LMFDB - Embedded newform 61.6.g.a.3.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [61,6,Mod(3,61)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(61, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("61.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 61 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	61.g (of order $10$, 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:	$9.78341300859$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$26$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			3.17
Character	$\chi$	$=$	61.3
Dual form			61.6.g.a.41.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.76517 + 1.22338i) q^{2} +(-4.80371 + 14.7843i) q^{3} +(-13.2087 - 9.59666i) q^{4} +(75.2721 + 54.6884i) q^{5} +(-36.1736 + 49.7887i) q^{6} +(-178.072 + 57.8590i) q^{7} +(-112.457 - 154.783i) q^{8} +(1.09088 + 0.792570i) q^{9} +O(q^{10})$	\(q+(3.76517 + 1.22338i) q^{2} +(-4.80371 + 14.7843i) q^{3} +(-13.2087 - 9.59666i) q^{4} +(75.2721 + 54.6884i) q^{5} +(-36.1736 + 49.7887i) q^{6} +(-178.072 + 57.8590i) q^{7} +(-112.457 - 154.783i) q^{8} +(1.09088 + 0.792570i) q^{9} +(216.508 + 297.998i) q^{10} -61.7027i q^{11} +(205.331 - 149.182i) q^{12} -497.808 q^{13} -741.254 q^{14} +(-1170.12 + 850.139i) q^{15} +(-72.6119 - 223.476i) q^{16} +(-1222.32 + 1682.38i) q^{17} +(3.13773 + 4.31872i) q^{18} +(-48.9603 + 150.684i) q^{19} +(-469.419 - 1444.72i) q^{20} -2910.61i q^{21} +(75.4858 - 232.321i) q^{22} +(1391.70 - 1915.51i) q^{23} +(2828.58 - 919.060i) q^{24} +(1709.39 + 5260.97i) q^{25} +(-1874.33 - 609.008i) q^{26} +(-3073.00 + 2232.66i) q^{27} +(2907.34 + 944.653i) q^{28} +1103.89i q^{29} +(-5445.73 + 1769.43i) q^{30} +(8004.45 - 2600.80i) q^{31} +5192.07i q^{32} +(912.233 + 296.402i) q^{33} +(-6660.42 + 4839.08i) q^{34} +(-16568.0 - 5383.28i) q^{35} +(-6.80303 - 20.9376i) q^{36} +(11379.1 - 3697.28i) q^{37} +(-368.688 + 507.456i) q^{38} +(2391.33 - 7359.76i) q^{39} -17801.0i q^{40} +(5748.40 + 17691.8i) q^{41} +(3560.77 - 10958.9i) q^{42} +(3785.41 + 5210.17i) q^{43} +(-592.140 + 815.011i) q^{44} +(38.7684 + 119.317i) q^{45} +(7583.37 - 5509.64i) q^{46} +8941.14 q^{47} +3652.75 q^{48} +(14764.7 - 10727.2i) q^{49} +21899.7i q^{50} +(-19001.1 - 26152.8i) q^{51} +(6575.39 + 4777.30i) q^{52} +(-831.480 - 1144.43i) q^{53} +(-14301.8 + 4646.92i) q^{54} +(3374.42 - 4644.50i) q^{55} +(28981.0 + 21055.9i) q^{56} +(-1992.57 - 1447.69i) q^{57} +(-1350.48 + 4156.35i) q^{58} +(-26595.9 - 8641.54i) q^{59} +23614.2 q^{60} +(7459.36 + 28088.3i) q^{61} +33319.9 q^{62} +(-240.112 - 78.0171i) q^{63} +(-8675.45 + 26700.3i) q^{64} +(-37471.1 - 27224.3i) q^{65} +(3072.10 + 2232.01i) q^{66} +(5926.05 - 8156.51i) q^{67} +(32290.4 - 10491.8i) q^{68} +(21634.1 + 29776.8i) q^{69} +(-55795.8 - 40538.0i) q^{70} +(-38817.0 - 53427.0i) q^{71} -257.980i q^{72} +(-14841.1 + 10782.7i) q^{73} +47367.3 q^{74} -85991.3 q^{75} +(2092.77 - 1520.48i) q^{76} +(3570.06 + 10987.5i) q^{77} +(18007.5 - 24785.3i) q^{78} +(-14664.9 - 20184.5i) q^{79} +(6755.91 - 20792.6i) q^{80} +(-18145.3 - 55845.6i) q^{81} +73645.0i q^{82} +(-28529.0 + 87803.2i) q^{83} +(-27932.1 + 38445.2i) q^{84} +(-184013. + 59789.4i) q^{85} +(7878.71 + 24248.2i) q^{86} +(-16320.3 - 5302.80i) q^{87} +(-9550.56 + 6938.89i) q^{88} +(64413.5 + 20929.2i) q^{89} +496.677i q^{90} +(88645.6 - 28802.7i) q^{91} +(-36764.9 + 11945.7i) q^{92} +130834. i q^{93} +(33664.9 + 10938.4i) q^{94} +(-11926.0 + 8664.77i) q^{95} +(-76761.2 - 24941.2i) q^{96} +(8909.69 + 27421.2i) q^{97} +(68715.1 - 22326.9i) q^{98} +(48.9037 - 67.3102i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9}+O(q^{10}) $ 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9	\( 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9} - 595 q^{10} + 1982 q^{12} + 2372 q^{13} - 4474 q^{14} - 1149 q^{15} - 8631 q^{16} + 950 q^{17} + 4340 q^{18} - 5597 q^{19} - 6627 q^{20} - 8639 q^{22} + 9065 q^{23} + 17220 q^{24} - 7694 q^{25} + 14810 q^{26} + 4500 q^{27} + 19835 q^{28} - 44585 q^{30} + 10905 q^{31} - 19205 q^{33} - 15376 q^{34} - 43790 q^{35} - 25135 q^{36} - 5 q^{37} + 17555 q^{38} + 29401 q^{39} - 21014 q^{41} + 62197 q^{42} - 31625 q^{43} + 146190 q^{44} + 153742 q^{45} + 13387 q^{46} + 27326 q^{47} - 82968 q^{48} + 14694 q^{49} + 34090 q^{51} + 90072 q^{52} - 40270 q^{53} - 13760 q^{54} + 25140 q^{55} - 97860 q^{56} + 114893 q^{57} - 18003 q^{58} - 117435 q^{59} - 536650 q^{60} - 121867 q^{61} - 157388 q^{62} - 160825 q^{63} + 132509 q^{64} - 155852 q^{65} + 308443 q^{66} + 101665 q^{67} + 303780 q^{68} + 281945 q^{69} + 264985 q^{70} + 160970 q^{71} + 127669 q^{73} - 133952 q^{74} - 139592 q^{75} - 641111 q^{76} + 128917 q^{77} + 1670 q^{78} + 187940 q^{79} + 785373 q^{80} - 453473 q^{81} - 301209 q^{83} + 100475 q^{84} - 340045 q^{85} - 462669 q^{86} + 189245 q^{87} - 881635 q^{88} - 201970 q^{89} + 93865 q^{91} - 622085 q^{92} - 285265 q^{94} - 113308 q^{95} + 1215465 q^{96} - 342131 q^{97} - 616150 q^{98} + 714235 q^{99}+O(q^{100}) \) 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9 - 595 * q^10 + 1982 * q^12 + 2372 * q^13 - 4474 * q^14 - 1149 * q^15 - 8631 * q^16 + 950 * q^17 + 4340 * q^18 - 5597 * q^19 - 6627 * q^20 - 8639 * q^22 + 9065 * q^23 + 17220 * q^24 - 7694 * q^25 + 14810 * q^26 + 4500 * q^27 + 19835 * q^28 - 44585 * q^30 + 10905 * q^31 - 19205 * q^33 - 15376 * q^34 - 43790 * q^35 - 25135 * q^36 - 5 * q^37 + 17555 * q^38 + 29401 * q^39 - 21014 * q^41 + 62197 * q^42 - 31625 * q^43 + 146190 * q^44 + 153742 * q^45 + 13387 * q^46 + 27326 * q^47 - 82968 * q^48 + 14694 * q^49 + 34090 * q^51 + 90072 * q^52 - 40270 * q^53 - 13760 * q^54 + 25140 * q^55 - 97860 * q^56 + 114893 * q^57 - 18003 * q^58 - 117435 * q^59 - 536650 * q^60 - 121867 * q^61 - 157388 * q^62 - 160825 * q^63 + 132509 * q^64 - 155852 * q^65 + 308443 * q^66 + 101665 * q^67 + 303780 * q^68 + 281945 * q^69 + 264985 * q^70 + 160970 * q^71 + 127669 * q^73 - 133952 * q^74 - 139592 * q^75 - 641111 * q^76 + 128917 * q^77 + 1670 * q^78 + 187940 * q^79 + 785373 * q^80 - 453473 * q^81 - 301209 * q^83 + 100475 * q^84 - 340045 * q^85 - 462669 * q^86 + 189245 * q^87 - 881635 * q^88 - 201970 * q^89 + 93865 * q^91 - 622085 * q^92 - 285265 * q^94 - 113308 * q^95 + 1215465 * q^96 - 342131 * q^97 - 616150 * q^98 + 714235 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	3.76517	+	1.22338i	0.665595	+	0.216265i	0.622278	−	0.782796i	$-0.286207\pi$
$2$	3.76517	+	1.22338i	0.665595	+	0.216265i	0.0433171	+	0.999061i	$0.486207\pi$
$3$	−4.80371	+	14.7843i	−0.308158	+	0.948414i	0.670321	+	0.742071i	$0.266156\pi$
$3$	−4.80371	+	14.7843i	−0.308158	+	0.948414i	−0.978480	+	0.206343i	$0.933844\pi$
$4$	−13.2087	−	9.59666i	−0.412771	−	0.299896i
$5$	75.2721	+	54.6884i	1.34651	+	0.978296i	0.999177	+	0.0405532i	$0.0129120\pi$
$5$	75.2721	+	54.6884i	1.34651	+	0.978296i	0.347331	+	0.937743i	$0.387088\pi$
$6$	−36.1736	+	49.7887i	−0.410217	+	0.564616i
$7$	−178.072	+	57.8590i	−1.37357	+	0.446299i	−0.900549	−	0.434754i	$-0.856835\pi$
$7$	−178.072	+	57.8590i	−1.37357	+	0.446299i	−0.473017	+	0.881053i	$0.656835\pi$
$8$	−112.457	−	154.783i	−0.621242	−	0.855066i
$9$	1.09088	+	0.792570i	0.00448921	+	0.00326160i
$10$	216.508	+	297.998i	0.684658	+	0.942351i
$11$		−	61.7027i		−	0.153753i	−0.997041	−	0.0768763i	$-0.975505\pi$
$11$		−	61.7027i		−	0.153753i	0.997041	−	0.0768763i	$-0.0244947\pi$
$12$	205.331	−	149.182i	0.411624	−	0.299062i
$13$	−497.808			−0.816966			−0.408483	−	0.912766i	$-0.633942\pi$
$13$	−497.808			−0.816966			−0.408483	+	0.912766i	$0.633942\pi$
$14$	−741.254			−1.01076
$15$	−1170.12	+	850.139i	−1.34277	+	0.975578i
$16$	−72.6119	−	223.476i	−0.0709100	−	0.218239i
$17$	−1222.32	+	1682.38i	−1.02580	+	1.41189i	−0.117739	+	0.993045i	$0.537565\pi$
$17$	−1222.32	+	1682.38i	−1.02580	+	1.41189i	−0.908058	+	0.418844i	$0.862435\pi$
$18$	3.13773	+	4.31872i	0.00228263	+	0.00314177i
$19$	−48.9603	+	150.684i	−0.0311143	+	0.0957600i	−0.965408	−	0.260745i	$-0.916032\pi$
$19$	−48.9603	+	150.684i	−0.0311143	+	0.0957600i	0.934293	+	0.356505i	$0.116032\pi$
$20$	−469.419	−	1444.72i	−0.262413	−	0.807624i
$21$		−	2910.61i		−	1.44024i
$22$	75.4858	−	232.321i	0.0332513	−	0.102337i
$23$	1391.70	−	1915.51i	0.548561	−	0.755030i	−0.441255	−	0.897382i	$-0.645467\pi$
$23$	1391.70	−	1915.51i	0.548561	−	0.755030i	0.989816	+	0.142352i	$0.0454665\pi$
$24$	2828.58	−	919.060i	1.00240	−	0.325699i
$25$	1709.39	+	5260.97i	0.547006	+	1.68351i
$26$	−1874.33	−	609.008i	−0.543768	−	0.176681i
$27$	−3073.00	+	2232.66i	−0.811246	+	0.589405i
$28$	2907.34	+	944.653i	0.700812	+	0.227707i
$29$			1103.89i			0.243743i	0.992546	+	0.121872i	$0.0388896\pi$
$29$			1103.89i			0.243743i	−0.992546	+	0.121872i	$0.961110\pi$
$30$	−5445.73	+	1769.43i	−1.10472	+	0.358946i
$31$	8004.45	−	2600.80i	1.49599	−	0.486075i	0.557142	−	0.830417i	$-0.311898\pi$
$31$	8004.45	−	2600.80i	1.49599	−	0.486075i	0.938844	+	0.344342i	$0.111898\pi$
$32$			5192.07i			0.896325i
$33$	912.233	+	296.402i	0.145821	+	0.0473802i
$34$	−6660.42	+	4839.08i	−0.988107	+	0.717902i
$35$	−16568.0	−	5383.28i	−2.28613	−	0.742809i
$36$	−6.80303	−	20.9376i	−0.000874876	−	0.00269259i
$37$	11379.1	−	3697.28i	1.36648	−	0.443995i	0.468276	−	0.883582i	$-0.344875\pi$
$37$	11379.1	−	3697.28i	1.36648	−	0.443995i	0.898200	+	0.439587i	$0.144875\pi$
$38$	−368.688	+	507.456i	−0.0414191	+	0.0570084i
$39$	2391.33	−	7359.76i	0.251755	−	0.774822i
$40$		−	17801.0i		−	1.75911i
$41$	5748.40	+	17691.8i	0.534057	+	1.64366i	0.745678	+	0.666306i	$0.232126\pi$
$41$	5748.40	+	17691.8i	0.534057	+	1.64366i	−0.211621	+	0.977352i	$0.567874\pi$
$42$	3560.77	−	10958.9i	0.311474	−	0.958617i
$43$	3785.41	+	5210.17i	0.312206	+	0.429715i	0.936068	−	0.351820i	$-0.114437\pi$
$43$	3785.41	+	5210.17i	0.312206	+	0.429715i	−0.623861	+	0.781535i	$0.714437\pi$
$44$	−592.140	+	815.011i	−0.0461098	+	0.0634646i
$45$	38.7684	+	119.317i	0.00285395	+	0.00878355i
$46$	7583.37	−	5509.64i	0.528406	−	0.383909i
$47$	8941.14			0.590402			0.295201	−	0.955435i	$-0.404613\pi$
$47$	8941.14			0.590402			0.295201	+	0.955435i	$0.404613\pi$
$48$	3652.75			0.228832
$49$	14764.7	−	10727.2i	0.878486	−	0.638257i
$50$			21899.7i			1.23883i
$51$	−19001.1	−	26152.8i	−1.02295	−	1.40797i
$52$	6575.39	+	4777.30i	0.337220	+	0.245004i
$53$	−831.480	−	1144.43i	−0.0406595	−	0.0559630i	0.788203	−	0.615415i	$-0.211012\pi$
$53$	−831.480	−	1144.43i	−0.0406595	−	0.0559630i	−0.828863	+	0.559452i	$0.811012\pi$
$54$	−14301.8	+	4646.92i	−0.667429	+	0.216861i
$55$	3374.42	−	4644.50i	0.150416	−	0.207029i
$56$	28981.0	+	21055.9i	1.23493	+	0.897230i
$57$	−1992.57	−	1447.69i	−0.0812320	−	0.0590185i
$58$	−1350.48	+	4156.35i	−0.0527131	+	0.162234i
$59$	−26595.9	−	8641.54i	−0.994684	−	0.323192i	−0.233945	−	0.972250i	$-0.575163\pi$
$59$	−26595.9	−	8641.54i	−0.994684	−	0.323192i	−0.760739	+	0.649057i	$0.775163\pi$
$60$	23614.2			0.846827
$61$	7459.36	+	28088.3i	0.256671	+	0.966499i
$61$	7459.36	+	28088.3i	0.256671	+	0.966499i
$62$	33319.9			1.10084
$63$	−240.112	−	78.0171i	−0.00762188	−	0.00247650i
$64$	−8675.45	+	26700.3i	−0.264754	+	0.814828i
$65$	−37471.1	−	27224.3i	−1.10005	−	0.799234i
$66$	3072.10	+	2232.01i	0.0868112	+	0.0630720i
$67$	5926.05	−	8156.51i	0.161279	−	0.221982i	−0.720728	−	0.693218i	$-0.756192\pi$
$67$	5926.05	−	8156.51i	0.161279	−	0.221982i	0.882007	+	0.471237i	$0.156192\pi$
$68$	32290.4	−	10491.8i	0.846839	−	0.275155i
$69$	21634.1	+	29776.8i	0.547037	+	0.752932i
$70$	−55795.8	−	40538.0i	−1.36099	−	0.988820i
$71$	−38817.0	−	53427.0i	−0.913852	−	1.25781i	−0.965834	−	0.259162i	$-0.916554\pi$
$71$	−38817.0	−	53427.0i	−0.913852	−	1.25781i	0.0519815	−	0.998648i	$-0.483446\pi$
$72$		−	257.980i		−	0.00586481i
$73$	−14841.1	+	10782.7i	−0.325955	+	0.236820i	−0.738712	−	0.674021i	$-0.764566\pi$
$73$	−14841.1	+	10782.7i	−0.325955	+	0.236820i	0.412757	+	0.910841i	$0.364566\pi$
$74$	47367.3			1.00554
$75$	−85991.3			−1.76523
$76$	2092.77	−	1520.48i	0.0415611	−	0.0301959i
$77$	3570.06	+	10987.5i	0.0686196	+	0.211190i
$78$	18007.5	−	24785.3i	0.335134	−	0.461272i
$79$	−14664.9	−	20184.5i	−0.264369	−	0.363873i	0.656109	−	0.754666i	$-0.272201\pi$
$79$	−14664.9	−	20184.5i	−0.264369	−	0.363873i	−0.920479	+	0.390793i	$0.872201\pi$
$80$	6755.91	−	20792.6i	0.118021	−	0.363231i
$81$	−18145.3	−	55845.6i	−0.307293	−	0.945750i
$82$			73645.0i			1.20951i
$83$	−28529.0	+	87803.2i	−0.454560	+	1.39899i	0.417091	+	0.908865i	$0.363050\pi$
$83$	−28529.0	+	87803.2i	−0.454560	+	1.39899i	−0.871651	+	0.490127i	$0.836950\pi$
$84$	−27932.1	+	38445.2i	−0.431922	+	0.594490i
$85$	−184013.	+	59789.4i	−2.76249	+	0.897587i
$86$	7878.71	+	24248.2i	0.114871	+	0.353536i
$87$	−16320.3	−	5302.80i	−0.231170	−	0.0751116i
$88$	−9550.56	+	6938.89i	−0.131469	+	0.0955176i
$89$	64413.5	+	20929.2i	0.861990	+	0.280077i	0.706459	−	0.707754i	$-0.250291\pi$
$89$	64413.5	+	20929.2i	0.861990	+	0.280077i	0.155530	+	0.987831i	$0.450291\pi$
$90$			496.677i			0.00646350i
$91$	88645.6	−	28802.7i	1.12216	−	0.364611i
$92$	−36764.9	+	11945.7i	−0.452860	+	0.147143i
$93$			130834.i			1.56860i
$94$	33664.9	+	10938.4i	0.392969	+	0.127683i
$95$	−11926.0	+	8664.77i	−0.135577	+	0.0985027i
$96$	−76761.2	−	24941.2i	−0.850088	−	0.276210i
$97$	8909.69	+	27421.2i	0.0961464	+	0.295908i	0.987551	−	0.157301i	$-0.0502792\pi$
$97$	8909.69	+	27421.2i	0.0961464	+	0.295908i	−0.891404	+	0.453209i	$0.850279\pi$
$98$	68715.1	−	22326.9i	0.722748	−	0.234835i
$99$	48.9037	−	67.3102i	0.000501480	−	0.000690228i
$100$	27908.9	−	85894.9i	0.279089	−	0.858949i
$101$			9077.98i			0.0885494i	0.999019	+	0.0442747i	$0.0140977\pi$
$101$			9077.98i			0.0885494i	−0.999019	+	0.0442747i	$0.985902\pi$
$102$	−39547.7	−	121715.i	−0.376375	−	1.15836i
$103$	−17584.6	+	54120.0i	−0.163320	+	0.502648i	−0.998909	−	0.0467078i	$-0.985127\pi$
$103$	−17584.6	+	54120.0i	−0.163320	+	0.502648i	0.835588	+	0.549356i	$0.185127\pi$
$104$	55981.9	+	77052.5i	0.507533	+	0.698559i
$105$	159176.	−	219087.i	1.40898	−	1.93930i
$106$	−1730.59	−	5326.20i	−0.0149599	−	0.0460419i
$107$	104683.	−	76056.9i	0.883931	−	0.642213i	−0.0503577	−	0.998731i	$-0.516036\pi$
$107$	104683.	−	76056.9i	0.883931	−	0.642213i	0.934288	+	0.356518i	$0.116036\pi$
$108$	62016.3			0.511619
$109$	−40231.6			−0.324340			−0.162170	−	0.986763i	$-0.551849\pi$
$109$	−40231.6			−0.324340			−0.162170	+	0.986763i	$0.551849\pi$
$110$	18387.3	−	13359.1i	0.144889	−	0.105268i
$111$			185992.i			1.43281i
$112$	25860.2	+	35593.6i	0.194799	+	0.268118i
$113$	−185149.	−	134519.i	−1.36403	−	0.991029i	−0.998177	−	0.0603584i	$-0.980776\pi$
$113$	−185149.	−	134519.i	−1.36403	−	0.991029i	−0.365858	−	0.930671i	$-0.619224\pi$
$114$	−5731.31	−	7888.47i	−0.0413040	−	0.0568501i
$115$	209512.	−	68074.6i	1.47728	−	0.479999i
$116$	10593.7	−	14581.0i	0.0730976	−	0.100610i
$117$	−543.048	−	394.548i	−0.00366753	−	0.00266462i
$118$	−89566.4	−	65073.8i	−0.592161	−	0.430230i
$119$	120320.	−	370305.i	0.778877	−	2.39714i
$120$	263175.	+	85510.7i	1.66837	+	0.542085i
$121$	157244.			0.976360
$122$	−6276.88	+	114883.i	−0.0381807	+	0.698806i
$123$	−289174.			−1.72344
$124$	−130687.	−	42462.9i	−0.763271	−	0.248002i
$125$	−69196.3	+	212964.i	−0.396103	+	1.21908i
$126$	−808.618	−	587.495i	−0.00453750	−	0.00329669i
$127$	125463.	+	91154.1i	0.690249	+	0.501495i	0.876742	−	0.480961i	$-0.159712\pi$
$127$	125463.	+	91154.1i	0.690249	+	0.501495i	−0.186493	+	0.982456i	$0.559712\pi$
$128$	32329.2	−	44497.3i	0.174409	−	0.240054i
$129$	−95212.8	+	30936.5i	−0.503757	+	0.163681i
$130$	−107779.	−	148346.i	−0.559342	−	0.769869i
$131$	110508.	+	80288.5i	0.562619	+	0.408767i	0.832416	−	0.554151i	$-0.186957\pi$
$131$	110508.	+	80288.5i	0.562619	+	0.408767i	−0.269798	+	0.962917i	$0.586957\pi$
$132$	−9204.91	−	12669.5i	−0.0459817	−	0.0632883i
$133$		−	29665.4i		−	0.145419i
$134$	32291.1	−	23460.9i	0.155353	−	0.112871i
$135$	−353412.			−1.66896
$136$	397862.			1.84453
$137$	−161196.	+	117116.i	−0.733759	+	0.533107i	−0.890750	−	0.454493i	$-0.849821\pi$
$137$	−161196.	+	117116.i	−0.733759	+	0.533107i	0.156991	+	0.987600i	$0.449821\pi$
$138$	45027.9	+	138582.i	0.201272	+	0.619453i
$139$	152527.	−	209936.i	0.669592	−	0.921615i	−0.330159	−	0.943925i	$-0.607102\pi$
$139$	152527.	−	209936.i	0.669592	−	0.921615i	0.999751	+	0.0223106i	$0.00710229\pi$
$140$	167180.	+	230104.i	0.720883	+	0.992211i
$141$	−42950.7	+	132189.i	−0.181937	+	0.559946i
$142$	−80791.2	−	248650.i	−0.336235	−	1.03483i
$143$			30716.1i			0.125611i
$144$	97.9098	−	301.336i	0.000393478	−	0.00121100i
$145$	−60370.2	+	83092.5i	−0.238453	+	0.328202i
$146$	−69070.5	+	22442.4i	−0.268170	+	0.0871337i
$147$	87668.7	+	269816.i	0.334619	+	1.02985i
$148$	−185784.	−	60364.8i	−0.697194	−	0.226532i
$149$	375097.	−	272524.i	1.38413	−	1.00563i	0.387653	−	0.921805i	$-0.373286\pi$
$149$	375097.	−	272524.i	1.38413	−	1.00563i	0.996480	−	0.0838268i	$-0.0267142\pi$
$150$	−323772.	−	105200.i	−1.17493	−	0.381757i
$151$		−	139940.i		−	0.499459i	−0.968316	−	0.249729i	$-0.919658\pi$
$151$		−	139940.i		−	0.499459i	0.968316	−	0.249729i	$-0.0803416\pi$
$152$	28829.4	−	9367.23i	0.101211	−	0.0328853i
$153$	−2666.80	+	866.495i	−0.00921004	+	0.00299252i
$154$			45737.4i			0.155407i
$155$	744746.	+	241983.i	2.48988	+	0.809012i
$156$	−102215.	+	74263.8i	−0.336283	+	0.244324i
$157$	−419907.	−	136436.i	−1.35958	−	0.441753i	−0.463675	−	0.886005i	$-0.653470\pi$
$157$	−419907.	−	136436.i	−1.35958	−	0.441753i	−0.895902	+	0.444252i	$0.853470\pi$
$158$	−30522.6	−	93938.8i	−0.0972699	−	0.299366i
$159$	20913.9	−	6795.32i	0.0656057	−	0.0213166i
$160$	−283946.	+	390818.i	−0.876871	+	1.20691i
$161$	−136993.	+	421620.i	−0.416516	+	1.28191i
$162$		−	232467.i		−	0.695943i
$163$	20717.5	+	63761.8i	0.0610756	+	0.187971i	0.976939	−	0.213519i	$-0.0684924\pi$
$163$	20717.5	+	63761.8i	0.0610756	+	0.187971i	−0.915863	+	0.401490i	$0.868492\pi$
$164$	93853.1	−	288850.i	0.272483	−	0.838616i
$165$	52455.9	+	72199.4i	0.149998	+	0.206454i
$166$	−214833.	+	295692.i	−0.605105	+	0.832856i
$167$	−36332.9	−	111821.i	−0.100811	−	0.310265i	0.887913	−	0.460011i	$-0.152154\pi$
$167$	−36332.9	−	111821.i	−0.100811	−	0.310265i	−0.988725	+	0.149746i	$0.952154\pi$
$168$	−450513.	+	327317.i	−1.23150	+	0.894737i
$169$	−123480.			−0.332567
$170$	−765985.			−2.03282
$171$	−172.838	+	125.574i	−0.000452010	+	0.000328404i
$172$		−	105147.i		−	0.271003i
$173$	162942.	+	224270.i	0.413921	+	0.569713i	0.964169	−	0.265288i	$-0.0854670\pi$
$173$	162942.	+	224270.i	0.413921	+	0.569713i	−0.550249	+	0.835001i	$0.685467\pi$
$174$	−54961.5	−	39931.9i	−0.137621	−	0.0999877i
$175$	−608789.	−	837926.i	−1.50270	−	2.06829i
$176$	−13789.1	+	4480.35i	−0.0335548	+	0.0109026i
$177$	255519.	−	351691.i	0.613041	−	0.843778i
$178$	216924.	+	157604.i	0.513165	+	0.372836i
$179$	−351040.	−	255046.i	−0.818887	−	0.594957i	0.0975062	−	0.995235i	$-0.468913\pi$
$179$	−351040.	−	255046.i	−0.818887	−	0.594957i	−0.916394	+	0.400278i	$0.868913\pi$
$180$	632.964	−	1948.06i	0.00145612	−	0.00448148i
$181$	716521.	+	232812.i	1.62567	+	0.528212i	0.973270	−	0.229663i	$-0.0737625\pi$
$181$	716521.	+	232812.i	1.62567	+	0.528212i	0.652399	+	0.757875i	$0.273763\pi$
$182$	369003.			0.825754
$183$	−451099.	−	24646.8i	−0.995737	−	0.0544042i
$184$	−452994.			−0.986389
$185$	1.05872e6	+	344000.i	2.27433	+	0.738975i
$186$	−160059.	+	492612.i	−0.339234	+	1.04405i
$187$	103807.	+	75420.3i	0.217082	+	0.157719i
$188$	−118101.	−	85805.1i	−0.243701	−	0.177059i
$189$	418034.	−	575374.i	0.851250	−	1.17164i
$190$	−55503.9	+	18034.3i	−0.111542	+	0.0362423i
$191$	339672.	+	467518.i	0.673714	+	0.927288i	0.999837	−	0.0180390i	$-0.00574230\pi$
$191$	339672.	+	467518.i	0.673714	+	0.927288i	−0.326123	+	0.945327i	$0.605742\pi$
$192$	−353071.	−	256521.i	−0.691209	−	0.502192i
$193$	−75536.7	−	103967.i	−0.145970	−	0.200911i	0.729771	−	0.683692i	$-0.239627\pi$
$193$	−75536.7	−	103967.i	−0.145970	−	0.200911i	−0.875741	+	0.482781i	$0.839627\pi$
$194$			114146.i			0.217748i
$195$	582494.	−	423206.i	1.09700	−	0.797014i
$196$	−297967.			−0.554024
$197$	−384718.			−0.706279			−0.353140	−	0.935571i	$-0.614886\pi$
$197$	−384718.			−0.706279			−0.353140	+	0.935571i	$0.614886\pi$
$198$	266.477	−	193.607i	0.000483055	−	0.000350960i
$199$	−214354.	−	659713.i	−0.383706	−	1.18093i	−0.937415	−	0.348215i	$-0.886788\pi$
$199$	−214354.	−	659713.i	−0.383706	−	1.18093i	0.553709	−	0.832710i	$-0.313212\pi$
$200$	622078.	−	856217.i	1.09969	−	1.51359i
$201$	92121.3	+	126794.i	0.160831	+	0.221365i
$202$	−11105.8	+	34180.2i	−0.0191501	+	0.0589381i
$203$	−63870.2	−	196572.i	−0.108782	−	0.334798i
$204$			527790.i			0.887945i
$205$	−534840.	+	1.64607e6i	−0.888872	+	2.73567i
$206$	−132418.	+	182258.i	−0.217410	+	0.299240i
$207$	3036.34	−	986.568i	0.00492521	−	0.00160030i
$208$	36146.8	+	111248.i	0.0579311	+	0.178294i
$209$	9297.64	+	3020.99i	0.0147234	+	0.00478391i
$210$	867353.	−	630169.i	1.35721	−	0.986073i
$211$	−358097.	−	116353.i	−0.553726	−	0.179917i	0.0187701	−	0.999824i	$-0.494025\pi$
$211$	−358097.	−	116353.i	−0.553726	−	0.179917i	−0.572496	+	0.819907i	$0.694025\pi$
$212$			23095.9i			0.0352935i
$213$	976347.	−	317235.i	1.47454	−	0.479106i
$214$	487197.	−	158300.i	0.727228	−	0.236291i
$215$			599199.i			0.884046i
$216$	691158.	+	224571.i	1.00796	+	0.327506i
$217$	−1.27489e6	+	926259.i	−1.83790	+	1.33531i
$218$	−151479.	−	49218.5i	−0.215879	−	0.0701434i
$219$	−88122.1	−	271212.i	−0.124158	−	0.382119i
$220$	−89143.3	+	28964.4i	−0.124174	+	0.0403467i
$221$	608480.	−	837501.i	0.838041	−	1.15346i
$222$	−227539.	+	700293.i	−0.309866	+	0.953668i
$223$			516506.i			0.695526i	0.937582	+	0.347763i	$0.113059\pi$
$223$			516506.i			0.695526i	−0.937582	+	0.347763i	$0.886941\pi$
$224$	−300408.	−	924561.i	−0.400029	−	1.23116i
$225$	−2304.95	+	7093.89i	−0.00303532	+	0.00934175i
$226$	−532551.	−	732993.i	−0.693570	−	0.954617i
$227$	−590913.	+	813321.i	−0.761129	+	1.04760i	0.235990	+	0.971756i	$0.424167\pi$
$227$	−590913.	+	813321.i	−0.761129	+	1.04760i	−0.997119	+	0.0758493i	$0.975833\pi$
$228$	12426.3	+	38244.1i	0.0158308	+	0.0487223i
$229$	−287295.	+	208732.i	−0.362025	+	0.263027i	−0.753896	−	0.656993i	$-0.771828\pi$
$229$	−287295.	+	208732.i	−0.362025	+	0.263027i	0.391871	+	0.920020i	$0.371828\pi$
$230$	872130.			1.08708
$231$	−179592.			−0.221441
$232$	170865.	−	124140.i	0.208417	−	0.151423i
$233$			219114.i			0.264411i	0.991222	+	0.132205i	$0.0422059\pi$
$233$			219114.i			0.264411i	−0.991222	+	0.132205i	$0.957794\pi$
$234$	−1561.99	−	2149.89i	−0.00186483	−	0.00256671i
$235$	673018.	+	488976.i	0.794982	+	0.577588i
$236$	268367.	+	369375.i	0.313653	+	0.431706i
$237$	368860.	−	119850.i	0.426570	−	0.138601i
$238$	906048.	−	1.24707e6i	1.03683	−	1.42708i
$239$	−36230.2	−	26322.8i	−0.0410276	−	0.0298083i	0.567082	−	0.823661i	$-0.308072\pi$
$239$	−36230.2	−	26322.8i	−0.0410276	−	0.0298083i	−0.608110	+	0.793853i	$0.708072\pi$
$240$	274950.	+	199763.i	0.308124	+	0.223866i
$241$	401906.	−	1.23694e6i	0.445740	−	1.37185i	−0.435931	−	0.899980i	$-0.643581\pi$
$241$	401906.	−	1.23694e6i	0.445740	−	1.37185i	0.881670	−	0.471866i	$-0.156419\pi$
$242$	592050.	+	192369.i	0.649860	+	0.211152i
$243$	−10215.3			−0.0110978
$244$	171026.	−	442594.i	0.183902	−	0.475917i
$245$	1.69802e6			1.80729
$246$	−1.08879e6	−	353770.i	−1.14711	−	0.372720i
$247$	24372.9	−	75011.9i	0.0254193	−	0.0782327i
$248$	−1.30272e6	−	946479.i	−1.34499	−	0.977196i
$249$	−1.16106e6	−	843563.i	−1.18675	−	0.862222i
$250$	−521072.	+	717194.i	−0.527288	+	0.725750i
$251$	−780441.	+	253581.i	−0.781908	+	0.254057i	−0.672655	−	0.739956i	$-0.734846\pi$
$251$	−780441.	+	253581.i	−0.781908	+	0.254057i	−0.109254	+	0.994014i	$0.534846\pi$
$252$	2422.85	+	3334.77i	0.00240340	+	0.00330800i
$253$	−118192.	−	85871.5i	−0.116088	−	0.0843428i
$254$	360873.	+	496700.i	0.350970	+	0.483069i
$255$		−	3.00771e6i		−	2.89658i
$256$	902966.	−	656043.i	0.861136	−	0.625652i
$257$	1.38768e6			1.31056			0.655281	−	0.755386i	$-0.272550\pi$
$257$	1.38768e6			1.31056			0.655281	+	0.755386i	$0.272550\pi$
$258$	−396340.			−0.370697
$259$	−1.81237e6	+	1.31676e6i	−1.67879	+	1.21971i
$260$	233681.	+	719195.i	0.214382	+	0.659801i
$261$	−874.913	+	1204.21i	−0.000794994	+	0.00109422i
$262$	317857.	+	437493.i	0.286074	+	0.393748i
$263$	−263342.	+	810483.i	−0.234763	+	0.722527i	0.762389	+	0.647119i	$0.224026\pi$
$263$	−263342.	+	810483.i	−0.234763	+	0.722527i	−0.997153	+	0.0754088i	$0.975974\pi$
$264$	−56708.5	−	174531.i	−0.0500770	−	0.154121i
$265$		−	131616.i		−	0.115132i
$266$	36292.0	−	111695.i	0.0314490	−	0.0967902i
$267$	−618849.	+	851772.i	−0.531259	+	0.731215i
$268$	−156550.	+	50866.3i	−0.133143	+	0.0432607i
$269$	408055.	+	1.25586e6i	0.343825	+	1.05819i	0.962210	+	0.272310i	$0.0877876\pi$
$269$	408055.	+	1.25586e6i	0.343825	+	1.05819i	−0.618384	+	0.785876i	$0.712212\pi$
$270$	−1.33066e6	−	432356.i	−1.11085	−	0.360938i
$271$	−654260.	+	475348.i	−0.541162	+	0.393177i	−0.824516	−	0.565838i	$-0.808553\pi$
$271$	−654260.	+	475348.i	−0.541162	+	0.393177i	0.283355	+	0.959015i	$0.408553\pi$
$272$	464726.	+	150999.i	0.380868	+	0.123752i
$273$			1.44892e6i			1.17663i
$274$	−750209.	+	243758.i	−0.603679	+	0.196147i
$275$	324616.	−	105474.i	0.258844	−	0.0841036i
$276$		−	600928.i		−	0.474843i
$277$	2.04779e6	+	665368.i	1.60356	+	0.521029i	0.967985	−	0.251007i	$-0.0807618\pi$
$277$	2.04779e6	+	665368.i	1.60356	+	0.521029i	0.635578	+	0.772037i	$0.280762\pi$
$278$	831123.	−	603846.i	0.644990	−	0.468613i
$279$	10793.2	+	3506.93i	0.00830118	+	0.00269722i
$280$	1.02995e6	+	3.16985e6i	0.785089	+	2.41626i
$281$	2.16388e6	−	703086.i	1.63481	−	0.531181i	0.659439	−	0.751758i	$-0.270794\pi$
$281$	2.16388e6	−	703086.i	1.63481	−	0.531181i	0.975370	+	0.220577i	$0.0707940\pi$
$282$	−323433.	+	445168.i	−0.242193	+	0.333350i
$283$	−239140.	+	735998.i	−0.177495	+	0.546274i	−0.999739	−	0.0228621i	$-0.992722\pi$
$283$	−239140.	+	735998.i	−0.177495	+	0.546274i	0.822244	+	0.569136i	$0.192722\pi$
$284$			1.07821e6i			0.793248i
$285$	−70813.4	−	217941.i	−0.0516420	−	0.158938i
$286$	−37577.5	+	115652.i	−0.0271652	+	0.0836058i
$287$	−2.04726e6	−	2.81781e6i	−1.46713	−	2.01933i
$288$	−4115.08	+	5663.92i	−0.00292346	+	0.00402379i
$289$	−897567.	−	2.76243e6i	−0.632153	−	1.94557i
$290$	−328958.	+	239002.i	−0.229692	+	0.166881i
$291$	−448203.			−0.310272
$292$	299508.			0.205566
$293$	−643516.	+	467542.i	−0.437916	+	0.318164i	−0.784806	−	0.619741i	$-0.787238\pi$
$293$	−643516.	+	467542.i	−0.437916	+	0.318164i	0.346891	+	0.937906i	$0.387238\pi$
$294$			1.12316e6i			0.757831i
$295$	−1.52934e6	−	2.10496e6i	−1.02317	−	1.40828i
$296$	−1.85193e6	−	1.34551e6i	−1.22856	−	0.892599i
$297$	137761.	+	189612.i	0.0906226	+	0.124731i
$298$	1.74571e6	−	567214.i	1.13876	−	0.370004i
$299$	−692798.	+	953555.i	−0.448156	+	0.616833i
$300$	1.13583e6	+	825229.i	0.728636	+	0.529385i
$301$	−975530.	−	708764.i	−0.620618	−	0.450905i
$302$	171200.	−	526898.i	0.108015	−	0.332437i
$303$	−134212.	−	43608.0i	−0.0839815	−	0.0272873i
$304$	37229.5			0.0231049
$305$	−974624.	+	2.52221e6i	−0.599912	+	1.55250i
$306$	−11101.0			−0.00677734
$307$	−978903.	−	318065.i	−0.592780	−	0.192606i	−0.00276254	−	0.999996i	$-0.500879\pi$
$307$	−978903.	−	318065.i	−0.592780	−	0.192606i	−0.590018	+	0.807390i	$0.700879\pi$
$308$	58287.7	−	179391.i	0.0350106	−	0.107752i
$309$	−715655.	−	519954.i	−0.426390	−	0.309791i
$310$	2.50806e6	+	1.82221e6i	1.48229	+	1.07695i
$311$	−932624.	+	1.28365e6i	−0.546771	+	0.752566i	−0.989570	−	0.144055i	$-0.953986\pi$
$311$	−932624.	+	1.28365e6i	−0.546771	+	0.752566i	0.442799	+	0.896621i	$0.353986\pi$
$312$	−1.40809e6	+	457516.i	−0.818924	+	0.266085i
$313$	−1.26890e6	−	1.74650e6i	−0.732095	−	1.00764i	−0.999035	−	0.0439294i	$-0.986012\pi$
$313$	−1.26890e6	−	1.74650e6i	−0.732095	−	1.00764i	0.266939	−	0.963713i	$-0.413988\pi$
$314$	−1.41411e6	−	1.02741e6i	−0.809392	−	0.588058i
$315$	−13807.1	−	19003.8i	−0.00784018	−	0.0107911i
$316$			407344.i			0.229480i
$317$	−106916.	+	77679.2i	−0.0597579	+	0.0434167i	−0.617263	−	0.786757i	$-0.711759\pi$
$317$	−106916.	+	77679.2i	−0.0597579	+	0.0434167i	0.557505	+	0.830173i	$0.311759\pi$
$318$	87057.5			0.0482768
$319$	68113.3			0.0374762
$320$	−2.11322e6	+	1.53534e6i	−1.15364	+	0.838166i
$321$	621580.	+	1.91303e6i	0.336693	+	1.03624i
$322$	−1.03160e6	+	1.41988e6i	−0.554462	+	0.763152i
$323$	−193663.	−	266554.i	−0.103286	−	0.142160i
$324$	−296255.	+	911781.i	−0.156785	+	0.482534i
$325$	−850950.	−	2.61896e6i	−0.446885	−	1.37537i
$326$			265419.i			0.138321i
$327$	193261.	−	594796.i	0.0999482	−	0.307609i
$328$	2.09195e6	−	2.87932e6i	1.07366	−	1.47776i
$329$	−1.59216e6	+	517325.i	−0.810957	+	0.263496i
$330$	109178.	+	336017.i	0.0551889	+	0.169854i
$331$	3.53423e6	+	1.14834e6i	1.77307	+	0.576104i	0.998415	−	0.0562835i	$-0.0179251\pi$
$331$	3.53423e6	+	1.14834e6i	1.77307	+	0.576104i	0.774652	+	0.632388i	$0.217925\pi$
$332$	1.21945e6	−	885981.i	0.607181	−	0.441143i
$333$	15343.5	+	4985.41i	0.00758254	+	0.00246372i
$334$		−	465474.i		−	0.228312i
$335$	892132.	−	289871.i	0.434327	−	0.141122i
$336$	−650452.	+	211345.i	−0.314316	+	0.102128i
$337$			1.95699e6i			0.938672i	0.883020	+	0.469336i	$0.155507\pi$
$337$			1.95699e6i			0.938672i	−0.883020	+	0.469336i	$0.844493\pi$
$338$	−464923.	−	151063.i	−0.221355	−	0.0719226i
$339$	2.87817e6	−	2.09111e6i	1.36024	−	0.988276i
$340$	3.00434e6	+	976170.i	1.40946	+	0.457961i
$341$	−160477.	−	493897.i	−0.0747354	−	0.230012i
$342$	−804.388	+	261.361i	−0.000371878	+	0.000120830i
$343$	−158829.	+	218609.i	−0.0728943	+	0.100330i
$344$	380753.	−	1.17184e6i	0.173479	−	0.533914i
$345$			3.42450e6i			1.54899i
$346$	339137.	+	1.04376e6i	0.152295	+	0.468715i
$347$	593914.	−	1.82788e6i	0.264789	−	0.814936i	−0.726953	−	0.686687i	$-0.759064\pi$
$347$	593914.	−	1.82788e6i	0.264789	−	0.814936i	0.991742	−	0.128249i	$-0.0409357\pi$
$348$	164681.	+	226664.i	0.0728945	+	0.100331i
$349$	41621.7	−	57287.3i	0.0182918	−	0.0251765i	−0.799773	−	0.600302i	$-0.795047\pi$
$349$	41621.7	−	57287.3i	0.0182918	−	0.0251765i	0.818065	+	0.575126i	$0.195047\pi$
$350$	−1.26709e6	−	3.89972e6i	−0.552890	−	1.70162i
$351$	1.52976e6	−	1.11144e6i	0.662760	−	0.481523i
$352$	320365.			0.137812
$353$	622816.			0.266025			0.133013	−	0.991114i	$-0.457535\pi$
$353$	622816.			0.266025			0.133013	+	0.991114i	$0.457535\pi$
$354$	1.39232e6	−	1.01158e6i	0.590516	−	0.429035i
$355$		−	6.14440e6i		−	2.58767i
$356$	−649967.	−	894602.i	−0.271810	−	0.374115i
$357$	4.89673e6	+	3.55768e6i	2.03346	+	1.47740i
$358$	−1.00971e6	−	1.38975e6i	−0.416379	−	0.573097i
$359$	−3.97749e6	+	1.29237e6i	−1.62882	+	0.529236i	−0.974000	−	0.226548i	$-0.927256\pi$
$359$	−3.97749e6	+	1.29237e6i	−1.62882	+	0.529236i	−0.654821	+	0.755784i	$0.727256\pi$
$360$	14108.5	−	19418.7i	0.00573752	−	0.00789702i
$361$	1.98290e6	+	1.44066e6i	0.800815	+	0.581826i
$362$	2.41301e6	+	1.75315e6i	0.967803	+	0.703150i
$363$	−755354.	+	2.32474e6i	−0.300874	+	0.925994i
$364$	−1.44730e6	−	470256.i	−0.572539	−	0.186029i
$365$	−1.70681e6			−0.670582
$366$	−1.66831e6	−	644665.i	−0.650991	−	0.251554i
$367$	2.80010e6			1.08520			0.542599	−	0.839992i	$-0.317440\pi$
$367$	2.80010e6			1.08520			0.542599	+	0.839992i	$0.317440\pi$
$368$	−529124.	−	171923.i	−0.203675	−	0.0661781i
$369$	−7751.15	+	23855.6i	−0.00296347	+	0.00912061i
$370$	3.56544e6	+	2.59044e6i	1.35397	+	0.983715i
$371$	214279.	+	155683.i	0.0808247	+	0.0587226i
$372$	1.25557e6	−	1.72814e6i	0.470417	−	0.647474i
$373$	202006.	−	65635.8i	0.0751784	−	0.0244269i	−0.271186	−	0.962527i	$-0.587416\pi$
$373$	202006.	−	65635.8i	0.0751784	−	0.0244269i	0.346365	+	0.938100i	$0.387416\pi$
$374$	298584.	+	410966.i	0.110379	+	0.151924i
$375$	−2.81613e6	−	2.04604e6i	−1.03413	−	0.751339i
$376$	−1.00549e6	−	1.38394e6i	−0.366783	−	0.504833i
$377$		−	549528.i		−	0.199130i
$378$	2.27787e6	−	1.65497e6i	0.819973	−	0.595745i
$379$	3.23639e6			1.15734			0.578672	−	0.815560i	$-0.303571\pi$
$379$	3.23639e6			1.15734			0.578672	+	0.815560i	$0.303571\pi$
$380$	240680.			0.0855029
$381$	−1.95034e6	+	1.41700e6i	−0.688331	+	0.500102i
$382$	706971.	+	2.17583e6i	0.247881	+	0.762899i
$383$	1.64824e6	−	2.26861e6i	0.574148	−	0.790246i	−0.418891	−	0.908037i	$-0.637581\pi$
$383$	1.64824e6	−	2.26861e6i	0.574148	−	0.790246i	0.993038	+	0.117790i	$0.0375811\pi$
$384$	502562.	+	691717.i	0.173925	+	0.239387i
$385$	−332163.	+	1.02229e6i	−0.114209	+	0.351499i
$386$	−157217.	−	483865.i	−0.0537071	−	0.165294i
$387$			8683.86i			0.00294738i
$388$	145467.	−	447701.i	0.0490552	−	0.150976i
$389$	−253495.	+	348906.i	−0.0849368	+	0.116906i	−0.849371	−	0.527796i	$-0.823018\pi$
$389$	−253495.	+	348906.i	−0.0849368	+	0.116906i	0.764434	+	0.644702i	$0.223018\pi$
$390$	2.71093e6	−	880835.i	0.902520	−	0.293247i
$391$	1.52151e6	+	4.68271e6i	0.503305	+	1.54901i
$392$	−3.32078e6	−	1.07899e6i	−1.09150	−	0.354651i
$393$	−1.71786e6	+	1.24810e6i	−0.561056	+	0.407631i
$394$	−1.44853e6	−	470655.i	−0.470096	−	0.152743i
$395$		−	2.32133e6i		−	0.748590i
$396$	−1291.91	+	419.766i	−0.000413993	+	0.000134514i
$397$	−2.32493e6	+	755414.i	−0.740343	+	0.240552i	−0.654821	−	0.755784i	$-0.727256\pi$
$397$	−2.32493e6	+	755414.i	−0.740343	+	0.240552i	−0.0855220	+	0.996336i	$0.527256\pi$
$398$		−	2.74617e6i		−	0.869000i
$399$	438583.	+	142504.i	0.137917	+	0.0448121i
$400$	1.05158e6	−	764018.i	0.328619	−	0.238756i
$401$	−611646.	−	198736.i	−0.189950	−	0.0617185i	0.212497	−	0.977162i	$-0.431840\pi$
$401$	−611646.	−	198736.i	−0.189950	−	0.0617185i	−0.402447	+	0.915443i	$0.631840\pi$
$402$	191735.	+	590101.i	0.0591749	+	0.182121i
$403$	−3.98468e6	+	1.29470e6i	−1.22217	+	0.397107i
$404$	87118.3	−	119908.i	0.0265556	−	0.0365506i
$405$	1.68827e6	−	5.19595e6i	0.511451	−	1.57408i
$406$		−	818267.i		−	0.246365i
$407$	−228132.	−	702119.i	−0.0682654	−	0.210099i
$408$	−1.91121e6	+	5.88211e6i	−0.568406	+	1.74937i
$409$	−668448.	−	920040.i	−0.197587	−	0.271956i	0.698714	−	0.715401i	$-0.253756\pi$
$409$	−668448.	−	920040.i	−0.197587	−	0.271956i	−0.896301	+	0.443445i	$0.853756\pi$
$410$	−4.02753e6	+	5.54342e6i	−1.18326	+	1.62861i
$411$	−957138.	−	2.94577e6i	−0.279492	−	0.860189i
$412$	751641.	−	546099.i	0.218156	−	0.158500i
$413$	5.23597e6			1.51051
$414$	12639.3			0.00362429
$415$	−6.94925e6	+	5.04893e6i	−1.98070	+	1.43906i
$416$		−	2.58466e6i		−	0.732267i
$417$	2.37106e6	+	3.26348e6i	0.667732	+	0.919054i
$418$	31311.4	+	22749.1i	0.00876520	+	0.00636829i
$419$	3.51506e6	+	4.83807e6i	0.978133	+	1.34628i	0.937829	+	0.347097i	$0.112833\pi$
$419$	3.51506e6	+	4.83807e6i	0.978133	+	1.34628i	0.0403037	+	0.999187i	$0.487167\pi$
$420$	−4.20502e6	+	1.36629e6i	−1.16317	+	0.377938i
$421$	1.97264e6	−	2.71510e6i	0.542428	−	0.746588i	−0.446533	−	0.894767i	$-0.647341\pi$
$421$	1.97264e6	−	2.71510e6i	0.542428	−	0.746588i	0.988960	+	0.148180i	$0.0473414\pi$
$422$	−1.20596e6	−	876178.i	−0.329648	−	0.239503i
$423$	9753.69	+	7086.47i	0.00265044	+	0.00192566i
$424$	−83633.8	+	257399.i	−0.0225927	+	0.0695331i
$425$	−1.09403e7	−	3.55473e6i	−2.93805	−	0.954629i
$426$	4.06422e6			1.08506
$427$	−2.95346e6	−	4.57014e6i	−0.783902	−	1.21300i
$428$	−2.11262e6			−0.557458
$429$	−454117.	−	147552.i	−0.119131	−	0.0387080i
$430$	−733047.	+	2.25609e6i	−0.191188	+	0.588416i
$431$	314283.	+	228340.i	0.0814944	+	0.0592091i	0.627786	−	0.778386i	$-0.283961\pi$
$431$	314283.	+	228340.i	0.0814944	+	0.0592091i	−0.546292	+	0.837595i	$0.683961\pi$
$432$	722083.	+	524624.i	0.186156	+	0.135251i
$433$	944950.	−	1.30061e6i	0.242208	−	0.333371i	−0.670555	−	0.741860i	$-0.733944\pi$
$433$	944950.	−	1.30061e6i	0.242208	−	0.333371i	0.912763	+	0.408488i	$0.133944\pi$
$434$	−5.93334e6	+	1.92786e6i	−1.51208	+	0.491304i
$435$	−938464.	−	1.29169e6i	−0.237791	−	0.327291i
$436$	531406.	+	386089.i	0.133878	+	0.0972682i
$437$	220499.	+	303491.i	0.0552336	+	0.0760225i
$438$		−	1.12897e6i		−	0.281187i
$439$	2.40987e6	−	1.75087e6i	0.596804	−	0.433603i	−0.247939	−	0.968776i	$-0.579753\pi$
$439$	2.40987e6	−	1.75087e6i	0.596804	−	0.433603i	0.844743	+	0.535172i	$0.179753\pi$
$440$	−1.09837e6			−0.270468
$441$	24608.5			0.00602545
$442$	3.31561e6	−	2.40893e6i	0.807250	−	0.586501i
$443$	−680250.	−	2.09359e6i	−0.164687	−	0.506854i	0.834326	−	0.551271i	$-0.185857\pi$
$443$	−680250.	−	2.09359e6i	−0.164687	−	0.506854i	−0.999013	+	0.0444169i	$0.985857\pi$
$444$	1.78490e6	−	2.45671e6i	0.429692	−	0.591421i
$445$	3.70396e6	+	5.09806e6i	0.886678	+	1.22041i
$446$	−631883.	+	1.94473e6i	−0.150418	+	0.462938i
$447$	2.22722e6	+	6.85468e6i	0.527223	+	1.62263i
$448$		−	5.25652e6i		−	1.23738i
$449$	−1.23066e6	+	3.78759e6i	−0.288087	+	0.886639i	0.697370	+	0.716711i	$0.254353\pi$
$449$	−1.23066e6	+	3.78759e6i	−0.288087	+	0.886639i	−0.985456	+	0.169928i	$0.945647\pi$
$450$	−17357.0	+	23889.9i	−0.00404058	+	0.00556139i
$451$	1.09163e6	−	354692.i	0.252717	−	0.0821127i
$452$	1.15464e6	+	3.55363e6i	0.265829	+	0.818136i
$453$	2.06892e6	+	672232.i	0.473694	+	0.153912i
$454$	−3.21989e6	+	2.33939e6i	−0.733164	+	0.532675i
$455$	8.24771e6	+	2.67984e6i	1.86769	+	0.606850i
$456$			471220.i			0.106123i
$457$	1.51555e6	−	492432.i	0.339453	−	0.110295i	−0.134330	−	0.990937i	$-0.542888\pi$
$457$	1.51555e6	−	492432.i	0.339453	−	0.110295i	0.473783	+	0.880642i	$0.342888\pi$
$458$	−1.33707e6	+	434441.i	−0.297846	+	0.0967760i
$459$		−	7.89895e6i		−	1.75000i
$460$	−3.42066e6	−	1.11144e6i	−0.753730	−	0.244902i
$461$	1.29705e6	−	942365.i	0.284253	−	0.206522i	−0.436517	−	0.899696i	$-0.643788\pi$
$461$	1.29705e6	−	942365.i	0.284253	−	0.206522i	0.720771	+	0.693174i	$0.243788\pi$
$462$	−676196.	−	219709.i	−0.147390	−	0.0478899i
$463$	518304.	+	1.59518e6i	0.112365	+	0.345825i	0.991388	−	0.130954i	$-0.0418041\pi$
$463$	518304.	+	1.59518e6i	0.112365	+	0.345825i	−0.879023	+	0.476779i	$0.841804\pi$
$464$	246694.	−	80155.9i	0.0531942	−	0.0172838i
$465$	−7.15510e6	+	9.84814e6i	−1.53456	+	2.11214i
$466$	−268059.	+	825000.i	−0.0571828	+	0.175991i
$467$			2.04881e6i			0.434720i	0.976092	+	0.217360i	$0.0697446\pi$
$467$			2.04881e6i			0.434720i	−0.976092	+	0.217360i	$0.930255\pi$
$468$	3386.61	+	10422.9i	0.000714743	+	0.00219975i
$469$	−583334.	+	1.79532e6i	−0.122457	+	0.376885i
$470$	1.93583e6	+	2.66444e6i	0.404224	+	0.556366i
$471$	4.03423e6	−	5.55264e6i	0.837930	−	1.15331i
$472$	1.65332e6	+	5.08841e6i	0.341588	+	1.05130i
$473$	321482.	−	233570.i	0.0660699	−	0.0480026i
$474$	1.53544e6			0.313898
$475$	−876438.			−0.178233
$476$	−5.14296e6	+	3.73658e6i	−1.04039	+	0.755886i
$477$		−	1907.44i		−	0.000383845i
$478$	−104210.	−	143433.i	−0.0208613	−	0.0287131i
$479$	−6.69501e6	−	4.86421e6i	−1.33325	−	0.968665i	−0.999663	−	0.0259467i	$-0.991740\pi$
$479$	−6.69501e6	−	4.86421e6i	−1.33325	−	0.968665i	−0.333590	−	0.942718i	$-0.608260\pi$
$480$	−4.41398e6	−	6.07533e6i	−0.874435	−	1.20356i
$481$	−5.66459e6	+	1.84054e6i	−1.11636	+	0.362729i
$482$	3.02649e6	−	4.16560e6i	0.593364	−	0.816696i
$483$	−5.57528e6	−	4.05068e6i	−1.08742	−	0.790060i
$484$	−2.07698e6	−	1.50902e6i	−0.403013	−	0.292806i
$485$	−828970.	+	2.55131e6i	−0.160024	+	0.492503i
$486$	−38462.5	−	12497.2i	−0.00738665	−	0.00240007i
$487$	1.64076e6			0.313490			0.156745	−	0.987639i	$-0.449900\pi$
$487$	1.64076e6			0.313490			0.156745	+	0.987639i	$0.449900\pi$
$488$	3.50875e6	−	4.31331e6i	0.666965	−	0.819900i
$489$	−1.04220e6			−0.197096
$490$	6.39335e6	+	2.07733e6i	1.20292	+	0.390854i
$491$	1.05553e6	−	3.24858e6i	0.197590	−	0.608121i	−0.802346	−	0.596859i	$-0.796415\pi$
$491$	1.05553e6	−	3.24858e6i	0.197590	−	0.608121i	0.999937	−	0.0112618i	$-0.00358483\pi$
$492$	3.81961e6	+	2.77511e6i	0.711387	+	0.516853i
$493$	−1.85717e6	−	1.34931e6i	−0.344138	−	0.250031i
$494$	183536.	−	252616.i	0.0338380	−	0.0465739i
$495$	7362.17	−	2392.11i	0.00135049	−	0.000438802i
$496$	−1.16244e6	−	1.59996e6i	−0.212161	−	0.292014i
$497$	1.00034e7	+	7.26792e6i	1.81660	+	1.31983i
$498$	−3.33961e6	−	4.59658e6i	−0.603424	−	0.830542i
$499$		−	3.19146e6i		−	0.573770i	−0.957965	−	0.286885i	$-0.907380\pi$
$499$		−	3.19146e6i		−	0.573770i	0.957965	−	0.286885i	$-0.0926198\pi$
$500$	2.95774e6	−	2.14892e6i	0.529096	−	0.384411i
$501$	1.82773e6			0.325325
$502$	−3.24872e6			−0.575378
$503$	6.34665e6	−	4.61111e6i	1.11847	−	0.812617i	0.134495	−	0.990914i	$-0.457059\pi$
$503$	6.34665e6	−	4.61111e6i	1.11847	−	0.812617i	0.983977	+	0.178297i	$0.0570589\pi$
$504$	14926.4	+	45938.9i	0.00261746	+	0.00805571i
$505$	−496460.	+	683319.i	−0.0866275	+	0.119233i
$506$	−339960.	−	467915.i	−0.0590271	−	0.0812438i
$507$	593162.	−	1.82556e6i	0.102483	−	0.315411i
$508$	−782423.	−	2.40805e6i	−0.134519	−	0.414005i
$509$		−	1.07018e7i		−	1.83089i	−0.402441	−	0.915446i	$-0.631838\pi$
$509$		−	1.07018e7i		−	1.83089i	0.402441	−	0.915446i	$-0.368162\pi$
$510$	3.67957e6	−	1.13246e7i	0.626429	−	1.92795i
$511$	2.01890e6	−	2.77878e6i	0.342029	−	0.470762i
$512$	2.52850e6	−	821560.i	0.426274	−	0.138505i
$513$	−185972.	−	572364.i	−0.0312000	−	0.0960239i
$514$	5.22486e6	+	1.69766e6i	0.872303	+	0.283428i
$515$	−4.28337e6	+	3.11205e6i	−0.711651	+	0.517045i
$516$	1.55452e6	+	505095.i	0.257023	+	0.0835120i
$517$		−	551693.i		−	0.0907760i
$518$	−8.43477e6	+	2.74062e6i	−1.38118	+	0.448771i
$519$	−4.09840e6	+	1.33165e6i	−0.667877	+	0.217006i
$520$			8.86146e6i			1.43713i
$521$	3.75849e6	+	1.22121e6i	0.606623	+	0.197104i	0.596192	−	0.802842i	$-0.296680\pi$
$521$	3.75849e6	+	1.22121e6i	0.606623	+	0.197104i	0.0104311	+	0.999946i	$0.496680\pi$
$522$	−4767.41	+	3463.73i	−0.000765784	+	0.000556375i
$523$	7.68987e6	+	2.49859e6i	1.22932	+	0.399430i	0.850467	−	0.526028i	$-0.176319\pi$
$523$	7.68987e6	+	2.49859e6i	1.22932	+	0.399430i	0.378851	+	0.925458i	$0.376319\pi$
$524$	−689158.	−	2.12101e6i	−0.109645	−	0.337454i
$525$	1.53126e7	−	4.97537e6i	2.42466	−	0.787820i
$526$	−1.98305e6	+	2.72944e6i	−0.312515	+	0.430139i
$527$	−5.40845e6	+	1.66455e7i	−0.848294	+	2.61078i
$528$		−	225385.i		−	0.0351836i
$529$	256595.	+	789717.i	0.0398665	+	0.122697i
$530$	161016.	−	495558.i	0.0248989	−	0.0766310i
$531$	−22163.9	−	30506.0i	−0.00341122	−	0.00469514i
$532$	−284689.	+	391841.i	−0.0436105	+	0.0600248i
$533$	−2.86160e6	−	8.80711e6i	−0.436306	−	1.34281i
$534$	−3.37211e6	+	2.44998e6i	−0.511739	+	0.371800i
$535$	1.20392e7			1.81849
$536$	−1.92892e6			−0.290002
$537$	5.45697e6	−	3.96472e6i	0.816612	−	0.593304i
$538$			5.22775e6i			0.778680i
$539$	−661897.	−	911023.i	−0.0981338	−	0.135070i
$540$	4.66810e6	+	3.39157e6i	0.688899	+	0.500514i
$541$	694192.	+	955473.i	0.101973	+	0.140354i	0.856954	−	0.515393i	$-0.172354\pi$
$541$	694192.	+	955473.i	0.101973	+	0.140354i	−0.754981	+	0.655747i	$0.772354\pi$
$542$	−3.04493e6	+	989358.i	−0.445225	+	0.144662i
$543$	−6.88392e6	+	9.47490e6i	−1.00193	+	1.37903i
$544$	−8.73501e6	−	6.34636e6i	−1.26551	−	0.919448i
$545$	−3.02832e6	−	2.20020e6i	−0.436727	−	0.317301i
$546$	−1.77258e6	+	5.45545e6i	−0.254463	+	0.783157i
$547$	−6.07692e6	−	1.97451e6i	−0.868391	−	0.282157i	−0.159262	−	0.987236i	$-0.550911\pi$
$547$	−6.07692e6	−	1.97451e6i	−0.868391	−	0.282157i	−0.709129	+	0.705079i	$0.750911\pi$
$548$	3.25311e6			0.462751
$549$	−14124.7	+	36553.0i	−0.00200008	+	0.00517598i
$550$	1.35127e6			0.190474
$551$	−166340.	−	54047.0i	−0.0233409	−	0.00758391i
$552$	2.17606e6	−	6.69721e6i	0.303964	−	0.935505i
$553$	3.77926e6	+	2.74579e6i	0.525525	+	0.381816i
$554$	6.89629e6	+	5.01045e6i	0.954643	+	0.693589i
$555$	−1.01716e7	+	1.40000e7i	−1.40171	+	1.92929i
$556$	−4.02936e6	+	1.30922e6i	−0.552777	+	0.179608i
$557$	3.79010e6	+	5.21663e6i	0.517623	+	0.712446i	0.985181	−	0.171516i	$-0.0548664\pi$
$557$	3.79010e6	+	5.21663e6i	0.517623	+	0.712446i	−0.467559	+	0.883962i	$0.654866\pi$
$558$	36348.0	+	26408.4i	0.00494191	+	0.00359051i
$559$	−1.88441e6	−	2.59367e6i	−0.255062	−	0.351063i
$560$			4.09346e6i			0.551595i
$561$	−1.61370e6	+	1.17242e6i	−0.216479	+	0.157281i
$562$	9.00751e6			1.20300
$563$	2.45776e6			0.326790			0.163395	−	0.986561i	$-0.447755\pi$
$563$	2.45776e6			0.326790			0.163395	+	0.986561i	$0.447755\pi$
$564$	1.83589e6	−	1.33385e6i	0.243024	−	0.176567i
$565$	−6.57995e6	−	2.02510e7i	−0.867165	−	2.66886i
$566$	−1.80081e6	+	2.47860e6i	−0.236280	+	0.325211i
$567$	6.46234e6	+	8.89465e6i	0.844174	+	1.16191i
$568$	−3.90438e6	+	1.20165e7i	−0.507787	+	1.56281i
$569$	−1.70951e6	−	5.26134e6i	−0.221356	−	0.681265i	−0.998641	−	0.0521157i	$-0.983404\pi$
$569$	−1.70951e6	−	5.26134e6i	−0.221356	−	0.681265i	0.777285	−	0.629149i	$-0.216596\pi$
$570$		−	907218.i		−	0.116957i
$571$	−1.57402e6	+	4.84434e6i	−0.202032	+	0.621791i	0.797790	+	0.602935i	$0.206002\pi$
$571$	−1.57402e6	+	4.84434e6i	−0.202032	+	0.621791i	−0.999822	+	0.0188554i	$0.993998\pi$
$572$	294772.	−	405719.i	0.0376701	−	0.0518484i
$573$	−8.54362e6	+	2.77599e6i	−1.08706	+	0.353209i
$574$	−4.26103e6	−	1.31141e7i	−0.539802	−	1.66134i
$575$	1.24564e7	+	4.04732e6i	1.57117	+	0.510503i
$576$	−30625.7	+	22250.9i	−0.00384618	+	0.00279441i
$577$	98009.2	+	31845.1i	0.0122554	+	0.00398202i	0.315138	−	0.949046i	$-0.397949\pi$
$577$	98009.2	+	31845.1i	0.0122554	+	0.00398202i	−0.302883	+	0.953028i	$0.597949\pi$
$578$		−	1.14991e7i		−	1.43167i
$579$	1.89994e6	−	617328.i	0.235529	−	0.0765279i
$580$	1.59482e6	−	518189.i	0.196853	−	0.0639614i
$581$		−	1.72859e7i		−	2.12448i
$582$	−1.68756e6	−	548322.i	−0.206515	−	0.0671009i
$583$	−70614.7	+	51304.6i	−0.00860446	+	0.00625151i
$584$	3.33796e6	+	1.08457e6i	0.404994	+	0.131590i
$585$	−19299.2	−	59396.9i	−0.00233158	−	0.00717586i
$586$	−2.99493e6	+	973112.i	−0.360282	+	0.117063i
$587$	−9.00506e6	+	1.23944e7i	−1.07868	+	1.48467i	−0.217707	+	0.976014i	$0.569858\pi$
$587$	−9.00506e6	+	1.23944e7i	−1.07868	+	1.48467i	−0.860969	+	0.508657i	$0.830142\pi$
$588$	1.43135e6	−	4.40524e6i	0.170727	−	0.525444i
$589$			1.33348e6i			0.158380i
$590$	−3.18307e6	−	9.79648e6i	−0.376458	−	1.15862i
$591$	1.84807e6	−	5.68778e6i	0.217646	−	0.669845i
$592$	−1.65251e6	−	2.27448e6i	−0.193794	−	0.266734i
$593$	3.51169e6	−	4.83343e6i	0.410090	−	0.564441i	−0.553150	−	0.833082i	$-0.686574\pi$
$593$	3.51169e6	−	4.83343e6i	0.410090	−	0.564441i	0.963240	+	0.268641i	$0.0865744\pi$
$594$	286728.	+	882457.i	0.0333429	+	0.102619i
$595$	2.93081e7	−	2.12936e7i	3.39387	−	2.46579i
$596$	−7.56986e6			−0.872915
$597$	1.07831e7			1.23825
$598$	−3.77507e6	+	2.74275e6i	−0.431690	+	0.313641i
$599$			4.37218e6i			0.497888i	0.968518	+	0.248944i	$0.0800835\pi$
$599$			4.37218e6i			0.497888i	−0.968518	+	0.248944i	$0.919917\pi$
$600$	9.67030e6	+	1.33100e7i	1.09663	+	1.50939i
$601$	−1.05860e7	−	7.69116e6i	−1.19549	−	0.868571i	−0.201653	−	0.979457i	$-0.564631\pi$
$601$	−1.05860e7	−	7.69116e6i	−1.19549	−	0.868571i	−0.993833	+	0.110886i	$0.964631\pi$
$602$	−2.80595e6	−	3.86206e6i	−0.315565	−	0.434338i
$603$	12929.2	−	4200.95i	0.00144803	−	0.000470494i
$604$	−1.34296e6	+	1.84842e6i	−0.149785	+	0.206162i
$605$	1.18361e7	+	8.59941e6i	1.31468	+	0.955169i
$606$	−451981.	−	328384.i	−0.0499964	−	0.0363245i
$607$	−3.35626e6	+	1.03295e7i	−0.369729	+	1.13791i	0.577238	+	0.816576i	$0.304131\pi$
$607$	−3.35626e6	+	1.03295e7i	−0.369729	+	1.13791i	−0.946967	+	0.321332i	$0.895869\pi$
$608$	−782364.	−	254205.i	−0.0858321	−	0.0278886i
$609$	3.21300e6			0.351049
$610$	−6.75524e6	+	8.30422e6i	−0.735049	+	0.903596i
$611$	−4.45097e6			−0.482339
$612$	43540.3	+	14147.1i	0.00469908	+	0.00152682i
$613$	−2.73960e6	+	8.43162e6i	−0.294466	+	0.906274i	0.688934	+	0.724824i	$0.258079\pi$
$613$	−2.73960e6	+	8.43162e6i	−0.294466	+	0.906274i	−0.983400	+	0.181450i	$0.941921\pi$
$614$	−3.29663e6	−	2.39514e6i	−0.352898	−	0.256395i
$615$	−2.17668e7	−	1.58145e7i	−2.32063	−	1.68604i
$616$	1.29921e6	−	1.78821e6i	0.137952	−	0.189874i
$617$	9.30585e6	−	3.02365e6i	0.984109	−	0.319756i	0.227611	−	0.973752i	$-0.426909\pi$
$617$	9.30585e6	−	3.02365e6i	0.984109	−	0.319756i	0.756498	+	0.653996i	$0.226909\pi$
$618$	−2.05846e6	−	2.83323e6i	−0.216806	−	0.298408i
$619$	−9.55393e6	−	6.94134e6i	−1.00220	−	0.728143i	−0.0396433	−	0.999214i	$-0.512622\pi$
$619$	−9.55393e6	−	6.94134e6i	−1.00220	−	0.728143i	−0.962559	+	0.271071i	$0.912622\pi$
$620$	−7.51488e6	−	1.03433e7i	−0.785132	−	1.08064i
$621$			8.99353e6i			0.935839i
$622$	−5.08188e6	+	3.69220e6i	−0.526682	+	0.382657i
$623$	−1.26812e7			−1.30900
$624$	−1.81837e6			−0.186948
$625$	−2.87008e6	+	2.08523e6i	−0.293896	+	0.213528i
$626$	−2.64101e6	−	8.12821e6i	−0.269361	−	0.829008i
$627$	−89326.4	+	122947.i	−0.00907426	+	0.0124896i
$628$	4.23708e6	+	5.83184e6i	0.428714	+	0.590074i
$629$	−7.68861e6	+	2.36631e7i	−0.774856	+	2.38476i
$630$	−28737.2	−	88444.1i	−0.00288465	−	0.00887804i
$631$			1.48809e7i			1.48784i	0.668269	+	0.743919i	$0.267035\pi$
$631$			1.48809e7i			1.48784i	−0.668269	+	0.743919i	$0.732965\pi$
$632$	−1.47506e6	+	4.53977e6i	−0.146898	+	0.452106i
$633$	3.44040e6	−	4.73530e6i	0.341271	−	0.469719i
$634$	−497589.	+	161677.i	−0.0491641	+	0.0159744i
$635$	4.45878e6	+	1.37227e7i	0.438816	+	1.35054i
$636$	−341457.	−	110946.i	−0.0334729	−	0.0108760i
$637$	−7.35000e6	+	5.34008e6i	−0.717693	+	0.521434i
$638$	256458.	+	83328.4i	0.0249440	+	0.00810478i
$639$		−	89047.5i		−	0.00862720i
$640$	4.86697e6	−	1.58138e6i	0.469688	−	0.152611i
$641$	−8.88142e6	+	2.88575e6i	−0.853763	+	0.277405i	−0.703021	−	0.711169i	$-0.748166\pi$
$641$	−8.88142e6	+	2.88575e6i	−0.853763	+	0.277405i	−0.150742	+	0.988573i	$0.548166\pi$
$642$			7.96331e6i			0.762528i
$643$	−9.58669e6	−	3.11490e6i	−0.914410	−	0.297110i	−0.186239	−	0.982505i	$-0.559630\pi$
$643$	−9.58669e6	−	3.11490e6i	−0.914410	−	0.297110i	−0.728172	+	0.685395i	$0.759630\pi$
$644$	5.85563e6	−	4.25436e6i	0.556364	−	0.404222i
$645$	−8.85874e6	−	2.87838e6i	−0.838441	−	0.272426i
$646$	−403077.	−	1.24054e6i	−0.0380020	−	0.116958i
$647$	1.27999e7	−	4.15893e6i	1.20211	−	0.390589i	0.361574	−	0.932344i	$-0.382240\pi$
$647$	1.27999e7	−	4.15893e6i	1.20211	−	0.390589i	0.840537	+	0.541754i	$0.182240\pi$
$648$	−6.60341e6	+	9.08881e6i	−0.617775	+	0.850295i
$649$	−533207.	+	1.64104e6i	−0.0496917	+	0.152935i
$650$		−	1.09019e7i		−	1.01208i
$651$	−7.56992e6	−	2.32978e7i	−0.700065	−	2.15458i
$652$	338250.	−	1.04103e6i	0.0311615	−	0.0959054i
$653$	1.03985e7	+	1.43123e7i	0.954303	+	1.31349i	0.949589	+	0.313497i	$0.101500\pi$
$653$	1.03985e7	+	1.43123e7i	0.954303	+	1.31349i	0.00471393	+	0.999989i	$0.498500\pi$
$654$	1.45532e6	−	2.00308e6i	0.133050	−	0.183128i
$655$	3.92730e6	+	1.20870e7i	0.357677	+	1.10082i
$656$	3.53629e6	−	2.56926e6i	0.320840	−	0.233104i
$657$	−24735.8			−0.00223570
$658$	−6.62766e6			−0.596754
$659$	5.20322e6	−	3.78036e6i	0.466722	−	0.339093i	−0.329440	−	0.944176i	$-0.606860\pi$
$659$	5.20322e6	−	3.78036e6i	0.466722	−	0.339093i	0.796162	+	0.605083i	$0.206860\pi$
$660$		−	1.45706e6i		−	0.130202i
$661$	−9.47714e6	−	1.30442e7i	−0.843672	−	1.16121i	−0.985222	−	0.171283i	$-0.945209\pi$
$661$	−9.47714e6	−	1.30442e7i	−0.843672	−	1.16121i	0.141550	−	0.989931i	$-0.454791\pi$
$662$	1.19021e7	+	8.64741e6i	1.05555	+	0.766904i
$663$	9.45891e6	+	1.30191e7i	0.835713	+	1.15026i
$664$	1.67988e7	−	5.45825e6i	1.47862	−	0.480433i
$665$	1.62235e6	−	2.23298e6i	0.142263	−	0.195808i
$666$	51672.0	+	37541.9i	0.00451408	+	0.00327967i
$667$	2.11452e6	+	1.53629e6i	0.184033	+	0.133708i
$668$	−593200.	+	1.82568e6i	−0.0514351	+	0.158301i
$669$	−7.63619e6	−	2.48115e6i	−0.659647	−	0.214332i
$670$	3.71366e6			0.319606
$671$	1.73313e6	−	460263.i	0.148602	−	0.0394639i
$672$	1.51121e7			1.29092
$673$	994062.	+	322990.i	0.0846010	+	0.0274885i	0.351012	−	0.936371i	$-0.385838\pi$
$673$	994062.	+	322990.i	0.0846010	+	0.0274885i	−0.266411	+	0.963860i	$0.585838\pi$
$674$	−2.39414e6	+	7.36840e6i	−0.203002	+	0.624775i
$675$	−1.69989e7	−	1.23504e7i	−1.43603	−	1.04333i
$676$	1.63100e6	+	1.18499e6i	0.137274	+	0.0997354i
$677$	−2.88233e6	+	3.96719e6i	−0.241698	+	0.332668i	−0.912582	−	0.408894i	$-0.865915\pi$
$677$	−2.88233e6	+	3.96719e6i	−0.241698	+	0.332668i	0.670884	+	0.741562i	$0.265915\pi$
$678$	1.33950e7	−	4.35231e6i	1.11910	−	0.363618i
$679$	−3.17313e6	−	4.36743e6i	−0.264127	−	0.363540i
$680$	2.99479e7	+	2.17584e7i	2.48367	+	1.80449i
$681$	−9.18582e6	−	1.26432e7i	−0.759015	−	1.04469i
$682$		−	2.05593e6i		−	0.169257i
$683$	−1.01568e7	+	7.37937e6i	−0.833118	+	0.605296i	−0.920440	−	0.390885i	$-0.872169\pi$
$683$	−1.01568e7	+	7.37937e6i	−0.833118	+	0.605296i	0.0873218	+	0.996180i	$0.472169\pi$
$684$	3488.05			0.000285064
$685$	−1.85385e7			−1.50955
$686$	−865459.	+	628793.i	−0.0702160	+	0.0510149i
$687$	−1.70588e6	−	5.25015e6i	−0.137897	−	0.424404i
$688$	889484.	−	1.22427e6i	0.0716419	−	0.0986066i
$689$	413918.	+	569709.i	0.0332174	+	0.0457198i
$690$	−4.18946e6	+	1.28938e7i	−0.334993	+	1.03100i
$691$	1.16285e6	+	3.57889e6i	0.0926466	+	0.285137i	0.986633	−	0.162957i	$-0.0521031\pi$
$691$	1.16285e6	+	3.57889e6i	0.0926466	+	0.285137i	−0.893987	+	0.448094i	$0.852103\pi$
$692$		−	4.52601e6i		−	0.359294i
$693$	−4813.87	+	14815.6i	−0.000380768	+	0.00117188i
$694$	4.47238e6	−	6.15570e6i	0.352484	−	0.485153i
$695$	2.29621e7	−	7.46084e6i	1.80322	−	0.585903i
$696$	1.01455e6	+	3.12245e6i	0.0793869	+	0.244328i
$697$	−3.67906e7	−	1.19540e7i	−2.86850	−	0.932031i
$698$	226797.	−	164778.i	0.0176197	−	0.0128015i
$699$	−3.23944e6	−	1.05256e6i	−0.250771	−	0.0814805i
$700$			1.69102e7i			1.30438i
$701$	1.58840e7	−	5.16101e6i	1.22085	−	0.396679i	0.373461	−	0.927646i	$-0.378171\pi$
$701$	1.58840e7	−	5.16101e6i	1.22085	−	0.396679i	0.847393	+	0.530967i	$0.178171\pi$
$702$	7.11953e6	−	2.31328e6i	0.545266	−	0.177168i
$703$			1.89567e6i			0.144668i
$704$	1.64748e6	+	535299.i	0.125282	+	0.0407066i
$705$	−1.04622e7	+	7.60121e6i	−0.792773	+	0.575983i
$706$	2.34501e6	+	761940.i	0.177065	+	0.0575319i
$707$	−525243.	−	1.61653e6i	−0.0395195	−	0.121629i
$708$	−6.75012e6	+	2.19325e6i	−0.506091	+	0.164439i
$709$	1.20835e7	−	1.66315e7i	0.902772	−	1.24256i	−0.0668032	−	0.997766i	$-0.521280\pi$
$709$	1.20835e7	−	1.66315e7i	0.902772	−	1.24256i	0.969575	−	0.244793i	$-0.0787200\pi$
$710$	7.51693e6	−	2.31347e7i	0.559622	−	1.72234i
$711$		−	33641.8i		−	0.00249577i
$712$	−4.00424e6	−	1.23238e7i	−0.296019	−	0.911054i
$713$	6.15792e6	−	1.89521e7i	0.453639	−	1.39616i
$714$	1.40846e7	+	1.93858e7i	1.03395	+	1.42311i
$715$	−1.67982e6	+	2.31207e6i	−0.122884	+	0.169136i
$716$	2.18919e6	+	6.73763e6i	0.159588	+	0.491162i
$717$	563204.	−	409192.i	0.0409136	−	0.0297255i
$718$	−1.65570e7			−1.19859
$719$	74764.6			0.00539354			0.00269677	−	0.999996i	$-0.499142\pi$
$719$	74764.6			0.00539354			0.00269677	+	0.999996i	$0.499142\pi$
$720$	23849.4	−	17327.6i	0.00171454	−	0.00124568i
$721$		−	1.06547e7i		−	0.763311i
$722$	5.70348e6	+	7.85017e6i	0.407190	+	0.560449i
$723$	1.63566e7	+	1.18838e7i	1.16372	+	0.845492i
$724$	−7.23007e6	−	9.95134e6i	−0.512621	−	0.705562i
$725$	−5.80756e6	+	1.88699e6i	−0.410344	+	0.133329i
$726$	−5.68808e6	+	7.82897e6i	−0.400520	+	0.551268i
$727$	1.16808e7	+	8.48656e6i	0.819662	+	0.595519i	0.916616	−	0.399770i	$-0.130910\pi$
$727$	1.16808e7	+	8.48656e6i	0.819662	+	0.595519i	−0.0969537	+	0.995289i	$0.530910\pi$
$728$	−1.44270e7	−	1.04818e7i	−1.00890	−	0.733006i
$729$	4.45839e6	−	1.37215e7i	0.310713	−	0.956275i
$730$	−6.42642e6	−	2.08807e6i	−0.446336	−	0.145023i
$731$	−1.33924e7			−0.926971
$732$	5.72190e6	+	4.65460e6i	0.394696	+	0.321074i
$733$	−1.01470e7			−0.697557			−0.348778	−	0.937205i	$-0.613403\pi$
$733$	−1.01470e7			−0.697557			−0.348778	+	0.937205i	$0.613403\pi$
$734$	1.05429e7	+	3.42559e6i	0.722302	+	0.234690i
$735$	−8.15682e6	+	2.51041e7i	−0.556933	+	1.71406i
$736$	9.94545e6	+	7.22579e6i	0.676752	+	0.491689i
$737$	−503279.	−	365653.i	−0.0341303	−	0.0247971i
$738$	−58368.8	+	80337.8i	−0.00394494	+	0.00542974i
$739$	1.00172e7	−	3.25480e6i	0.674740	−	0.219236i	0.0484492	−	0.998826i	$-0.484572\pi$
$739$	1.00172e7	−	3.25480e6i	0.674740	−	0.219236i	0.626291	+	0.779589i	$0.284572\pi$
$740$	−1.06831e7	−	1.47040e7i	−0.717162	−	0.987089i
$741$	991920.	+	720672.i	0.0663638	+	0.0482161i
$742$	616338.	+	848316.i	0.0410969	+	0.0565650i
$743$		−	2.51503e7i		−	1.67136i	−0.549216	−	0.835681i	$-0.685073\pi$
$743$		−	2.51503e7i		−	1.67136i	0.549216	−	0.835681i	$-0.314927\pi$
$744$	2.02509e7	−	1.47132e7i	1.34126	−	0.974481i
$745$	4.31383e7			2.84755
$746$	840886.			0.0553210
$747$	−100712.	+	73171.4i	−0.00660357	+	0.00479778i
$748$	−647371.	−	1.99240e6i	−0.0423058	−	0.130204i
$749$	−1.42406e7	+	1.96005e7i	−0.927519	+	1.27662i
$750$	−8.10014e6	−	1.11489e7i	−0.525823	−	0.723733i
$751$	−2.90663e6	+	8.94569e6i	−0.188057	+	0.578781i	−0.999988	−	0.00497359i	$-0.998417\pi$
$751$	−2.90663e6	+	8.94569e6i	−0.188057	+	0.578781i	0.811930	+	0.583754i	$0.198417\pi$
$752$	−649233.	−	1.99813e6i	−0.0418655	−	0.128849i
$753$		−	1.27564e7i		−	0.819863i
$754$	672281.	−	2.06907e6i	0.0430648	−	0.132540i
$755$	7.65309e6	−	1.05336e7i	0.488618	−	0.672525i
$756$	−1.10433e7	+	3.58820e6i	−0.702742	+	0.228335i
$757$	−2.44957e6	−	7.53901e6i	−0.155364	−	0.478161i	0.842834	−	0.538174i	$-0.180886\pi$
$757$	−2.44957e6	−	7.53901e6i	−0.155364	−	0.478161i	−0.998198	+	0.0600129i	$0.980886\pi$
$758$	1.21856e7	+	3.95933e6i	0.770323	+	0.250293i
$759$	1.83731e6	−	1.33489e6i	0.115765	−	0.0841084i
$760$	2.68233e6	+	871540.i	0.168453	+	0.0547335i
$761$			1.61360e7i			1.01003i	0.863110	+	0.505015i	$0.168513\pi$
$761$			1.61360e7i			1.01003i	−0.863110	+	0.505015i	$0.831487\pi$
$762$	−9.07689e6	+	2.94926e6i	−0.566304	+	0.184003i
$763$	7.16411e6	−	2.32776e6i	0.445503	−	0.144753i
$764$		−	9.43500e6i		−	0.584802i
$765$	−248123.	−	80620.0i	−0.0153290	−	0.00498069i
$766$	8.98128e6	−	6.52528e6i	0.553052	−	0.401816i
$767$	1.32397e7	+	4.30183e6i	0.812623	+	0.264037i
$768$	5.36156e6	+	1.65012e7i	0.328011	+	1.00951i
$769$	2.05540e7	−	6.67842e6i	1.25338	−	0.407247i	0.394247	−	0.919005i	$-0.371006\pi$
$769$	2.05540e7	−	6.67842e6i	1.25338	−	0.407247i	0.859130	+	0.511758i	$0.171006\pi$
$770$	−2.50131e6	+	3.44275e6i	−0.152034	+	0.209256i
$771$	−6.66603e6	+	2.05159e7i	−0.403860	+	1.24295i
$772$			2.09817e6i			0.126706i
$773$	2.43884e6	+	7.50599e6i	0.146803	+	0.451814i	0.997238	−	0.0742660i	$-0.0236614\pi$
$773$	2.43884e6	+	7.50599e6i	0.146803	+	0.451814i	−0.850435	+	0.526080i	$0.823661\pi$
$774$	−10623.7	+	32696.3i	−0.000637414	+	0.00196176i
$775$	2.73655e7	+	3.76654e7i	1.63663	+	2.25262i
$776$	3.24239e6	−	4.46277e6i	0.193291	−	0.266042i
$777$	−1.07613e7	−	3.31200e7i	−0.639460	−	1.96805i
$778$	−1.38130e6	+	1.00357e6i	−0.0818161	+	0.0594429i
$779$	−2.94732e6			−0.174014
$780$	−1.17553e7			−0.691829
$781$	−3.29659e6	+	2.39511e6i	−0.193392	+	0.140507i
$782$			1.94926e7i			1.13986i
$783$	−2.46462e6	−	3.39226e6i	−0.143663	−	0.197736i
$784$	−3.46937e6	−	2.52064e6i	−0.201586	−	0.146461i
$785$	−2.41458e7	−	3.32339e7i	−1.39852	−	1.92489i
$786$	−7.99493e6	+	2.59771e6i	−0.461592	+	0.149980i
$787$	1.96424e7	−	2.70355e7i	1.13047	−	1.55596i	0.343290	−	0.939229i	$-0.388459\pi$
$787$	1.96424e7	−	2.70355e7i	1.13047	−	1.55596i	0.787178	−	0.616726i	$-0.211541\pi$
$788$	5.08161e6	+	3.69200e6i	0.291532	+	0.211810i
$789$	−1.07174e7	−	7.78665e6i	−0.612911	−	0.445306i
$790$	2.83987e6	−	8.74021e6i	0.161894	−	0.498258i
$791$	4.07529e7	+	1.32414e7i	2.31589	+	0.752478i
$792$	−15918.1			−0.000901731
$793$	−3.71333e6	−	1.39826e7i	−0.209692	−	0.789596i
$794$	−9.67790e6			−0.544791
$795$	1.94586e6	+	632247.i	0.109192	+	0.0354788i
$796$	−3.49971e6	+	1.07710e7i	−0.195772	+	0.602523i
$797$	−1.27555e7	−	9.26741e6i	−0.711298	−	0.516788i	0.172294	−	0.985046i	$-0.444882\pi$
$797$	−1.27555e7	−	9.26741e6i	−0.711298	−	0.516788i	−0.883592	+	0.468257i	$0.844882\pi$
$798$	1.47700e6	+	1.07311e6i	0.0821059	+	0.0596534i
$799$	−1.09289e7	+	1.50423e7i	−0.605633	+	0.833583i
$800$	−2.73153e7	+	8.87529e6i	−1.50897	+	0.490295i
$801$	53679.5	+	73883.5i	0.00295615	+	0.00406880i
$802$	−2.05982e6	−	1.49655e6i	−0.113082	−	0.0821590i
$803$	665320.	+	915734.i	0.0364118	+	0.0501165i
$804$		−	2.55884e6i		−	0.139606i
$805$	−3.33694e7	+	2.42443e7i	−1.81493	+	1.31862i
$806$	−1.65869e7			−0.899350
$807$	−2.05273e7			−1.10955
$808$	1.40512e6	−	1.02088e6i	0.0757156	−	0.0550106i
$809$	8.08190e6	+	2.48735e7i	0.434153	+	1.33618i	0.893953	+	0.448162i	$0.147921\pi$
$809$	8.08190e6	+	2.48735e7i	0.434153	+	1.33618i	−0.459800	+	0.888022i	$0.652079\pi$
$810$	1.27132e7	−	1.74983e7i	0.680838	−	0.937093i
$811$	1.00487e7	+	1.38309e7i	0.536486	+	0.738409i	0.988101	−	0.153803i	$-0.0491522\pi$
$811$	1.00487e7	+	1.38309e7i	0.536486	+	0.738409i	−0.451616	+	0.892213i	$0.649152\pi$
$812$	−1.04280e6	+	3.20940e6i	−0.0555022	+	0.170818i
$813$	−3.88481e6	−	1.19562e7i	−0.206131	−	0.634406i
$814$		−	2.92269e6i		−	0.154604i
$815$	−1.92758e6	+	5.93249e6i	−0.101653	+	0.312855i
$816$	−4.46482e6	+	6.14530e6i	−0.234735	+	0.323086i
$817$	−970426.	+	315311.i	−0.0508636	+	0.0165266i
$818$	−1.39127e6	−	4.28187e6i	−0.0726987	−	0.223744i
$819$	119530.	+	38837.5i	0.00622682	+	0.00202322i
$820$	2.28613e7	−	1.66097e7i	1.18731	−	0.862635i
$821$	−5.97564e6	−	1.94160e6i	−0.309404	−	0.100532i	0.150199	−	0.988656i	$-0.452008\pi$
$821$	−5.97564e6	−	1.94160e6i	−0.309404	−	0.100532i	−0.459604	+	0.888124i	$0.652008\pi$
$822$		−	1.22623e7i		−	0.632982i
$823$	4.06583e6	−	1.32107e6i	0.209242	−	0.0679870i	−0.202520	−	0.979278i	$-0.564913\pi$
$823$	4.06583e6	−	1.32107e6i	0.209242	−	0.0679870i	0.411763	+	0.911291i	$0.364913\pi$
$824$	1.03544e7	−	3.36434e6i	0.531259	−	0.172616i
$825$			5.30590e6i			0.271409i
$826$	1.97143e7	+	6.40558e6i	1.00538	+	0.326669i
$827$	7.76160e6	−	5.63913e6i	0.394628	−	0.286714i	−0.372722	−	0.927943i	$-0.621575\pi$
$827$	7.76160e6	−	5.63913e6i	0.394628	−	0.286714i	0.767349	+	0.641229i	$0.221575\pi$
$828$	−49573.8	−	16107.5i	−0.00251291	−	0.000816493i
$829$	−693357.	−	2.13393e6i	−0.0350405	−	0.107844i	0.932006	−	0.362442i	$-0.118057\pi$
$829$	−693357.	−	2.13393e6i	−0.0350405	−	0.107844i	−0.967047	+	0.254598i	$0.918057\pi$
$830$	−3.23419e7	+	1.05085e7i	−1.62956	+	0.529476i
$831$	−1.96740e7	+	2.70789e7i	−0.988303	+	1.36028i
$832$	4.31871e6	−	1.32916e7i	0.216295	−	0.665687i
$833$			3.79518e7i			1.89505i
$834$	4.93497e6	+	1.51883e7i	0.245680	+	0.756125i
$835$	3.38046e6	−	1.04040e7i	0.167788	−	0.516397i
$836$	−93818.1	−	129129.i	−0.00464270	−	0.00639013i
$837$	−1.87909e7	+	2.58635e7i	−0.927118	+	1.27607i
$838$	7.31603e6	+	2.25164e7i	0.359886	+	1.10762i
$839$	−2.69409e7	+	1.95737e7i	−1.32132	+	0.959992i	−0.321401	+	0.946943i	$0.604154\pi$
$839$	−2.69409e7	+	1.95737e7i	−1.32132	+	0.959992i	−0.999915	+	0.0130486i	$0.995846\pi$
$840$	−5.18116e7			−2.53354
$841$	1.92926e7			0.940589
$842$	1.07489e7	−	7.80955e6i	0.522498	−	0.379617i
$843$			3.53689e7i			1.71416i
$844$	3.61339e6	+	4.97341e6i	0.174606	+	0.240324i
$845$	−9.29458e6	−	6.75291e6i	−0.447804	−	0.325349i
$846$	28054.9	+	38614.3i	0.00134767	+	0.00185491i
$847$	−2.80007e7	+	9.09797e6i	−1.34110	+	0.435748i
$848$	−195379.	+	268916.i	−0.00933012	+	0.0128418i
$849$	−9.73246e6	−	7.07105e6i	−0.463397	−	0.336678i
$850$	−3.68435e7	−	2.67684e7i	−1.74910	−	1.27079i
$851$	8.75404e6	−	2.69422e7i	0.414366	−	1.27529i
$852$	−1.59406e7	−	5.17943e6i	−0.752327	−	0.244446i
$853$	−2.45882e7			−1.15706			−0.578528	−	0.815663i	$-0.696373\pi$
$853$	−2.45882e7			−1.15706			−0.578528	+	0.815663i	$0.696373\pi$
$854$	−5.52928e6	−	2.08206e7i	−0.259432	−	0.976896i
$855$	−19877.3			−0.000929912
$856$	−2.35447e7	−	7.65014e6i	−1.09827	−	0.356849i
$857$	−4.46163e6	+	1.37315e7i	−0.207511	+	0.638653i	0.792090	+	0.610404i	$0.208993\pi$
$857$	−4.46163e6	+	1.37315e7i	−0.207511	+	0.638653i	−0.999601	+	0.0282488i	$0.991007\pi$
$858$	−1.52932e6	−	1.11111e6i	−0.0709218	−	0.0515277i
$859$	−1.27136e7	−	9.23696e6i	−0.587875	−	0.427116i	0.253680	−	0.967288i	$-0.418359\pi$
$859$	−1.27136e7	−	9.23696e6i	−0.587875	−	0.427116i	−0.841555	+	0.540172i	$0.818359\pi$
$860$	5.75031e6	−	7.91462e6i	0.265121	−	0.364908i
$861$	5.14937e7	−	1.67313e7i	2.36726	−	0.769171i
$862$	903983.	+	1.24423e6i	0.0414374	+	0.0570337i
$863$	−1.16230e6	−	844460.i	−0.0531240	−	0.0385969i	0.560906	−	0.827879i	$-0.310453\pi$
$863$	−1.16230e6	−	844460.i	−0.0531240	−	0.0385969i	−0.614030	+	0.789282i	$0.710453\pi$
$864$	−1.15921e7	−	1.59552e7i	−0.528298	−	0.727140i
$865$			2.57923e7i			1.17206i
$866$	5.14904e6	−	3.74100e6i	0.233309	−	0.169509i
$867$	4.51523e7			2.04001
$868$	2.57286e7			1.15909
$869$	−1.24544e6	+	904864.i	−0.0559465	+	0.0406475i
$870$	−1.95326e6	−	6.01151e6i	−0.0874907	−	0.269269i
$871$	−2.95004e6	+	4.06038e6i	−0.131760	+	0.181351i
$872$	4.52431e6	+	6.22718e6i	0.201494	+	0.277332i
$873$	−12013.8	+	36974.8i	−0.000533514	+	0.00164199i
$874$	458933.	+	1.41245e6i	0.0203222	+	0.0625452i
$875$		−	4.19265e7i		−	1.85127i
$876$	−1.43875e6	+	4.42803e6i	−0.0633470	+	0.194962i
$877$	3.97091e6	−	5.46549e6i	0.174338	−	0.239955i	−0.712902	−	0.701263i	$-0.752620\pi$
$877$	3.97091e6	−	5.46549e6i	0.174338	−	0.239955i	0.887240	+	0.461308i	$0.152620\pi$
$878$	1.12155e7	−	3.64415e6i	0.491003	−	0.159536i
$879$	−3.82102e6	−	1.17599e7i	−0.166804	−	0.513370i
$880$	−1.28296e6	−	416858.i	−0.0558478	−	0.0181460i
$881$	5.13531e6	−	3.73102e6i	0.222909	−	0.161953i	−0.470726	−	0.882279i	$-0.656008\pi$
$881$	5.13531e6	−	3.73102e6i	0.222909	−	0.161953i	0.693635	+	0.720327i	$0.256008\pi$
$882$	92655.4	+	30105.6i	0.00401051	+	0.00130309i
$883$		−	9.72216e6i		−	0.419625i	−0.977742	−	0.209812i	$-0.932715\pi$
$883$		−	9.72216e6i		−	0.419625i	0.977742	−	0.209812i	$-0.0672853\pi$
$884$	−1.60744e7	+	5.22290e6i	−0.691838	+	0.224792i
$885$	3.84668e7	−	1.24986e7i	1.65093	−	0.536419i
$886$		−	8.71495e6i		−	0.372976i
$887$	2.43551e7	+	7.91344e6i	1.03939	+	0.337720i	0.778498	−	0.627647i	$-0.215982\pi$
$887$	2.43551e7	+	7.91344e6i	1.03939	+	0.337720i	0.260896	+	0.965367i	$0.415982\pi$
$888$	2.87885e7	−	2.09161e7i	1.22514	−	0.890119i
$889$	−2.76155e7	−	8.97281e6i	−1.17192	−	0.380780i
$890$	7.70918e6	+	2.37264e7i	0.326237	+	1.00405i
$891$	−3.44583e6	+	1.11962e6i	−0.145412	+	0.0472471i
$892$	4.95673e6	−	6.82236e6i	0.208585	−	0.287093i
$893$	−437761.	+	1.34729e6i	−0.0183700	+	0.0565369i
$894$			2.85338e7i			1.19403i
$895$	−1.24755e7	−	3.83956e7i	−0.520595	−	1.60223i
$896$	−3.18234e6	+	9.79425e6i	−0.132427	+	0.407569i
$897$	−1.07697e7	−	1.48232e7i	−0.446911	−	0.615120i
$898$	−9.26731e6	+	1.27554e7i	−0.383498	+	0.527840i
$899$	2.87101e6	+	8.83608e6i	0.118478	+	0.364637i
$900$	98522.9	−	71581.1i	0.00405444	−	0.00294572i
$901$	2.94170e6			0.120722
$902$	4.54410e6			0.185965
$903$	1.51648e7	−	1.10178e7i	0.618894	−	0.449652i
$904$			4.37855e7i			1.78201i
$905$	4.12019e7	+	5.67096e7i	1.67223	+	2.30163i
$906$	6.96744e6	+	5.06214e6i	0.282002	+	0.204887i
$907$	−1.73640e7	−	2.38994e7i	−0.700859	−	0.964650i	−0.999946	−	0.0104237i	$-0.996682\pi$
$907$	−1.73640e7	−	2.38994e7i	−0.700859	−	0.964650i	0.299087	−	0.954226i	$-0.403318\pi$
$908$	1.56103e7	−	5.07211e6i	0.628344	−	0.204161i
$909$	−7194.93	+	9902.97i	−0.000288813	+	0.000397517i
$910$	2.77756e7	+	2.01802e7i	1.11189	+	0.807832i
$911$	−796759.	−	578879.i	−0.0318076	−	0.0231096i	0.571768	−	0.820415i	$-0.306258\pi$
$911$	−796759.	−	578879.i	−0.0318076	−	0.0231096i	−0.603575	+	0.797306i	$0.706258\pi$
$912$	−178840.	+	550413.i	−0.00711996	+	0.0219130i
$913$	5.41770e6	+	1.76032e6i	0.215099	+	0.0698898i
$914$	6.30874e6			0.249791
$915$	−3.26073e7	−	2.65251e7i	−1.28754	−	1.04738i
$916$	5.79791e6			0.228314
$917$	−2.43237e7	−	7.90325e6i	−0.955227	−	0.310372i
$918$	9.66341e6	−	2.97409e7i	0.378463	−	1.16479i
$919$	−2.06345e7	−	1.49918e7i	−0.805944	−	0.585552i	0.106708	−	0.994290i	$-0.465969\pi$
$919$	−2.06345e7	−	1.49918e7i	−0.805944	−	0.585552i	−0.912652	+	0.408738i	$0.865969\pi$
$920$	−3.40978e7	−	2.47735e7i	−1.32818	−	0.964980i
$921$	9.40475e6	−	1.29445e7i	0.365341	−	0.502848i
$922$	6.03650e6	−	1.96138e6i	0.233861	−	0.0759861i
$923$	1.93234e7	+	2.65964e7i	0.746586	+	1.02759i
$924$	2.37218e6	+	1.72349e6i	0.0914044	+	0.0664092i
$925$	3.89026e7	+	5.35448e7i	1.49494	+	2.05761i
$926$			6.64020e6i			0.254480i
$927$	−62076.5	+	45101.2i	−0.00237262	+	0.00172381i
$928$	−5.73150e6			−0.218473
$929$	1.38087e7			0.524943			0.262472	−	0.964940i	$-0.415462\pi$
$929$	1.38087e7			0.524943			0.262472	+	0.964940i	$0.415462\pi$
$930$	−3.89882e7	+	2.83266e7i	−1.47817	+	1.07396i
$931$	893535.	+	2.75002e6i	0.0337860	+	0.103983i
$932$	2.10276e6	−	2.89420e6i	0.0792957	−	0.109141i
$933$	−1.44978e7	−	1.99545e7i	−0.545252	−	0.750475i
$934$	−2.50647e6	+	7.71413e6i	−0.0940147	+	0.289347i
$935$	3.68917e6	+	1.13541e7i	0.138006	+	0.424740i
$936$			128424.i			0.00479135i
$937$	−9.04629e6	+	2.78416e7i	−0.336606	+	1.03597i	0.629320	+	0.777147i	$0.283334\pi$
$937$	−9.04629e6	+	2.78416e7i	−0.336606	+	1.03597i	−0.965926	+	0.258820i	$0.916666\pi$
$938$	−4.39271e6	+	6.04604e6i	−0.163014	+	0.224370i
$939$	3.19162e7	−	1.03702e7i	1.18126	−	0.383816i
$940$	−4.19714e6	−	1.29175e7i	−0.154929	−	0.476823i
$941$	3.74042e7	+	1.21534e7i	1.37704	+	0.447427i	0.901695	−	0.432373i	$-0.142324\pi$
$941$	3.74042e7	+	1.21534e7i	1.37704	+	0.447427i	0.475344	+	0.879800i	$0.342324\pi$
$942$	2.19825e7	−	1.59712e7i	0.807143	−	0.586424i
$943$	4.18887e7	+	1.36105e7i	1.53397	+	0.498418i
$944$			6.57104e6i			0.239996i
$945$	6.29326e7	−	2.04480e7i	2.29243	−	0.744856i
$946$	1.49618e6	−	486138.i	0.0543570	−	0.0176617i
$947$		−	6.07047e6i		−	0.219962i	−0.993934	−	0.109981i	$-0.964921\pi$
$947$		−	6.07047e6i		−	0.219962i	0.993934	−	0.109981i	$-0.0350790\pi$
$948$	−6.02231e6	−	1.95677e6i	−0.217642	−	0.0707161i
$949$	7.38801e6	−	5.36770e6i	0.266294	−	0.193474i
$950$	−3.29994e6	−	1.07222e6i	−0.118631	−	0.0385455i
$951$	−634838.	−	1.95383e6i	−0.0227621	−	0.0700545i
$952$	−7.08479e7	+	2.30199e7i	−2.53358	+	0.823210i
$953$	3.20952e7	−	4.41753e7i	1.14474	−	1.57561i	0.388319	−	0.921525i	$-0.373056\pi$
$953$	3.20952e7	−	4.41753e7i	1.14474	−	1.57561i	0.756425	−	0.654080i	$-0.226944\pi$
$954$	2333.53	−	7181.85i	8.30121e−5	−	0.000255485i
$955$			5.37672e7i			1.90769i
$956$	225942.	+	695378.i	0.00799563	+	0.0246080i
$957$	−327197.	+	1.00701e6i	−0.0115486	+	0.0355429i
$958$	−1.92571e7	−	2.65051e7i	−0.677918	−	0.933074i
$959$	2.19283e7	−	3.01817e7i	0.769942	−	1.05973i
$960$	−1.25477e7	−	3.86178e7i	−0.439426	−	1.35241i
$961$	3.41456e7	−	2.48083e7i	1.19269	−	0.866538i
$962$	−2.35798e7			−0.821492
$963$	174477.			0.00606280
$964$	−1.71791e7	+	1.24814e7i	−0.595399	+	0.432583i
$965$		−	1.19568e7i		−	0.413330i
$966$	−1.60364e7	−	2.20722e7i	−0.552922	−	0.761032i
$967$	−2.67680e7	−	1.94481e7i	−0.920556	−	0.668823i	0.0231060	−	0.999733i	$-0.492644\pi$
$967$	−2.67680e7	−	1.94481e7i	−0.920556	−	0.668823i	−0.943662	+	0.330910i	$0.892644\pi$
$968$	−1.76831e7	−	2.43387e7i	−0.606556	−	0.834852i
$969$	4.87111e6	−	1.58272e6i	0.166655	−	0.0541496i
$970$	−6.24243e6	+	8.59197e6i	−0.213022	+	0.293200i
$971$	−9.08170e6	−	6.59824e6i	−0.309114	−	0.224585i	0.422402	−	0.906409i	$-0.361187\pi$
$971$	−9.08170e6	−	6.59824e6i	−0.309114	−	0.224585i	−0.731516	+	0.681824i	$0.761187\pi$
$972$	134931.	+	98033.2i	0.00458086	+	0.00332819i
$973$	−1.50141e7	+	4.62087e7i	−0.508414	+	1.56474i
$974$	6.17776e6	+	2.00727e6i	0.208657	+	0.0677968i
$975$	4.28072e7			1.44213
$976$	5.73544e6	−	3.70654e6i	0.192727	−	0.124550i
$977$	−3.60700e7			−1.20895			−0.604477	−	0.796623i	$-0.706618\pi$
$977$	−3.60700e7			−1.20895			−0.604477	+	0.796623i	$0.706618\pi$
$978$	−3.92404e6	−	1.27500e6i	−0.131186	−	0.0426248i
$979$	1.29139e6	−	3.97449e6i	0.0430627	−	0.132533i
$980$	−2.24286e7	−	1.62954e7i	−0.745998	−	0.541999i
$981$	−43887.8	−	31886.3i	−0.00145603	−	0.00105787i
$982$	7.94849e6	−	1.09402e7i	0.263030	−	0.362030i
$983$	868604.	−	282226.i	0.0286707	−	0.00931566i	−0.294647	−	0.955606i	$-0.595202\pi$
$983$	868604.	−	282226.i	0.0286707	−	0.00931566i	0.323317	+	0.946291i	$0.395202\pi$
$984$	3.25196e7	+	4.47594e7i	1.07067	+	1.47366i
$985$	−2.89585e7	−	2.10396e7i	−0.951011	−	0.690950i
$986$	−5.34183e6	−	7.35240e6i	−0.174984	−	0.240845i
$987$		−	2.60241e7i		−	0.850322i
$988$	−1.04180e6	+	756910.i	−0.0339540	+	0.0246690i
$989$	1.52483e7			0.495712
$990$	30646.3			0.000993780
$991$	−4.26030e7	+	3.09529e7i	−1.37802	+	1.00119i	−0.380960	+	0.924592i	$0.624406\pi$
$991$	−4.26030e7	+	3.09529e7i	−1.37802	+	1.00119i	−0.997062	+	0.0765996i	$0.975594\pi$
$992$	1.35036e7	+	4.15597e7i	0.435682	+	1.34089i
$993$	−3.39549e7	+	4.67349e7i	−1.09277	+	1.50407i
$994$	2.87733e7	+	3.96030e7i	0.923683	+	1.27134i
$995$	1.99438e7	−	6.13806e7i	0.638631	−	1.96550i
$996$	7.24074e6	+	2.22847e7i	0.231278	+	0.711801i
$997$		−	7.57897e6i		−	0.241475i	−0.992684	−	0.120738i	$-0.961474\pi$
$997$		−	7.57897e6i		−	0.241475i	0.992684	−	0.120738i	$-0.0385260\pi$
$998$	3.90437e6	−	1.20164e7i	0.124086	−	0.381899i
$999$	−2.67130e7	+	3.67673e7i	−0.846856	+	1.16560i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.6.g.a.3.17	✓	104
61.41	even	10	inner	61.6.g.a.41.17	yes	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.6.g.a.3.17	✓	104	1.1	even	1	trivial
61.6.g.a.41.17	yes	104	61.41	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	61.g (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.76517 + 1.22338i) q^{2} +(-4.80371 + 14.7843i) q^{3} +(-13.2087 - 9.59666i) q^{4} +(75.2721 + 54.6884i) q^{5} +(-36.1736 + 49.7887i) q^{6} +(-178.072 + 57.8590i) q^{7} +(-112.457 - 154.783i) q^{8} +(1.09088 + 0.792570i) q^{9} +O(q^{10})\)	\(q+(3.76517 + 1.22338i) q^{2} +(-4.80371 + 14.7843i) q^{3} +(-13.2087 - 9.59666i) q^{4} +(75.2721 + 54.6884i) q^{5} +(-36.1736 + 49.7887i) q^{6} +(-178.072 + 57.8590i) q^{7} +(-112.457 - 154.783i) q^{8} +(1.09088 + 0.792570i) q^{9} +(216.508 + 297.998i) q^{10} -61.7027i q^{11} +(205.331 - 149.182i) q^{12} -497.808 q^{13} -741.254 q^{14} +(-1170.12 + 850.139i) q^{15} +(-72.6119 - 223.476i) q^{16} +(-1222.32 + 1682.38i) q^{17} +(3.13773 + 4.31872i) q^{18} +(-48.9603 + 150.684i) q^{19} +(-469.419 - 1444.72i) q^{20} -2910.61i q^{21} +(75.4858 - 232.321i) q^{22} +(1391.70 - 1915.51i) q^{23} +(2828.58 - 919.060i) q^{24} +(1709.39 + 5260.97i) q^{25} +(-1874.33 - 609.008i) q^{26} +(-3073.00 + 2232.66i) q^{27} +(2907.34 + 944.653i) q^{28} +1103.89i q^{29} +(-5445.73 + 1769.43i) q^{30} +(8004.45 - 2600.80i) q^{31} +5192.07i q^{32} +(912.233 + 296.402i) q^{33} +(-6660.42 + 4839.08i) q^{34} +(-16568.0 - 5383.28i) q^{35} +(-6.80303 - 20.9376i) q^{36} +(11379.1 - 3697.28i) q^{37} +(-368.688 + 507.456i) q^{38} +(2391.33 - 7359.76i) q^{39} -17801.0i q^{40} +(5748.40 + 17691.8i) q^{41} +(3560.77 - 10958.9i) q^{42} +(3785.41 + 5210.17i) q^{43} +(-592.140 + 815.011i) q^{44} +(38.7684 + 119.317i) q^{45} +(7583.37 - 5509.64i) q^{46} +8941.14 q^{47} +3652.75 q^{48} +(14764.7 - 10727.2i) q^{49} +21899.7i q^{50} +(-19001.1 - 26152.8i) q^{51} +(6575.39 + 4777.30i) q^{52} +(-831.480 - 1144.43i) q^{53} +(-14301.8 + 4646.92i) q^{54} +(3374.42 - 4644.50i) q^{55} +(28981.0 + 21055.9i) q^{56} +(-1992.57 - 1447.69i) q^{57} +(-1350.48 + 4156.35i) q^{58} +(-26595.9 - 8641.54i) q^{59} +23614.2 q^{60} +(7459.36 + 28088.3i) q^{61} +33319.9 q^{62} +(-240.112 - 78.0171i) q^{63} +(-8675.45 + 26700.3i) q^{64} +(-37471.1 - 27224.3i) q^{65} +(3072.10 + 2232.01i) q^{66} +(5926.05 - 8156.51i) q^{67} +(32290.4 - 10491.8i) q^{68} +(21634.1 + 29776.8i) q^{69} +(-55795.8 - 40538.0i) q^{70} +(-38817.0 - 53427.0i) q^{71} -257.980i q^{72} +(-14841.1 + 10782.7i) q^{73} +47367.3 q^{74} -85991.3 q^{75} +(2092.77 - 1520.48i) q^{76} +(3570.06 + 10987.5i) q^{77} +(18007.5 - 24785.3i) q^{78} +(-14664.9 - 20184.5i) q^{79} +(6755.91 - 20792.6i) q^{80} +(-18145.3 - 55845.6i) q^{81} +73645.0i q^{82} +(-28529.0 + 87803.2i) q^{83} +(-27932.1 + 38445.2i) q^{84} +(-184013. + 59789.4i) q^{85} +(7878.71 + 24248.2i) q^{86} +(-16320.3 - 5302.80i) q^{87} +(-9550.56 + 6938.89i) q^{88} +(64413.5 + 20929.2i) q^{89} +496.677i q^{90} +(88645.6 - 28802.7i) q^{91} +(-36764.9 + 11945.7i) q^{92} +130834. i q^{93} +(33664.9 + 10938.4i) q^{94} +(-11926.0 + 8664.77i) q^{95} +(-76761.2 - 24941.2i) q^{96} +(8909.69 + 27421.2i) q^{97} +(68715.1 - 22326.9i) q^{98} +(48.9037 - 67.3102i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9}+O(q^{10}) \) 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9	\( 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9} - 595 q^{10} + 1982 q^{12} + 2372 q^{13} - 4474 q^{14} - 1149 q^{15} - 8631 q^{16} + 950 q^{17} + 4340 q^{18} - 5597 q^{19} - 6627 q^{20} - 8639 q^{22} + 9065 q^{23} + 17220 q^{24} - 7694 q^{25} + 14810 q^{26} + 4500 q^{27} + 19835 q^{28} - 44585 q^{30} + 10905 q^{31} - 19205 q^{33} - 15376 q^{34} - 43790 q^{35} - 25135 q^{36} - 5 q^{37} + 17555 q^{38} + 29401 q^{39} - 21014 q^{41} + 62197 q^{42} - 31625 q^{43} + 146190 q^{44} + 153742 q^{45} + 13387 q^{46} + 27326 q^{47} - 82968 q^{48} + 14694 q^{49} + 34090 q^{51} + 90072 q^{52} - 40270 q^{53} - 13760 q^{54} + 25140 q^{55} - 97860 q^{56} + 114893 q^{57} - 18003 q^{58} - 117435 q^{59} - 536650 q^{60} - 121867 q^{61} - 157388 q^{62} - 160825 q^{63} + 132509 q^{64} - 155852 q^{65} + 308443 q^{66} + 101665 q^{67} + 303780 q^{68} + 281945 q^{69} + 264985 q^{70} + 160970 q^{71} + 127669 q^{73} - 133952 q^{74} - 139592 q^{75} - 641111 q^{76} + 128917 q^{77} + 1670 q^{78} + 187940 q^{79} + 785373 q^{80} - 453473 q^{81} - 301209 q^{83} + 100475 q^{84} - 340045 q^{85} - 462669 q^{86} + 189245 q^{87} - 881635 q^{88} - 201970 q^{89} + 93865 q^{91} - 622085 q^{92} - 285265 q^{94} - 113308 q^{95} + 1215465 q^{96} - 342131 q^{97} - 616150 q^{98} + 714235 q^{99}+O(q^{100}) \) 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9 - 595 * q^10 + 1982 * q^12 + 2372 * q^13 - 4474 * q^14 - 1149 * q^15 - 8631 * q^16 + 950 * q^17 + 4340 * q^18 - 5597 * q^19 - 6627 * q^20 - 8639 * q^22 + 9065 * q^23 + 17220 * q^24 - 7694 * q^25 + 14810 * q^26 + 4500 * q^27 + 19835 * q^28 - 44585 * q^30 + 10905 * q^31 - 19205 * q^33 - 15376 * q^34 - 43790 * q^35 - 25135 * q^36 - 5 * q^37 + 17555 * q^38 + 29401 * q^39 - 21014 * q^41 + 62197 * q^42 - 31625 * q^43 + 146190 * q^44 + 153742 * q^45 + 13387 * q^46 + 27326 * q^47 - 82968 * q^48 + 14694 * q^49 + 34090 * q^51 + 90072 * q^52 - 40270 * q^53 - 13760 * q^54 + 25140 * q^55 - 97860 * q^56 + 114893 * q^57 - 18003 * q^58 - 117435 * q^59 - 536650 * q^60 - 121867 * q^61 - 157388 * q^62 - 160825 * q^63 + 132509 * q^64 - 155852 * q^65 + 308443 * q^66 + 101665 * q^67 + 303780 * q^68 + 281945 * q^69 + 264985 * q^70 + 160970 * q^71 + 127669 * q^73 - 133952 * q^74 - 139592 * q^75 - 641111 * q^76 + 128917 * q^77 + 1670 * q^78 + 187940 * q^79 + 785373 * q^80 - 453473 * q^81 - 301209 * q^83 + 100475 * q^84 - 340045 * q^85 - 462669 * q^86 + 189245 * q^87 - 881635 * q^88 - 201970 * q^89 + 93865 * q^91 - 622085 * q^92 - 285265 * q^94 - 113308 * q^95 + 1215465 * q^96 - 342131 * q^97 - 616150 * q^98 + 714235 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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