LMFDB - Embedded newform 102.5.g.d.83.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [102,5,Mod(53,102)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(102, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("102.53");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 102 = 2 \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	102.g (of order $8$, degree $4$, 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:	$10.5437362346$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			83.7
Character	$\chi$	$=$	102.83
Dual form			102.5.g.d.59.7

$q$-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 - 2.00000i) q^{2} +(1.73792 - 8.83061i) q^{3} -8.00000i q^{4} +(-7.65773 - 18.4874i) q^{5} +(-14.1854 - 21.1371i) q^{6} +(3.64521 + 1.50990i) q^{7} +(-16.0000 - 16.0000i) q^{8} +(-74.9592 - 30.6938i) q^{9} +(-52.2903 - 21.6593i) q^{10} +(25.7810 + 10.6788i) q^{11} +(-70.6449 - 13.9034i) q^{12} -9.18287i q^{13} +(10.3102 - 4.27063i) q^{14} +(-176.563 + 35.4927i) q^{15} -64.0000 q^{16} +(106.428 + 268.690i) q^{17} +(-211.306 + 88.5308i) q^{18} +(-360.583 - 360.583i) q^{19} +(-147.899 + 61.2618i) q^{20} +(19.6684 - 29.5653i) q^{21} +(72.9196 - 30.2043i) q^{22} +(240.696 + 99.6995i) q^{23} +(-169.096 + 113.483i) q^{24} +(158.799 - 158.799i) q^{25} +(-18.3657 - 18.3657i) q^{26} +(-401.319 + 608.592i) q^{27} +(12.0792 - 29.1617i) q^{28} +(13.8218 + 33.3687i) q^{29} +(-282.141 + 424.112i) q^{30} +(-540.837 - 1305.70i) q^{31} +(-128.000 + 128.000i) q^{32} +(139.106 - 209.103i) q^{33} +(750.235 + 324.524i) q^{34} -78.9528i q^{35} +(-245.551 + 599.674i) q^{36} +(56.2456 + 135.789i) q^{37} -1442.33 q^{38} +(-81.0903 - 15.9591i) q^{39} +(-173.275 + 418.322i) q^{40} +(520.910 - 1257.59i) q^{41} +(-19.7939 - 98.4674i) q^{42} +(868.612 - 868.612i) q^{43} +(85.4306 - 206.248i) q^{44} +(6.56867 + 1620.85i) q^{45} +(680.790 - 281.993i) q^{46} +2737.29 q^{47} +(-111.227 + 565.159i) q^{48} +(-1686.76 - 1686.76i) q^{49} -635.195i q^{50} +(2557.66 - 472.860i) q^{51} -73.4630 q^{52} +(1559.93 - 1559.93i) q^{53} +(414.547 + 2019.82i) q^{54} -558.399i q^{55} +(-34.1650 - 82.4817i) q^{56} +(-3810.83 + 2557.50i) q^{57} +(94.3809 + 39.0938i) q^{58} +(2222.40 + 2222.40i) q^{59} +(283.942 + 1412.51i) q^{60} +(1138.60 + 471.625i) q^{61} +(-3693.07 - 1529.72i) q^{62} +(-226.898 - 225.066i) q^{63} +512.000i q^{64} +(-169.767 + 70.3200i) q^{65} +(-139.994 - 696.417i) q^{66} +7869.59 q^{67} +(2149.52 - 851.423i) q^{68} +(1298.72 - 1952.22i) q^{69} +(-157.906 - 157.906i) q^{70} +(-1085.42 + 449.597i) q^{71} +(708.247 + 1690.45i) q^{72} +(2739.63 - 1134.79i) q^{73} +(384.069 + 159.087i) q^{74} +(-1126.31 - 1678.27i) q^{75} +(-2884.66 + 2884.66i) q^{76} +(77.8532 + 77.8532i) q^{77} +(-194.099 + 130.262i) q^{78} +(1484.13 - 3583.01i) q^{79} +(490.095 + 1183.19i) q^{80} +(4676.78 + 4601.57i) q^{81} +(-1473.36 - 3557.00i) q^{82} +(-1937.39 + 1937.39i) q^{83} +(-236.523 - 157.347i) q^{84} +(4152.38 - 4025.13i) q^{85} -3474.45i q^{86} +(318.687 - 64.0623i) q^{87} +(-241.634 - 583.357i) q^{88} -3544.63 q^{89} +(3254.83 + 3228.56i) q^{90} +(13.8652 - 33.4735i) q^{91} +(797.596 - 1925.57i) q^{92} +(-12470.0 + 2506.72i) q^{93} +(5474.57 - 5474.57i) q^{94} +(-3904.99 + 9427.49i) q^{95} +(907.864 + 1352.77i) q^{96} +(-8873.53 + 3675.54i) q^{97} -6747.02 q^{98} +(-1604.75 - 1591.79i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 88 q^{2} - 4 q^{3} + 72 q^{5} - 40 q^{6} + 132 q^{7} - 704 q^{8} + 324 q^{9} + 384 q^{10} - 616 q^{11} - 128 q^{12} + 416 q^{14} - 908 q^{15} - 2816 q^{16} + 424 q^{17} + 1016 q^{18} + 568 q^{19}+ \cdots + 91704 q^{99}+O(q^{100}) $ 44 * q + 88 * q^2 - 4 * q^3 + 72 * q^5 - 40 * q^6 + 132 * q^7 - 704 * q^8 + 324 * q^9 + 384 * q^10 - 616 * q^11 - 128 * q^12 + 416 * q^14 - 908 * q^15 - 2816 * q^16 + 424 * q^17 + 1016 * q^18 + 568 * q^19 + 960 * q^20 + 1020 * q^21 + 424 * q^22 + 332 * q^23 - 192 * q^24 + 1888 * q^25 - 1008 * q^26 - 436 * q^27 + 608 * q^28 - 6688 * q^29 - 2000 * q^30 - 1428 * q^31 - 5632 * q^32 + 2224 * q^33 + 512 * q^34 + 1472 * q^36 + 296 * q^37 + 2272 * q^38 - 3720 * q^39 + 768 * q^40 + 4592 * q^41 + 3328 * q^42 - 228 * q^43 + 6624 * q^44 + 8228 * q^45 + 1872 * q^46 + 10712 * q^47 + 256 * q^48 + 5304 * q^49 - 3984 * q^51 - 4032 * q^52 - 5656 * q^53 - 9288 * q^54 - 896 * q^56 - 13364 * q^57 - 11472 * q^58 + 3620 * q^59 - 736 * q^60 - 10448 * q^61 - 3536 * q^62 + 28248 * q^63 - 13760 * q^65 + 12952 * q^66 - 18584 * q^67 - 1344 * q^68 + 6500 * q^69 - 9664 * q^70 + 36660 * q^71 - 2240 * q^72 + 18008 * q^73 - 144 * q^74 + 30268 * q^75 + 4544 * q^76 - 5704 * q^77 - 22576 * q^78 - 7324 * q^79 - 4608 * q^80 - 33668 * q^81 + 11160 * q^82 - 12620 * q^83 + 5152 * q^84 - 10896 * q^85 + 23860 * q^87 + 23104 * q^88 - 5040 * q^89 - 8784 * q^90 + 52368 * q^91 + 4832 * q^92 - 1304 * q^93 + 21424 * q^94 + 16032 * q^95 + 2560 * q^96 - 40164 * q^97 + 21216 * q^98 + 91704 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/102\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	2.00000	−	2.00000i	0.500000	−	0.500000i
$2$	2.00000	−	2.00000i	0.500000	−	0.500000i
$3$	1.73792	−	8.83061i	0.193103	−	0.981179i
$3$	1.73792	−	8.83061i	0.193103	−	0.981179i
$4$		−	8.00000i		−	0.500000i
$5$	−7.65773	−	18.4874i	−0.306309	−	0.739496i	−0.999819	−	0.0190482i	$-0.993936\pi$
$5$	−7.65773	−	18.4874i	−0.306309	−	0.739496i	0.693509	−	0.720448i	$-0.256064\pi$
$6$	−14.1854	−	21.1371i	−0.394038	−	0.587141i
$7$	3.64521	+	1.50990i	0.0743920	+	0.0308142i	0.419569	−	0.907723i	$-0.362181\pi$
$7$	3.64521	+	1.50990i	0.0743920	+	0.0308142i	−0.345177	+	0.938538i	$0.612181\pi$
$8$	−16.0000	−	16.0000i	−0.250000	−	0.250000i
$9$	−74.9592	−	30.6938i	−0.925423	−	0.378936i
$10$	−52.2903	−	21.6593i	−0.522903	−	0.216593i
$11$	25.7810	+	10.6788i	0.213066	+	0.0882548i	0.486664	−	0.873589i	$-0.338214\pi$
$11$	25.7810	+	10.6788i	0.213066	+	0.0882548i	−0.273598	+	0.961844i	$0.588214\pi$
$12$	−70.6449	−	13.9034i	−0.490589	−	0.0965513i
$13$		−	9.18287i		−	0.0543365i	−0.999631	−	0.0271683i	$-0.991351\pi$
$13$		−	9.18287i		−	0.0543365i	0.999631	−	0.0271683i	$-0.00864899\pi$
$14$	10.3102	−	4.27063i	0.0526031	−	0.0217889i
$15$	−176.563	+	35.4927i	−0.784727	+	0.157745i
$16$	−64.0000			−0.250000
$17$	106.428	+	268.690i	0.368262	+	0.929722i
$17$	106.428	+	268.690i	0.368262	+	0.929722i
$18$	−211.306	+	88.5308i	−0.652179	+	0.273243i
$19$	−360.583	−	360.583i	−0.998845	−	0.998845i	0.00115466	−	0.999999i	$-0.499632\pi$
$19$	−360.583	−	360.583i	−0.998845	−	0.998845i	−0.999999	+	0.00115466i	$0.999632\pi$
$20$	−147.899	+	61.2618i	−0.369748	+	0.153155i
$21$	19.6684	−	29.5653i	0.0445995	−	0.0670416i
$22$	72.9196	−	30.2043i	0.150660	−	0.0624056i
$23$	240.696	+	99.6995i	0.455001	+	0.188468i	0.598400	−	0.801197i	$-0.295803\pi$
$23$	240.696	+	99.6995i	0.455001	+	0.188468i	−0.143399	+	0.989665i	$0.545803\pi$
$24$	−169.096	+	113.483i	−0.293570	+	0.197019i
$25$	158.799	−	158.799i	0.254078	−	0.254078i
$26$	−18.3657	−	18.3657i	−0.0271683	−	0.0271683i
$27$	−401.319	+	608.592i	−0.550506	+	0.834831i
$28$	12.0792	−	29.1617i	0.0154071	−	0.0371960i
$29$	13.8218	+	33.3687i	0.0164349	+	0.0396774i	0.931884	−	0.362757i	$-0.118164\pi$
$29$	13.8218	+	33.3687i	0.0164349	+	0.0396774i	−0.915449	+	0.402434i	$0.868164\pi$
$30$	−282.141	+	424.112i	−0.313491	+	0.471236i
$31$	−540.837	−	1305.70i	−0.562786	−	1.35869i	−0.907529	−	0.419989i	$-0.862034\pi$
$31$	−540.837	−	1305.70i	−0.562786	−	1.35869i	0.344743	−	0.938697i	$-0.387966\pi$
$32$	−128.000	+	128.000i	−0.125000	+	0.125000i
$33$	139.106	−	209.103i	0.127737	−	0.192014i
$34$	750.235	+	324.524i	0.648992	+	0.280730i
$35$		−	78.9528i		−	0.0644513i
$36$	−245.551	+	599.674i	−0.189468	+	0.462711i
$37$	56.2456	+	135.789i	0.0410852	+	0.0991884i	0.943090	−	0.332537i	$-0.107905\pi$
$37$	56.2456	+	135.789i	0.0410852	+	0.0991884i	−0.902005	+	0.431726i	$0.857905\pi$
$38$	−1442.33			−0.998845
$39$	−81.0903	−	15.9591i	−0.0533138	−	0.0104925i
$40$	−173.275	+	418.322i	−0.108297	+	0.261451i
$41$	520.910	−	1257.59i	0.309881	−	0.748119i	−0.689827	−	0.723974i	$-0.742314\pi$
$41$	520.910	−	1257.59i	0.309881	−	0.748119i	0.999708	−	0.0241453i	$-0.00768644\pi$
$42$	−19.7939	−	98.4674i	−0.0112210	−	0.0558205i
$43$	868.612	−	868.612i	0.469774	−	0.469774i	−0.432067	−	0.901841i	$-0.642216\pi$
$43$	868.612	−	868.612i	0.469774	−	0.469774i	0.901841	+	0.432067i	$0.142216\pi$
$44$	85.4306	−	206.248i	0.0441274	−	0.106533i
$45$	6.56867	+	1620.85i	0.00324379	+	0.800418i
$46$	680.790	−	281.993i	0.321735	−	0.133267i
$47$	2737.29			1.23915			0.619576	−	0.784937i	$-0.287305\pi$
$47$	2737.29			1.23915			0.619576	+	0.784937i	$0.287305\pi$
$48$	−111.227	+	565.159i	−0.0482756	+	0.245295i
$49$	−1686.76	−	1686.76i	−0.702522	−	0.702522i
$50$		−	635.195i		−	0.254078i
$51$	2557.66	−	472.860i	0.983336	−	0.181799i
$52$	−73.4630			−0.0271683
$53$	1559.93	−	1559.93i	0.555334	−	0.555334i	−0.372641	−	0.927975i	$-0.621548\pi$
$53$	1559.93	−	1559.93i	0.555334	−	0.555334i	0.927975	+	0.372641i	$0.121548\pi$
$54$	414.547	+	2019.82i	0.142163	+	0.692669i
$55$		−	558.399i		−	0.184595i
$56$	−34.1650	−	82.4817i	−0.0108945	−	0.0263016i
$57$	−3810.83	+	2557.50i	−1.17292	+	0.787166i
$58$	94.3809	+	39.0938i	0.0280561	+	0.0116212i
$59$	2222.40	+	2222.40i	0.638436	+	0.638436i	0.950170	−	0.311733i	$-0.100910\pi$
$59$	2222.40	+	2222.40i	0.638436	+	0.638436i	−0.311733	+	0.950170i	$0.600910\pi$
$60$	283.942	+	1412.51i	0.0788727	+	0.392363i
$61$	1138.60	+	471.625i	0.305994	+	0.126747i	0.530397	−	0.847750i	$-0.322043\pi$
$61$	1138.60	+	471.625i	0.305994	+	0.126747i	−0.224402	+	0.974497i	$0.572043\pi$
$62$	−3693.07	−	1529.72i	−0.960736	−	0.397950i
$63$	−226.898	−	225.066i	−0.0571675	−	0.0567060i
$64$			512.000i			0.125000i
$65$	−169.767	+	70.3200i	−0.0401816	+	0.0166438i
$66$	−139.994	−	696.417i	−0.0321381	−	0.159875i
$67$	7869.59			1.75308			0.876542	−	0.481325i	$-0.159844\pi$
$67$	7869.59			1.75308			0.876542	+	0.481325i	$0.159844\pi$
$68$	2149.52	−	851.423i	0.464861	−	0.184131i
$69$	1298.72	−	1952.22i	0.272782	−	0.410044i
$70$	−157.906	−	157.906i	−0.0322256	−	0.0322256i
$71$	−1085.42	+	449.597i	−0.215319	+	0.0891882i	−0.487736	−	0.872991i	$-0.662177\pi$
$71$	−1085.42	+	449.597i	−0.215319	+	0.0891882i	0.272417	+	0.962179i	$0.412177\pi$
$72$	708.247	+	1690.45i	0.136622	+	0.326090i
$73$	2739.63	−	1134.79i	0.514098	−	0.212946i	−0.110524	−	0.993873i	$-0.535253\pi$
$73$	2739.63	−	1134.79i	0.514098	−	0.212946i	0.624622	+	0.780927i	$0.285253\pi$
$74$	384.069	+	159.087i	0.0701368	+	0.0290516i
$75$	−1126.31	−	1678.27i	−0.200233	−	0.298359i
$76$	−2884.66	+	2884.66i	−0.499422	+	0.499422i
$77$	77.8532	+	77.8532i	0.0131309	+	0.0131309i
$78$	−194.099	+	130.262i	−0.0319032	+	0.0214107i
$79$	1484.13	−	3583.01i	0.237803	−	0.574108i	−0.759252	−	0.650797i	$-0.774435\pi$
$79$	1484.13	−	3583.01i	0.237803	−	0.574108i	0.997055	+	0.0766890i	$0.0244349\pi$
$80$	490.095	+	1183.19i	0.0765773	+	0.184874i
$81$	4676.78	+	4601.57i	0.712815	+	0.701352i
$82$	−1473.36	−	3557.00i	−0.219119	−	0.529000i
$83$	−1937.39	+	1937.39i	−0.281230	+	0.281230i	−0.833599	−	0.552369i	$-0.813724\pi$
$83$	−1937.39	+	1937.39i	−0.281230	+	0.281230i	0.552369	+	0.833599i	$0.313724\pi$
$84$	−236.523	−	157.347i	−0.0335208	−	0.0222998i
$85$	4152.38	−	4025.13i	0.574723	−	0.557111i
$86$		−	3474.45i		−	0.469774i
$87$	318.687	−	64.0623i	0.0421042	−	0.00846378i
$88$	−241.634	−	583.357i	−0.0312028	−	0.0753302i
$89$	−3544.63			−0.447498			−0.223749	−	0.974647i	$-0.571830\pi$
$89$	−3544.63			−0.447498			−0.223749	+	0.974647i	$0.571830\pi$
$90$	3254.83	+	3228.56i	0.401831	+	0.398587i
$91$	13.8652	−	33.4735i	0.00167434	−	0.00404220i
$92$	797.596	−	1925.57i	0.0942339	−	0.227501i
$93$	−12470.0	+	2506.72i	−1.44179	+	0.289828i
$94$	5474.57	−	5474.57i	0.619576	−	0.619576i
$95$	−3904.99	+	9427.49i	−0.432686	+	1.04460i
$96$	907.864	+	1352.77i	0.0985095	+	0.146785i
$97$	−8873.53	+	3675.54i	−0.943089	+	0.390640i	−0.800629	−	0.599160i	$-0.795501\pi$
$97$	−8873.53	+	3675.54i	−0.943089	+	0.390640i	−0.142460	+	0.989801i	$0.545501\pi$
$98$	−6747.02			−0.702522
$99$	−1604.75	−	1591.79i	−0.163733	−	0.162411i
$100$	−1270.39	−	1270.39i	−0.127039	−	0.127039i
$101$			9636.92i			0.944704i	0.881410	+	0.472352i	$0.156595\pi$
$101$			9636.92i			0.944704i	−0.881410	+	0.472352i	$0.843405\pi$
$102$	4169.59	−	6061.03i	0.400768	−	0.582568i
$103$	1449.19			0.136600			0.0682999	−	0.997665i	$-0.478243\pi$
$103$	1449.19			0.136600			0.0682999	+	0.997665i	$0.478243\pi$
$104$	−146.926	+	146.926i	−0.0135841	+	0.0135841i
$105$	−697.201	−	137.214i	−0.0632382	−	0.0124457i
$106$		−	6239.73i		−	0.555334i
$107$	1634.82	+	3946.81i	0.142792	+	0.344730i	0.979054	−	0.203599i	$-0.0652640\pi$
$107$	1634.82	+	3946.81i	0.142792	+	0.344730i	−0.836262	+	0.548329i	$0.815264\pi$
$108$	4868.74	+	3210.55i	0.417416	+	0.275253i
$109$	−13150.6	−	5447.14i	−1.10686	−	0.458475i	−0.247003	−	0.969015i	$-0.579446\pi$
$109$	−13150.6	−	5447.14i	−1.10686	−	0.458475i	−0.859854	+	0.510539i	$0.829446\pi$
$110$	−1116.80	−	1116.80i	−0.0922973	−	0.0922973i
$111$	1296.85	−	260.692i	0.105255	−	0.0211584i
$112$	−233.293	−	96.6333i	−0.0185980	−	0.00770355i
$113$	−8386.48	−	3473.79i	−0.656784	−	0.272049i	0.0293004	−	0.999571i	$-0.490672\pi$
$113$	−8386.48	−	3473.79i	−0.656784	−	0.272049i	−0.686085	+	0.727522i	$0.740672\pi$
$114$	−2506.66	+	12736.7i	−0.192879	+	0.980045i
$115$		−	5213.31i		−	0.394201i
$116$	266.949	−	110.574i	0.0198387	−	0.00821745i
$117$	−281.858	+	688.341i	−0.0205901	+	0.0502843i
$118$	8889.58			0.638436
$119$	−17.7415	+	1140.12i	−0.00125284	+	0.0805116i
$120$	3392.90	+	2257.13i	0.235618	+	0.156745i
$121$	−9802.13	−	9802.13i	−0.669499	−	0.669499i
$122$	3220.46	−	1333.96i	0.216371	−	0.0896236i
$123$	−10200.0	−	6785.55i	−0.674200	−	0.448512i
$124$	−10445.6	+	4326.70i	−0.679343	+	0.281393i
$125$	−15706.4	−	6505.82i	−1.00521	−	0.416372i
$126$	−903.928	+	3.66327i	−0.0569367	+	0.000230743i
$127$	−17937.9	+	17937.9i	−1.11215	+	1.11215i	−0.119294	+	0.992859i	$0.538063\pi$
$127$	−17937.9	+	17937.9i	−1.11215	+	1.11215i	−0.992859	+	0.119294i	$0.961937\pi$
$128$	1024.00	+	1024.00i	0.0625000	+	0.0625000i
$129$	−6160.79	−	9179.95i	−0.370218	−	0.551647i
$130$	−198.895	+	480.175i	−0.0117689	+	0.0284127i
$131$	2720.48	+	6567.83i	0.158527	+	0.382718i	0.983108	−	0.183025i	$-0.0585891\pi$
$131$	2720.48	+	6567.83i	0.158527	+	0.382718i	−0.824581	+	0.565744i	$0.808589\pi$
$132$	−1672.82	−	1112.85i	−0.0960068	−	0.0638686i
$133$	−769.958	−	1858.84i	−0.0435275	−	0.105085i
$134$	15739.2	−	15739.2i	0.876542	−	0.876542i
$135$	14324.5	+	2758.90i	0.785979	+	0.151380i
$136$	2596.19	−	6001.88i	0.140365	−	0.324496i
$137$		−	5706.00i		−	0.304012i	−0.988380	−	0.152006i	$-0.951427\pi$
$137$		−	5706.00i		−	0.304012i	0.988380	−	0.152006i	$-0.0485733\pi$
$138$	−1307.00	−	6501.87i	−0.0686308	−	0.341413i
$139$	6644.04	+	16040.1i	0.343877	+	0.830192i	0.997316	+	0.0732131i	$0.0233253\pi$
$139$	6644.04	+	16040.1i	0.343877	+	0.830192i	−0.653440	+	0.756979i	$0.726675\pi$
$140$	−631.622			−0.0322256
$141$	4757.19	−	24171.9i	0.239283	−	1.21583i
$142$	−1271.65	+	3070.04i	−0.0630655	+	0.152254i
$143$	98.0623	−	236.743i	0.00479546	−	0.0115773i
$144$	4797.39	+	1964.41i	0.231356	+	0.0947340i
$145$	511.057	−	511.057i	0.0243071	−	0.0243071i
$146$	3209.67	−	7748.84i	0.150576	−	0.363522i
$147$	−17826.5	+	11963.6i	−0.824958	+	0.553641i
$148$	1086.31	−	449.965i	0.0495942	−	0.0205426i
$149$	41062.4			1.84957			0.924786	−	0.380487i	$-0.124244\pi$
$149$	41062.4			1.84957			0.924786	+	0.380487i	$0.124244\pi$
$150$	−5609.16	−	1103.92i	−0.249296	−	0.0490631i
$151$	3339.40	+	3339.40i	0.146458	+	0.146458i	0.776534	−	0.630075i	$-0.216976\pi$
$151$	3339.40	+	3339.40i	0.146458	+	0.146458i	−0.630075	+	0.776534i	$0.716976\pi$
$152$			11538.7i			0.499422i
$153$	269.364	−	23407.5i	0.0115069	−	0.999934i
$154$	311.413			0.0131309
$155$	−19997.3	+	19997.3i	−0.832356	+	0.832356i
$156$	−127.673	+	648.723i	−0.00524626	+	0.0266569i
$157$			21128.2i			0.857161i	0.903504	+	0.428580i	$0.140986\pi$
$157$			21128.2i			0.857161i	−0.903504	+	0.428580i	$0.859014\pi$
$158$	−4197.76	−	10134.3i	−0.168152	−	0.405956i
$159$	−11064.1	−	16486.2i	−0.437645	−	0.652118i
$160$	3346.58	+	1386.20i	0.130726	+	0.0541483i
$161$	726.851	+	726.851i	0.0280410	+	0.0280410i
$162$	18556.7	−	150.409i	0.707084	−	0.00573117i
$163$	43002.1	+	17812.1i	1.61851	+	0.670407i	0.993875	−	0.110512i	$-0.0352490\pi$
$163$	43002.1	+	17812.1i	1.61851	+	0.670407i	0.624632	+	0.780919i	$0.285249\pi$
$164$	−10060.7	−	4167.28i	−0.374060	−	0.154941i
$165$	−4931.00	−	970.454i	−0.181120	−	0.0356457i
$166$			7749.58i			0.281230i
$167$	27959.3	−	11581.1i	1.00252	−	0.415257i	0.179799	−	0.983703i	$-0.442455\pi$
$167$	27959.3	−	11581.1i	1.00252	−	0.415257i	0.822720	+	0.568446i	$0.192455\pi$
$168$	−787.740	+	158.351i	−0.0279103	+	0.00561051i
$169$	28476.7			0.997048
$170$	254.500	−	16355.0i	0.00880622	−	0.565917i
$171$	15961.4	+	38096.7i	0.545855	+	1.30285i
$172$	−6948.90	−	6948.90i	−0.234887	−	0.234887i
$173$	−4652.59	+	1927.17i	−0.155454	+	0.0643913i	−0.459054	−	0.888408i	$-0.651812\pi$
$173$	−4652.59	+	1927.17i	−0.155454	+	0.0643913i	0.303600	+	0.952800i	$0.401812\pi$
$174$	509.249	−	765.498i	0.0168202	−	0.0252840i
$175$	818.624	−	339.085i	0.0267306	−	0.0110722i
$176$	−1649.98	−	683.445i	−0.0532665	−	0.0220637i
$177$	23487.5	−	15762.8i	0.749703	−	0.503136i
$178$	−7089.27	+	7089.27i	−0.223749	+	0.223749i
$179$	34759.9	+	34759.9i	1.08486	+	1.08486i	0.996049	+	0.0888096i	$0.0283063\pi$
$179$	34759.9	+	34759.9i	1.08486	+	1.08486i	0.0888096	+	0.996049i	$0.471694\pi$
$180$	12966.8	−	52.5494i	0.400209	−	0.00162189i
$181$	−15577.4	+	37607.1i	−0.475486	+	1.14792i	0.486219	+	0.873837i	$0.338376\pi$
$181$	−15577.4	+	37607.1i	−0.475486	+	1.14792i	−0.961705	+	0.274087i	$0.911624\pi$
$182$	−39.2166	−	94.6774i	−0.00118393	−	0.00285827i
$183$	6143.55	−	9234.92i	0.183450	−	0.275760i
$184$	−2255.94	−	5446.32i	−0.0666334	−	0.160867i
$185$	2079.67	−	2079.67i	0.0607646	−	0.0607646i
$186$	−19926.6	+	29953.5i	−0.575980	+	0.865808i
$187$	−125.478	+	8063.61i	−0.00358825	+	0.230593i
$188$		−	21898.3i		−	0.619576i
$189$	−2381.80	+	1612.50i	−0.0666779	+	0.0451414i
$190$	11045.0	+	26665.0i	0.305955	+	0.738641i
$191$	14758.9			0.404564			0.202282	−	0.979327i	$-0.435164\pi$
$191$	14758.9			0.404564			0.202282	+	0.979327i	$0.435164\pi$
$192$	4521.27	+	889.817i	0.122647	+	0.0241378i
$193$	5517.11	−	13319.5i	0.148114	−	0.357580i	−0.832358	−	0.554239i	$-0.813009\pi$
$193$	5517.11	−	13319.5i	0.148114	−	0.357580i	0.980472	+	0.196659i	$0.0630094\pi$
$194$	−10396.0	+	25098.1i	−0.276224	+	0.666865i
$195$	325.925	+	1621.36i	0.00857134	+	0.0426393i
$196$	−13494.0	+	13494.0i	−0.351261	+	0.351261i
$197$	16639.3	−	40170.9i	0.428749	−	1.03509i	−0.550936	−	0.834548i	$-0.685729\pi$
$197$	16639.3	−	40170.9i	0.428749	−	1.03509i	0.979685	−	0.200544i	$-0.0642710\pi$
$198$	−6393.09	+	25.9087i	−0.163072	+	0.000660870i
$199$	−37170.3	+	15396.4i	−0.938619	+	0.388789i	−0.798942	−	0.601408i	$-0.794607\pi$
$199$	−37170.3	+	15396.4i	−0.938619	+	0.388789i	−0.139677	+	0.990197i	$0.544607\pi$
$200$	−5081.56			−0.127039
$201$	13676.7	−	69493.3i	0.338525	−	1.72009i
$202$	19273.8	+	19273.8i	0.472352	+	0.472352i
$203$			142.505i			0.00345811i
$204$	−3782.88	−	20461.2i	−0.0908997	−	0.491668i
$205$	−27238.5			−0.648151
$206$	2898.37	−	2898.37i	0.0682999	−	0.0682999i
$207$	−14982.2	−	14861.3i	−0.349651	−	0.346829i
$208$			587.704i			0.0135841i
$209$	−5445.58	−	13146.8i	−0.124667	−	0.300973i
$210$	−1668.83	+	1119.97i	−0.0378420	+	0.0253963i
$211$	64039.7	+	26526.1i	1.43842	+	0.595811i	0.959414	−	0.282002i	$-0.0909986\pi$
$211$	64039.7	+	26526.1i	1.43842	+	0.595811i	0.479002	+	0.877814i	$0.340999\pi$
$212$	−12479.5	−	12479.5i	−0.277667	−	0.277667i
$213$	2083.83	+	10366.3i	0.0459308	+	0.228489i
$214$	11163.3	+	4623.98i	0.243761	+	0.100969i
$215$	−22710.0	−	9406.78i	−0.491292	−	0.203500i
$216$	16158.6	−	3316.38i	0.346334	−	0.0710815i
$217$		−	5576.15i		−	0.118417i
$218$	−37195.4	+	15406.9i	−0.782666	+	0.324191i
$219$	−5259.63	−	26164.8i	−0.109665	−	0.545542i
$220$	−4467.19			−0.0922973
$221$	2467.34	−	977.313i	0.0505179	−	0.0200101i
$222$	2072.31	−	3115.08i	0.0420484	−	0.0632068i
$223$	−60969.0	−	60969.0i	−1.22602	−	1.22602i	−0.965455	−	0.260569i	$-0.916090\pi$
$223$	−60969.0	−	60969.0i	−1.22602	−	1.22602i	−0.260569	−	0.965455i	$-0.583910\pi$
$224$	−659.853	+	273.320i	−0.0131508	+	0.00544723i
$225$	−16777.6	+	7029.29i	−0.331409	+	0.138850i
$226$	−23720.5	+	9825.37i	−0.464417	+	0.192368i
$227$	−20563.0	−	8517.48i	−0.399057	−	0.165295i	0.174124	−	0.984724i	$-0.444291\pi$
$227$	−20563.0	−	8517.48i	−0.399057	−	0.165295i	−0.573181	+	0.819429i	$0.694291\pi$
$228$	20460.0	+	30486.7i	0.393583	+	0.586462i
$229$	−11283.6	+	11283.6i	−0.215168	+	0.215168i	−0.806459	−	0.591291i	$-0.798619\pi$
$229$	−11283.6	+	11283.6i	−0.215168	+	0.215168i	0.591291	+	0.806459i	$0.298619\pi$
$230$	−10426.6	−	10426.6i	−0.197101	−	0.197101i
$231$	822.793	−	552.188i	0.0154194	−	0.0103482i
$232$	312.751	−	755.047i	0.00581062	−	0.0140281i
$233$	−29829.3	−	72014.3i	−0.549454	−	1.32650i	−0.917886	−	0.396844i	$-0.870105\pi$
$233$	−29829.3	−	72014.3i	−0.549454	−	1.32650i	0.368432	−	0.929655i	$-0.379895\pi$
$234$	812.967	+	1940.40i	0.0148471	+	0.0354372i
$235$	−20961.4	−	50605.3i	−0.379564	−	0.916348i
$236$	17779.2	−	17779.2i	0.319218	−	0.319218i
$237$	−29060.8	−	19332.8i	−0.517382	−	0.344189i
$238$	2244.77	+	2315.73i	0.0396294	+	0.0408822i
$239$			76724.2i			1.34319i	0.740920	+	0.671593i	$0.234390\pi$
$239$			76724.2i			1.34319i	−0.740920	+	0.671593i	$0.765610\pi$
$240$	11300.1	−	2271.54i	0.196182	−	0.0394364i
$241$	−23413.2	−	56524.4i	−0.403112	−	0.973199i	−0.986906	−	0.161297i	$-0.948432\pi$
$241$	−23413.2	−	56524.4i	−0.403112	−	0.973199i	0.583794	−	0.811902i	$-0.301568\pi$
$242$	−39208.5			−0.669499
$243$	48762.6	−	33301.6i	0.825798	−	0.563966i
$244$	3773.00	−	9108.84i	0.0633735	−	0.152997i
$245$	−18267.0	+	44100.4i	−0.304323	+	0.734701i
$246$	−33971.0	+	6828.85i	−0.561356	+	0.112844i
$247$	−3311.19	+	3311.19i	−0.0542737	+	0.0542737i
$248$	−12237.8	+	29544.5i	−0.198975	+	0.480368i
$249$	13741.3	+	20475.4i	0.221631	+	0.330243i
$250$	−44424.5	+	18401.2i	−0.710792	+	0.294420i
$251$	47451.2			0.753181			0.376591	−	0.926380i	$-0.377096\pi$
$251$	47451.2			0.753181			0.376591	+	0.926380i	$0.377096\pi$
$252$	−1800.53	+	1815.18i	−0.0283530	+	0.0285837i
$253$	5140.70	+	5140.70i	0.0803121	+	0.0803121i
$254$			71751.7i			1.11215i
$255$	−28327.8	−	43663.4i	−0.435645	−	0.671486i
$256$	4096.00			0.0625000
$257$	−29392.3	+	29392.3i	−0.445008	+	0.445008i	−0.893691	−	0.448683i	$-0.851893\pi$
$257$	−29392.3	+	29392.3i	−0.445008	+	0.445008i	0.448683	+	0.893691i	$0.351893\pi$
$258$	−30681.5	−	6038.32i	−0.460932	−	0.0907146i
$259$			579.904i			0.00864483i
$260$	562.560	+	1358.14i	0.00832189	+	0.0200908i
$261$	−11.8561	−	2925.53i	−0.000174044	−	0.0429461i
$262$	18576.6	+	7694.69i	0.270623	+	0.112096i
$263$	47064.5	+	47064.5i	0.680427	+	0.680427i	0.960096	−	0.279669i	$-0.0902248\pi$
$263$	47064.5	+	47064.5i	0.680427	+	0.680427i	−0.279669	+	0.960096i	$0.590225\pi$
$264$	−5571.34	+	1119.95i	−0.0799377	+	0.0160691i
$265$	−40784.7	−	16893.6i	−0.580771	−	0.240563i
$266$	−5257.60	−	2177.77i	−0.0743061	−	0.0307786i
$267$	−6160.30	+	31301.3i	−0.0864131	+	0.439076i
$268$		−	62956.7i		−	0.876542i
$269$	−18730.4	+	7758.39i	−0.258847	+	0.107218i	−0.508333	−	0.861160i	$-0.669738\pi$
$269$	−18730.4	+	7758.39i	−0.258847	+	0.107218i	0.249486	+	0.968378i	$0.419738\pi$
$270$	34166.7	−	23131.1i	0.468680	−	0.317300i
$271$	63003.2			0.857875			0.428938	−	0.903334i	$-0.358888\pi$
$271$	63003.2			0.857875			0.428938	+	0.903334i	$0.358888\pi$
$272$	−6811.38	−	17196.1i	−0.0920656	−	0.232430i
$273$	−271.495	−	180.612i	−0.00364281	−	0.00242338i
$274$	−11412.0	−	11412.0i	−0.152006	−	0.152006i
$275$	5789.77	−	2398.20i	0.0765590	−	0.0317118i
$276$	−15617.8	−	10389.7i	−0.205022	−	0.136391i
$277$	−31105.9	+	12884.5i	−0.405400	+	0.167922i	−0.576059	−	0.817408i	$-0.695410\pi$
$277$	−31105.9	+	12884.5i	−0.405400	+	0.167922i	0.170659	+	0.985330i	$0.445410\pi$
$278$	45368.3	+	18792.2i	0.587034	+	0.243158i
$279$	463.921	+	114474.i	0.00595986	+	1.47062i
$280$	−1263.24	+	1263.24i	−0.0161128	+	0.0161128i
$281$	89307.1	+	89307.1i	1.13103	+	1.13103i	0.990006	+	0.141022i	$0.0450388\pi$
$281$	89307.1	+	89307.1i	1.13103	+	1.13103i	0.141022	+	0.990006i	$0.454961\pi$
$282$	−38829.4	−	57858.2i	−0.488273	−	0.727556i
$283$	8808.36	−	21265.3i	0.109982	−	0.265520i	−0.859300	−	0.511472i	$-0.829100\pi$
$283$	8808.36	−	21265.3i	0.109982	−	0.265520i	0.969282	+	0.245952i	$0.0791004\pi$
$284$	3596.78	+	8683.39i	0.0445941	+	0.107660i
$285$	76463.8	+	50867.7i	0.941383	+	0.626257i
$286$	−277.362	−	669.612i	−0.00339090	−	0.00818636i
$287$	3797.65	−	3797.65i	0.0461054	−	0.0461054i
$288$	13523.6	−	5665.97i	0.163045	−	0.0683108i
$289$	−60867.2	+	57192.1i	−0.728766	+	0.684763i
$290$		−	2044.23i		−	0.0243071i
$291$	17035.7	+	84746.4i	0.201175	+	1.00077i
$292$	−9078.33	−	21917.0i	−0.106473	−	0.257049i
$293$	−163331.			−1.90253			−0.951267	−	0.308367i	$-0.900218\pi$
$293$	−163331.			−1.90253			−0.951267	+	0.308367i	$0.900218\pi$
$294$	−11725.8	+	59580.3i	−0.135659	+	0.689300i
$295$	24067.8	−	58104.8i	0.276562	−	0.667680i
$296$	1272.69	−	3072.55i	0.0145258	−	0.0350684i
$297$	−16845.4	+	11404.5i	−0.190972	+	0.129289i
$298$	82124.7	−	82124.7i	0.924786	−	0.924786i
$299$	915.527	−	2210.28i	0.0102407	−	0.0247232i
$300$	−13426.2	+	9010.48i	−0.149180	+	0.100116i
$301$	4477.79	−	1854.76i	0.0494232	−	0.0204717i
$302$	13357.6			0.146458
$303$	85099.9	+	16748.2i	0.926923	+	0.182425i
$304$	23077.3	+	23077.3i	0.249711	+	0.249711i
$305$		−	24661.4i		−	0.265105i
$306$	−46276.2	−	47353.6i	−0.494213	−	0.505720i
$307$	80499.5			0.854115			0.427057	−	0.904224i	$-0.359550\pi$
$307$	80499.5			0.854115			0.427057	+	0.904224i	$0.359550\pi$
$308$	622.825	−	622.825i	0.00656545	−	0.00656545i
$309$	2518.57	−	12797.2i	0.0263778	−	0.134029i
$310$			79989.4i			0.832356i
$311$	−54500.3	−	131575.i	−0.563479	−	1.36036i	−0.906967	−	0.421202i	$-0.861608\pi$
$311$	−54500.3	−	131575.i	−0.563479	−	1.36036i	0.343487	−	0.939157i	$-0.388392\pi$
$312$	1042.10	+	1552.79i	0.0107053	+	0.0159516i
$313$	111542.	+	46202.1i	1.13854	+	0.471599i	0.870676	−	0.491857i	$-0.163682\pi$
$313$	111542.	+	46202.1i	1.13854	+	0.471599i	0.267866	+	0.963456i	$0.413682\pi$
$314$	42256.3	+	42256.3i	0.428580	+	0.428580i
$315$	−2423.36	+	5918.24i	−0.0244229	+	0.0596447i
$316$	−28664.1	−	11873.0i	−0.287054	−	0.118902i
$317$	−153750.	−	63685.2i	−1.53002	−	0.633753i	−0.550448	−	0.834869i	$-0.685543\pi$
$317$	−153750.	−	63685.2i	−1.53002	−	0.633753i	−0.979567	+	0.201116i	$0.935543\pi$
$318$	−55100.6	−	10844.2i	−0.544882	−	0.107236i
$319$			1007.88i			0.00990436i
$320$	9465.55	−	3920.76i	0.0924370	−	0.0382886i
$321$	37694.0	−	7577.23i	0.365815	−	0.0735361i
$322$	2907.40			0.0280410
$323$	58508.8	−	135261.i	0.560811	−	1.29648i
$324$	36812.6	−	37414.2i	0.350676	−	0.356407i
$325$	−1458.23	−	1458.23i	−0.0138057	−	0.0138057i
$326$	121628.	−	50380.1i	1.14446	−	0.474050i
$327$	−70956.3	+	106661.i	−0.663583	+	0.997492i
$328$	−28456.0	+	11786.9i	−0.264500	+	0.109560i
$329$	9977.98	+	4133.02i	0.0921830	+	0.0381835i
$330$	−11802.9	+	7921.09i	−0.108383	+	0.0727373i
$331$	94383.8	−	94383.8i	0.861473	−	0.861473i	−0.130036	−	0.991509i	$-0.541509\pi$
$331$	94383.8	−	94383.8i	0.861473	−	0.861473i	0.991509	+	0.130036i	$0.0415094\pi$
$332$	15499.2	+	15499.2i	0.140615	+	0.140615i
$333$	−48.2465	−	11905.0i	−0.000435088	−	0.107360i
$334$	32756.3	−	79080.8i	0.293631	−	0.708888i
$335$	−60263.2	−	145488.i	−0.536986	−	1.29640i
$336$	−1258.78	+	1892.18i	−0.0111499	+	0.0167604i
$337$	13216.3	+	31906.9i	0.116372	+	0.280947i	0.971324	−	0.237760i	$-0.0764133\pi$
$337$	13216.3	+	31906.9i	0.116372	+	0.280947i	−0.854952	+	0.518708i	$0.826413\pi$
$338$	56953.3	−	56953.3i	0.498524	−	0.498524i
$339$	−45250.8	+	68020.5i	−0.393755	+	0.591889i
$340$	−32201.0	−	33219.0i	−0.278555	−	0.287362i
$341$		−	39437.7i		−	0.339158i
$342$	108116.	+	44270.7i	0.924354	+	0.378498i
$343$	−7227.01	−	17447.6i	−0.0614286	−	0.148302i
$344$	−27795.6			−0.234887
$345$	−46036.7	−	9060.33i	−0.386782	−	0.0761212i
$346$	−5450.85	+	13159.5i	−0.0455315	+	0.109923i
$347$	−52640.7	+	127086.i	−0.437182	+	1.05545i	0.539735	+	0.841835i	$0.318524\pi$
$347$	−52640.7	+	127086.i	−0.437182	+	1.05545i	−0.976918	+	0.213617i	$0.931476\pi$
$348$	−512.499	−	2549.49i	−0.00423189	−	0.0210521i
$349$	47215.9	−	47215.9i	0.387648	−	0.387648i	−0.486200	−	0.873848i	$-0.661617\pi$
$349$	47215.9	−	47215.9i	0.387648	−	0.387648i	0.873848	+	0.486200i	$0.161617\pi$
$350$	959.078	−	2315.42i	0.00782921	−	0.0189014i
$351$	5588.62	+	3685.26i	0.0453618	+	0.0299126i
$352$	−4666.86	+	1933.07i	−0.0376651	+	0.0156014i
$353$	161461.			1.29574			0.647871	−	0.761750i	$-0.275660\pi$
$353$	161461.			1.29574			0.647871	+	0.761750i	$0.275660\pi$
$354$	15449.4	−	78500.4i	0.123284	−	0.626420i
$355$	16623.8	+	16623.8i	0.131909	+	0.131909i
$356$			28357.1i			0.223749i
$357$	10037.2	+	2138.12i	0.0787543	+	0.0167763i
$358$	139040.			1.08486
$359$	150183.	−	150183.i	1.16529	−	1.16529i	0.181985	−	0.983301i	$-0.441748\pi$
$359$	150183.	−	150183.i	1.16529	−	1.16529i	0.983301	−	0.181985i	$-0.0582524\pi$
$360$	25828.4	−	26038.6i	0.199294	−	0.200915i
$361$			129719.i			0.995381i
$362$	44059.5	+	106369.i	0.336219	+	0.811705i
$363$	−103594.	+	69523.4i	−0.786180	+	0.527616i
$364$	−267.788	−	110.921i	−0.00202110	−	0.000837168i
$365$	−41958.7	−	41958.7i	−0.314946	−	0.314946i
$366$	−6182.75	−	30756.9i	−0.0461551	−	0.229605i
$367$	−222937.	−	92343.6i	−1.65520	−	0.685606i	−0.657503	−	0.753452i	$-0.728387\pi$
$367$	−222937.	−	92343.6i	−1.65520	−	0.685606i	−0.997696	+	0.0678462i	$0.978387\pi$
$368$	−15404.5	−	6380.76i	−0.113750	−	0.0471169i
$369$	−77647.2	+	78279.2i	−0.570261	+	0.574901i
$370$		−	8318.68i		−	0.0607646i
$371$	8041.62	−	3330.95i	0.0584246	−	0.0242003i
$372$	20053.8	+	99760.2i	0.144914	+	0.720894i
$373$	179287.			1.28864			0.644320	−	0.764756i	$-0.277140\pi$
$373$	179287.			1.28864			0.644320	+	0.764756i	$0.277140\pi$
$374$	15876.3	+	16378.2i	0.113502	+	0.117091i
$375$	−84746.9	+	127391.i	−0.602645	+	0.905890i
$376$	−43796.6	−	43796.6i	−0.309788	−	0.309788i
$377$	306.420	−	126.923i	0.00215593	−	0.000893016i
$378$	−1538.61	+	7988.60i	−0.0107682	+	0.0559097i
$379$	−121091.	+	50157.7i	−0.843015	+	0.349188i	−0.762042	−	0.647528i	$-0.775803\pi$
$379$	−121091.	+	50157.7i	−0.843015	+	0.349188i	−0.0809733	+	0.996716i	$0.525803\pi$
$380$	75419.9	+	31239.9i	0.522298	+	0.216343i
$381$	127228.	+	189577.i	0.876461	+	1.30598i
$382$	29517.8	−	29517.8i	0.202282	−	0.202282i
$383$	98554.0	+	98554.0i	0.671857	+	0.671857i	0.958144	−	0.286287i	$-0.0924210\pi$
$383$	98554.0	+	98554.0i	0.671857	+	0.671857i	−0.286287	+	0.958144i	$0.592421\pi$
$384$	10822.2	−	7262.91i	0.0733926	−	0.0492548i
$385$	843.124	−	2035.48i	0.00568813	−	0.0137324i
$386$	−15604.7	−	37673.2i	−0.104733	−	0.252847i
$387$	−91771.6	+	38449.5i	−0.612754	+	0.256725i
$388$	29404.3	+	70988.2i	0.195320	+	0.471545i
$389$	−193844.	+	193844.i	−1.28101	+	1.28101i	−0.340915	+	0.940094i	$0.610737\pi$
$389$	−193844.	+	193844.i	−1.28101	+	1.28101i	−0.940094	+	0.340915i	$0.889263\pi$
$390$	3894.57	+	2590.87i	0.0256053	+	0.0170340i
$391$	−1171.48	+	75283.3i	−0.00766270	+	0.492430i
$392$			53976.2i			0.351261i
$393$	62725.9	−	12609.1i	0.406127	−	0.0816395i
$394$	−47063.1	−	113620.i	−0.303171	−	0.731921i
$395$	−77605.6			−0.497392
$396$	−12734.4	+	12838.0i	−0.0812057	+	0.0818666i
$397$	14842.4	−	35832.8i	0.0941724	−	0.227352i	−0.869773	−	0.493452i	$-0.835735\pi$
$397$	14842.4	−	35832.8i	0.0941724	−	0.227352i	0.963946	+	0.266099i	$0.0857350\pi$
$398$	−43547.7	+	105133.i	−0.274915	+	0.663704i
$399$	−17752.8	+	3568.67i	−0.111512	+	0.0224161i
$400$	−10163.1	+	10163.1i	−0.0635195	+	0.0635195i
$401$	17541.7	−	42349.3i	0.109089	−	0.263365i	−0.859902	−	0.510459i	$-0.829476\pi$
$401$	17541.7	−	42349.3i	0.109089	−	0.263365i	0.968992	+	0.247094i	$0.0794756\pi$
$402$	−111633.	−	166340.i	−0.690782	−	1.02931i
$403$	−11990.0	+	4966.44i	−0.0738263	+	0.0305798i
$404$	77095.4			0.472352
$405$	49257.6	−	121699.i	0.300305	−	0.741954i
$406$	285.010	+	285.010i	0.00172905	+	0.00172905i
$407$			4101.41i			0.0247596i
$408$	−48488.3	−	33356.7i	−0.291284	−	0.200384i
$409$	−135299.			−0.808811			−0.404405	−	0.914580i	$-0.632521\pi$
$409$	−135299.			−0.808811			−0.404405	+	0.914580i	$0.632521\pi$
$410$	−54477.1	+	54477.1i	−0.324075	+	0.324075i
$411$	−50387.4	−	9916.58i	−0.298290	−	0.0587054i
$412$		−	11593.5i		−	0.0682999i
$413$	4745.51	+	11456.7i	0.0278217	+	0.0671675i
$414$	−59687.0	+	241.889i	−0.348240	+	0.00141128i
$415$	50653.4	+	20981.3i	0.294112	+	0.121825i
$416$	1175.41	+	1175.41i	0.00679207	+	0.00679207i
$417$	153191.	−	30794.4i	0.880970	−	0.177092i
$418$	−37184.7	−	15402.4i	−0.212820	−	0.0881528i
$419$	116918.	+	48429.1i	0.665970	+	0.275854i	0.689948	−	0.723859i	$-0.257633\pi$
$419$	116918.	+	48429.1i	0.665970	+	0.275854i	−0.0239785	+	0.999712i	$0.507633\pi$
$420$	−1097.71	+	5577.61i	−0.00622285	+	0.0316191i
$421$		−	93479.0i		−	0.527412i	−0.964603	−	0.263706i	$-0.915055\pi$
$421$		−	93479.0i		−	0.527412i	0.964603	−	0.263706i	$-0.0849449\pi$
$422$	181132.	−	75027.2i	1.01711	−	0.421302i
$423$	−205185.	−	84017.8i	−1.14674	−	0.469560i
$424$	−49917.9			−0.277667
$425$	59568.2	+	25767.0i	0.329789	+	0.142655i
$426$	24900.3	+	16565.0i	0.137210	+	0.0912791i
$427$	3438.35	+	3438.35i	0.0188579	+	0.0188579i
$428$	31574.5	−	13078.6i	0.172365	−	0.0713959i
$429$	−1920.16	−	1277.39i	−0.0104333	−	0.00694080i
$430$	−64233.5	+	26606.4i	−0.347396	+	0.143896i
$431$	−151204.	−	62630.9i	−0.813973	−	0.337159i	−0.0634350	−	0.997986i	$-0.520206\pi$
$431$	−151204.	−	62630.9i	−0.813973	−	0.337159i	−0.750538	+	0.660827i	$0.770206\pi$
$432$	25684.4	−	38949.9i	0.137626	−	0.208708i
$433$	228799.	−	228799.i	1.22033	−	1.22033i	0.252816	−	0.967514i	$-0.418643\pi$
$433$	228799.	−	228799.i	1.22033	−	1.22033i	0.967514	−	0.252816i	$-0.0813567\pi$
$434$	−11152.3	−	11152.3i	−0.0592086	−	0.0592086i
$435$	−3624.76	−	5401.12i	−0.0191558	−	0.0285434i
$436$	−43577.2	+	105205.i	−0.229238	+	0.553429i
$437$	−50840.9	−	122741.i	−0.266226	−	0.642726i
$438$	−62848.8	−	41810.2i	−0.327604	−	0.217939i
$439$	−106414.	−	256907.i	−0.552168	−	1.33305i	−0.915847	−	0.401527i	$-0.868480\pi$
$439$	−106414.	−	256907.i	−0.552168	−	1.33305i	0.363680	−	0.931524i	$-0.381520\pi$
$440$	−8934.38	+	8934.38i	−0.0461487	+	0.0461487i
$441$	74664.9	+	178211.i	0.383919	+	0.916341i
$442$	2980.06	−	6889.31i	0.0152539	−	0.0352640i
$443$		−	181174.i		−	0.923186i	−0.887092	−	0.461593i	$-0.847278\pi$
$443$		−	181174.i		−	0.923186i	0.887092	−	0.461593i	$-0.152722\pi$
$444$	−2085.54	−	10374.8i	−0.0105792	−	0.0526276i
$445$	27143.9	+	65531.1i	0.137073	+	0.330923i
$446$	−243876.			−1.22602
$447$	71363.2	−	362606.i	0.357157	−	1.81476i
$448$	−773.066	+	1866.35i	−0.00385177	+	0.00929900i
$449$	−84436.8	+	203849.i	−0.418831	+	1.01115i	0.563855	+	0.825874i	$0.309318\pi$
$449$	−84436.8	+	203849.i	−0.418831	+	1.01115i	−0.982687	+	0.185275i	$0.940682\pi$
$450$	−19496.6	+	47613.7i	−0.0962794	+	0.235130i
$451$	26859.1	−	26859.1i	0.132050	−	0.132050i
$452$	−27790.3	+	67091.8i	−0.136024	+	0.328392i
$453$	35292.5	−	23685.3i	0.171983	−	0.115420i
$454$	−58161.0	+	24091.1i	−0.282176	+	0.116881i
$455$	−725.014			−0.00350206
$456$	101893.	+	20053.3i	0.490022	+	0.0964397i
$457$	−214809.	−	214809.i	−1.02854	−	1.02854i	−0.999581	−	0.0289573i	$-0.990781\pi$
$457$	−214809.	−	214809.i	−1.02854	−	1.02854i	−0.0289573	−	0.999581i	$-0.509219\pi$
$458$			45134.5i			0.215168i
$459$	−206234.	−	43059.0i	−0.978892	−	0.204380i
$460$	−41706.5			−0.197101
$461$	−119716.	+	119716.i	−0.563315	+	0.563315i	−0.930248	−	0.366933i	$-0.880408\pi$
$461$	−119716.	+	119716.i	−0.563315	+	0.563315i	0.366933	+	0.930248i	$0.380408\pi$
$462$	541.211	−	2749.96i	0.00253561	−	0.0128838i
$463$			351733.i			1.64078i	0.571803	+	0.820391i	$0.306244\pi$
$463$			351733.i			1.64078i	−0.571803	+	0.820391i	$0.693756\pi$
$464$	−884.592	−	2135.60i	−0.00410873	−	0.00991934i
$465$	141835.	+	211343.i	0.655960	+	0.977420i
$466$	−203687.	−	84370.0i	−0.937976	−	0.388523i
$467$	−95324.8	−	95324.8i	−0.437091	−	0.437091i	0.453941	−	0.891032i	$-0.350018\pi$
$467$	−95324.8	−	95324.8i	−0.437091	−	0.437091i	−0.891032	+	0.453941i	$0.850018\pi$
$468$	5506.73	+	2254.86i	0.0251421	+	0.0102950i
$469$	28686.3	+	11882.3i	0.130415	+	0.0540199i
$470$	−143133.	−	59287.8i	−0.647956	−	0.268392i
$471$	186574.	+	36719.1i	0.841028	+	0.165520i
$472$		−	71116.7i		−	0.319218i
$473$	31669.4	−	13117.9i	0.141553	−	0.0586330i
$474$	−96787.2	+	19456.1i	−0.430786	+	0.0865964i
$475$	−114520.			−0.507569
$476$	9121.00	+	141.932i	0.0402558	+	0.000626420i
$477$	−164812.	+	69051.1i	−0.724355	+	0.303483i
$478$	153448.	+	153448.i	0.671593	+	0.671593i
$479$	63633.3	−	26357.8i	0.277341	−	0.114878i	−0.239678	−	0.970852i	$-0.577042\pi$
$479$	63633.3	−	26357.8i	0.277341	−	0.114878i	0.517019	+	0.855974i	$0.327042\pi$
$480$	18057.1	−	27143.2i	0.0783726	−	0.117809i
$481$	1246.93	−	516.496i	0.00538955	−	0.00223243i
$482$	−159875.	−	66222.4i	−0.688155	−	0.285043i
$483$	7681.75	−	5155.32i	0.0329280	−	0.0220984i
$484$	−78417.0	+	78417.0i	−0.334749	+	0.334749i
$485$	135902.	+	135902.i	0.577754	+	0.577754i
$486$	30921.9	−	164128.i	0.130916	−	0.694882i
$487$	−180234.	+	435124.i	−0.759939	+	1.83466i	−0.270139	+	0.962821i	$0.587070\pi$
$487$	−180234.	+	435124.i	−0.759939	+	1.83466i	−0.489801	+	0.871835i	$0.662930\pi$
$488$	−10671.7	−	25763.7i	−0.0448118	−	0.108185i
$489$	232026.	−	348779.i	0.970327	−	1.45859i
$490$	51666.9	+	124735.i	0.215189	+	0.519512i
$491$	143418.	−	143418.i	0.594897	−	0.594897i	−0.344053	−	0.938950i	$-0.611800\pi$
$491$	143418.	−	143418.i	0.594897	−	0.594897i	0.938950	+	0.344053i	$0.111800\pi$
$492$	−54284.4	+	81599.7i	−0.224256	+	0.337100i
$493$	−7494.80	+	7265.12i	−0.0308366	+	0.0298916i
$494$			13244.7i			0.0542737i
$495$	−17139.4	+	41857.2i	−0.0699496	+	0.170828i
$496$	34613.6	+	83564.6i	0.140696	+	0.339671i
$497$	−4635.44			−0.0187663
$498$	68433.5	+	13468.2i	0.275937	+	0.0543062i
$499$	−125369.	+	302668.i	−0.503488	+	1.21553i	0.444083	+	0.895986i	$0.353529\pi$
$499$	−125369.	+	302668.i	−0.503488	+	1.21553i	−0.947572	+	0.319543i	$0.896471\pi$
$500$	−52046.6	+	125651.i	−0.208186	+	0.502606i
$501$	−53677.2	−	267024.i	−0.213852	−	1.06384i
$502$	94902.3	−	94902.3i	0.376591	−	0.376591i
$503$	29057.8	−	70151.6i	0.114849	−	0.277269i	−0.855994	−	0.516985i	$-0.827054\pi$
$503$	29057.8	−	70151.6i	0.114849	−	0.277269i	0.970843	+	0.239716i	$0.0770543\pi$
$504$	29.3062	+	7231.42i	0.000115371	+	0.0284684i
$505$	178162.	−	73797.0i	0.698605	−	0.289371i
$506$	20562.8			0.0803121
$507$	49490.3	−	251466.i	0.192532	−	0.978282i
$508$	143503.	+	143503.i	0.556077	+	0.556077i
$509$			371895.i			1.43544i	0.696332	+	0.717720i	$0.254814\pi$
$509$			371895.i			1.43544i	−0.696332	+	0.717720i	$0.745186\pi$
$510$	−143982.	−	30671.1i	−0.553565	−	0.117921i
$511$	11699.9			0.0448066
$512$	8192.00	−	8192.00i	0.0312500	−	0.0312500i
$513$	364157.	−	74739.3i	1.38374	−	0.283997i
$514$			117569.i			0.445008i
$515$	−11097.5	−	26791.7i	−0.0418418	−	0.101015i
$516$	−73439.6	+	49286.3i	−0.275823	+	0.185109i
$517$	70569.9	+	29231.0i	0.264021	+	0.109361i
$518$	1159.81	+	1159.81i	0.00432242	+	0.00432242i
$519$	8932.20	+	44434.5i	0.0331607	+	0.164963i
$520$	3841.40	+	1591.16i	0.0142064	+	0.00588446i
$521$	−81849.0	−	33903.0i	−0.301535	−	0.124900i	0.226786	−	0.973945i	$-0.427178\pi$
$521$	−81849.0	−	33903.0i	−0.301535	−	0.124900i	−0.528321	+	0.849045i	$0.677178\pi$
$522$	−5874.78	−	5827.35i	−0.0215601	−	0.0213860i
$523$		−	24048.8i		−	0.0879203i	−0.999033	−	0.0439602i	$-0.986003\pi$
$523$		−	24048.8i		−	0.0879203i	0.999033	−	0.0439602i	$-0.0139975\pi$
$524$	52542.6	−	21763.9i	0.191359	−	0.0792636i
$525$	−1571.62	−	7818.25i	−0.00570203	−	0.0283655i
$526$	188258.			0.680427
$527$	293267.	−	284280.i	1.05595	−	1.02359i
$528$	−8902.78	+	13382.6i	−0.0319343	+	0.0480034i
$529$	−149883.	−	149883.i	−0.535601	−	0.535601i
$530$	−115356.	+	47782.2i	−0.410667	+	0.170104i
$531$	−98375.3	−	234803.i	−0.348897	−	0.832750i
$532$	−14870.7	+	6159.66i	−0.0525423	+	0.0217638i
$533$	−11548.3	−	4783.45i	−0.0406502	−	0.0168379i
$534$	50282.0	+	74923.2i	0.176331	+	0.262744i
$535$	60447.3	−	60447.3i	0.211188	−	0.211188i
$536$	−125913.	−	125913.i	−0.438271	−	0.438271i
$537$	367362.	−	246541.i	1.27393	−	0.854951i
$538$	−21944.0	+	52977.6i	−0.0758145	+	0.183032i
$539$	−25473.6	−	61498.8i	−0.0876826	−	0.211684i
$540$	22071.2	−	114596.i	0.0756900	−	0.392990i
$541$	75142.1	+	181409.i	0.256737	+	0.619818i	0.998719	−	0.0506018i	$-0.0161139\pi$
$541$	75142.1	+	181409.i	0.256737	+	0.619818i	−0.741982	+	0.670420i	$0.766114\pi$
$542$	126006.	−	126006.i	0.428938	−	0.428938i
$543$	305022.	+	202916.i	1.03450	+	0.688203i
$544$	−48015.0	−	20769.5i	−0.162248	−	0.0701824i
$545$			284833.i			0.958951i
$546$	−904.214	+	181.765i	−0.00303309	+	0.000609712i
$547$	24992.8	+	60337.9i	0.0835296	+	0.201658i	0.960126	−	0.279568i	$-0.0901914\pi$
$547$	24992.8	+	60337.9i	0.0835296	+	0.201658i	−0.876596	+	0.481227i	$0.840191\pi$
$548$	−45648.0			−0.152006
$549$	−70872.9	−	70300.8i	−0.235145	−	0.233247i
$550$	6783.14	−	16376.0i	0.0224236	−	0.0541354i
$551$	7048.28	−	17016.1i	0.0232156	−	0.0560475i
$552$	−52015.0	+	10456.0i	−0.170707	+	0.0343154i
$553$	10819.9	−	10819.9i	0.0353814	−	0.0353814i
$554$	−36442.9	+	87980.9i	−0.118739	+	0.286661i
$555$	−14750.4	−	21979.0i	−0.0478871	−	0.0713547i
$556$	128321.	−	53152.3i	0.415096	−	0.171938i
$557$	−215024.			−0.693070			−0.346535	−	0.938037i	$-0.612642\pi$
$557$	−215024.			−0.693070			−0.346535	+	0.938037i	$0.612642\pi$
$558$	229877.	+	228021.i	0.738289	+	0.732329i
$559$	−7976.36	−	7976.36i	−0.0255259	−	0.0255259i
$560$			5052.98i			0.0161128i
$561$	70988.5	+	15122.0i	0.225560	+	0.0480488i
$562$	357229.			1.13103
$563$	394055.	−	394055.i	1.24320	−	1.24320i	0.284532	−	0.958666i	$-0.408162\pi$
$563$	394055.	−	394055.i	1.24320	−	1.24320i	0.958666	−	0.284532i	$-0.0918383\pi$
$564$	−193375.	−	38057.5i	−0.607915	−	0.119642i
$565$			181646.i			0.569020i
$566$	−24913.8	−	60147.3i	−0.0777691	−	0.187751i
$567$	10099.9	+	23835.1i	0.0314161	+	0.0741398i
$568$	24560.3	+	10173.2i	0.0761269	+	0.0315328i
$569$	26247.4	+	26247.4i	0.0810704	+	0.0810704i	0.746479	−	0.665409i	$-0.231743\pi$
$569$	26247.4	+	26247.4i	0.0810704	+	0.0810704i	−0.665409	+	0.746479i	$0.731743\pi$
$570$	254663.	−	51192.3i	0.783820	−	0.157563i
$571$	326207.	+	135119.i	1.00051	+	0.414424i	0.821983	−	0.569512i	$-0.192868\pi$
$571$	326207.	+	135119.i	1.00051	+	0.414424i	0.178525	+	0.983935i	$0.442868\pi$
$572$	−1893.95	−	784.499i	−0.00578863	−	0.00239773i
$573$	25649.8	−	130330.i	0.0781224	−	0.396950i
$574$		−	15190.6i		−	0.0461054i
$575$	54054.3	−	22390.0i	0.163491	−	0.0677204i
$576$	15715.2	−	38379.1i	0.0473670	−	0.115678i
$577$	−10497.6			−0.0315310			−0.0157655	−	0.999876i	$-0.505019\pi$
$577$	−10497.6			−0.0315310			−0.0157655	+	0.999876i	$0.505019\pi$
$578$	−7350.26	+	236119.i	−0.0220012	+	0.706764i
$579$	−108031.	−	71867.7i	−0.322248	−	0.214376i
$580$	−4088.45	−	4088.45i	−0.0121535	−	0.0121535i
$581$	−9987.47	+	4136.95i	−0.0295872	+	0.0122554i
$582$	203564.	+	135421.i	0.600974	+	0.399799i
$583$	56874.9	−	23558.3i	0.167334	−	0.0693119i
$584$	−61990.7	−	25677.4i	−0.181761	−	0.0752879i
$585$	14884.0	−	60.3193i	0.0434919	−	0.000176256i
$586$	−326661.	+	326661.i	−0.951267	+	0.951267i
$587$	187273.	+	187273.i	0.543499	+	0.543499i	0.924553	−	0.381053i	$-0.124439\pi$
$587$	187273.	+	187273.i	0.543499	+	0.543499i	−0.381053	+	0.924553i	$0.624439\pi$
$588$	95709.0	+	142612.i	0.276820	+	0.412479i
$589$	−275795.	+	665829.i	−0.794980	+	1.91925i
$590$	−68074.0	−	164345.i	−0.195559	−	0.472121i
$591$	−325815.	−	216749.i	−0.932817	−	0.620558i
$592$	−3599.72	−	8690.49i	−0.0102713	−	0.0247971i
$593$	5315.48	−	5315.48i	0.0151159	−	0.0151159i	−0.699508	−	0.714624i	$-0.746598\pi$
$593$	5315.48	−	5315.48i	0.0151159	−	0.0151159i	0.714624	+	0.699508i	$0.246598\pi$
$594$	−10881.9	+	56499.9i	−0.0308412	+	0.160131i
$595$	21213.8	−	8402.78i	0.0599218	−	0.0237350i
$596$		−	328499.i		−	0.924786i
$597$	71360.8	+	354994.i	0.200222	+	0.996029i
$598$	−2589.50	−	6251.61i	−0.00724126	−	0.0174819i
$599$	−319000.			−0.889072			−0.444536	−	0.895761i	$-0.646632\pi$
$599$	−319000.			−0.889072			−0.444536	+	0.895761i	$0.646632\pi$
$600$	−8831.36	+	44873.3i	−0.0245316	+	0.124648i
$601$	179660.	−	433737.i	0.497396	−	1.20082i	−0.453486	−	0.891264i	$-0.649820\pi$
$601$	179660.	−	433737.i	0.497396	−	1.20082i	0.950881	−	0.309556i	$-0.100180\pi$
$602$	5246.05	−	12665.1i	0.0144757	−	0.0349474i
$603$	−589899.	−	241548.i	−1.62234	−	0.664307i
$604$	26715.2	−	26715.2i	0.0732292	−	0.0732292i
$605$	−106154.	+	256278.i	−0.290018	+	0.700165i
$606$	203696.	−	136703.i	0.554674	−	0.372249i
$607$	188048.	−	77891.9i	0.510377	−	0.211405i	−0.112607	−	0.993640i	$-0.535920\pi$
$607$	188048.	−	77891.9i	0.510377	−	0.211405i	0.622984	+	0.782235i	$0.285920\pi$
$608$	92309.2			0.249711
$609$	1258.41	+	247.663i	0.00339302	+	0.000667770i
$610$	−49322.8	−	49322.8i	−0.132553	−	0.132553i
$611$		−	25136.2i		−	0.0673312i
$612$	−187260.	−	2154.92i	−0.499967	−	0.00575344i
$613$	208486.			0.554825			0.277412	−	0.960751i	$-0.410523\pi$
$613$	208486.			0.554825			0.277412	+	0.960751i	$0.410523\pi$
$614$	160999.	−	160999.i	0.427057	−	0.427057i
$615$	−47338.5	+	240533.i	−0.125160	+	0.635951i
$616$		−	2491.30i		−	0.00656545i
$617$	277983.	+	671111.i	0.730211	+	1.76289i	0.641893	+	0.766794i	$0.278149\pi$
$617$	277983.	+	671111.i	0.730211	+	1.76289i	0.0883180	+	0.996092i	$0.471851\pi$
$618$	−20557.2	−	30631.5i	−0.0538255	−	0.0802033i
$619$	−627433.	−	259891.i	−1.63752	−	0.678282i	−0.641474	−	0.767145i	$-0.721677\pi$
$619$	−627433.	−	259891.i	−1.63752	−	0.678282i	−0.996044	+	0.0888625i	$0.971677\pi$
$620$	159979.	+	159979.i	0.416178	+	0.416178i
$621$	−157272.	+	106474.i	−0.407820	+	0.276097i
$622$	−372151.	−	154150.i	−0.961920	−	0.398440i
$623$	−12920.9	−	5352.03i	−0.0332903	−	0.0137893i
$624$	5189.78	+	1021.38i	0.0133285	+	0.00262313i
$625$			199831.i			0.511568i
$626$	315488.	−	130679.i	0.805071	−	0.333471i
$627$	−125558.	+	25239.6i	−0.319381	+	0.0642019i
$628$	169025.			0.428580
$629$	−30499.0	+	29564.3i	−0.0770875	+	0.0747251i
$630$	6989.76	+	16683.2i	0.0176109	+	0.0420338i
$631$	−19904.6	−	19904.6i	−0.0499913	−	0.0499913i	0.681669	−	0.731661i	$-0.261254\pi$
$631$	−19904.6	−	19904.6i	−0.0499913	−	0.0499913i	−0.731661	+	0.681669i	$0.761254\pi$
$632$	−81074.2	+	33582.0i	−0.202978	+	0.0840762i
$633$	345538.	−	519409.i	0.862359	−	1.29629i
$634$	−434870.	+	180129.i	−1.08188	+	0.448131i
$635$	468989.	+	194262.i	1.16310	+	0.481770i
$636$	−131890.	+	88512.9i	−0.326059	+	0.218823i
$637$	−15489.3	+	15489.3i	−0.0381726	+	0.0381726i
$638$	2015.75	+	2015.75i	0.00495218	+	0.00495218i
$639$	95162.5	−	385.657i	0.233058	−	0.000944495i
$640$	11089.6	−	26772.6i	0.0270742	−	0.0653628i
$641$	−258660.	−	624460.i	−0.629525	−	1.51981i	−0.840214	−	0.542254i	$-0.817571\pi$
$641$	−258660.	−	624460.i	−0.629525	−	1.51981i	0.210689	−	0.977553i	$-0.432429\pi$
$642$	60233.5	−	90542.4i	0.146140	−	0.219676i
$643$	−145562.	−	351417.i	−0.352067	−	0.849965i	−0.996365	−	0.0851901i	$-0.972850\pi$
$643$	−145562.	−	351417.i	−0.352067	−	0.849965i	0.644298	−	0.764775i	$-0.277150\pi$
$644$	5814.81	−	5814.81i	0.0140205	−	0.0140205i
$645$	−122536.	+	184195.i	−0.294539	+	0.442749i
$646$	−153504.	−	387540.i	−0.367837	−	0.928648i
$647$			465441.i			1.11187i	0.831224	+	0.555937i	$0.187641\pi$
$647$			465441.i			1.11187i	−0.831224	+	0.555937i	$0.812359\pi$
$648$	−1203.27	−	148454.i	−0.00286559	−	0.353542i
$649$	33563.0	+	81028.1i	0.0796839	+	0.192374i
$650$	−5832.92			−0.0138057
$651$	−49240.8	−	9690.91i	−0.116188	−	0.0228667i
$652$	142496.	−	344017.i	0.335204	−	0.809253i
$653$	171755.	−	414652.i	0.402793	−	0.972428i	−0.584192	−	0.811616i	$-0.698588\pi$
$653$	171755.	−	414652.i	0.402793	−	0.972428i	0.986985	−	0.160813i	$-0.0514116\pi$
$654$	71409.1	+	355234.i	0.166954	+	0.830537i
$655$	100589.	−	100589.i	0.234460	−	0.234460i
$656$	−33338.3	+	80485.7i	−0.0774703	+	0.187030i
$657$	−240192.	+	973.405i	−0.556451	+	0.00225508i
$658$	28222.0	−	11689.9i	0.0651833	−	0.0269998i
$659$	−56441.4			−0.129965			−0.0649826	−	0.997886i	$-0.520699\pi$
$659$	−56441.4			−0.129965			−0.0649826	+	0.997886i	$0.520699\pi$
$660$	−7763.63	+	39448.0i	−0.0178228	+	0.0905601i
$661$	−150787.	−	150787.i	−0.345112	−	0.345112i	0.513173	−	0.858285i	$-0.328470\pi$
$661$	−150787.	−	150787.i	−0.345112	−	0.345112i	−0.858285	+	0.513173i	$0.828470\pi$
$662$		−	377535.i		−	0.861473i
$663$	−4342.22	−	23486.6i	−0.00987835	−	0.0534310i
$664$	61996.6			0.140615
$665$	−28469.0	+	28469.0i	−0.0643768	+	0.0643768i
$666$	−23906.5	−	23713.6i	−0.0538975	−	0.0534624i
$667$			9409.72i			0.0211507i
$668$	−92648.9	−	223674.i	−0.207629	−	0.501260i
$669$	−644352.	+	432434.i	−1.43970	+	0.966201i
$670$	−411503.	−	170450.i	−0.916692	−	0.379706i
$671$	24317.9	+	24317.9i	0.0540109	+	0.0540109i
$672$	1266.81	+	6301.92i	0.00280526	+	0.0139551i
$673$	−18859.1	−	7811.71i	−0.0416382	−	0.0172471i	0.361767	−	0.932268i	$-0.382174\pi$
$673$	−18859.1	−	7811.71i	−0.0416382	−	0.0172471i	−0.403405	+	0.915021i	$0.632174\pi$
$674$	90246.3	+	37381.3i	0.198660	+	0.0822875i
$675$	32914.8	+	160373.i	0.0722410	+	0.351984i
$676$		−	227813.i		−	0.498524i
$677$	−821025.	+	340080.i	−1.79134	+	0.741999i	−0.801833	+	0.597548i	$0.796142\pi$
$677$	−821025.	+	340080.i	−1.79134	+	0.741999i	−0.989512	+	0.144451i	$0.953858\pi$
$678$	45539.5	+	226543.i	0.0990670	+	0.492822i
$679$	−37895.5			−0.0821956
$680$	−130840.	−	2036.00i	−0.282959	−	0.00440311i
$681$	−110951.	+	166781.i	−0.239243	+	0.359628i
$682$	−78875.3	−	78875.3i	−0.169579	−	0.169579i
$683$	−393162.	+	162853.i	−0.842811	+	0.349104i	−0.761961	−	0.647622i	$-0.775763\pi$
$683$	−393162.	+	162853.i	−0.842811	+	0.349104i	−0.0808499	+	0.996726i	$0.525763\pi$
$684$	304774.	−	127691.i	0.651426	−	0.272928i
$685$	−105489.	+	43695.0i	−0.224815	+	0.0931216i
$686$	−49349.1	−	20441.1i	−0.104865	−	0.0434366i
$687$	80031.2	+	119251.i	0.169569	+	0.252668i
$688$	−55591.2	+	55591.2i	−0.117444	+	0.117444i
$689$	−14324.7	−	14324.7i	−0.0301749	−	0.0301749i
$690$	−110194.	+	73952.7i	−0.231451	+	0.155330i
$691$	−34236.2	+	82653.4i	−0.0717016	+	0.173103i	−0.955667	−	0.294449i	$-0.904864\pi$
$691$	−34236.2	+	82653.4i	−0.0717016	+	0.173103i	0.883966	+	0.467552i	$0.154864\pi$
$692$	15417.3	+	37220.7i	0.0321956	+	0.0777271i
$693$	−3446.20	−	8225.43i	−0.00717587	−	0.0171274i
$694$	148890.	+	359453.i	0.309135	+	0.746317i
$695$	245662.	−	245662.i	0.508591	−	0.508591i
$696$	−6123.99	−	4073.99i	−0.0126420	−	0.00841011i
$697$	393340.	+	6120.76i	0.809660	+	0.0125991i
$698$		−	188864.i		−	0.387648i
$699$	−687771.	+	138256.i	−1.40763	+	0.282962i
$700$	−2712.68	−	6549.00i	−0.00553609	−	0.0133653i
$701$	−612377.			−1.24619			−0.623093	−	0.782147i	$-0.714124\pi$
$701$	−612377.			−1.24619			−0.623093	+	0.782147i	$0.714124\pi$
$702$	18547.8	−	3806.73i	0.0376372	−	0.00772464i
$703$	28681.9	−	69244.3i	0.0580361	−	0.140111i
$704$	−5467.56	+	13199.9i	−0.0110319	+	0.0266332i
$705$	−483305.	+	97153.8i	−0.972395	+	0.195471i
$706$	322922.	−	322922.i	0.647871	−	0.647871i
$707$	−14550.7	+	35128.6i	−0.0291103	+	0.0702784i
$708$	−126102.	−	187900.i	−0.251568	−	0.374852i
$709$	−201767.	+	83574.6i	−0.401382	+	0.166258i	−0.574236	−	0.818690i	$-0.694701\pi$
$709$	−201767.	+	83574.6i	−0.401382	+	0.166258i	0.172855	+	0.984947i	$0.444701\pi$
$710$	66495.1			0.131909
$711$	−221226.	+	223026.i	−0.437619	+	0.441180i
$712$	56714.2	+	56714.2i	0.111875	+	0.111875i
$713$		−	368197.i		−	0.724271i
$714$	24350.6	−	15798.1i	0.0477653	−	0.0309890i
$715$	−5127.70			−0.0100302
$716$	278080.	−	278080.i	0.542429	−	0.542429i
$717$	677521.	+	133341.i	1.31791	+	0.259373i
$718$		−	600733.i		−	1.16529i
$719$	96058.7	+	231906.i	0.185814	+	0.448595i	0.989146	−	0.146937i	$-0.0469414\pi$
$719$	96058.7	+	231906.i	0.185814	+	0.448595i	−0.803332	+	0.595532i	$0.796941\pi$
$720$	−420.395	−	103734.i	−0.000810947	−	0.200104i
$721$	5282.59	+	2188.12i	0.0101619	+	0.00420921i
$722$	259438.	+	259438.i	0.497691	+	0.497691i
$723$	−539835.	+	108517.i	−1.03272	+	0.207598i
$724$	300857.	+	124619.i	0.573962	+	0.237743i
$725$	7493.78	+	3104.03i	0.0142569	+	0.00590540i
$726$	−68141.4	+	346235.i	−0.129282	+	0.656898i
$727$		−	748794.i		−	1.41675i	−0.705835	−	0.708376i	$-0.749428\pi$
$727$		−	748794.i		−	1.41675i	0.705835	−	0.708376i	$-0.250572\pi$
$728$	−757.419	+	313.733i	−0.00142914	+	0.000591967i
$729$	−209328.	−	488479.i	−0.393887	−	0.919159i
$730$	−167835.			−0.314946
$731$	325832.	+	140943.i	0.609759	+	0.263759i
$732$	−73879.4	−	49148.4i	−0.137880	−	0.0917248i
$733$	207003.	+	207003.i	0.385274	+	0.385274i	0.872998	−	0.487724i	$-0.162173\pi$
$733$	207003.	+	207003.i	0.385274	+	0.385274i	−0.487724	+	0.872998i	$0.662173\pi$
$734$	−630561.	+	261187.i	−1.17040	+	0.484796i
$735$	357687.	+	237952.i	0.662107	+	0.440468i
$736$	−43570.6	+	18047.5i	−0.0804337	+	0.0333167i
$737$	202886.	+	84038.1i	0.373522	+	0.154718i
$738$	1263.82	+	311853.i	0.00232045	+	0.572581i
$739$	529085.	−	529085.i	0.968806	−	0.968806i	−0.0307216	−	0.999528i	$-0.509781\pi$
$739$	529085.	−	529085.i	0.968806	−	0.968806i	0.999528	+	0.0307216i	$0.00978054\pi$
$740$	−16637.4	−	16637.4i	−0.0303823	−	0.0303823i
$741$	23485.2	+	34994.4i	0.0427718	+	0.0637326i
$742$	9421.34	−	22745.1i	0.0171122	−	0.0413124i
$743$	175876.	+	424602.i	0.318588	+	0.769139i	0.999329	+	0.0366152i	$0.0116576\pi$
$743$	175876.	+	424602.i	0.318588	+	0.769139i	−0.680742	+	0.732524i	$0.738342\pi$
$744$	239628.	+	159413.i	0.432904	+	0.287990i
$745$	−314444.	−	759136.i	−0.566541	−	1.36775i
$746$	358574.	−	358574.i	0.644320	−	0.644320i
$747$	204692.	−	85759.5i	0.366825	−	0.153688i
$748$	64508.9	+	1003.82i	0.115296	+	0.00179413i
$749$			16855.4i			0.0300452i
$750$	85287.7	+	424275.i	0.151623	+	0.754267i
$751$	209211.	+	505081.i	0.370942	+	0.895532i	0.993591	+	0.113032i	$0.0360562\pi$
$751$	209211.	+	505081.i	0.370942	+	0.895532i	−0.622650	+	0.782501i	$0.713944\pi$
$752$	−175186.			−0.309788
$753$	82466.5	−	419023.i	0.145441	−	0.739005i
$754$	358.994	−	866.687i	0.000631457	−	0.00152447i
$755$	36164.6	−	87309.0i	0.0634438	−	0.153167i
$756$	12900.0	+	19054.4i	0.0225707	+	0.0333389i
$757$	−103914.	+	103914.i	−0.181336	+	0.181336i	−0.791938	−	0.610602i	$-0.790928\pi$
$757$	−103914.	+	103914.i	−0.181336	+	0.181336i	0.610602	+	0.791938i	$0.290928\pi$
$758$	−141868.	+	342498.i	−0.246913	+	0.596102i
$759$	54329.6	−	36461.4i	0.0943090	−	0.0632921i
$760$	213320.	−	88359.9i	0.369321	−	0.152978i
$761$	800853.			1.38288			0.691439	−	0.722435i	$-0.256977\pi$
$761$	800853.			1.38288			0.691439	+	0.722435i	$0.256977\pi$
$762$	633611.	+	124699.i	1.09122	+	0.214760i
$763$	−39712.0	−	39712.0i	−0.0682138	−	0.0682138i
$764$		−	118071.i		−	0.202282i
$765$	−434806.	+	174268.i	−0.742972	+	0.297780i
$766$	394216.			0.671857
$767$	20408.0	−	20408.0i	0.0346904	−	0.0346904i
$768$	7118.53	−	36170.2i	0.0120689	−	0.0613237i
$769$		−	366030.i		−	0.618963i	−0.950906	−	0.309481i	$-0.899845\pi$
$769$		−	366030.i		−	0.618963i	0.950906	−	0.309481i	$-0.100155\pi$
$770$	−2384.71	−	5757.21i	−0.00402212	−	0.00971025i
$771$	208470.	+	310633.i	0.350700	+	0.522564i
$772$	−106556.	−	44136.9i	−0.178790	−	0.0740571i
$773$	−49199.6	−	49199.6i	−0.0823385	−	0.0823385i	0.664738	−	0.747077i	$-0.268543\pi$
$773$	−49199.6	−	49199.6i	−0.0823385	−	0.0823385i	−0.747077	+	0.664738i	$0.768543\pi$
$774$	−106644.	+	260442.i	−0.178014	+	0.434740i
$775$	−293227.	−	121459.i	−0.488204	−	0.202221i
$776$	200785.	+	83167.9i	0.333432	+	0.138112i
$777$	5120.90	+	1007.83i	0.00848212	+	0.00166934i
$778$			775374.i			1.28101i
$779$	−641296.	+	265634.i	−1.05678	+	0.437732i
$780$	12970.9	−	2607.40i	0.0213197	−	0.00428567i
$781$	−32784.5			−0.0537485
$782$	148224.	+	152909.i	0.242384	+	0.250047i
$783$	−25854.8	−	4979.66i	−0.0421714	−	0.00812224i
$784$	107952.	+	107952.i	0.175631	+	0.175631i
$785$	390605.	−	161794.i	0.633867	−	0.262556i
$786$	100234.	−	150670.i	0.162244	−	0.243883i
$787$	814032.	−	337183.i	1.31429	−	0.544398i	0.388158	−	0.921593i	$-0.373111\pi$
$787$	814032.	−	337183.i	1.31429	−	0.544398i	0.926134	+	0.377195i	$0.123111\pi$
$788$	−321367.	−	133115.i	−0.517546	−	0.214375i
$789$	497402.	−	333813.i	0.799013	−	0.536228i
$790$	−155211.	+	155211.i	−0.248696	+	0.248696i
$791$	−25325.4	−	25325.4i	−0.0404766	−	0.0404766i
$792$	207.270	+	51144.7i	0.000330435	+	0.0815361i
$793$	4330.88	−	10455.7i	0.00688699	−	0.0166267i
$794$	−41980.7	−	101350.i	−0.0665900	−	0.160762i
$795$	−220061.	+	330794.i	−0.348184	+	0.523387i
$796$	123171.	+	297362.i	0.194394	+	0.469310i
$797$	−404700.	+	404700.i	−0.637113	+	0.637113i	−0.949842	−	0.312729i	$-0.898757\pi$
$797$	−404700.	+	404700.i	−0.637113	+	0.637113i	0.312729	+	0.949842i	$0.398757\pi$
$798$	−28368.3	+	42643.0i	−0.0445480	+	0.0669641i
$799$	291323.	+	735481.i	0.456333	+	1.15207i
$800$			40652.5i			0.0635195i
$801$	265703.	+	108798.i	0.414125	+	0.169573i
$802$	−49615.3	−	119782.i	−0.0771378	−	0.186227i
$803$	82748.5			0.128330
$804$	−555946.	−	109414.i	−0.860044	−	0.169262i
$805$	7871.55	−	19003.6i	0.0121470	−	0.0293254i
$806$	−14047.2	+	33913.0i	−0.0216232	+	0.0522030i
$807$	35959.3	+	178884.i	0.0552159	+	0.274679i
$808$	154191.	−	154191.i	0.236176	−	0.236176i
$809$	−322081.	+	777572.i	−0.492116	+	1.18807i	0.461525	+	0.887127i	$0.347303\pi$
$809$	−322081.	+	777572.i	−0.492116	+	1.18807i	−0.953641	+	0.300946i	$0.902697\pi$
$810$	−144883.	−	341913.i	−0.220824	−	0.521130i
$811$	−74134.0	+	30707.3i	−0.112713	+	0.0466874i	−0.438327	−	0.898815i	$-0.644429\pi$
$811$	−74134.0	+	30707.3i	−0.112713	+	0.0466874i	0.325614	+	0.945503i	$0.394429\pi$
$812$	1140.04			0.00172905
$813$	109495.	−	556356.i	0.165658	−	0.841729i
$814$	8202.81	+	8202.81i	0.0123798	+	0.0123798i
$815$		−	931397.i		−	1.40223i
$816$	−163690.	+	30263.1i	−0.245834	+	0.0454499i
$817$	−626413.			−0.938463
$818$	−270597.	+	270597.i	−0.404405	+	0.404405i
$819$	−2066.75	+	2083.57i	−0.00308121	+	0.00310628i
$820$			217908.i			0.324075i
$821$	119012.	+	287321.i	0.176565	+	0.426267i	0.987242	−	0.159228i	$-0.0509004\pi$
$821$	119012.	+	287321.i	0.176565	+	0.426267i	−0.810676	+	0.585494i	$0.800900\pi$
$822$	−120608.	+	80941.7i	−0.178498	+	0.119792i
$823$	614882.	+	254692.i	0.907804	+	0.376025i	0.787216	−	0.616678i	$-0.211522\pi$
$823$	614882.	+	254692.i	0.907804	+	0.376025i	0.120588	+	0.992703i	$0.461522\pi$
$824$	−23187.0	−	23187.0i	−0.0341499	−	0.0341499i
$825$	−11115.4	−	55295.1i	−0.0163312	−	0.0812417i
$826$	32404.4	+	13422.3i	0.0474946	+	0.0196729i
$827$	919796.	+	380992.i	1.34487	+	0.557064i	0.934860	−	0.355017i	$-0.115525\pi$
$827$	919796.	+	380992.i	1.34487	+	0.557064i	0.410011	+	0.912081i	$0.365525\pi$
$828$	−118890.	+	119858.i	−0.173414	+	0.174826i
$829$			1.18877e6i			1.72977i	0.501972	+	0.864884i	$0.332608\pi$
$829$			1.18877e6i			1.72977i	−0.501972	+	0.864884i	$0.667392\pi$
$830$	143269.	−	59344.2i	0.207968	−	0.0861434i
$831$	59718.3	+	297077.i	0.0864779	+	0.430196i
$832$	4701.63			0.00679207
$833$	273696.	−	632731.i	0.394438	−	0.911863i
$834$	244793.	−	367971.i	0.351939	−	0.529031i
$835$	−428209.	−	428209.i	−0.614162	−	0.614162i
$836$	−105174.	+	43564.6i	−0.150486	+	0.0623335i
$837$	1.01168e6	+	194851.i	1.44409	+	0.278133i
$838$	330695.	−	136978.i	0.470912	−	0.195058i
$839$	388267.	+	160825.i	0.551577	+	0.228471i	0.641024	−	0.767521i	$-0.278510\pi$
$839$	388267.	+	160825.i	0.551577	+	0.228471i	−0.0894470	+	0.995992i	$0.528510\pi$
$840$	8959.80	+	13350.6i	0.0126981	+	0.0189210i
$841$	499201.	−	499201.i	0.705803	−	0.705803i
$842$	−186958.	−	186958.i	−0.263706	−	0.263706i
$843$	943845.	−	633427.i	1.32815	−	0.891336i
$844$	212209.	−	512318.i	0.297906	−	0.719208i
$845$	−218067.	−	526460.i	−0.305405	−	0.737312i
$846$	−578406.	+	242334.i	−0.808149	+	0.338590i
$847$	−20930.6	−	50531.0i	−0.0291753	−	0.0704354i
$848$	−99835.7	+	99835.7i	−0.138834	+	0.138834i
$849$	−172477.	−	114741.i	−0.239285	−	0.159185i
$850$	170670.	−	67602.4i	0.236222	−	0.0935674i
$851$			38291.5i			0.0528741i
$852$	82930.6	−	16670.7i	0.114245	−	0.0229654i
$853$	−292242.	−	705533.i	−0.401646	−	0.969660i	−0.987267	−	0.159075i	$-0.949149\pi$
$853$	−292242.	−	705533.i	−0.401646	−	0.969660i	0.585620	−	0.810586i	$-0.300851\pi$
$854$	13753.4			0.0188579
$855$	582081.	−	586818.i	0.796253	−	0.802733i
$856$	36991.8	−	89306.2i	0.0504845	−	0.121880i
$857$	491745.	−	1.18718e6i	0.669543	−	1.61642i	−0.112834	−	0.993614i	$-0.535993\pi$
$857$	491745.	−	1.18718e6i	0.669543	−	1.61642i	0.782377	−	0.622805i	$-0.214007\pi$
$858$	−6395.11	+	1285.54i	−0.00868707	+	0.00174627i
$859$	−722268.	+	722268.i	−0.978840	+	0.978840i	−0.999781	−	0.0209404i	$-0.993334\pi$
$859$	−722268.	+	722268.i	−0.978840	+	0.978840i	0.0209404	+	0.999781i	$0.493334\pi$
$860$	−75254.2	+	181680.i	−0.101750	+	0.245646i
$861$	−26935.6	−	40135.6i	−0.0363345	−	0.0541407i
$862$	−427671.	+	177147.i	−0.575566	+	0.238407i
$863$	−302134.			−0.405675			−0.202838	−	0.979212i	$-0.565016\pi$
$863$	−302134.			−0.405675			−0.202838	+	0.979212i	$0.565016\pi$
$864$	−26531.0	−	129269.i	−0.0355407	−	0.173167i
$865$	71256.6	+	71256.6i	0.0952342	+	0.0952342i
$866$		−	915194.i		−	1.22033i
$867$	399258.	+	636890.i	0.531148	+	0.847279i
$868$	−44609.2			−0.0592086
$869$	76524.7	−	76524.7i	0.101336	−	0.101336i
$870$	−18051.8	−	3552.71i	−0.0238496	−	0.00469376i
$871$		−	72265.5i		−	0.0952565i
$872$	123255.	+	297563.i	0.162095	+	0.391333i
$873$	777969.	−	3152.81i	1.02078	−	0.00413685i
$874$	−347163.	−	143800.i	−0.454476	−	0.188250i
$875$	−47430.2	−	47430.2i	−0.0619496	−	0.0619496i
$876$	−209318.	+	42077.0i	−0.272771	+	0.0548324i
$877$	−93795.8	−	38851.5i	−0.121951	−	0.0505136i	0.320874	−	0.947122i	$-0.396023\pi$
$877$	−93795.8	−	38851.5i	−0.121951	−	0.0505136i	−0.442824	+	0.896608i	$0.646023\pi$
$878$	−726642.	−	300985.i	−0.942609	−	0.390442i
$879$	−283856.	+	1.44231e6i	−0.367384	+	1.86673i
$880$			35737.5i			0.0461487i
$881$	−895774.	+	371042.i	−1.15411	+	0.478047i	−0.875909	−	0.482476i	$-0.839738\pi$
$881$	−895774.	+	371042.i	−1.15411	+	0.478047i	−0.278199	+	0.960523i	$0.589738\pi$
$882$	505752.	+	207092.i	0.650130	+	0.266211i
$883$	−118179.			−0.151572			−0.0757860	−	0.997124i	$-0.524147\pi$
$883$	−118179.			−0.151572			−0.0757860	+	0.997124i	$0.524147\pi$
$884$	−7818.51	−	19738.7i	−0.0100050	−	0.0252589i
$885$	−471273.	−	313515.i	−0.601708	−	0.400287i
$886$	−362349.	−	362349.i	−0.461593	−	0.461593i
$887$	−289818.	+	120047.i	−0.368365	+	0.152582i	−0.559184	−	0.829043i	$-0.688886\pi$
$887$	−289818.	+	120047.i	−0.368365	+	0.152582i	0.190819	+	0.981625i	$0.438886\pi$
$888$	−24920.7	−	16578.5i	−0.0316034	−	0.0210242i
$889$	−92471.9	+	38303.1i	−0.117005	+	0.0484652i
$890$	185350.	+	76774.4i	0.233998	+	0.0969252i
$891$	71432.5	+	168576.i	0.0899788	+	0.212344i
$892$	−487752.	+	487752.i	−0.613012	+	0.613012i
$893$	−987019.	−	987019.i	−1.23772	−	1.23772i
$894$	−582485.	−	867938.i	−0.728802	−	1.08596i
$895$	376439.	−	908803.i	0.469946	−	1.13455i
$896$	2186.56	+	5278.83i	0.00272362	+	0.00657539i
$897$	−17927.0	−	11926.0i	−0.0222804	−	0.0148221i
$898$	238823.	+	576571.i	0.296159	+	0.714990i
$899$	36094.0	−	36094.0i	0.0446597	−	0.0446597i
$900$	56234.3	+	134221.i	0.0694251	+	0.165704i
$901$	585158.	+	253118.i	0.720815	+	0.311798i
$902$		−	107437.i		−	0.132050i
$903$	−8596.61	−	42765.0i	−0.0105427	−	0.0524461i
$904$	78603.0	+	189764.i	0.0961838	+	0.232208i
$905$	814545.			0.994531
$906$	23214.5	−	117956.i	0.0282815	−	0.143702i
$907$	217795.	−	525804.i	0.264748	−	0.639159i	−0.734472	−	0.678639i	$-0.762570\pi$
$907$	217795.	−	525804.i	0.264748	−	0.639159i	0.999220	+	0.0394799i	$0.0125701\pi$
$908$	−68139.9	+	164504.i	−0.0826475	+	0.199529i
$909$	295794.	−	722377.i	0.357982	−	0.874250i
$910$	−1450.03	+	1450.03i	−0.00175103	+	0.00175103i
$911$	−61399.5	+	148231.i	−0.0739823	+	0.178609i	−0.956544	−	0.291587i	$-0.905817\pi$
$911$	−61399.5	+	148231.i	−0.0739823	+	0.178609i	0.882562	+	0.470196i	$0.155817\pi$
$912$	243893.	−	163680.i	0.293231	−	0.196791i
$913$	−70637.0	+	29258.8i	−0.0847404	+	0.0351006i
$914$	−859236.			−1.02854
$915$	−217775.	−	42859.6i	−0.260116	−	0.0511925i
$916$	90269.0	+	90269.0i	0.107584	+	0.107584i
$917$			28048.8i			0.0333561i
$918$	−498586.	+	326350.i	−0.591636	+	0.387256i
$919$	109207.			0.129306			0.0646531	−	0.997908i	$-0.479406\pi$
$919$	109207.			0.129306			0.0646531	+	0.997908i	$0.479406\pi$
$920$	−83412.9	+	83412.9i	−0.0985503	+	0.0985503i
$921$	139902.	−	710859.i	0.164932	−	0.838039i
$922$			478865.i			0.563315i
$923$	4128.60	+	9967.31i	0.00484617	+	0.0116997i
$924$	−4417.50	−	6582.35i	−0.00517408	−	0.00770969i
$925$	30494.8	+	12631.4i	0.0356404	+	0.0147627i
$926$	703465.	+	703465.i	0.820391	+	0.820391i
$927$	−108630.	−	44481.1i	−0.126413	−	0.0517626i
$928$	−6040.37	−	2502.01i	−0.00701404	−	0.00290531i
$929$	1.02709e6	+	425435.i	1.19008	+	0.492948i	0.887782	−	0.460264i	$-0.152245\pi$
$929$	1.02709e6	+	425435.i	1.19008	+	0.492948i	0.302301	+	0.953213i	$0.402245\pi$
$930$	706355.	+	139015.i	0.816690	+	0.160730i
$931$			1.21643e6i			1.40342i
$932$	−576114.	+	238634.i	−0.663249	+	0.274727i
$933$	−1.25661e6	+	252603.i	−1.44357	+	0.290185i
$934$	−381299.			−0.437091
$935$	150036.	−	59429.2i	0.171622	−	0.0679793i
$936$	15523.2	−	6503.74i	0.0177186	−	0.00742355i
$937$	−503245.	−	503245.i	−0.573193	−	0.573193i	0.359827	−	0.933019i	$-0.382836\pi$
$937$	−503245.	−	503245.i	−0.573193	−	0.573193i	−0.933019	+	0.359827i	$0.882836\pi$
$938$	81137.2	−	33608.1i	0.0922177	−	0.0381978i
$939$	601844.	−	904686.i	0.682579	−	1.02605i
$940$	−404842.	+	167691.i	−0.458174	+	0.189782i
$941$	−846692.	−	350712.i	−0.956195	−	0.396069i	−0.150639	−	0.988589i	$-0.548133\pi$
$941$	−846692.	−	350712.i	−0.956195	−	0.396069i	−0.805556	+	0.592520i	$0.798133\pi$
$942$	446587.	−	299711.i	0.503274	−	0.337754i
$943$	250762.	−	250762.i	0.281993	−	0.281993i
$944$	−142233.	−	142233.i	−0.159609	−	0.159609i
$945$	48050.1	+	31685.2i	0.0538060	+	0.0354808i
$946$	37103.1	−	89574.7i	0.0414598	−	0.100093i
$947$	394174.	+	951620.i	0.439529	+	1.06112i	0.976112	+	0.217270i	$0.0697151\pi$
$947$	394174.	+	951620.i	0.439529	+	1.06112i	−0.536582	+	0.843848i	$0.680285\pi$
$948$	−154662.	+	232487.i	−0.172095	+	0.258691i
$949$	−10420.6	−	25157.7i	−0.0115708	−	0.0279343i
$950$	−229041.	+	229041.i	−0.253784	+	0.253784i
$951$	−829584.	+	1.24702e6i	−0.917275	+	1.37884i
$952$	18525.9	−	17958.1i	0.0204411	−	0.0198147i
$953$		−	138030.i		−	0.151980i	−0.997109	−	0.0759901i	$-0.975788\pi$
$953$		−	138030.i		−	0.151980i	0.997109	−	0.0759901i	$-0.0242117\pi$
$954$	−191521.	+	467726.i	−0.210436	+	0.513919i
$955$	−113020.	−	272854.i	−0.123922	−	0.299173i
$956$	613793.			0.671593
$957$	8900.17	+	1751.61i	0.00971794	+	0.00191256i
$958$	74551.1	−	179982.i	0.0812312	−	0.196110i
$959$	8615.46	−	20799.6i	0.00936788	−	0.0226161i
$960$	−18172.3	−	90400.5i	−0.0197182	−	0.0980908i
$961$	−759311.	+	759311.i	−0.822192	+	0.822192i
$962$	1460.87	−	3526.86i	0.00157856	−	0.00381099i
$963$	−1402.32	−	346029.i	−0.00151215	−	0.373130i
$964$	−452195.	+	187305.i	−0.486599	+	0.201556i
$965$	−288491.			−0.309797
$966$	5052.84	−	25674.1i	0.00541479	−	0.0275132i
$967$	382407.	+	382407.i	0.408952	+	0.408952i	0.881373	−	0.472421i	$-0.156620\pi$
$967$	382407.	+	382407.i	0.408952	+	0.408952i	−0.472421	+	0.881373i	$0.656620\pi$
$968$			313668.i			0.334749i
$969$	−1.09275e6	−	751742.i	−1.16379	−	0.800610i
$970$	543609.			0.577754
$971$	−238234.	+	238234.i	−0.252677	+	0.252677i	−0.822067	−	0.569390i	$-0.807179\pi$
$971$	−238234.	+	238234.i	−0.252677	+	0.252677i	0.569390	+	0.822067i	$0.307179\pi$
$972$	−266413.	−	390101.i	−0.281983	−	0.412899i
$973$			68501.5i			0.0723559i
$974$	509779.	+	1.23072e6i	0.537358	+	1.29730i
$975$	−15411.3	+	10342.8i	−0.0162118	+	0.0108800i
$976$	−72870.7	−	30184.0i	−0.0764986	−	0.0316867i
$977$	787891.	+	787891.i	0.825424	+	0.825424i	0.986880	−	0.161456i	$-0.0516190\pi$
$977$	787891.	+	787891.i	0.825424	+	0.825424i	−0.161456	+	0.986880i	$0.551619\pi$
$978$	−233506.	−	1.16161e6i	−0.244130	−	1.21446i
$979$	−91384.2	−	37852.6i	−0.0953467	−	0.0394939i
$980$	352803.	+	146136.i	0.367351	+	0.152162i
$981$	818563.	+	811955.i	0.850578	+	0.843712i
$982$		−	573674.i		−	0.594897i
$983$	−1.35162e6	+	559860.i	−1.39878	+	0.579392i	−0.949434	−	0.313968i	$-0.898342\pi$
$983$	−1.35162e6	+	559860.i	−1.39878	+	0.579392i	−0.449342	+	0.893360i	$0.648342\pi$
$984$	54630.8	+	271768.i	0.0564218	+	0.280678i
$985$	−870074.			−0.896776
$986$	−459.357	+	29519.8i	−0.000472495	+	0.0303641i
$987$	53838.0	−	80928.8i	0.0552656	−	0.0830747i
$988$	26489.5	+	26489.5i	0.0271369	+	0.0271369i
$989$	295671.	−	122471.i	0.302285	−	0.125211i
$990$	49435.5	+	117993.i	0.0504392	+	0.120389i
$991$	−231419.	+	95857.0i	−0.235642	+	0.0976060i	−0.497380	−	0.867533i	$-0.665704\pi$
$991$	−231419.	+	95857.0i	−0.235642	+	0.0976060i	0.261738	+	0.965139i	$0.415704\pi$
$992$	236356.	+	97902.0i	0.240184	+	0.0994874i
$993$	−669435.	−	997498.i	−0.678906	−	1.01161i
$994$	−9270.89	+	9270.89i	−0.00938315	+	0.00938315i
$995$	569280.	+	569280.i	0.575016	+	0.575016i
$996$	163803.	−	109931.i	0.165122	−	0.110815i
$997$	502856.	−	1.21400e6i	0.505887	−	1.22132i	−0.440345	−	0.897829i	$-0.645144\pi$
$997$	502856.	−	1.21400e6i	0.505887	−	1.22132i	0.946231	−	0.323490i	$-0.104856\pi$
$998$	354597.	+	856074.i	0.356020	+	0.859509i
$999$	−105212.	−	20264.0i	−0.105423	−	0.0203046i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	102.5.g.d.83.7	yes	44
3.2	odd	2		102.5.g.c.83.3	yes	44
17.8	even	8		102.5.g.c.59.3	✓	44
51.8	odd	8	inner	102.5.g.d.59.7	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.5.g.c.59.3	✓	44	17.8	even	8
102.5.g.c.83.3	yes	44	3.2	odd	2
102.5.g.d.59.7	yes	44	51.8	odd	8	inner
102.5.g.d.83.7	yes	44	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 102 = 2 \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	102.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 - 2.00000i) q^{2} +(1.73792 - 8.83061i) q^{3} -8.00000i q^{4} +(-7.65773 - 18.4874i) q^{5} +(-14.1854 - 21.1371i) q^{6} +(3.64521 + 1.50990i) q^{7} +(-16.0000 - 16.0000i) q^{8} +(-74.9592 - 30.6938i) q^{9} +(-52.2903 - 21.6593i) q^{10} +(25.7810 + 10.6788i) q^{11} +(-70.6449 - 13.9034i) q^{12} -9.18287i q^{13} +(10.3102 - 4.27063i) q^{14} +(-176.563 + 35.4927i) q^{15} -64.0000 q^{16} +(106.428 + 268.690i) q^{17} +(-211.306 + 88.5308i) q^{18} +(-360.583 - 360.583i) q^{19} +(-147.899 + 61.2618i) q^{20} +(19.6684 - 29.5653i) q^{21} +(72.9196 - 30.2043i) q^{22} +(240.696 + 99.6995i) q^{23} +(-169.096 + 113.483i) q^{24} +(158.799 - 158.799i) q^{25} +(-18.3657 - 18.3657i) q^{26} +(-401.319 + 608.592i) q^{27} +(12.0792 - 29.1617i) q^{28} +(13.8218 + 33.3687i) q^{29} +(-282.141 + 424.112i) q^{30} +(-540.837 - 1305.70i) q^{31} +(-128.000 + 128.000i) q^{32} +(139.106 - 209.103i) q^{33} +(750.235 + 324.524i) q^{34} -78.9528i q^{35} +(-245.551 + 599.674i) q^{36} +(56.2456 + 135.789i) q^{37} -1442.33 q^{38} +(-81.0903 - 15.9591i) q^{39} +(-173.275 + 418.322i) q^{40} +(520.910 - 1257.59i) q^{41} +(-19.7939 - 98.4674i) q^{42} +(868.612 - 868.612i) q^{43} +(85.4306 - 206.248i) q^{44} +(6.56867 + 1620.85i) q^{45} +(680.790 - 281.993i) q^{46} +2737.29 q^{47} +(-111.227 + 565.159i) q^{48} +(-1686.76 - 1686.76i) q^{49} -635.195i q^{50} +(2557.66 - 472.860i) q^{51} -73.4630 q^{52} +(1559.93 - 1559.93i) q^{53} +(414.547 + 2019.82i) q^{54} -558.399i q^{55} +(-34.1650 - 82.4817i) q^{56} +(-3810.83 + 2557.50i) q^{57} +(94.3809 + 39.0938i) q^{58} +(2222.40 + 2222.40i) q^{59} +(283.942 + 1412.51i) q^{60} +(1138.60 + 471.625i) q^{61} +(-3693.07 - 1529.72i) q^{62} +(-226.898 - 225.066i) q^{63} +512.000i q^{64} +(-169.767 + 70.3200i) q^{65} +(-139.994 - 696.417i) q^{66} +7869.59 q^{67} +(2149.52 - 851.423i) q^{68} +(1298.72 - 1952.22i) q^{69} +(-157.906 - 157.906i) q^{70} +(-1085.42 + 449.597i) q^{71} +(708.247 + 1690.45i) q^{72} +(2739.63 - 1134.79i) q^{73} +(384.069 + 159.087i) q^{74} +(-1126.31 - 1678.27i) q^{75} +(-2884.66 + 2884.66i) q^{76} +(77.8532 + 77.8532i) q^{77} +(-194.099 + 130.262i) q^{78} +(1484.13 - 3583.01i) q^{79} +(490.095 + 1183.19i) q^{80} +(4676.78 + 4601.57i) q^{81} +(-1473.36 - 3557.00i) q^{82} +(-1937.39 + 1937.39i) q^{83} +(-236.523 - 157.347i) q^{84} +(4152.38 - 4025.13i) q^{85} -3474.45i q^{86} +(318.687 - 64.0623i) q^{87} +(-241.634 - 583.357i) q^{88} -3544.63 q^{89} +(3254.83 + 3228.56i) q^{90} +(13.8652 - 33.4735i) q^{91} +(797.596 - 1925.57i) q^{92} +(-12470.0 + 2506.72i) q^{93} +(5474.57 - 5474.57i) q^{94} +(-3904.99 + 9427.49i) q^{95} +(907.864 + 1352.77i) q^{96} +(-8873.53 + 3675.54i) q^{97} -6747.02 q^{98} +(-1604.75 - 1591.79i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 88 q^{2} - 4 q^{3} + 72 q^{5} - 40 q^{6} + 132 q^{7} - 704 q^{8} + 324 q^{9} + 384 q^{10} - 616 q^{11} - 128 q^{12} + 416 q^{14} - 908 q^{15} - 2816 q^{16} + 424 q^{17} + 1016 q^{18} + 568 q^{19}+ \cdots + 91704 q^{99}+O(q^{100}) \) 44 * q + 88 * q^2 - 4 * q^3 + 72 * q^5 - 40 * q^6 + 132 * q^7 - 704 * q^8 + 324 * q^9 + 384 * q^10 - 616 * q^11 - 128 * q^12 + 416 * q^14 - 908 * q^15 - 2816 * q^16 + 424 * q^17 + 1016 * q^18 + 568 * q^19 + 960 * q^20 + 1020 * q^21 + 424 * q^22 + 332 * q^23 - 192 * q^24 + 1888 * q^25 - 1008 * q^26 - 436 * q^27 + 608 * q^28 - 6688 * q^29 - 2000 * q^30 - 1428 * q^31 - 5632 * q^32 + 2224 * q^33 + 512 * q^34 + 1472 * q^36 + 296 * q^37 + 2272 * q^38 - 3720 * q^39 + 768 * q^40 + 4592 * q^41 + 3328 * q^42 - 228 * q^43 + 6624 * q^44 + 8228 * q^45 + 1872 * q^46 + 10712 * q^47 + 256 * q^48 + 5304 * q^49 - 3984 * q^51 - 4032 * q^52 - 5656 * q^53 - 9288 * q^54 - 896 * q^56 - 13364 * q^57 - 11472 * q^58 + 3620 * q^59 - 736 * q^60 - 10448 * q^61 - 3536 * q^62 + 28248 * q^63 - 13760 * q^65 + 12952 * q^66 - 18584 * q^67 - 1344 * q^68 + 6500 * q^69 - 9664 * q^70 + 36660 * q^71 - 2240 * q^72 + 18008 * q^73 - 144 * q^74 + 30268 * q^75 + 4544 * q^76 - 5704 * q^77 - 22576 * q^78 - 7324 * q^79 - 4608 * q^80 - 33668 * q^81 + 11160 * q^82 - 12620 * q^83 + 5152 * q^84 - 10896 * q^85 + 23860 * q^87 + 23104 * q^88 - 5040 * q^89 - 8784 * q^90 + 52368 * q^91 + 4832 * q^92 - 1304 * q^93 + 21424 * q^94 + 16032 * q^95 + 2560 * q^96 - 40164 * q^97 + 21216 * q^98 + 91704 * q^99

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