i	$0.227639\pi$
$182$	−202971.	+	278925.i	−0.454210	+	0.624180i
$183$			510550.i			1.12696i
$184$	198060.	+	390889.i	0.431273	+	0.851156i
$185$			72608.5i			0.155976i
$186$	−218503.	−	159003.i	−0.463101	−	0.336995i
$187$	−10953.9	+	10953.9i	−0.0229069	+	0.0229069i
$188$	763788.	−	246902.i	1.57608	−	0.509483i
$189$	−83879.2	−	83879.2i	−0.170805	−	0.170805i
$190$	28268.2	−	4455.47i	0.0568085	−	0.00895385i
$191$	−76724.8			−0.152178			−0.0760891	−	0.997101i	$-0.524243\pi$
$191$	−76724.8			−0.152178			−0.0760891	+	0.997101i	$0.524243\pi$
$192$	−291486.	+	44821.2i	−0.570643	+	0.0877466i
$193$	14493.3			0.0280075			0.0140037	−	0.999902i	$-0.495542\pi$
$193$	14493.3			0.0280075			0.0140037	+	0.999902i	$0.495542\pi$
$194$	−561872.	+	88559.2i	−1.07185	+	0.168939i
$195$	12299.3	+	12299.3i	0.0231630	+	0.0231630i
$196$	−294466.	+	95188.9i	−0.547513	+	0.176989i
$197$	−227729.	+	227729.i	−0.418074	+	0.418074i	−0.884539	−	0.466466i	$-0.845527\pi$
$197$	−227729.	+	227729.i	−0.418074	+	0.418074i	0.466466	+	0.884539i	$0.345527\pi$
$198$	102694.	+	74729.6i	0.186158	+	0.135466i
$199$		−	978533.i		−	1.75163i	−0.482645	−	0.875816i	$-0.660324\pi$
$199$		−	978533.i		−	1.75163i	0.482645	−	0.875816i	$-0.339676\pi$
$200$	253503.	+	500312.i	0.448135	+	0.884436i
$201$			7117.09i			0.0124255i
$202$	203314.	−	279396.i	0.350581	−	0.481772i
$203$	155911.	−	155911.i	0.265544	−	0.265544i
$204$	14330.4	+	7328.86i	0.0241093	+	0.0123299i
$205$	−7841.55	−	7841.55i	−0.0130322	−	0.0130322i
$206$	15402.8	+	97724.2i	0.0252889	+	0.160448i
$207$	−196081.			−0.318061
$208$	−378845.	−	61170.6i	−0.607161	−	0.0980357i
$209$	271902.			0.430574
$210$	6651.67	+	42202.1i	0.0104084	+	0.0660368i
$211$	346114.	+	346114.i	0.535197	+	0.535197i	0.922114	−	0.386917i	$-0.126460\pi$
$211$	346114.	+	346114.i	0.535197	+	0.535197i	−0.386917	+	0.922114i	$0.626460\pi$
$212$	112519.	−	220013.i	0.171943	−	0.336208i
$213$	−332515.	+	332515.i	−0.502183	+	0.502183i
$214$	−769238.	+	1.05710e6i	−1.14822	+	1.57790i
$215$			94404.0i			0.139282i
$216$	41061.6	−	125412.i	0.0598826	−	0.182896i
$217$		−	863698.i		−	1.24512i
$218$	161641.	+	117625.i	0.230362	+	0.167633i
$219$	302406.	−	302406.i	0.426070	−	0.426070i
$220$	−14069.8	−	43524.8i	−0.0195989	−	0.0606289i
$221$	14810.0	+	14810.0i	0.0203974	+	0.0203974i
$222$	708065.	−	111601.i	0.964252	−	0.151980i
$223$	923010.			1.24292			0.621462	−	0.783444i	$-0.286539\pi$
$223$	923010.			1.24292			0.621462	+	0.783444i	$0.286539\pi$
$224$	−663995.	−	669001.i	−0.884188	−	0.890854i
$225$	−250971.			−0.330496
$226$	1.05991e6	−	167057.i	1.38038	−	0.217568i
$227$	81686.9	+	81686.9i	0.105217	+	0.105217i	0.757756	−	0.652538i	$-0.226296\pi$
$227$	81686.9	+	81686.9i	0.105217	+	0.105217i	−0.652538	+	0.757756i	$0.726296\pi$
$228$	−86898.0	−	268818.i	−0.110706	−	0.342469i
$229$	374714.	−	374714.i	0.472184	−	0.472184i	−0.430436	−	0.902621i	$-0.641640\pi$
$229$	374714.	−	374714.i	0.472184	−	0.472184i	0.902621	+	0.430436i	$0.141640\pi$
$230$	57101.8	+	41552.4i	0.0711754	+	0.0517937i
$231$			405929.i			0.500518i
$232$	233110.	+	76323.3i	0.284342	+	0.0930974i
$233$		−	372770.i		−	0.449833i	−0.974378	−	0.224917i	$-0.927789\pi$
$233$		−	372770.i		−	0.449833i	0.974378	−	0.224917i	$-0.0722110\pi$
$234$	101036.	−	138845.i	0.120625	−	0.165765i
$235$	91473.1	−	91473.1i	0.108050	−	0.108050i
$236$	560348.	−	1.09567e6i	0.654904	−	1.28056i
$237$	−388241.	−	388241.i	−0.448983	−	0.448983i
$238$	8009.47	+	50816.8i	0.00916561	+	0.0581521i
$239$	−1.52030e6			−1.72161			−0.860806	−	0.508934i	$-0.830040\pi$
$239$	−1.52030e6			−1.72161			−0.860806	+	0.508934i	$0.830040\pi$
$240$	−38534.4	+	27820.4i	−0.0431838	+	0.0311770i
$241$	−1.23857e6			−1.37366			−0.686828	−	0.726820i	$-0.740998\pi$
$241$	−1.23857e6			−1.37366			−0.686828	+	0.726820i	$0.740998\pi$
$242$	74176.0	+	470616.i	0.0814189	+	0.516569i
$243$	41753.9	+	41753.9i	0.0453609	+	0.0453609i
$244$	−1.61619e6	−	826552.i	−1.73788	−	0.888783i
$245$	−35265.9	+	35265.9i	−0.0375353	+	0.0375353i
$246$	−64416.7	+	88522.1i	−0.0678673	+	0.0932639i
$247$		−	367620.i		−	0.383404i
$248$	857084.	−	434276.i	0.884900	−	0.448370i
$249$			229169.i			0.234238i
$250$	146800.	+	106825.i	0.148551	+	0.108099i
$251$	741761.	−	741761.i	0.743156	−	0.743156i	−0.230028	−	0.973184i	$-0.573882\pi$
$251$	741761.	−	741761.i	0.743156	−	0.743156i	0.973184	+	0.230028i	$0.0738818\pi$
$252$	401323.	−	129732.i	0.398101	−	0.128690i
$253$	474462.	+	474462.i	0.466015	+	0.466015i
$254$	−102932.	+	16223.6i	−0.100108	+	0.0157784i
$255$	2593.97			0.00249813
$256$	330015.	−	995290.i	0.314726	−	0.949182i
$257$	−664351.			−0.627430			−0.313715	−	0.949517i	$-0.601574\pi$
$257$	−664351.			−0.627430			−0.313715	+	0.949517i	$0.601574\pi$
$258$	920611.	−	145102.i	0.861047	−	0.135713i
$259$	1.61998e6	+	1.61998e6i	1.50059	+	1.50059i
$260$	−58846.7	+	19022.8i	−0.0539869	+	0.0174518i
$261$	−77610.3	+	77610.3i	−0.0705210	+	0.0705210i
$262$	−1.53696e6	−	1.11843e6i	−1.38328	−	1.00660i
$263$			1.42038e6i			1.26624i	0.774055	+	0.633119i	$0.218225\pi$
$263$			1.42038e6i			1.26624i	−0.774055	+	0.633119i	$0.781775\pi$
$264$	−402820.	+	204105.i	−0.355714	+	0.180237i
$265$		−	39824.8i		−	0.0348369i
$266$	531290.	−	730105.i	0.460392	−	0.632676i
$267$	618811.	−	618811.i	0.531227	−	0.531227i
$268$	−22529.8	−	11522.2i	−0.0191611	−	0.00979937i
$269$	390301.	+	390301.i	0.328866	+	0.328866i	0.852155	−	0.523289i	$-0.175295\pi$
$269$	390301.	+	390301.i	0.328866	+	0.328866i	−0.523289	+	0.852155i	$0.675295\pi$
$270$	−3311.11	−	21007.6i	−0.00276417	−	0.0175375i
$271$	−674625.			−0.558006			−0.279003	−	0.960290i	$-0.590004\pi$
$271$	−674625.			−0.558006			−0.279003	+	0.960290i	$0.590004\pi$
$272$	−46400.4	+	33499.3i	−0.0380277	+	0.0274545i
$273$	548827.			0.445686
$274$	298808.	+	1.89582e6i	0.240445	+	1.52553i
$275$	607279.	+	607279.i	0.484236	+	0.484236i
$276$	317445.	−	620713.i	0.250839	−	0.490477i
$277$	−937284.	+	937284.i	−0.733959	+	0.733959i	−0.971402	−	0.237442i	$-0.923691\pi$
$277$	−937284.	+	937284.i	−0.733959	+	0.733959i	0.237442	+	0.971402i	$0.423691\pi$
$278$	−1.14423e6	+	1.57242e6i	−0.887978	+	1.22027i
$279$			429938.i			0.330670i
$280$	−144363.	−	47266.4i	−0.110043	−	0.0360295i
$281$			2.25402e6i			1.70291i	0.524427	+	0.851456i	$0.324280\pi$
$281$			2.25402e6i			1.70291i	−0.524427	+	0.851456i	$0.675720\pi$
$282$	−1.03263e6	−	751433.i	−0.773251	−	0.562687i
$283$	−143799.	+	143799.i	−0.106731	+	0.106731i	−0.758455	−	0.651725i	$-0.774046\pi$
$283$	−143799.	+	143799.i	−0.106731	+	0.106731i	0.651725	+	0.758455i	$0.274046\pi$
$284$	−514283.	−	1.59093e6i	−0.378361	−	1.17046i
$285$	−32194.3	−	32194.3i	−0.0234783	−	0.0234783i
$286$	−580447.	+	91486.9i	−0.419612	+	0.0661369i
$287$	−349909.			−0.250756
$288$	330528.	+	333020.i	0.234815	+	0.236586i
$289$	−1.41673e6			−0.997800
$290$	39048.0	−	6154.54i	0.0272649	−	0.00429735i
$291$	639910.	+	639910.i	0.442982	+	0.442982i
$292$	467716.	+	1.44688e6i	0.321015	+	0.993057i
$293$	−1.88124e6	+	1.88124e6i	−1.28020	+	1.28020i	−0.339640	+	0.940556i	$0.610305\pi$
$293$	−1.88124e6	+	1.88124e6i	−1.28020	+	1.28020i	−0.940556	+	0.339640i	$0.889695\pi$
$294$	398112.	+	289702.i	0.268619	+	0.195472i
$295$		−	198329.i		−	0.132688i
$296$	−793034.	+	2.42212e6i	−0.526093	+	1.60682i
$297$		−	202066.i		−	0.132923i
$298$	654073.	−	898834.i	0.426664	−	0.586325i
$299$	641485.	−	641485.i	0.414962	−	0.414962i
$300$	406308.	−	794472.i	0.260647	−	0.509654i
$301$	2.10627e6	+	2.10627e6i	1.33998	+	1.33998i
$302$	137484.	+	872279.i	0.0867429	+	0.550349i
$303$	−549752.			−0.344002
$304$	991651.	+	160118.i	0.615425	+	0.0993701i
$305$	−292549.			−0.180073
$306$	−3987.01	−	25295.9i	−0.00243413	−	0.0154435i
$307$	−1.10939e6	−	1.10939e6i	−0.671798	−	0.671798i	0.286332	−	0.958130i	$-0.407564\pi$
$307$	−1.10939e6	−	1.10939e6i	−0.671798	−	0.671798i	−0.958130	+	0.286332i	$0.907564\pi$
$308$	−1.28501e6	−	657176.i	−0.771841	−	0.394735i
$309$	111297.	−	111297.i	0.0663112	−	0.0663112i
$310$	91110.0	−	125204.i	0.0538470	−	0.0739971i
$311$		−	169801.i		−	0.0995496i	−0.998760	−	0.0497748i	$-0.984150\pi$
$311$		−	169801.i		−	0.0995496i	0.998760	−	0.0497748i	$-0.0158504\pi$
$312$	275955.	+	544624.i	0.160492	+	0.316745i
$313$		−	3.05307e6i		−	1.76147i	−0.473607	−	0.880736i	$-0.657048\pi$
$313$		−	3.05307e6i		−	1.76147i	0.473607	−	0.880736i	$-0.342952\pi$
$314$	−410435.	−	298670.i	−0.234920	−	0.170949i
$315$	48063.5	−	48063.5i	0.0272922	−	0.0272922i
$316$	1.85755e6	−	600472.i	1.04646	−	0.338279i
$317$	−1.21009e6	−	1.21009e6i	−0.676347	−	0.676347i	0.282825	−	0.959172i	$-0.408728\pi$
$317$	−1.21009e6	−	1.21009e6i	−0.676347	−	0.676347i	−0.959172	+	0.282825i	$0.908728\pi$
$318$	−388364.	+	61211.9i	−0.215363	+	0.0339444i
$319$	375591.			0.206651
$320$	−25682.9	−	167024.i	−0.0140207	−	0.0911809i
$321$	2.07999e6			1.12667
$322$	2.20110e6	−	346925.i	1.18304	−	0.186464i
$323$	−38766.1	−	38766.1i	−0.0206750	−	0.0206750i
$324$	−199773.	+	64578.7i	−0.105724	+	0.0341764i
$325$	821058.	−	821058.i	0.431187	−	0.431187i
$326$	−716119.	−	521113.i	−0.373200	−	0.271574i
$327$		−	318053.i		−	0.164487i
$328$	−175938.	−	347230.i	−0.0902973	−	0.178210i
$329$		−	4.08176e6i		−	2.07901i
$330$	−42820.7	+	58844.6i	−0.0216455	+	0.0297455i
$331$	−254903.	+	254903.i	−0.127881	+	0.127881i	−0.768150	−	0.640269i	$-0.778823\pi$
$331$	−254903.	+	254903.i	−0.127881	+	0.127881i	0.640269	+	0.768150i	$0.278823\pi$
$332$	−725457.	−	371012.i	−0.361215	−	0.184732i
$333$	−806406.	−	806406.i	−0.398514	−	0.398514i
$334$	−270659.	−	1.71722e6i	−0.132757	−	0.842288i
$335$	−4078.15			−0.00198542
$336$	−239043.	+	1.48046e6i	−0.115512	+	0.715397i
$337$	−1.26633e6			−0.607394			−0.303697	−	0.952769i	$-0.598221\pi$
$337$	−1.26633e6			−0.607394			−0.303697	+	0.952769i	$0.598221\pi$
$338$	−203316.	−	1.28996e6i	−0.0968010	−	0.614163i
$339$	−1.20712e6	−	1.20712e6i	−0.570493	−	0.570493i
$340$	−4199.50	+	8211.46i	−0.00197015	+	0.00385233i
$341$	1.04033e6	−	1.04033e6i	0.484490	−	0.484490i
$342$	−264469.	+	363436.i	−0.122267	+	0.168021i
$343$		−	1.16119e6i		−	0.532926i
$344$	−1.03109e6	+	3.14919e6i	−0.469785	+	1.43484i
$345$		−	112356.i		−	0.0508217i
$346$	1.28487e6	+	934987.i	0.576990	+	0.419871i
$347$	984991.	−	984991.i	0.439146	−	0.439146i	−0.452579	−	0.891724i	$-0.649496\pi$
$347$	984991.	−	984991.i	0.439146	−	0.439146i	0.891724	+	0.452579i	$0.149496\pi$
$348$	−120036.	−	371330.i	−0.0531328	−	0.164366i
$349$	2.78799e6	+	2.78799e6i	1.22526	+	1.22526i	0.965737	+	0.259523i	$0.0835655\pi$
$349$	2.78799e6	+	2.78799e6i	1.22526	+	1.22526i	0.259523	+	0.965737i	$0.416435\pi$
$350$	2.81726e6	−	444041.i	1.22930	−	0.193755i
$351$	−273199.			−0.118362
$352$	6030.23	−	1.60560e6i	0.00259404	−	0.690686i
$353$	2.13019e6			0.909874			0.454937	−	0.890524i	$-0.349662\pi$
$353$	2.13019e6			0.909874			0.454937	+	0.890524i	$0.349662\pi$
$354$	−1.93407e6	+	304837.i	−0.820283	+	0.129288i
$355$	−190534.	−	190534.i	−0.0802418	−	0.0802418i
$356$	957083.	+	2.96073e6i	0.400244	+	1.23815i
$357$	57874.7	−	57874.7i	0.0240336	−	0.0240336i
$358$	−2.14408e6	−	1.56023e6i	−0.884165	−	0.643399i
$359$			55146.1i			0.0225828i	0.999936	+	0.0112914i	$0.00359425\pi$
$359$			55146.1i			0.0225828i	−0.999936	+	0.0112914i	$0.996406\pi$
$360$	71862.2	+	23528.6i	0.0292243	+	0.00956841i
$361$		−	1.51383e6i		−	0.611378i
$362$	205945.	−	283012.i	0.0826000	−	0.113510i
$363$	535979.	−	535979.i	0.213492	−	0.213492i
$364$	−888521.	+	1.73736e6i	−0.351491	+	0.687285i
$365$	173281.	+	173281.i	0.0680800	+	0.0680800i
$366$	449656.	+	2.85289e6i	0.175460	+	1.11322i
$367$	−2.96183e6			−1.14787			−0.573937	−	0.818899i	$-0.694585\pi$
$367$	−2.96183e6			−1.14787			−0.573937	+	0.818899i	$0.694585\pi$
$368$	1.45100e6	+	2.00980e6i	0.558532	+	0.773631i
$369$	174180.			0.0665936
$370$	63948.5	+	405727.i	0.0242843	+	0.154074i
$371$	−888541.	−	888541.i	−0.335153	−	0.335153i
$372$	−1.36101e6	−	696046.i	−0.509921	−	0.260784i
$373$	−714947.	+	714947.i	−0.266074	+	0.266074i	−0.827516	−	0.561442i	$-0.810247\pi$
$373$	−714947.	+	714947.i	−0.266074	+	0.266074i	0.561442	+	0.827516i	$0.310247\pi$
$374$	−51561.6	+	70856.5i	−0.0190611	+	0.0261939i
$375$		−	288851.i		−	0.106071i
$376$	4.05050e6	−	2.05235e6i	1.47754	−	0.748654i
$377$		−	507809.i		−	0.184012i
$378$	−542581.	−	394831.i	−0.195315	−	0.142129i
$379$	−2.66192e6	+	2.66192e6i	−0.951912	+	0.951912i	−0.998896	−	0.0469835i	$-0.985039\pi$
$379$	−2.66192e6	+	2.66192e6i	−0.951912	+	0.951912i	0.0469835	+	0.998896i	$0.485039\pi$
$380$	154035.	−	49793.2i	0.0547217	−	0.0176893i
$381$	117228.	+	117228.i	0.0413733	+	0.0413733i
$382$	−428729.	+	67573.8i	−0.150322	+	0.0236930i
$383$	−282296.			−0.0983351			−0.0491675	−	0.998791i	$-0.515657\pi$
$383$	−282296.			−0.0983351			−0.0491675	+	0.998791i	$0.515657\pi$
$384$	−1.58931e6	+	507175.i	−0.550023	+	0.175521i
$385$	−232600.			−0.0799758
$386$	80986.6	−	12764.7i	0.0276659	−	0.00436055i
$387$	−1.04847e6	−	1.04847e6i	−0.355860	−	0.355860i
$388$	−3.06167e6	+	989715.i	−1.03247	+	0.333757i
$389$	2.92623e6	−	2.92623e6i	0.980469	−	0.980469i	−0.0193439	−	0.999813i	$-0.506158\pi$
$389$	2.92623e6	−	2.92623e6i	0.980469	−	0.980469i	0.999813	+	0.0193439i	$0.00615773\pi$
$390$	79559.5	+	57894.7i	0.0264869	+	0.0192742i
$391$		−	135291.i		−	0.0447536i
$392$	−1.56160e6	+	791248.i	−0.513281	+	0.260074i
$393$			3.02420e6i			0.987710i
$394$	−1.07195e6	+	1.47309e6i	−0.347885	+	0.478066i
$395$	222465.	−	222465.i	0.0717413	−	0.0717413i
$396$	639658.	+	327134.i	0.204979	+	0.104830i
$397$	526136.	+	526136.i	0.167541	+	0.167541i	0.785898	−	0.618357i	$-0.212201\pi$
$397$	526136.	+	526136.i	0.167541	+	0.167541i	−0.618357	+	0.785898i	$0.712201\pi$
$398$	−861824.	−	5.46792e6i	−0.272716	−	1.73027i
$399$	−1.43659e6			−0.451752
$400$	1.85718e6	+	2.57241e6i	0.580370	+	0.803879i
$401$	5.32508e6			1.65373			0.826867	−	0.562398i	$-0.190121\pi$
$401$	5.32508e6			1.65373			0.826867	+	0.562398i	$0.190121\pi$
$402$	6268.24	+	39769.4i	0.00193455	+	0.0122739i
$403$	−1.40655e6	−	1.40655e6i	−0.431413	−	0.431413i
$404$	890019.	−	1.74029e6i	0.271298	−	0.530480i
$405$	−23925.4	+	23925.4i	−0.00724804	+	0.00724804i
$406$	733894.	−	1.00853e6i	0.220962	−	0.303649i
$407$			3.90256e6i			1.16779i
$408$	86531.4	+	28331.5i	0.0257350	+	0.00842595i
$409$			4.12155e6i			1.21829i	0.793057	+	0.609147i	$0.208488\pi$
$409$			4.12155e6i			1.21829i	−0.793057	+	0.609147i	$0.791512\pi$
$410$	−50723.9	−	36911.3i	−0.0149023	−	0.0108443i
$411$	2.15912e6	−	2.15912e6i	0.630482	−	0.630482i
$412$	172137.	+	532505.i	0.0499611	+	0.154554i
$413$	−4.42496e6	−	4.42496e6i	−1.27654	−	1.27654i
$414$	−1.09568e6	+	172694.i	−0.314182	+	0.0495197i
$415$	−131316.			−0.0374280
$416$	−2.17081e6	−	8153.04i	−0.615020	−	0.00230986i
$417$	3.09396e6			0.871313
$418$	1.51936e6	−	239473.i	0.425323	−	0.0670371i
$419$	3.90317e6	+	3.90317e6i	1.08613	+	1.08613i	0.995923	+	0.0902085i	$0.0287533\pi$
$419$	3.90317e6	+	3.90317e6i	1.08613	+	1.08613i	0.0902085	+	0.995923i	$0.471247\pi$
$420$	74337.3	+	229962.i	0.0205629	+	0.0636110i
$421$	572324.	−	572324.i	0.157375	−	0.157375i	−0.624027	−	0.781403i	$-0.714505\pi$
$421$	572324.	−	572324.i	0.157375	−	0.157375i	0.781403	+	0.624027i	$0.214505\pi$
$422$	2.23888e6	+	1.62921e6i	0.611997	+	0.445344i
$423$			2.03184e6i			0.552127i
$424$	434969.	−	1.32850e6i	0.117502	−	0.358879i
$425$		−	173164.i		−	0.0465034i
$426$	−1.56519e6	+	2.15091e6i	−0.417873	+	0.574245i
$427$	−6.52713e6	+	6.52713e6i	−1.73242	+	1.73242i
$428$	−3.36739e6	+	6.58440e6i	−0.888555	+	1.73743i
$429$	661064.	+	661064.i	0.173420	+	0.173420i
$430$	83144.4	+	527517.i	0.0216851	+	0.137583i
$431$	1.81882e6			0.471625			0.235812	−	0.971799i	$-0.424225\pi$
$431$	1.81882e6			0.471625			0.235812	+	0.971799i	$0.424225\pi$
$432$	118992.	−	736951.i	0.0306768	−	0.189989i
$433$	−4.04485e6			−1.03677			−0.518386	−	0.855147i	$-0.673467\pi$
$433$	−4.04485e6			−1.03677			−0.518386	+	0.855147i	$0.673467\pi$
$434$	−760685.	−	4.82624e6i	−0.193857	−	1.22994i
$435$	−44471.3	−	44471.3i	−0.0112683	−	0.0112683i
$436$	1.00683e6	+	514911.i	0.253652	+	0.129723i
$437$	−1.67913e6	+	1.67913e6i	−0.420610	+	0.420610i
$438$	1.42347e6	−	1.95615e6i	0.354538	−	0.487210i
$439$		−	4.21750e6i		−	1.04446i	−0.852803	−	0.522232i	$-0.825099\pi$
$439$		−	4.21750e6i		−	1.04446i	0.852803	−	0.522232i	$-0.174901\pi$
$440$	−116954.	−	230819.i	−0.0287993	−	0.0568382i
$441$		−	783343.i		−	0.191803i
$442$	95800.0	+	69712.8i	0.0233244	+	0.0169729i
$443$	548536.	−	548536.i	0.132799	−	0.132799i	−0.637583	−	0.770382i	$-0.720066\pi$
$443$	548536.	−	548536.i	0.132799	−	0.132799i	0.770382	+	0.637583i	$0.220066\pi$
$444$	3.85828e6	−	1.24723e6i	0.928831	−	0.300254i
$445$	354584.	+	354584.i	0.0848826	+	0.0848826i
$446$	5.15766e6	−	812923.i	1.22777	−	0.193514i
$447$	−1.76859e6			−0.418656
$448$	−4.29953e6	−	3.15349e6i	−1.01210	−	0.742329i
$449$	−5.03237e6			−1.17803			−0.589015	−	0.808122i	$-0.700484\pi$
$449$	−5.03237e6			−1.17803			−0.589015	+	0.808122i	$0.700484\pi$
$450$	−1.40239e6	+	221037.i	−0.326466	+	0.0514558i
$451$	−421467.	−	421467.i	−0.0975714	−	0.0975714i
$452$	5.77551e6	−	1.86699e6i	1.32967	−	0.429829i
$453$	993428.	−	993428.i	0.227453	−	0.227453i
$454$	528400.	+	384512.i	0.120316	+	0.0875528i
$455$			314482.i			0.0712143i
$456$	−722331.	−	1.42559e6i	−0.162676	−	0.321056i
$457$			5.30120e6i			1.18736i	0.804700	+	0.593681i	$0.202326\pi$
$457$			5.30120e6i			1.18736i	−0.804700	+	0.593681i	$0.797674\pi$
$458$	1.76383e6	−	2.42388e6i	0.392911	−	0.539942i
$459$	−28809.2	+	28809.2i	−0.00638263	+	0.00638263i
$460$	355674.	+	181898.i	0.0783713	+	0.0400806i
$461$	1.11380e6	+	1.11380e6i	0.244092	+	0.244092i	0.818541	−	0.574449i	$-0.194784\pi$
$461$	1.11380e6	+	1.11380e6i	0.244092	+	0.244092i	−0.574449	+	0.818541i	$0.694784\pi$
$462$	357513.	+	2.26828e6i	0.0779269	+	0.494414i
$463$	4.85131e6			1.05173			0.525867	−	0.850567i	$-0.323741\pi$
$463$	4.85131e6			1.05173			0.525867	+	0.850567i	$0.323741\pi$
$464$	1.36981e6	+	221178.i	0.295370	+	0.0476921i
$465$	−246358.			−0.0528365
$466$	−328310.	−	2.08299e6i	−0.0700357	−	0.444348i
$467$	−1.92617e6	−	1.92617e6i	−0.408697	−	0.408697i	0.472587	−	0.881284i	$-0.343320\pi$
$467$	−1.92617e6	−	1.92617e6i	−0.408697	−	0.408697i	−0.881284	+	0.472587i	$0.843320\pi$
$468$	442294.	−	864836.i	0.0933461	−	0.182524i
$469$	−90988.6	+	90988.6i	−0.0191009	+	0.0191009i
$470$	430577.	−	591703.i	0.0899096	−	0.123555i
$471$			807591.i			0.167741i
$472$	2.16616e6	−	6.61599e6i	0.447544	−	1.36691i
$473$			5.07402e6i			1.04280i
$474$	−2.51138e6	−	1.82750e6i	−0.513412	−	0.373605i
$475$	−2.14917e6	+	2.14917e6i	−0.437056	+	0.437056i
$476$	89511.8	+	276904.i	0.0181077	+	0.0560159i
$477$	442304.	+	442304.i	0.0890071	+	0.0890071i
$478$	−8.49525e6	+	1.33898e6i	−1.70062	+	0.268042i
$479$	8.33508e6			1.65986			0.829929	−	0.557868i	$-0.188381\pi$
$479$	8.33508e6			1.65986			0.829929	+	0.557868i	$0.188381\pi$
$480$	−190823.	+	189395.i	−0.0378031	+	0.0375202i
$481$	5.27636e6			1.03985
$482$	−6.92097e6	+	1.09085e6i	−1.35691	+	0.213868i
$483$	−2.50680e6	−	2.50680e6i	−0.488936	−	0.488936i
$484$	828972.	+	2.56442e6i	0.160852	+	0.497594i
$485$	−366673.	+	366673.i	−0.0707824	+	0.0707824i
$486$	270090.	+	196542.i	0.0518701	+	0.0377454i
$487$		−	7.34631e6i		−	1.40361i	−0.712369	−	0.701805i	$-0.752378\pi$
$487$		−	7.34631e6i		−	1.40361i	0.712369	−	0.701805i	$-0.247622\pi$
$488$	−9.75905e6	−	3.19524e6i	−1.85506	−	0.607370i
$489$			1.40907e6i			0.266477i
$490$	−166002.	+	228121.i	−0.0312336	+	0.0429216i
$491$	416502.	−	416502.i	0.0779675	−	0.0779675i	−0.667048	−	0.745015i	$-0.732442\pi$
$491$	416502.	−	416502.i	0.0779675	−	0.0779675i	0.745015	+	0.667048i	$0.232442\pi$
$492$	−281988.	+	551384.i	−0.0525192	+	0.102693i
$493$	−53549.3	−	53549.3i	−0.00992285	−	0.00992285i
$494$	−323774.	−	2.05421e6i	−0.0596931	−	0.378728i
$495$	115785.			0.0212393
$496$	4.40680e6	−	3.18154e6i	0.804301	−	0.580675i
$497$	−8.50208e6			−1.54395
$498$	201836.	+	1.28057e6i	0.0364691	+	0.231382i
$499$	3.88288e6	+	3.88288e6i	0.698076	+	0.698076i	0.963995	−	0.265919i	$-0.0856755\pi$
$499$	3.88288e6	+	3.88288e6i	0.698076	+	0.698076i	−0.265919	+	0.963995i	$0.585675\pi$
$500$	914385.	+	467634.i	0.163570	+	0.0836529i
$501$	−1.95572e6	+	1.95572e6i	−0.348108	+	0.348108i
$502$	3.49158e6	−	4.79816e6i	0.618390	−	0.849797i
$503$			2.93190e6i			0.516689i	0.966053	+	0.258344i	$0.0831769\pi$
$503$			2.93190e6i			0.516689i	−0.966053	+	0.258344i	$0.916823\pi$
$504$	2.12829e6	−	1.07838e6i	0.373210	−	0.189102i
$505$		−	315012.i		−	0.0549667i
$506$	3.06910e6	+	2.23336e6i	0.532887	+	0.387777i
$507$	−1.46912e6	+	1.46912e6i	−0.253826	+	0.253826i
$508$	−560883.	+	181311.i	−0.0964303	+	0.0311720i
$509$	−6.01194e6	−	6.01194e6i	−1.02854	−	1.02854i	−0.999581	−	0.0289562i	$-0.990782\pi$
$509$	−6.01194e6	−	6.01194e6i	−1.02854	−	1.02854i	−0.0289562	−	0.999581i	$-0.509218\pi$
$510$	14494.8	−	2284.59i	0.00246766	−	0.000388940i
$511$	7.73224e6			1.30994
$512$	967498.	−	5.85221e6i	0.163108	−	0.986608i
$513$	715114.			0.119973
$514$	−3.71231e6	+	585114.i	−0.619778	+	0.0976861i
$515$	63774.1	+	63774.1i	0.0105956	+	0.0105956i
$516$	5.01646e6	−	1.62162e6i	0.829417	−	0.268117i
$517$	4.91649e6	−	4.91649e6i	0.808964	−	0.808964i
$518$	1.04790e7	+	7.62550e6i	1.71592	+	1.24866i
$519$		−	2.52817e6i		−	0.411991i
$520$	−312074.	+	158125.i	−0.0506115	+	0.0256443i
$521$			2.06494e6i			0.333282i	0.986018	+	0.166641i	$0.0532922\pi$
$521$			2.06494e6i			0.333282i	−0.986018	+	0.166641i	$0.946708\pi$
$522$	−365323.	+	502030.i	−0.0586814	+	0.0806406i
$523$	3.60309e6	−	3.60309e6i	0.575999	−	0.575999i	−0.357800	−	0.933798i	$-0.616473\pi$
$523$	3.60309e6	−	3.60309e6i	0.575999	−	0.575999i	0.933798	+	0.357800i	$0.116473\pi$
$524$	−9.57340e6	−	4.89602e6i	−1.52313	−	0.778960i
$525$	−3.20854e6	−	3.20854e6i	−0.508053	−	0.508053i
$526$	1.25097e6	+	7.93690e6i	0.197144	+	1.25080i
$527$	−296647.			−0.0465279
$528$	−2.07114e6	+	1.49529e6i	−0.323315	+	0.233421i
$529$	576291.			0.0895371
$530$	−35074.9	−	222536.i	−0.00542384	−	0.0344121i
$531$	2.20269e6	+	2.20269e6i	0.339013	+	0.339013i
$532$	2.32576e6	−	4.54765e6i	0.356275	−	0.696640i
$533$	−569835.	+	569835.i	−0.0868823	+	0.0868823i
$534$	2.91283e6	−	4.00284e6i	0.442041	−	0.607457i
$535$			1.19185e6i			0.180027i
$536$	−136042.	−	44541.8i	−0.0204532	−	0.00669663i
$537$			4.21879e6i			0.631324i
$538$	2.52470e6	+	1.83720e6i	0.376058	+	0.273654i
$539$	−1.89547e6	+	1.89547e6i	−0.281025	+	0.281025i
$540$	−37004.1	−	114472.i	−0.00546092	−	0.0168933i
$541$	−5.55110e6	−	5.55110e6i	−0.815428	−	0.815428i	0.170013	−	0.985442i	$-0.445619\pi$
$541$	−5.55110e6	−	5.55110e6i	−0.815428	−	0.815428i	−0.985442	+	0.170013i	$0.945619\pi$
$542$	−3.76972e6	+	594162.i	−0.551202	+	0.0868774i
$543$	−556867.			−0.0810499
$544$	−229776.	+	228056.i	−0.0332895	+	0.0330404i
$545$	182247.			0.0262827
$546$	3.06677e6	−	483368.i	0.440251	−	0.0693899i
$547$	−5.10331e6	−	5.10331e6i	−0.729262	−	0.729262i	0.241211	−	0.970473i	$-0.422455\pi$
$547$	−5.10331e6	−	5.10331e6i	−0.729262	−	0.729262i	−0.970473	+	0.241211i	$0.922455\pi$
$548$	3.33941e6	+	1.03304e7i	0.475026	+	1.46949i
$549$	3.24912e6	−	3.24912e6i	0.460081	−	0.460081i
$550$	3.92825e6	+	2.85855e6i	0.553722	+	0.402939i
$551$			1.32922e6i			0.186517i
$552$	1.22716e6	−	3.74805e6i	0.171417	−	0.523549i
$553$		−	9.92694e6i		−	1.38039i
$554$	−4.41193e6	+	6.06292e6i	−0.610737	+	0.839281i
$555$	462077.	−	462077.i	0.0636770	−	0.0636770i
$556$	−5.00895e6	+	9.79422e6i	−0.687163	+	1.34364i
$557$	−5.89744e6	−	5.89744e6i	−0.805425	−	0.805425i	0.178512	−	0.983938i	$-0.442872\pi$
$557$	−5.89744e6	−	5.89744e6i	−0.805425	−	0.805425i	−0.983938	+	0.178512i	$0.942872\pi$
$558$	378659.	+	2.40244e6i	0.0514829	+	0.326638i
$559$	6.86022e6			0.928556
$560$	−848313.	−	136974.i	−0.114311	−	0.0184573i
$561$	139421.			0.0187034
$562$	1.98518e6	+	1.25952e7i	0.265131	+	1.68215i
$563$	3.13721e6	+	3.13721e6i	0.417132	+	0.417132i	0.884214	−	0.467082i	$-0.154695\pi$
$563$	3.13721e6	+	3.13721e6i	0.417132	+	0.417132i	−0.467082	+	0.884214i	$0.654695\pi$
$564$	−6.43199e6	−	3.28944e6i	−0.851428	−	0.435436i
$565$	691689.	−	691689.i	0.0911569	−	0.0911569i
$566$	−676881.	+	930176.i	−0.0888119	+	0.122046i
$567$			1.06761e6i			0.139461i
$568$	−4.27493e6	−	8.43697e6i	−0.555979	−	1.09728i
$569$			6.99379e6i			0.905590i	0.891615	+	0.452795i	$0.149573\pi$
$569$			6.99379e6i			0.905590i	−0.891615	+	0.452795i	$0.850427\pi$
$570$	−208252.	−	151543.i	−0.0268474	−	0.0195366i
$571$	5.99466e6	−	5.99466e6i	0.769439	−	0.769439i	−0.208569	−	0.978008i	$-0.566881\pi$
$571$	5.99466e6	−	5.99466e6i	0.769439	−	0.769439i	0.978008	+	0.208569i	$0.0668805\pi$
$572$	−3.16289e6	+	1.02243e6i	−0.404198	+	0.130661i
$573$	488274.	+	488274.i	0.0621265	+	0.0621265i
$574$	−1.95525e6	+	308175.i	−0.247698	+	0.0390408i
$575$	−7.50048e6			−0.946061
$576$	2.14025e6	+	1.56977e6i	0.268787	+	0.197142i
$577$	−245005.			−0.0306362			−0.0153181	−	0.999883i	$-0.504876\pi$
$577$	−245005.			−0.0306362			−0.0153181	+	0.999883i	$0.504876\pi$
$578$	−7.91653e6	+	1.24776e6i	−0.985633	+	0.155350i
$579$	−92234.7	−	92234.7i	−0.0114340	−	0.0114340i
$580$	212775.	−	68781.6i	0.0262634	−	0.00848989i
$581$	−2.92982e6	+	2.92982e6i	−0.360081	+	0.360081i
$582$	4.13932e6	+	3.01215e6i	0.506549	+	0.368611i
$583$		−	2.14050e6i		−	0.260822i
$584$	3.88785e6	+	7.67302e6i	0.471712	+	0.930967i
$585$		−	156545.i		−	0.0189125i
$586$	−8.85529e6	+	1.21690e7i	−1.06527	+	1.46390i
$587$	−6.48947e6	+	6.48947e6i	−0.777345	+	0.777345i	−0.979379	−	0.202033i	$-0.935245\pi$
$587$	−6.48947e6	+	6.48947e6i	−0.777345	+	0.777345i	0.202033	+	0.979379i	$0.435245\pi$
$588$	2.47975e6	+	1.26819e6i	0.295777	+	0.151266i
$589$	3.68174e6	+	3.68174e6i	0.437285	+	0.437285i
$590$	−174674.	−	1.10824e6i	−0.0206585	−	0.131070i
$591$	2.89852e6			0.341356
$592$	−2.29814e6	+	1.42330e7i	−0.269508	+	1.66913i
$593$	2.77540e6			0.324107			0.162054	−	0.986782i	$-0.448188\pi$
$593$	2.77540e6			0.324107			0.162054	+	0.986782i	$0.448188\pi$
$594$	−177965.	−	1.12912e6i	−0.0206952	−	0.131303i
$595$	33162.7	+	33162.7i	0.00384023	+	0.00384023i
$596$	2.86325e6	−	5.59863e6i	0.330174	−	0.645604i
$597$	−6.22735e6	+	6.22735e6i	−0.715101	+	0.715101i
$598$	3.01956e6	−	4.14951e6i	0.345295	−	0.474509i
$599$		−	2.73343e6i		−	0.311273i	−0.987814	−	0.155637i	$-0.950257\pi$
$599$		−	2.73343e6i		−	0.311273i	0.987814	−	0.155637i	$-0.0497429\pi$
$600$	1.57068e6	−	4.79725e6i	0.178119	−	0.544020i
$601$			8.93445e6i			1.00898i	0.863418	+	0.504489i	$0.168319\pi$
$601$			8.93445e6i			1.00898i	−0.863418	+	0.504489i	$0.831681\pi$
$602$	1.36246e7	+	9.91451e6i	1.53226	+	1.11501i
$603$	45292.9	−	45292.9i	0.00507267	−	0.00507267i
$604$	1.53648e6	+	4.75310e6i	0.171370	+	0.530132i
$605$	307121.	+	307121.i	0.0341131	+	0.0341131i
$606$	−3.07194e6	+	484183.i	−0.339807	+	0.0535585i
$607$	−4.08474e6			−0.449979			−0.224990	−	0.974361i	$-0.572235\pi$
$607$	−4.08474e6			−0.449979			−0.224990	+	0.974361i	$0.572235\pi$
$608$	5.68224e6	+	21341.1i	0.623391	+	0.00234130i
$609$	−1.98442e6			−0.216816
$610$	−1.63473e6	+	257657.i	−0.177877	+	0.0280361i
$611$	−6.64723e6	−	6.64723e6i	−0.720341	−	0.720341i
$612$	−44557.8	−	137839.i	−0.00480889	−	0.0148762i
$613$	1.04847e6	−	1.04847e6i	0.112695	−	0.112695i	−0.648511	−	0.761205i	$-0.724608\pi$
$613$	1.04847e6	−	1.04847e6i	0.112695	−	0.112695i	0.761205	+	0.648511i	$0.224608\pi$
$614$	−7.17621e6	−	5.22206e6i	−0.768200	−	0.559012i
$615$			99806.6i			0.0106407i
$616$	−7.75924e6	−	2.54047e6i	−0.823887	−	0.269751i
$617$		−	1.21315e7i		−	1.28293i	−0.767153	−	0.641465i	$-0.778327\pi$
$617$		−	1.21315e7i		−	1.28293i	0.767153	−	0.641465i	$-0.221673\pi$
$618$	523891.	−	719936.i	0.0551784	−	0.0758268i
$619$	3.81725e6	−	3.81725e6i	0.400428	−	0.400428i	−0.477956	−	0.878384i	$-0.658622\pi$
$619$	3.81725e6	−	3.81725e6i	0.400428	−	0.400428i	0.878384	+	0.477956i	$0.158622\pi$
$620$	398840.	−	779869.i	0.0416696	−	0.0814784i
$621$	1.24785e6	+	1.24785e6i	0.129848	+	0.129848i
$622$	−149549.	−	948827.i	−0.0154991	−	0.0983356i
$623$	1.58224e7			1.63325
$624$	2.02167e6	+	2.80024e6i	0.207849	+	0.287895i
$625$	−9.51700e6			−0.974541
$626$	−2.68893e6	−	1.70602e7i	−0.274248	−	1.73999i
$627$	−1.73038e6	−	1.73038e6i	−0.175781	−	0.175781i
$628$	−2.55651e6	−	1.30745e6i	−0.258671	−	0.132289i
$629$	556401.	−	556401.i	0.0560740	−	0.0560740i
$630$	226242.	−	310903.i	0.0227102	−	0.0312086i
$631$			3.74112e6i			0.374049i	0.982355	+	0.187025i	$0.0598844\pi$
$631$			3.74112e6i			0.374049i	−0.982355	+	0.187025i	$0.940116\pi$
$632$	9.85092e6	−	4.99137e6i	0.981034	−	0.497080i
$633$		−	4.40532e6i		−	0.436986i
$634$	−7.82759e6	−	5.69606e6i	−0.773401	−	0.562797i
$635$	−67172.8	+	67172.8i	−0.00661087	+	0.00661087i
$636$	−2.11622e6	+	684088.i	−0.207452	+	0.0670609i
$637$	2.56273e6	+	2.56273e6i	0.250239	+	0.250239i
$638$	2.09875e6	−	330794.i	0.204131	−	0.0321741i
$639$	4.23222e6			0.410031
$640$	−290616.	−	910689.i	−0.0280459	−	0.0878861i
$641$	1.45993e7			1.40342			0.701710	−	0.712462i	$-0.252420\pi$
$641$	1.45993e7			1.40342			0.701710	+	0.712462i	$0.252420\pi$
$642$	1.16227e7	−	1.83191e6i	1.11294	−	0.175415i
$643$	−572991.	−	572991.i	−0.0546538	−	0.0546538i	0.679252	−	0.733905i	$-0.262304\pi$
$643$	−572991.	−	572991.i	−0.0546538	−	0.0546538i	−0.733905	+	0.679252i	$0.762304\pi$
$644$	1.19939e7	−	3.87714e6i	1.13958	−	0.368381i
$645$	600783.	−	600783.i	0.0568615	−	0.0568615i
$646$	−250762.	−	182478.i	−0.0236418	−	0.0172039i
$647$		−	1.05180e7i		−	0.987809i	−0.869516	−	0.493904i	$-0.835569\pi$
$647$		−	1.05180e7i		−	0.987809i	0.869516	−	0.493904i	$-0.164431\pi$
$648$	−1.05943e6	+	536804.i	−0.0991141	+	0.0502202i
$649$		−	1.06598e7i		−	0.993427i
$650$	3.86484e6	−	5.31110e6i	0.358796	−	0.493061i
$651$	−5.49654e6	+	5.49654e6i	−0.508320	+	0.508320i
$652$	−4.46054e6	−	2.28121e6i	−0.410931	−	0.210158i
$653$	1.35182e7	+	1.35182e7i	1.24062	+	1.24062i	0.959746	+	0.280870i	$0.0906230\pi$
$653$	1.35182e7	+	1.35182e7i	1.24062	+	1.24062i	0.280870	+	0.959746i	$0.409377\pi$
$654$	−280119.	−	1.77724e6i	−0.0256093	−	0.162481i
$655$	−1.73289e6			−0.157822
$656$	−1.28893e6	−	1.78532e6i	−0.116942	−	0.161978i
$657$	−3.84900e6			−0.347884
$658$	−3.59492e6	−	2.28083e7i	−0.323687	−	2.05366i
$659$	2.14478e6	+	2.14478e6i	0.192384	+	0.192384i	0.796726	−	0.604341i	$-0.206564\pi$
$659$	2.14478e6	+	2.14478e6i	0.192384	+	0.192384i	−0.604341	+	0.796726i	$0.706564\pi$
$660$	−187450.	+	366529.i	−0.0167504	+	0.0327528i
$661$	−3.56700e6	+	3.56700e6i	−0.317541	+	0.317541i	−0.847822	−	0.530281i	$-0.822086\pi$
$661$	−3.56700e6	+	3.56700e6i	−0.317541	+	0.317541i	0.530281	+	0.847822i	$0.322086\pi$
$662$	−1.19987e6	+	1.64887e6i	−0.106411	+	0.146232i
$663$		−	188501.i		−	0.0166544i
$664$	−4.38052e6	−	1.43424e6i	−0.385572	−	0.126241i
$665$		−	823177.i		−	0.0721837i
$666$	−5.21632e6	−	3.79587e6i	−0.455700	−	0.331609i
$667$	−2.31945e6	+	2.31945e6i	−0.201869	+	0.201869i
$668$	−3.02482e6	−	9.35724e6i	−0.262276	−	0.811347i
$669$	−5.87400e6	−	5.87400e6i	−0.507421	−	0.507421i
$670$	−22788.2	+	3591.75i	−0.00196120	+	0.000309114i
$671$	−1.57239e7			−1.34820
$672$	−31860.5	+	8.48313e6i	−0.00272164	+	0.724658i
$673$	8.98348e6			0.764552			0.382276	−	0.924048i	$-0.375140\pi$
$673$	8.98348e6			0.764552			0.382276	+	0.924048i	$0.375140\pi$
$674$	−7.07606e6	+	1.11529e6i	−0.599987	+	0.0945667i
$675$	1.59717e6	+	1.59717e6i	0.134925	+	0.134925i
$676$	−2.27221e6	−	7.02905e6i	−0.191241	−	0.591602i
$677$	2.71205e6	−	2.71205e6i	0.227418	−	0.227418i	−0.584195	−	0.811613i	$-0.698590\pi$
$677$	2.71205e6	−	2.71205e6i	0.227418	−	0.227418i	0.811613	+	0.584195i	$0.198590\pi$
$678$	−7.80837e6	−	5.68208e6i	−0.652358	−	0.474715i
$679$			1.63619e7i			1.36194i
$680$	−16234.2	+	49583.2i	−0.00134635	+	0.00411209i
$681$		−	1.03970e6i		−	0.0859096i
$682$	4.89698e6	−	6.72947e6i	0.403150	−	0.554013i
$683$	6.16980e6	−	6.16980e6i	0.506080	−	0.506080i	−0.407241	−	0.913321i	$-0.633509\pi$
$683$	6.16980e6	−	6.16980e6i	0.506080	−	0.506080i	0.913321	+	0.407241i	$0.133509\pi$
$684$	−1.15773e6	+	2.26376e6i	−0.0946166	+	0.185008i
$685$	1.23720e6	+	1.23720e6i	0.100742	+	0.100742i
$686$	−1.02269e6	−	6.48857e6i	−0.0829726	−	0.526427i
$687$	−4.76934e6			−0.385537
$688$	−2.98799e6	+	1.85054e7i	−0.240662	+	1.49048i
$689$	−2.89402e6			−0.232249
$690$	−98955.4	−	627831.i	−0.00791255	−	0.0502019i
$691$	1.29063e6	+	1.29063e6i	0.102827	+	0.102827i	0.756648	−	0.653822i	$-0.226835\pi$
$691$	1.29063e6	+	1.29063e6i	0.102827	+	0.102827i	−0.653822	+	0.756648i	$0.726835\pi$
$692$	8.00315e6	+	4.09297e6i	0.635325	+	0.324917i
$693$	2.58331e6	−	2.58331e6i	0.204336	−	0.204336i
$694$	4.63649e6	−	6.37152e6i	0.365419	−	0.502162i
$695$			1.77286e6i			0.139224i
$696$	−997787.	−	1.96922e6i	−0.0780755	−	0.154089i
$697$			120180.i			0.00937024i
$698$	1.80344e7	+	1.31235e7i	1.40108	+	1.01955i
$699$	−2.37230e6	+	2.37230e6i	−0.183644	+	0.183644i
$700$	1.53514e7	−	4.96248e6i	1.18414	−	0.382784i
$701$	6.68875e6	+	6.68875e6i	0.514103	+	0.514103i	0.915781	−	0.401678i	$-0.131573\pi$
$701$	6.68875e6	+	6.68875e6i	0.514103	+	0.514103i	−0.401678	+	0.915781i	$0.631573\pi$
$702$	−1.52660e6	+	240614.i	−0.116918	+	0.0184280i
$703$	−1.38112e7			−1.05401
$704$	−1.38040e6	−	8.97719e6i	−0.104972	−	0.682667i
$705$	−1.16426e6			−0.0882223
$706$	1.19032e7	−	1.87612e6i	0.898779	−	0.141661i
$707$	−7.02832e6	−	7.02832e6i	−0.528814	−	0.528814i
$708$	−1.05388e7	+	3.40678e6i	−0.790150	+	0.255424i
$709$	−2.01767e6	+	2.01767e6i	−0.150742	+	0.150742i	−0.778449	−	0.627707i	$-0.783993\pi$
$709$	−2.01767e6	+	2.01767e6i	−0.150742	+	0.150742i	0.627707	+	0.778449i	$0.283993\pi$
$710$	−1.23249e6	−	896869.i	−0.0917564	−	0.0667703i
$711$			4.94150e6i			0.366593i
$712$	7.95566e6	+	1.57012e7i	0.588134	+	1.16074i
$713$			1.28491e7i			0.946558i
$714$	272424.	−	374368.i	0.0199986	−	0.0274823i
$715$	−378795.	+	378795.i	−0.0277102	+	0.0277102i
$716$	−1.33550e7	−	6.83000e6i	−0.973556	−	0.497895i
$717$	9.67514e6	+	9.67514e6i	0.702845	+	0.702845i
$718$	48568.8	+	308149.i	0.00351598	+	0.0223075i
$719$	−1.74845e7			−1.26134			−0.630668	−	0.776053i	$-0.717219\pi$
$719$	−1.74845e7			−1.26134			−0.630668	+	0.776053i	$0.717219\pi$
$720$	422279.	+	68183.7i	0.0303577	+	0.00490173i
$721$	2.84576e6			0.203873
$722$	−1.33328e6	−	8.45910e6i	−0.0951869	−	0.603922i
$723$	7.88221e6	+	7.88221e6i	0.560793	+	0.560793i
$724$	901538.	−	1.76282e6i	0.0639202	−	0.124986i
$725$	−2.96874e6	+	2.96874e6i	−0.209762	+	0.209762i
$726$	2.52293e6	−	3.46704e6i	0.177649	−	0.244128i
$727$			7.94320e6i			0.557390i	0.960380	+	0.278695i	$0.0899019\pi$
$727$			7.94320e6i			0.557390i	−0.960380	+	0.278695i	$0.910098\pi$
$728$	−3.43479e6	+	1.04907e7i	−0.240199	+	0.733629i
$729$		−	531441.i		−	0.0370370i
$730$	1.12089e6	+	815660.i	0.0778494	+	0.0566503i
$731$	723421.	−	723421.i	0.0500723	−	0.0500723i
$732$	5.02524e6	+	1.55455e7i	0.346641	+	1.07233i
$733$	−9.59680e6	−	9.59680e6i	−0.659731	−	0.659731i	0.295586	−	0.955316i	$-0.404485\pi$
$733$	−9.59680e6	−	9.59680e6i	−0.659731	−	0.659731i	−0.955316	+	0.295586i	$0.904485\pi$
$734$	−1.65503e7	+	2.60857e6i	−1.13388	+	0.178715i
$735$	448862.			0.0306475
$736$	9.87810e6	+	9.95258e6i	0.672170	+	0.677238i
$737$	−219192.			−0.0148647
$738$	973296.	−	153406.i	0.0657816	−	0.0103681i
$739$	1.08023e7	+	1.08023e7i	0.727618	+	0.727618i	0.970145	−	0.242527i	$-0.0779762\pi$
$739$	1.08023e7	+	1.08023e7i	0.727618	+	0.727618i	−0.242527	+	0.970145i	$0.577976\pi$
$740$	714672.	+	2.21083e6i	0.0479763	+	0.148414i
$741$	−2.33952e6	+	2.33952e6i	−0.156524	+	0.156524i
$742$	−5.74762e6	−	4.18249e6i	−0.383246	−	0.278885i
$743$			2.01692e6i			0.134034i	0.997752	+	0.0670172i	$0.0213482\pi$
$743$			2.01692e6i			0.134034i	−0.997752	+	0.0670172i	$0.978652\pi$
$744$	−8.21817e6	−	2.69073e6i	−0.544305	−	0.178213i
$745$		−	1.01341e6i		−	0.0668954i
$746$	−3.36536e6	+	4.62471e6i	−0.221403	+	0.304255i
$747$	1.45842e6	−	1.45842e6i	0.0956274	−	0.0956274i
$748$	−225714.	+	441349.i	−0.0147505	+	0.0288422i
$749$	2.65917e7	+	2.65917e7i	1.73197	+	1.73197i
$750$	−254400.	−	1.61406e6i	−0.0165144	−	0.104777i
$751$	−3.01809e7			−1.95269			−0.976343	−	0.216230i	$-0.930624\pi$
$751$	−3.01809e7			−1.95269			−0.976343	+	0.216230i	$0.930624\pi$
$752$	2.08261e7	−	1.50356e7i	1.34296	−	0.969566i
$753$	−9.44108e6			−0.606784
$754$	−447242.	−	2.83757e6i	−0.0286493	−	0.181768i
$755$	569242.	+	569242.i	0.0363437	+	0.0363437i
$756$	−3.37961e6	−	1.72840e6i	−0.215061	−	0.109987i
$757$	−7.18933e6	+	7.18933e6i	−0.455983	+	0.455983i	−0.897334	−	0.441351i	$-0.854499\pi$
$757$	−7.18933e6	+	7.18933e6i	−0.455983	+	0.455983i	0.441351	+	0.897334i	$0.354499\pi$
$758$	−1.25300e7	+	1.72189e7i	−0.792099	+	1.08851i
$759$		−	6.03891e6i		−	0.380499i
$760$	816873.	−	413901.i	0.0513003	−	0.0259934i
$761$		−	2.93863e6i		−	0.183943i	−0.995762	−	0.0919714i	$-0.970683\pi$
$761$		−	2.93863e6i		−	0.183943i	0.995762	−	0.0919714i	$-0.0293168\pi$
$762$	758303.	+	551810.i	0.0473103	+	0.0344272i
$763$	4.06616e6	−	4.06616e6i	0.252856	−	0.252856i
$764$	−2.33617e6	+	755188.i	−0.144801	+	0.0468082i
$765$	−16507.9	−	16507.9i	−0.00101986	−	0.00101986i
$766$	−1.57744e6	+	248627.i	−0.0971359	+	0.0153100i
$767$	−1.44123e7			−0.884596
$768$	−8.43419e6	+	4.23379e6i	−0.515989	+	0.259016i
$769$	2.59963e7			1.58524			0.792620	−	0.609716i	$-0.208716\pi$
$769$	2.59963e7			1.58524			0.792620	+	0.609716i	$0.208716\pi$
$770$	−1.29974e6	+	204858.i	−0.0790005	+	0.0124516i
$771$	4.22791e6	+	4.22791e6i	0.256147	+	0.256147i
$772$	441301.	−	142655.i	0.0266496	−	0.00861475i
$773$	1.89206e7	−	1.89206e7i	1.13890	−	1.13890i	0.150251	−	0.988648i	$-0.451992\pi$
$773$	1.89206e7	−	1.89206e7i	1.13890	−	1.13890i	0.988648	−	0.150251i	$-0.0480081\pi$
$774$	−6.78215e6	−	4.93531e6i	−0.406926	−	0.296116i
$775$			1.64459e7i			0.983568i
$776$	−1.62366e7	+	8.22691e6i	−0.967921	+	0.490436i
$777$		−	2.06190e7i		−	1.22522i
$778$	1.37742e7	−	1.89286e7i	0.815861	−	1.12116i
$779$	1.49158e6	−	1.49158e6i	0.0880649	−	0.0880649i
$780$	495558.	+	253438.i	0.0291647	+	0.0149154i
$781$	−1.02408e7	−	1.02408e7i	−0.600767	−	0.600767i
$782$	−119155.	−	755991.i	−0.00696780	−	0.0442079i
$783$	987818.			0.0575801
$784$	−8.02915e6	+	5.79674e6i	−0.466530	+	0.336817i
$785$	−462756.			−0.0268027
$786$	2.66351e6	+	1.68989e7i	0.153779	+	0.975666i
$787$	1.44576e6	+	1.44576e6i	0.0832072	+	0.0832072i	0.747485	−	0.664278i	$-0.231261\pi$
$787$	1.44576e6	+	1.44576e6i	0.0832072	+	0.0832072i	−0.664278	+	0.747485i	$0.731261\pi$
$788$	−4.69254e6	+	9.17553e6i	−0.269211	+	0.526400i
$789$	9.03924e6	−	9.03924e6i	0.516939	−	0.516939i
$790$	1.04718e6	−	1.43904e6i	0.0596969	−	0.0820361i
$791$		−	3.08649e7i		−	1.75397i
$792$	3.86245e6	+	1.26461e6i	0.218801	+	0.0716383i
$793$			2.12592e7i			1.20050i
$794$	3.40336e6	+	2.47659e6i	0.191583	+	0.139413i
$795$	−253444.	+	253444.i	−0.0142221	+	0.0142221i
$796$	−9.63152e6	−	2.97950e7i	−0.538781	−	1.66671i
$797$	894713.	+	894713.i	0.0498928	+	0.0498928i	0.731613	−	0.681720i	$-0.238768\pi$
$797$	894713.	+	894713.i	0.0498928	+	0.0498928i	−0.681720	+	0.731613i	$0.738768\pi$
$798$	−8.02747e6	+	1.26525e6i	−0.446243	+	0.0703344i
$799$	−1.40192e6			−0.0776886
$800$	1.26433e7	+	1.27386e7i	0.698451	+	0.703717i
$801$	−7.87618e6			−0.433745
$802$	2.97559e7	−	4.68996e6i	1.63357	−	0.257474i
$803$	9.31352e6	+	9.31352e6i	0.509712	+	0.509712i
$804$	70052.2	+	216706.i	0.00382192	+	0.0118231i
$805$	1.43642e6	−	1.43642e6i	0.0781252	−	0.0781252i
$806$	−9.09843e6	−	6.62085e6i	−0.493320	−	0.358985i
$807$		−	4.96772e6i		−	0.268518i
$808$	3.44058e6	−	1.05084e7i	0.185398	−	0.566250i
$809$		−	3.34488e7i		−	1.79684i	−0.439138	−	0.898419i	$-0.644716\pi$
$809$		−	3.34488e7i		−	1.79684i	0.439138	−	0.898419i	$-0.355284\pi$
$810$	−112620.	+	154764.i	−0.00603119	+	0.00828812i
$811$	1.33105e7	−	1.33105e7i	0.710628	−	0.710628i	−0.256039	−	0.966667i	$-0.582417\pi$
$811$	1.33105e7	−	1.33105e7i	0.710628	−	0.710628i	0.966667	+	0.256039i	$0.0824175\pi$
$812$	3.21267e6	−	6.28187e6i	0.170992	−	0.334348i
$813$	4.29329e6	+	4.29329e6i	0.227805	+	0.227805i
$814$	3.43710e6	+	2.18070e7i	0.181816	+	1.15355i
$815$	−807408.			−0.0425794
$816$	508479.	+	82102.0i	0.0267330	+	0.00431647i
$817$	−1.79570e7			−0.941195
$818$	3.62997e6	+	2.30307e7i	0.189679	+	1.20344i
$819$	−3.49271e6	−	3.49271e6i	−0.181950	−	0.181950i
$820$	−315947.	−	161582.i	−0.0164089	−	0.00839184i
$821$	−1.21428e7	+	1.21428e7i	−0.628728	+	0.628728i	−0.947748	−	0.319020i	$-0.896646\pi$
$821$	−1.21428e7	+	1.21428e7i	−0.628728	+	0.628728i	0.319020	+	0.947748i	$0.396646\pi$
$822$	1.01633e7	−	1.39665e7i	0.524632	−	0.720955i
$823$		−	8.69291e6i		−	0.447369i	−0.974662	−	0.223684i	$-0.928191\pi$
$823$		−	8.69291e6i		−	0.447369i	0.974662	−	0.223684i	$-0.0718085\pi$
$824$	1.43087e6	+	2.82396e6i	0.0734148	+	0.144891i
$825$		−	7.72940e6i		−	0.395377i
$826$	−2.86233e7	−	2.08289e7i	−1.45972	−	1.06223i
$827$	−50332.2	+	50332.2i	−0.00255907	+	0.00255907i	−0.708385	−	0.705826i	$-0.750576\pi$
$827$	−50332.2	+	50332.2i	−0.00255907	+	0.00255907i	0.705826	+	0.708385i	$0.250576\pi$
$828$	−5.97040e6	+	1.92999e6i	−0.302641	+	0.0978316i
$829$	−1.04563e7	−	1.04563e7i	−0.528435	−	0.528435i	0.391670	−	0.920106i	$-0.371897\pi$
$829$	−1.04563e7	−	1.04563e7i	−0.528435	−	0.528435i	−0.920106	+	0.391670i	$0.871897\pi$
$830$	−733776.	+	115654.i	−0.0369716	+	0.00582726i
$831$	1.19297e7			0.599275
$832$	−1.21374e7	+	1.86634e6i	−0.607880	+	0.0934724i
$833$	540488.			0.0269882
$834$	1.72886e7	−	2.72494e6i	0.860688	−	0.135657i
$835$	−1.12065e6	−	1.12065e6i	−0.0556227	−	0.0556227i
$836$	8.27906e6	−	2.67628e6i	0.409699	−	0.132439i
$837$	2.73611e6	−	2.73611e6i	0.134995	−	0.134995i
$838$	2.52481e7	+	1.83728e7i	1.24199	+	0.903784i
$839$			2.27011e7i			1.11338i	0.830721	+	0.556688i	$0.187928\pi$
$839$			2.27011e7i			1.11338i	−0.830721	+	0.556688i	$0.812072\pi$
$840$	617921.	+	1.21953e6i	0.0302159	+	0.0596338i
$841$		−	1.86750e7i		−	0.910482i
$842$	2.69401e6	−	3.70214e6i	0.130954	−	0.179959i
$843$	1.43445e7	−	1.43445e7i	0.695211	−	0.695211i
$844$	1.39455e7	+	7.13197e6i	0.673870	+	0.344630i
$845$	−841816.	−	841816.i	−0.0405579	−	0.0405579i
$846$	1.78951e6	+	1.13537e7i	0.0859621	+	0.545395i
$847$	1.37045e7			0.656378
$848$	1.26050e6	−	7.80660e6i	0.0601939	−	0.372797i
$849$	1.83026e6			0.0871451
$850$	−152511.	−	967618.i	−0.00724024	−	0.0459363i
$851$	−2.41001e7	−	2.41001e7i	−1.14076	−	1.14076i
$852$	−6.85174e6	+	1.33975e7i	−0.323371	+	0.632302i
$853$	−2.54709e7	+	2.54709e7i	−1.19859	+	1.19859i	−0.224007	+	0.974587i	$0.571914\pi$
$853$	−2.54709e7	+	2.54709e7i	−1.19859	+	1.19859i	−0.974587	+	0.224007i	$0.928086\pi$
$854$	−3.07241e7	+	4.22214e7i	−1.44157	+	1.98102i
$855$			409766.i			0.0191699i
$856$	−1.30175e7	+	3.97586e7i	−0.607214	+	1.85458i
$857$		−	6.42467e6i		−	0.298812i	−0.988776	−	0.149406i	$-0.952264\pi$
$857$		−	6.42467e6i		−	0.298812i	0.988776	−	0.149406i	$-0.0477362\pi$
$858$	4.27616e6	+	3.11172e6i	0.198306	+	0.144305i
$859$	1.66700e6	−	1.66700e6i	0.0770818	−	0.0770818i	−0.667515	−	0.744597i	$-0.732642\pi$
$859$	1.66700e6	−	1.66700e6i	0.0770818	−	0.0770818i	0.744597	+	0.667515i	$0.232642\pi$
$860$	929201.	+	2.87447e6i	0.0428414	+	0.132529i
$861$	2.22681e6	+	2.22681e6i	0.102371	+	0.102371i
$862$	1.01633e7	−	1.60189e6i	0.465874	−	0.0734285i
$863$	6.48401e6			0.296358			0.148179	−	0.988961i	$-0.452659\pi$
$863$	6.48401e6			0.296358			0.148179	+	0.988961i	$0.452659\pi$
$864$	15859.8	−	4.22279e6i	0.000722790	−	0.192449i
$865$	1.44866e6			0.0658304
$866$	−2.26021e7	+	3.56242e6i	−1.02413	+	0.161418i
$867$	9.01604e6	+	9.01604e6i	0.407350	+	0.407350i
$868$	−8.50122e6	−	2.62984e7i	−0.382985	−	1.18476i
$869$	1.19570e7	−	1.19570e7i	0.537124	−	0.537124i
$870$	−287667.	−	209333.i	−0.0128852	−	0.00937647i
$871$			296354.i			0.0132363i
$872$	6.07952e6	+	1.99051e6i	0.270756	+	0.0886490i
$873$		−	8.14472e6i		−	0.361693i
$874$	−7.90389e6	+	1.08616e7i	−0.349995	+	0.480967i
$875$	3.69282e6	−	3.69282e6i	0.163056	−	0.163056i
$876$	6.23133e6	−	1.21844e7i	0.274360	−	0.536468i
$877$	−3.33213e6	−	3.33213e6i	−0.146293	−	0.146293i	0.630167	−	0.776460i	$-0.282986\pi$
$877$	−3.33213e6	−	3.33213e6i	−0.146293	−	0.146293i	−0.776460	+	0.630167i	$0.782986\pi$
$878$	−3.71448e6	−	2.35668e7i	−0.162615	−	1.03173i
$879$	2.39443e7			1.04528
$880$	−856812.	−	1.18678e6i	−0.0372974	−	0.0516612i
$881$	−3.62141e7			−1.57195			−0.785974	−	0.618260i	$-0.787838\pi$
$881$	−3.62141e7			−1.57195			−0.785974	+	0.618260i	$0.787838\pi$
$882$	−689914.	−	4.37722e6i	−0.0298623	−	0.189464i
$883$	−5.61515e6	−	5.61515e6i	−0.242359	−	0.242359i	0.575466	−	0.817825i	$-0.304821\pi$
$883$	−5.61515e6	−	5.61515e6i	−0.242359	−	0.242359i	−0.817825	+	0.575466i	$0.804821\pi$
$884$	596716.	+	305172.i	0.0256825	+	0.0131345i
$885$	−1.26216e6	+	1.26216e6i	−0.0541696	+	0.0541696i
$886$	2.58204e6	−	3.54826e6i	0.110504	−	0.151856i
$887$		−	2.90982e7i		−	1.24181i	−0.783884	−	0.620907i	$-0.786764\pi$
$887$		−	2.90982e7i		−	1.24181i	0.783884	−	0.620907i	$-0.213236\pi$
$888$	2.04611e7	−	1.03675e7i	0.870757	−	0.441204i
$889$			2.99741e6i			0.127202i
$890$	2.29366e6	+	1.66908e6i	0.0970631	+	0.0706319i
$891$	−1.28594e6	+	1.28594e6i	−0.0542658	+	0.0542658i
$892$	2.81044e7	−	9.08502e6i	1.18267	−	0.382308i
$893$	1.73996e7	+	1.73996e7i	0.730145	+	0.730145i
$894$	−9.88264e6	+	1.55765e6i	−0.413551	+	0.0651816i
$895$	−2.41740e6			−0.100877
$896$	−2.68026e7	−	1.38346e7i	−1.11534	−	0.575700i
$897$	−8.16477e6			−0.338815
$898$	−2.81202e7	+	4.43216e6i	−1.16366	+	0.183411i
$899$	5.08575e6	+	5.08575e6i	0.209873	+	0.209873i
$900$	−7.64172e6	+	2.47026e6i	−0.314474	+	0.101657i
$901$	−305179.	+	305179.i	−0.0125240	+	0.0125240i
$902$	−2.72630e6	−	1.98391e6i	−0.111573	−	0.0811904i
$903$		−	2.68084e7i		−	1.09409i
$904$	3.06285e7	−	1.55192e7i	1.24653	−	0.631607i
$905$		−	319090.i		−	0.0129506i
$906$	4.67621e6	−	6.42609e6i	0.189266	−	0.260092i
$907$	2.98113e7	−	2.98113e7i	1.20327	−	1.20327i	0.230102	−	0.973167i	$-0.426094\pi$
$907$	2.98113e7	−	2.98113e7i	1.20327	−	1.20327i	0.973167	−	0.230102i	$-0.0739058\pi$
$908$	3.29128e6	+	1.68322e6i	0.132480	+	0.0677528i
$909$	3.49860e6	+	3.49860e6i	0.140438	+	0.140438i
$910$	276974.	+	1.75729e6i	0.0110875	+	0.0703459i
$911$	5.88622e6			0.234985			0.117493	−	0.993074i	$-0.462514\pi$
$911$	5.88622e6			0.234985			0.117493	+	0.993074i	$0.462514\pi$
$912$	−5.29185e6	−	7.32982e6i	−0.210679	−	0.291814i
$913$	−7.05796e6			−0.280222
$914$	4.66892e6	+	2.96224e7i	0.184864	+	1.17288i
$915$	1.86177e6	+	1.86177e6i	0.0735146	+	0.0735146i
$916$	7.72130e6	−	1.50978e7i	0.304055	−	0.594531i
$917$	−3.86630e7	+	3.86630e7i	−1.51835	+	1.51835i
$918$	−135609.	+	186355.i	−0.00531107	+	0.00729853i
$919$			3.26295e7i			1.27445i	0.770679	+	0.637224i	$0.219917\pi$
$919$			3.26295e7i			1.27445i	−0.770679	+	0.637224i	$0.780083\pi$
$920$	2.14766e6	+	703173.i	0.0836559	+	0.0273900i
$921$			1.41202e7i			0.548521i
$922$	7.20470e6	+	5.24279e6i	0.279118	+	0.203112i
$923$	−1.38458e7	+	1.38458e7i	−0.534952	+	0.534952i
$924$	3.99548e6	+	1.23600e7i	0.153953	+	0.476253i
$925$	−3.08466e7	−	3.08466e7i	−1.18537	−	1.18537i
$926$	2.71085e7	−	4.27269e6i	1.03891	−	0.163747i
$927$	−1.41658e6			−0.0541429
$928$	7.84913e6	+	29479.4i	0.299193	+	0.00112369i
$929$	3.95087e7			1.50194			0.750972	−	0.660334i	$-0.229585\pi$
$929$	3.95087e7			1.50194			0.750972	+	0.660334i	$0.229585\pi$
$930$	−1.37662e6	+	216975.i	−0.0521922	+	0.00822624i
$931$	−6.70811e6	−	6.70811e6i	−0.253645	−	0.253645i
$932$	−3.66911e6	−	1.13503e7i	−0.138363	−	0.428025i
$933$	−1.08061e6	+	1.08061e6i	−0.0406410	+	0.0406410i
$934$	−1.24596e7	−	9.06674e6i	−0.467344	−	0.340082i
$935$			79889.1i			0.00298854i
$936$	1.70979e6	−	5.22213e6i	0.0637902	−	0.194831i
$937$			2.56610e7i			0.954825i	0.878679	+	0.477413i	$0.158425\pi$
$937$			2.56610e7i			0.954825i	−0.878679	+	0.477413i	$0.841575\pi$
$938$	−428296.	+	588569.i	−0.0158941	+	0.0218419i
$939$	−1.94296e7	+	1.94296e7i	−0.719118	+	0.719118i
$940$	1.88488e6	−	3.68558e6i	0.0695767	−	0.136046i
$941$	−1.58947e7	−	1.58947e7i	−0.585166	−	0.585166i	0.351153	−	0.936318i	$-0.385790\pi$
$941$	−1.58947e7	−	1.58947e7i	−0.585166	−	0.585166i	−0.936318	+	0.351153i	$0.885790\pi$
$942$	711270.	+	4.51272e6i	0.0261160	+	0.165696i
$943$	5.20552e6			0.190627
$944$	6.27732e6	−	3.88771e7i	0.229269	−	1.41992i
$945$	−611748.			−0.0222840
$946$	4.46884e6	+	2.83530e7i	0.162356	+	1.03008i
$947$	3.26052e7	+	3.26052e7i	1.18144	+	1.18144i	0.979371	+	0.202069i	$0.0647666\pi$
$947$	3.26052e7	+	3.26052e7i	1.18144	+	1.18144i	0.202069	+	0.979371i	$0.435233\pi$
$948$	−1.56428e7	−	8.00002e6i	−0.565319	−	0.289115i
$949$	1.25921e7	−	1.25921e7i	0.453872	−	0.453872i
$950$	−1.01165e7	+	1.39021e7i	−0.363680	+	0.499773i
$951$			1.54019e7i			0.552235i
$952$	744058.	+	1.46847e6i	0.0266081	+	0.0525136i
$953$			3.93496e7i			1.40349i	0.712431	+	0.701743i	$0.247594\pi$
$953$			3.93496e7i			1.40349i	−0.712431	+	0.701743i	$0.752406\pi$
$954$	2.86109e6	+	2.08199e6i	0.101779	+	0.0740640i
$955$	−279785.	+	279785.i	−0.00992695	+	0.00992695i
$956$	−4.62911e7	+	1.49640e7i	−1.63815	+	0.529547i
$957$	−2.39024e6	−	2.39024e6i	−0.0843650	−	0.0843650i
$958$	4.65754e7	−	7.34096e6i	1.63962	−	0.258428i
$959$	5.52067e7			1.93841
$960$	−899489.	+	1.22638e6i	−0.0315005	+	0.0429484i
$961$	−455659.			−0.0159159
$962$	2.94837e7	−	4.64705e6i	1.02717	−	0.161897i
$963$	−1.32370e7	−	1.32370e7i	−0.459963	−	0.459963i
$964$	−3.77128e7	+	1.21910e7i	−1.30706	+	0.422520i
$965$	52851.2	−	52851.2i	0.00182699	−	0.00182699i
$966$	−1.62155e7	−	1.17999e7i	−0.559098	−	0.406850i
$967$			4.06989e7i			1.39964i	0.714319	+	0.699820i	$0.246737\pi$
$967$			4.06989e7i			1.39964i	−0.714319	+	0.699820i	$0.753263\pi$
$968$	6.89075e6	+	1.35995e7i	0.236362	+	0.466483i
$969$			493412.i			0.0168811i
$970$	−1.72598e6	+	2.37186e6i	−0.0588989	+	0.0809395i
$971$	−1.81122e7	+	1.81122e7i	−0.616486	+	0.616486i	−0.944628	−	0.328143i	$-0.893577\pi$
$971$	−1.81122e7	+	1.81122e7i	−0.616486	+	0.616486i	0.328143	+	0.944628i	$0.393577\pi$
$972$	1.68233e6	+	860374.i	0.0571143	+	0.0292093i
$973$	3.95548e7	+	3.95548e7i	1.33942	+	1.33942i
$974$	−6.47011e6	−	4.10502e7i	−0.218532	−	1.38649i
$975$	−1.04504e7			−0.352063
$976$	−5.73465e7	−	9.25950e6i	−1.92700	−	0.311145i
$977$	−4.58366e7			−1.53630			−0.768150	−	0.640270i	$-0.778822\pi$
$977$	−4.58366e7			−1.53630			−0.768150	+	0.640270i	$0.778822\pi$
$978$	1.24101e6	+	7.87370e6i	0.0414885	+	0.263228i
$979$	1.90581e7	+	1.90581e7i	0.635512	+	0.635512i
$980$	−726684.	+	1.42092e6i	−0.0241702	+	0.0472610i
$981$	−2.02408e6	+	2.02408e6i	−0.0671513	+	0.0671513i
$982$	1.96053e6	−	2.69419e6i	0.0648777	−	0.0891556i
$983$			2.19349e6i			0.0724022i	0.999345	+	0.0362011i	$0.0115257\pi$
$983$			2.19349e6i			0.0724022i	−0.999345	+	0.0362011i	$0.988474\pi$
$984$	−1.09009e6	+	3.32942e6i	−0.0358902	+	0.109618i
$985$			1.66087e6i			0.0545439i
$986$	−346389.	−	252064.i	−0.0113468	−	0.00825693i
$987$	−2.59761e7	+	2.59761e7i	−0.848754	+	0.848754i
$988$	−3.61841e6	−	1.11935e7i	−0.117930	−	0.364816i
$989$	−3.13345e7	−	3.13345e7i	−1.01867	−	1.01867i
$990$	646994.	−	101976.i	0.0209803	−	0.00330680i
$991$	−4.58885e6			−0.148429			−0.0742147	−	0.997242i	$-0.523645\pi$
$991$	−4.58885e6			−0.148429			−0.0742147	+	0.997242i	$0.523645\pi$
$992$	2.18225e7	−	2.16592e7i	0.704087	−	0.698818i
$993$	3.24439e6			0.104414
$994$	−4.75085e7	+	7.48804e6i	−1.52513	+	0.240382i
$995$	−3.56832e6	−	3.56832e6i	−0.114263	−	0.114263i
$996$	2.25567e6	+	6.97789e6i	0.0720488	+	0.222882i
$997$	4.40125e6	−	4.40125e6i	0.140229	−	0.140229i	−0.633507	−	0.773737i	$-0.718385\pi$
$997$	4.40125e6	−	4.40125e6i	0.140229	−	0.140229i	0.773737	+	0.633507i	$0.218385\pi$
$998$	2.51168e7	+	1.82773e7i	0.798249	+	0.580878i
$999$			1.02639e7i			0.325385i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.6.j.a.13.19	✓	40
3.2	odd	2		144.6.k.c.109.2		40
4.3	odd	2		192.6.j.a.145.17		40
8.3	odd	2		384.6.j.b.289.4		40
8.5	even	2		384.6.j.a.289.17		40
12.11	even	2		576.6.k.c.145.11		40
16.3	odd	4		384.6.j.b.97.4		40
16.5	even	4	inner	48.6.j.a.37.19	yes	40
16.11	odd	4		192.6.j.a.49.17		40
16.13	even	4		384.6.j.a.97.17		40
48.5	odd	4		144.6.k.c.37.2		40
48.11	even	4		576.6.k.c.433.11		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.6.j.a.13.19	✓	40	1.1	even	1	trivial
48.6.j.a.37.19	yes	40	16.5	even	4	inner
144.6.k.c.37.2		40	48.5	odd	4
144.6.k.c.109.2		40	3.2	odd	2
192.6.j.a.49.17		40	16.11	odd	4
192.6.j.a.145.17		40	4.3	odd	2
384.6.j.a.97.17		40	16.13	even	4
384.6.j.a.289.17		40	8.5	even	2
384.6.j.b.97.4		40	16.3	odd	4
384.6.j.b.289.4		40	8.3	odd	2
576.6.k.c.145.11		40	12.11	even	2
576.6.k.c.433.11		40	48.11	even	4

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	48.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(5.58787 - 0.880730i) q^{2} +(-6.36396 - 6.36396i) q^{3} +(30.4486 - 9.84281i) q^{4} +(3.64660 - 3.64660i) q^{5} +(-41.1659 - 29.9561i) q^{6} -162.720i q^{7} +(161.474 - 81.8174i) q^{8} +81.0000i q^{9} +O(q^{10})\)	\(q+(5.58787 - 0.880730i) q^{2} +(-6.36396 - 6.36396i) q^{3} +(30.4486 - 9.84281i) q^{4} +(3.64660 - 3.64660i) q^{5} +(-41.1659 - 29.9561i) q^{6} -162.720i q^{7} +(161.474 - 81.8174i) q^{8} +81.0000i q^{9} +(17.1651 - 23.5884i) q^{10} +(195.997 - 195.997i) q^{11} +(-256.413 - 131.135i) q^{12} +(-264.994 - 264.994i) q^{13} +(-143.313 - 909.260i) q^{14} -46.4137 q^{15} +(830.238 - 599.400i) q^{16} -55.8881 q^{17} +(71.3391 + 452.618i) q^{18} +(693.638 + 693.638i) q^{19} +(75.1412 - 146.927i) q^{20} +(-1035.55 + 1035.55i) q^{21} +(922.588 - 1267.83i) q^{22} +2420.75i q^{23} +(-1548.30 - 506.933i) q^{24} +3098.40i q^{25} +(-1714.14 - 1247.36i) q^{26} +(515.481 - 515.481i) q^{27} +(-1601.63 - 4954.61i) q^{28} +(958.152 + 958.152i) q^{29} +(-259.354 + 40.8779i) q^{30} +5307.87 q^{31} +(4111.35 - 4080.59i) q^{32} -2494.64 q^{33} +(-312.295 + 49.2223i) q^{34} +(-593.376 - 593.376i) q^{35} +(797.268 + 2466.34i) q^{36} +(-9955.63 + 9955.63i) q^{37} +(4486.87 + 3265.05i) q^{38} +3372.82i q^{39} +(290.477 - 887.187i) q^{40} -2150.37i q^{41} +(-4874.46 + 6698.53i) q^{42} +(-12944.1 + 12944.1i) q^{43} +(4038.69 - 7897.02i) q^{44} +(295.375 + 295.375i) q^{45} +(2132.03 + 13526.9i) q^{46} +25084.5 q^{47} +(-9098.16 - 1469.04i) q^{48} -9670.91 q^{49} +(2728.86 + 17313.5i) q^{50} +(355.670 + 355.670i) q^{51} +(-10677.0 - 5460.42i) q^{52} +(5460.54 - 5460.54i) q^{53} +(2426.44 - 3334.44i) q^{54} -1429.45i q^{55} +(-13313.4 - 26275.1i) q^{56} -8828.57i q^{57} +(6197.90 + 4510.16i) q^{58} +(27193.7 - 27193.7i) q^{59} +(-1413.23 + 456.841i) q^{60} +(-40112.6 - 40112.6i) q^{61} +(29659.7 - 4674.80i) q^{62} +13180.3 q^{63} +(19379.8 - 26422.8i) q^{64} -1932.65 q^{65} +(-13939.7 + 2197.10i) q^{66} +(-559.172 - 559.172i) q^{67} +(-1701.72 + 550.096i) q^{68} +(15405.6 - 15405.6i) q^{69} +(-3838.31 - 2793.11i) q^{70} -52249.6i q^{71} +(6627.21 + 13079.4i) q^{72} +47518.6i q^{73} +(-46862.6 + 64399.0i) q^{74} +(19718.1 - 19718.1i) q^{75} +(27947.7 + 14293.0i) q^{76} +(-31892.8 - 31892.8i) q^{77} +(2970.54 + 18846.9i) q^{78} +61006.2 q^{79} +(841.774 - 5213.32i) q^{80} -6561.00 q^{81} +(-1893.90 - 12016.0i) q^{82} +(-18005.2 - 18005.2i) q^{83} +(-21338.3 + 41723.6i) q^{84} +(-203.802 + 203.802i) q^{85} +(-60929.7 + 83730.3i) q^{86} -12195.3i q^{87} +(15612.5 - 47684.5i) q^{88} +97236.7i q^{89} +(1910.66 + 1390.37i) q^{90} +(-43119.9 + 43119.9i) q^{91} +(23827.0 + 73708.7i) q^{92} +(-33779.1 - 33779.1i) q^{93} +(140169. - 22092.7i) q^{94} +5058.84 q^{95} +(-52133.2 - 195.799i) q^{96} -100552. q^{97} +(-54039.8 + 8517.46i) q^{98} +(15875.8 + 15875.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 44 q^{4} - 492 q^{8}+O(q^{10}) \) 40 * q + 44 * q^4 - 492 * q^8	\( 40 q + 44 q^{4} - 492 q^{8} + 968 q^{10} + 1208 q^{11} - 792 q^{12} + 324 q^{14} - 1800 q^{15} - 384 q^{16} - 324 q^{18} + 2360 q^{19} - 7600 q^{20} - 1024 q^{22} + 5220 q^{24} - 12980 q^{26} + 10472 q^{28} - 8144 q^{29} - 1368 q^{30} + 23064 q^{31} + 44160 q^{32} + 4864 q^{34} - 4776 q^{35} - 1620 q^{36} + 21296 q^{37} - 72088 q^{38} - 90864 q^{40} - 14220 q^{42} + 31416 q^{43} + 43768 q^{44} + 90664 q^{46} + 44784 q^{48} - 96040 q^{49} + 106212 q^{50} + 10440 q^{51} - 116432 q^{52} - 49456 q^{53} - 14580 q^{54} - 158592 q^{56} - 111472 q^{58} + 28960 q^{59} + 49464 q^{60} + 48080 q^{61} + 191100 q^{62} + 31752 q^{63} + 369032 q^{64} - 55376 q^{65} + 63720 q^{66} + 101488 q^{67} - 122336 q^{68} - 22320 q^{69} - 460192 q^{70} - 28836 q^{72} - 94996 q^{74} - 96624 q^{75} + 211304 q^{76} - 14896 q^{77} + 200124 q^{78} - 71960 q^{79} + 623368 q^{80} - 262440 q^{81} + 33880 q^{82} - 126440 q^{83} - 116856 q^{84} + 132400 q^{85} - 581168 q^{86} - 466400 q^{88} - 46008 q^{90} + 429496 q^{91} - 12752 q^{92} + 524120 q^{94} - 76848 q^{95} + 51840 q^{96} + 477736 q^{98} + 97848 q^{99}+O(q^{100}) \) 40 * q + 44 * q^4 - 492 * q^8 + 968 * q^10 + 1208 * q^11 - 792 * q^12 + 324 * q^14 - 1800 * q^15 - 384 * q^16 - 324 * q^18 + 2360 * q^19 - 7600 * q^20 - 1024 * q^22 + 5220 * q^24 - 12980 * q^26 + 10472 * q^28 - 8144 * q^29 - 1368 * q^30 + 23064 * q^31 + 44160 * q^32 + 4864 * q^34 - 4776 * q^35 - 1620 * q^36 + 21296 * q^37 - 72088 * q^38 - 90864 * q^40 - 14220 * q^42 + 31416 * q^43 + 43768 * q^44 + 90664 * q^46 + 44784 * q^48 - 96040 * q^49 + 106212 * q^50 + 10440 * q^51 - 116432 * q^52 - 49456 * q^53 - 14580 * q^54 - 158592 * q^56 - 111472 * q^58 + 28960 * q^59 + 49464 * q^60 + 48080 * q^61 + 191100 * q^62 + 31752 * q^63 + 369032 * q^64 - 55376 * q^65 + 63720 * q^66 + 101488 * q^67 - 122336 * q^68 - 22320 * q^69 - 460192 * q^70 - 28836 * q^72 - 94996 * q^74 - 96624 * q^75 + 211304 * q^76 - 14896 * q^77 + 200124 * q^78 - 71960 * q^79 + 623368 * q^80 - 262440 * q^81 + 33880 * q^82 - 126440 * q^83 - 116856 * q^84 + 132400 * q^85 - 581168 * q^86 - 466400 * q^88 - 46008 * q^90 + 429496 * q^91 - 12752 * q^92 + 524120 * q^94 - 76848 * q^95 + 51840 * q^96 + 477736 * q^98 + 97848 * q^99

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