LMFDB - Embedded newform 22.7.d.a.17.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [22,7,Mod(7,22)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("22.7"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(22, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	22.d (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.06118983964$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			17.2
Character	$\chi$	$=$	22.17
Dual form			22.7.d.a.13.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.37999 + 1.74806i) q^{2} +(0.0235888 + 0.0171383i) q^{3} +(25.8885 - 18.8091i) q^{4} +(-27.6593 + 85.1266i) q^{5} +(-0.156866 - 0.0509689i) q^{6} +(-308.398 - 424.474i) q^{7} +(-106.400 + 146.448i) q^{8} +(-225.273 - 693.319i) q^{9} -506.330i q^{10} +(59.6730 - 1329.66i) q^{11} +0.933035 q^{12} +(-3288.96 + 1068.65i) q^{13} +(2401.19 + 1744.56i) q^{14} +(-2.11137 + 1.53400i) q^{15} +(316.433 - 973.882i) q^{16} +(4097.66 + 1331.41i) q^{17} +(2423.93 + 3336.26i) q^{18} +(-713.540 + 982.104i) q^{19} +(885.098 + 2724.05i) q^{20} -15.2982i q^{21} +(2003.29 + 7257.88i) q^{22} -5453.35 q^{23} +(-5.01972 + 1.63100i) q^{24} +(6159.39 + 4475.06i) q^{25} +(15826.5 - 11498.6i) q^{26} +(13.1367 - 40.4307i) q^{27} +(-15968.0 - 5188.31i) q^{28} +(-25717.5 - 35397.1i) q^{29} +(8.67762 - 11.9437i) q^{30} +(7047.50 + 21690.0i) q^{31} +5792.62i q^{32} +(24.1957 - 30.3424i) q^{33} -24372.8 q^{34} +(44664.1 - 14512.3i) q^{35} +(-18872.7 - 13711.8i) q^{36} +(-27038.8 + 19644.8i) q^{37} +(2122.06 - 6531.02i) q^{38} +(-95.8972 - 31.1589i) q^{39} +(-9523.63 - 13108.2i) q^{40} +(-16920.8 + 23289.5i) q^{41} +(26.7423 + 82.3043i) q^{42} -68945.6i q^{43} +(-23464.9 - 35545.4i) q^{44} +65250.8 q^{45} +(29339.0 - 9532.80i) q^{46} +(109540. + 79585.2i) q^{47} +(24.1549 - 17.5496i) q^{48} +(-48713.0 + 149923. i) q^{49} +(-40960.1 - 13308.7i) q^{50} +(73.8408 + 101.633i) q^{51} +(-65046.0 + 89528.1i) q^{52} +(-9195.10 - 28299.6i) q^{53} +240.481i q^{54} +(111539. + 41857.3i) q^{55} +94977.0 q^{56} +(-33.6631 + 10.9378i) q^{57} +(200236. + 145480. i) q^{58} +(158898. - 115446. i) q^{59} +(-25.8071 + 79.4261i) q^{60} +(-331837. - 107821. i) q^{61} +(-75831.0 - 104372. i) q^{62} +(-224822. + 309441. i) q^{63} +(-10125.9 - 31164.2i) q^{64} -309536. i q^{65} +(-77.1321 + 205.537i) q^{66} -207777. q^{67} +(131125. - 42605.2i) q^{68} +(-128.638 - 93.4609i) q^{69} +(-214924. + 156151. i) q^{70} +(215284. - 662575. i) q^{71} +(125504. + 40778.8i) q^{72} +(-218584. - 300855. i) q^{73} +(111128. - 152954. i) q^{74} +(68.5978 + 211.122i) q^{75} +38846.3i q^{76} +(-582810. + 384736. i) q^{77} +570.394 q^{78} +(495869. - 161118. i) q^{79} +(74150.9 + 53873.8i) q^{80} +(-429943. + 312372. i) q^{81} +(50322.1 - 154876. i) q^{82} +(360535. + 117145. i) q^{83} +(-287.746 - 396.049i) q^{84} +(-226677. + 311994. i) q^{85} +(120521. + 370926. i) q^{86} -1275.73i q^{87} +(188377. + 150216. i) q^{88} +801254. q^{89} +(-351049. + 114063. i) q^{90} +(1.46792e6 + 1.06651e6i) q^{91} +(-141179. + 102573. i) q^{92} +(-205.486 + 632.422i) q^{93} +(-728442. - 236685. i) q^{94} +(-63867.2 - 87905.6i) q^{95} +(-99.2754 + 136.641i) q^{96} +(44176.6 + 135962. i) q^{97} -891739. i q^{98} +(-935323. + 258165. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 52 q^{3} + 192 q^{4} - 368 q^{5} + 400 q^{6} + 720 q^{7} - 3814 q^{9} + 4366 q^{11} + 3456 q^{12} + 3600 q^{13} - 4288 q^{14} - 2148 q^{15} - 6144 q^{16} - 5880 q^{17} + 18400 q^{18} - 23850 q^{19}+ \cdots + 4890070 q^{99}+O(q^{100}) $ 24 * q + 52 * q^3 + 192 * q^4 - 368 * q^5 + 400 * q^6 + 720 * q^7 - 3814 * q^9 + 4366 * q^11 + 3456 * q^12 + 3600 * q^13 - 4288 * q^14 - 2148 * q^15 - 6144 * q^16 - 5880 * q^17 + 18400 * q^18 - 23850 * q^19 + 11776 * q^20 - 1056 * q^22 - 40096 * q^23 + 12800 * q^24 + 69978 * q^25 + 52224 * q^26 + 4222 * q^27 - 32640 * q^28 - 204800 * q^29 - 134160 * q^30 + 71568 * q^31 + 11242 * q^33 + 88896 * q^34 + 469520 * q^35 + 25728 * q^36 + 309120 * q^37 - 73392 * q^38 - 328640 * q^39 - 107520 * q^40 - 541660 * q^41 - 177760 * q^42 + 213888 * q^44 + 811664 * q^45 + 213120 * q^46 - 299820 * q^47 + 53248 * q^48 - 374658 * q^49 - 364480 * q^50 - 1347330 * q^51 - 291840 * q^52 + 612820 * q^53 + 440004 * q^55 + 70656 * q^56 + 1416050 * q^57 + 552576 * q^58 + 927550 * q^59 + 206336 * q^60 - 1184160 * q^61 - 226640 * q^62 - 921200 * q^63 + 196608 * q^64 + 128672 * q^66 - 515100 * q^67 - 188160 * q^68 + 957220 * q^69 + 207984 * q^70 + 217572 * q^71 - 896000 * q^72 - 590340 * q^73 - 610400 * q^74 - 2208402 * q^75 - 2221964 * q^77 + 3228512 * q^78 + 93240 * q^79 + 196608 * q^80 + 1034076 * q^81 + 312960 * q^82 + 4588350 * q^83 + 2357760 * q^84 + 4132920 * q^85 + 1057632 * q^86 - 772608 * q^88 - 4638852 * q^89 - 6535040 * q^90 - 3916044 * q^91 - 2350208 * q^92 - 556628 * q^93 - 2410800 * q^94 + 661320 * q^95 - 342342 * q^97 + 4890070 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−5.37999	+	1.74806i	−0.672499	+	0.218508i
$2$	−5.37999	+	1.74806i	−0.672499	+	0.218508i
$3$	0.0235888	+	0.0171383i	0.000873659	+	0.000634750i	0.588222	−	0.808700i	$-0.299828\pi$
$3$	0.0235888	+	0.0171383i	0.000873659	+	0.000634750i	−0.587348	+	0.809334i	$0.699828\pi$
$4$	25.8885	−	18.8091i	0.404508	−	0.293893i
$5$	−27.6593	+	85.1266i	−0.221275	+	0.681013i	0.777374	+	0.629039i	$0.216551\pi$
$5$	−27.6593	+	85.1266i	−0.221275	+	0.681013i	−0.998648	+	0.0519742i	$0.983449\pi$
$6$	−0.156866	−	0.0509689i	−0.000726232	−	0.000235967i
$7$	−308.398	−	424.474i	−0.899121	−	1.23753i	−0.970748	−	0.240102i	$-0.922819\pi$
$7$	−308.398	−	424.474i	−0.899121	−	1.23753i	0.0716272	−	0.997431i	$-0.477181\pi$
$8$	−106.400	+	146.448i	−0.207813	+	0.286031i
$9$	−225.273	−	693.319i	−0.309017	−	0.951055i
$10$		−	506.330i		−	0.506330i
$11$	59.6730	−	1329.66i	0.0448332	−	0.998994i
$11$	59.6730	−	1329.66i	0.0448332	−	0.998994i
$12$	0.933035			0.000539951
$13$	−3288.96	+	1068.65i	−1.49702	+	0.486412i	−0.939148	−	0.343514i	$-0.888383\pi$
$13$	−3288.96	+	1068.65i	−1.49702	+	0.486412i	−0.557874	+	0.829926i	$0.688383\pi$
$14$	2401.19	+	1744.56i	0.875068	+	0.635774i
$15$	−2.11137	+	1.53400i	−0.000625592	+	0.000454519i
$16$	316.433	−	973.882i	0.0772542	−	0.237764i
$17$	4097.66	+	1331.41i	0.834045	+	0.270998i	0.694748	−	0.719253i	$-0.255516\pi$
$17$	4097.66	+	1331.41i	0.834045	+	0.270998i	0.139297	+	0.990251i	$0.455516\pi$
$18$	2423.93	+	3336.26i	0.415626	+	0.572061i
$19$	−713.540	+	982.104i	−0.104030	+	0.143185i	−0.857858	−	0.513887i	$-0.828205\pi$
$19$	−713.540	+	982.104i	−0.104030	+	0.143185i	0.753828	+	0.657072i	$0.228205\pi$
$20$	885.098	+	2724.05i	0.110637	+	0.340506i
$21$		−	15.2982i		−	0.00165190i
$22$	2003.29	+	7257.88i	0.188138	+	0.681619i
$23$	−5453.35			−0.448208			−0.224104	−	0.974565i	$-0.571946\pi$
$23$	−5453.35			−0.448208			−0.224104	+	0.974565i	$0.571946\pi$
$24$	−5.01972	+	1.63100i	−0.000363116	+	0.000117984i
$25$	6159.39	+	4475.06i	0.394201	+	0.286404i
$26$	15826.5	−	11498.6i	0.900460	−	0.654223i
$27$	13.1367	−	40.4307i	0.000667415	−	0.00205409i
$28$	−15968.0	−	5188.31i	−0.727404	−	0.236348i
$29$	−25717.5	−	35397.1i	−1.05447	−	1.45135i	−0.884868	−	0.465842i	$-0.845752\pi$
$29$	−25717.5	−	35397.1i	−1.05447	−	1.45135i	−0.169603	−	0.985512i	$-0.554248\pi$
$30$	8.67762	−	11.9437i	0.000321393	−	0.000442360i
$31$	7047.50	+	21690.0i	0.236565	+	0.728072i	0.996910	+	0.0785525i	$0.0250298\pi$
$31$	7047.50	+	21690.0i	0.236565	+	0.728072i	−0.760345	+	0.649519i	$0.774970\pi$
$32$			5792.62i			0.176777i
$33$	24.1957	−	30.3424i	0.000673281	−	0.000844322i
$34$	−24372.8			−0.620109
$35$	44664.1	−	14512.3i	1.04173	−	0.338478i
$36$	−18872.7	−	13711.8i	−0.404508	−	0.293892i
$37$	−27038.8	+	19644.8i	−0.533804	+	0.387831i	−0.821779	−	0.569807i	$-0.807018\pi$
$37$	−27038.8	+	19644.8i	−0.533804	+	0.387831i	0.287975	+	0.957638i	$0.407018\pi$
$38$	2122.06	−	6531.02i	0.0386729	−	0.119023i
$39$	−95.8972	−	31.1589i	−0.00161664	−	0.000525277i
$40$	−9523.63	−	13108.2i	−0.148807	−	0.204815i
$41$	−16920.8	+	23289.5i	−0.245510	+	0.337915i	−0.913932	−	0.405866i	$-0.866970\pi$
$41$	−16920.8	+	23289.5i	−0.245510	+	0.337915i	0.668423	+	0.743782i	$0.266970\pi$
$42$	26.7423	+	82.3043i	0.000360953	+	0.00111090i
$43$		−	68945.6i		−	0.867163i	−0.901114	−	0.433582i	$-0.857250\pi$
$43$		−	68945.6i		−	0.867163i	0.901114	−	0.433582i	$-0.142750\pi$
$44$	−23464.9	−	35545.4i	−0.275462	−	0.417278i
$45$	65250.8			0.716059
$46$	29339.0	−	9532.80i	0.301419	−	0.0979371i
$47$	109540.	+	79585.2i	1.05506	+	0.766547i	0.973168	−	0.230094i	$-0.0739035\pi$
$47$	109540.	+	79585.2i	1.05506	+	0.766547i	0.0818929	+	0.996641i	$0.473903\pi$
$48$	24.1549	−	17.5496i	0.000218415	−	0.000158688i
$49$	−48713.0	+	149923.i	−0.414054	+	1.27433i
$50$	−40960.1	−	13308.7i	−0.327681	−	0.106470i
$51$	73.8408	+	101.633i	0.000556655	+	0.000766170i
$52$	−65046.0	+	89528.1i	−0.462605	+	0.636721i
$53$	−9195.10	−	28299.6i	−0.0617631	−	0.190087i	0.915414	−	0.402514i	$-0.131863\pi$
$53$	−9195.10	−	28299.6i	−0.0617631	−	0.190087i	−0.977177	+	0.212426i	$0.931863\pi$
$54$			240.481i			0.00152721i
$55$	111539.	+	41857.3i	0.670408	+	0.251584i
$56$	94977.0			0.540822
$57$	−33.6631	+	10.9378i	−0.000181773	+	5.90617e-5i
$58$	200236.	+	145480.i	1.02626	+	0.745623i
$59$	158898.	−	115446.i	0.773680	−	0.562111i	−0.129396	−	0.991593i	$-0.541304\pi$
$59$	158898.	−	115446.i	0.773680	−	0.562111i	0.903076	+	0.429482i	$0.141304\pi$
$60$	−25.8071	+	79.4261i	−0.000119477	+	0.000367713i
$61$	−331837.	−	107821.i	−1.46196	−	0.475020i	−0.533293	−	0.845931i	$-0.679046\pi$
$61$	−331837.	−	107821.i	−1.46196	−	0.475020i	−0.928669	+	0.370911i	$0.879046\pi$
$62$	−75831.0	−	104372.i	−0.318179	−	0.437936i
$63$	−224822.	+	309441.i	−0.899120	+	1.23753i
$64$	−10125.9	−	31164.2i	−0.0386271	−	0.118882i
$65$		−	309536.i		−	1.12712i
$66$	−77.1321	+	205.537i	−0.000268289	+	0.000714923i
$67$	−207777.			−0.690834			−0.345417	−	0.938449i	$-0.612263\pi$
$67$	−207777.			−0.690834			−0.345417	+	0.938449i	$0.612263\pi$
$68$	131125.	−	42605.2i	0.417023	−	0.135499i
$69$	−128.638	−	93.4609i	−0.000391581	−	0.000284500i
$70$	−214924.	+	156151.i	−0.626601	+	0.455252i
$71$	215284.	−	662575.i	0.601501	−	1.85123i	0.0822419	−	0.996612i	$-0.473792\pi$
$71$	215284.	−	662575.i	0.601501	−	1.85123i	0.519259	−	0.854617i	$-0.326208\pi$
$72$	125504.	+	40778.8i	0.336249	+	0.109254i
$73$	−218584.	−	300855.i	−0.561888	−	0.773373i	0.429677	−	0.902983i	$-0.358628\pi$
$73$	−218584.	−	300855.i	−0.561888	−	0.773373i	−0.991565	+	0.129610i	$0.958628\pi$
$74$	111128.	−	152954.i	0.274238	−	0.377456i
$75$	68.5978	+	211.122i	0.000162602	+	0.000500438i
$76$			38846.3i			0.0884930i
$77$	−582810.	+	384736.i	−1.27660	+	0.842734i
$78$	570.394			0.00120196
$79$	495869.	−	161118.i	1.00574	−	0.326785i	0.240583	−	0.970629i	$-0.422661\pi$
$79$	495869.	−	161118.i	1.00574	−	0.326785i	0.765157	+	0.643844i	$0.222661\pi$
$80$	74150.9	+	53873.8i	0.144826	+	0.105222i
$81$	−429943.	+	312372.i	−0.809014	+	0.587783i
$82$	50322.1	−	154876.i	0.0912678	−	0.280893i
$83$	360535.	+	117145.i	0.630540	+	0.204875i	0.606814	−	0.794844i	$-0.292447\pi$
$83$	360535.	+	117145.i	0.630540	+	0.204875i	0.0237256	+	0.999719i	$0.492447\pi$
$84$	−287.746	−	396.049i	−0.000485481	−	0.000668207i
$85$	−226677.	+	311994.i	−0.369106	+	0.508031i
$86$	120521.	+	370926.i	0.189482	+	0.583166i
$87$		−	1275.73i		−	0.00193731i
$88$	188377.	+	150216.i	0.276426	+	0.220428i
$89$	801254.			1.13658			0.568290	−	0.822828i	$-0.307605\pi$
$89$	801254.			1.13658			0.568290	+	0.822828i	$0.307605\pi$
$90$	−351049.	+	114063.i	−0.481548	+	0.156465i
$91$	1.46792e6	+	1.06651e6i	1.94795	+	1.41527i
$92$	−141179.	+	102573.i	−0.181304	+	0.131725i
$93$	−205.486	+	632.422i	−0.000255467	+	0.000786246i
$94$	−728442.	−	236685.i	−0.877024	−	0.284962i
$95$	−63867.2	−	87905.6i	−0.0744915	−	0.102529i
$96$	−99.2754	+	136.641i	−0.000112209	+	0.000154442i
$97$	44176.6	+	135962.i	0.0484036	+	0.148971i	0.972337	−	0.233582i	$-0.0750449\pi$
$97$	44176.6	+	135962.i	0.0484036	+	0.148971i	−0.923933	+	0.382553i	$0.875045\pi$
$98$		−	891739.i		−	0.947457i
$99$	−935323.	+	258165.i	−0.963953	+	0.266067i
$100$	243629.			0.243629
$101$	266849.	−	86704.4i	0.259001	−	0.0841544i	−0.176638	−	0.984276i	$-0.556522\pi$
$101$	266849.	−	86704.4i	0.259001	−	0.0841544i	0.435639	+	0.900121i	$0.356522\pi$
$102$	−574.924	−	417.707i	−0.000541764	−	0.000393615i
$103$	−141703.	+	102953.i	−0.129678	+	0.0942168i	−0.650734	−	0.759306i	$-0.725539\pi$
$103$	−141703.	+	102953.i	−0.129678	+	0.0942168i	0.521055	+	0.853523i	$0.325539\pi$
$104$	193446.	−	595365.i	0.171973	−	0.529277i
$105$	1302.29	+	423.139i	0.00112496	+	0.000365523i
$106$	98939.0	+	136178.i	0.0830711	+	0.114338i
$107$	−166133.	+	228662.i	−0.135614	+	0.186656i	−0.871423	−	0.490533i	$-0.836802\pi$
$107$	−166133.	+	228662.i	−0.135614	+	0.186656i	0.735809	+	0.677189i	$0.236802\pi$
$108$	−420.376	−	1293.78i	−0.000333708	−	0.00102705i
$109$		−	2.30355e6i		−	1.77877i	−0.457163	−	0.889383i	$-0.651135\pi$
$109$		−	2.30355e6i		−	1.77877i	0.457163	−	0.889383i	$-0.348865\pi$
$110$	−673248.	−	30214.3i	−0.505821	−	0.0227004i
$111$	−974.490			−0.000712538
$112$	−510975.	+	166026.i	−0.363702	+	0.118174i
$113$	150407.	+	109277.i	0.104239	+	0.0757343i	0.638684	−	0.769469i	$-0.279479\pi$
$113$	150407.	+	109277.i	0.104239	+	0.0757343i	−0.534445	+	0.845204i	$0.679479\pi$
$114$	161.987	−	117.691i	0.000109337	−	7.94377e-5i
$115$	150836.	−	464225.i	0.0991771	−	0.305236i
$116$	−1.33158e6	−	432655.i	−0.853085	−	0.277184i
$117$	1.48183e6	+	2.03956e6i	0.925209	+	1.27344i
$118$	−653060.	+	898861.i	−0.397473	+	0.547074i
$119$	−698563.	−	2.14996e6i	−0.414539	−	1.27582i
$120$		−	472.424i		−	0.000273394i
$121$	−1.76444e6	−	158690.i	−0.995980	−	0.0895763i
$122$	1.97376e6			1.08696
$123$	−798.281	+	259.377i	−0.000428984	+	0.000139385i
$124$	590419.	+	428965.i	0.309667	+	0.224987i
$125$	−1.68276e6	+	1.22260e6i	−0.861575	+	0.625971i
$126$	668617.	−	2.05779e6i	0.334246	−	1.02870i
$127$	389288.	+	126487.i	0.190046	+	0.0617498i	0.402494	−	0.915423i	$-0.368143\pi$
$127$	389288.	+	126487.i	0.190046	+	0.0617498i	−0.212448	+	0.977172i	$0.568143\pi$
$128$	108954.	+	149962.i	0.0519534	+	0.0715077i
$129$	1181.61	−	1626.34i	0.000550432	−	0.000757605i
$130$	541088.	+	1.66530e6i	0.246285	+	0.757988i
$131$			189516.i			0.0843011i	0.999111	+	0.0421505i	$0.0134209\pi$
$131$			189516.i			0.0843011i	−0.999111	+	0.0421505i	$0.986579\pi$
$132$	55.6770	−	1240.62i	2.42077e−5	−	0.000539408i
$133$	636932.			0.270731
$134$	1.11784e6	−	363208.i	0.464585	−	0.150953i
$135$	3078.38	+	2236.57i	0.00125118	+	0.000909037i
$136$	−630976.	+	458431.i	−0.250839	+	0.182246i
$137$	112848.	−	347309.i	0.0438865	−	0.135069i	−0.926712	−	0.375771i	$-0.877378\pi$
$137$	112848.	−	347309.i	0.0438865	−	0.135069i	0.970599	+	0.240703i	$0.0773778\pi$
$138$	855.446	+	277.951i	0.000325503	+	0.000105762i
$139$	−2.77563e6	−	3.82033e6i	−1.03352	−	1.42251i	−0.902274	−	0.431163i	$-0.858104\pi$
$139$	−2.77563e6	−	3.82033e6i	−1.03352	−	1.42251i	−0.131242	−	0.991350i	$-0.541896\pi$
$140$	883326.	−	1.21579e6i	0.321912	−	0.443074i
$141$	1219.96	+	3754.64i	0.000435198	+	0.00133940i
$142$			3.94098e6i			1.37638i
$143$	1.22468e6	+	4.43697e6i	0.418806	+	1.51732i
$144$	−746495.			−0.250000
$145$	3.72456e6	−	1.21018e6i	1.22172	−	0.396961i
$146$	1.70189e6	+	1.23650e6i	0.546857	+	0.397315i
$147$	−3718.50	+	2701.65i	−0.00117062	+	0.000850506i
$148$	−330493.	+	1.01715e6i	−0.101947	+	0.313762i
$149$	1.75615e6	+	570609.i	0.530889	+	0.172496i	0.562181	−	0.827014i	$-0.309962\pi$
$149$	1.75615e6	+	570609.i	0.530889	+	0.172496i	−0.0312922	+	0.999510i	$0.509962\pi$
$150$	−738.110	−	1015.92i	−0.000218699	−	0.000301014i
$151$	−2.71774e6	+	3.74065e6i	−0.789365	+	1.08647i	0.204822	+	0.978799i	$0.434338\pi$
$151$	−2.71774e6	+	3.74065e6i	−0.789365	+	1.08647i	−0.994187	+	0.107668i	$0.965662\pi$
$152$	−67905.9	−	208993.i	−0.0193364	−	0.0595114i
$153$		−	3.14092e6i		−	0.876966i
$154$	2.46297e6	−	3.08866e6i	0.674367	−	0.845684i
$155$	−2.04132e6			−0.548172
$156$	−3068.71	+	997.085i	−0.000808318	+	0.000262638i
$157$	−1.00370e6	−	729231.i	−0.259361	−	0.188437i	0.450504	−	0.892774i	$-0.351244\pi$
$157$	−1.00370e6	−	729231.i	−0.259361	−	0.188437i	−0.709865	+	0.704337i	$0.751244\pi$
$158$	−2.38612e6	+	1.73362e6i	−0.604953	+	0.439524i
$159$	268.105	−	825.141i	6.66980e−5	−	0.000205275i
$160$	−493106.	−	160220.i	−0.120387	−	0.0391162i
$161$	1.68180e6	+	2.31480e6i	0.402993	+	0.554673i
$162$	1.76704e6	−	2.43213e6i	0.415625	−	0.572059i
$163$	−803.737	−	2473.65i	−0.000185589	−	0.000571183i	0.950964	−	0.309303i	$-0.100096\pi$
$163$	−803.737	−	2473.65i	−0.000185589	−	0.000571183i	−0.951149	+	0.308731i	$0.900096\pi$
$164$			921196.i			0.208843i
$165$	1913.71	+	2898.95i	0.000426015	+	0.000645340i
$166$	−2.14445e6			−0.468804
$167$	−5.15495e6	+	1.67494e6i	−1.10681	+	0.359626i	−0.804721	−	0.593653i	$-0.797685\pi$
$167$	−5.15495e6	+	1.67494e6i	−1.10681	+	0.359626i	−0.302093	+	0.953279i	$0.597685\pi$
$168$	2240.39	+	1627.74i	0.000472494	+	0.000343287i
$169$	5.77026e6	−	4.19234e6i	1.19546	−	0.868553i
$170$	674134.	−	2.07477e6i	0.137214	−	0.422303i
$171$	841653.	+	273470.i	0.168324	+	0.0546916i
$172$	−1.29681e6	−	1.78490e6i	−0.254853	−	0.350775i
$173$	−138678.	+	190874.i	−0.0267836	+	0.0368644i	−0.822199	−	0.569200i	$-0.807253\pi$
$173$	−138678.	+	190874.i	−0.0267836	+	0.0368644i	0.795415	+	0.606065i	$0.207253\pi$
$174$	2230.05	+	6863.40i	0.000423319	+	0.00130284i
$175$		−	3.99460e6i		−	0.745348i
$176$	−1.27605e6	−	478864.i	−0.234061	−	0.0878363i
$177$	5726.74			0.00103273
$178$	−4.31073e6	+	1.40064e6i	−0.764348	+	0.248352i
$179$	−3.47125e6	−	2.52201e6i	−0.605239	−	0.439732i	0.242495	−	0.970153i	$-0.422034\pi$
$179$	−3.47125e6	−	2.52201e6i	−0.605239	−	0.439732i	−0.847735	+	0.530420i	$0.822034\pi$
$180$	1.68925e6	−	1.22731e6i	0.289652	−	0.210444i
$181$	−2.01376e6	+	6.19770e6i	−0.339603	+	1.04519i	0.624808	+	0.780779i	$0.285177\pi$
$181$	−2.01376e6	+	6.19770e6i	−0.339603	+	1.04519i	−0.964410	+	0.264411i	$0.914823\pi$
$182$	−9.76172e6	−	3.17178e6i	−1.61924	−	0.526124i
$183$	−5979.79	−	8230.47i	−0.000975736	−	0.00134299i
$184$	580239.	−	798631.i	0.0931437	−	0.128201i
$185$	−924423.	−	2.84508e6i	−0.146001	−	0.449345i
$186$		−	3761.63i		−	0.000584571i
$187$	2.01485e6	−	5.36906e6i	0.308118	−	0.821057i
$188$	4.33275e6			0.652064
$189$	−21213.1	+	6892.57i	−0.00314210	+	0.00102093i
$190$	497269.	+	361287.i	0.0724988	+	0.0526735i
$191$	7.61896e6	−	5.53550e6i	1.09344	−	0.794432i	0.113464	−	0.993542i	$-0.463805\pi$
$191$	7.61896e6	−	5.53550e6i	1.09344	−	0.794432i	0.979977	+	0.199111i	$0.0638053\pi$
$192$	295.243	−	908.666i	4.17135e−5	−	0.000128381i
$193$	1.07057e7	+	3.47850e6i	1.48917	+	0.483861i	0.936838	−	0.349763i	$-0.113738\pi$
$193$	1.07057e7	+	3.47850e6i	1.48917	+	0.483861i	0.552333	+	0.833624i	$0.313738\pi$
$194$	−475339.	−	654249.i	−0.0651027	−	0.0896061i
$195$	5304.90	−	7301.57i	0.000715441	−	0.000984720i
$196$	1.55882e6	+	4.79754e6i	0.207027	+	0.637163i
$197$			1.23291e7i			1.61262i	0.591494	+	0.806309i	$0.298538\pi$
$197$			1.23291e7i			1.61262i	−0.591494	+	0.806309i	$0.701462\pi$
$198$	4.58074e6	−	3.02393e6i	0.590119	−	0.389561i
$199$	−7.28149e6			−0.923976			−0.461988	−	0.886886i	$-0.652864\pi$
$199$	−7.28149e6			−0.923976			−0.461988	+	0.886886i	$0.652864\pi$
$200$	−1.31072e6	+	425880.i	−0.163840	+	0.0532350i
$201$	−4901.22	−	3560.94i	−0.000603553	−	0.000438507i
$202$	−1.28408e6	+	932937.i	−0.155789	+	0.113187i
$203$	−7.09391e6	+	2.18328e7i	−0.848003	+	2.60989i
$204$	3823.26	+	1242.25i	0.000450343	+	0.000146325i
$205$	−1.51454e6	−	2.08458e6i	−0.175800	−	0.241967i
$206$	582391.	−	801593.i	0.0666213	−	0.0916964i
$207$	1.22849e6	+	3.78091e6i	0.138504	+	0.426271i
$208$			3.54121e6i			0.393515i
$209$	1.26329e6	+	1.00737e6i	0.138377	+	0.110345i
$210$	−7745.96			−0.000836407
$211$	1.48868e7	−	4.83703e6i	1.58473	−	0.514910i	0.621460	−	0.783446i	$-0.286540\pi$
$211$	1.48868e7	−	4.83703e6i	1.58473	−	0.514910i	0.963270	+	0.268536i	$0.0865397\pi$
$212$	−770338.	−	559684.i	−0.0808489	−	0.0587402i
$213$	16433.7	−	11939.8i	0.00170057	−	0.00123554i
$214$	494076.	−	1.52061e6i	0.0504142	−	0.155159i
$215$	5.86910e6	+	1.90699e6i	0.590550	+	0.191881i
$216$	4523.23	+	6225.69i	0.000448836	+	0.000617770i
$217$	7.03340e6	−	9.68064e6i	0.688313	−	0.947381i
$218$	4.02676e6	+	1.23931e7i	0.388675	+	1.19622i
$219$		−	10843.0i		−	0.00103232i
$220$	3.67488e6	−	1.01433e6i	0.345124	−	0.0952600i
$221$	−1.48999e7			−1.38040
$222$	5242.74	−	1703.47i	0.000479181	−	0.000155695i
$223$	−1.33168e7	−	9.67519e6i	−1.20084	−	0.872459i	−0.206470	−	0.978453i	$-0.566198\pi$
$223$	−1.33168e7	−	9.67519e6i	−1.20084	−	0.872459i	−0.994367	+	0.105994i	$0.966198\pi$
$224$	2.45882e6	−	1.78643e6i	0.218767	−	0.158944i
$225$	1.71510e6	−	5.27853e6i	0.150571	−	0.463410i
$226$	−1.00021e6	−	324988.i	−0.0866494	−	0.0281541i
$227$	9732.30	+	13395.4i	0.000832028	+	0.00114519i	0.809433	−	0.587213i	$-0.199775\pi$
$227$	9732.30	+	13395.4i	0.000832028	+	0.00114519i	−0.808601	+	0.588358i	$0.799775\pi$
$228$	−665.758	+	916.337i	−5.61710e−5	+	7.73127e-5i
$229$	−6.22498e6	−	1.91585e7i	−0.518360	−	1.59535i	−0.777084	−	0.629397i	$-0.783302\pi$
$229$	−6.22498e6	−	1.91585e7i	−0.518360	−	1.59535i	0.258724	−	0.965951i	$-0.416698\pi$
$230$			2.76120e6i			0.226941i
$231$	−20341.5	−	912.891i	−0.00165024	−	7.40599e-5i
$232$	7.92018e6			0.634265
$233$	−1.29114e7	+	4.19517e6i	−1.02072	+	0.331651i	−0.771114	−	0.636697i	$-0.780300\pi$
$233$	−1.29114e7	+	4.19517e6i	−1.02072	+	0.331651i	−0.249603	+	0.968348i	$0.580300\pi$
$234$	−1.15375e7	−	8.38248e6i	−0.900459	−	0.654222i
$235$	−9.80461e6	+	7.12347e6i	−0.755487	+	0.548893i
$236$	1.94219e6	−	5.97745e6i	0.147760	−	0.454758i
$237$	14458.2	+	4697.76i	0.00108610	+	0.000352895i
$238$	7.51652e6	+	1.03456e7i	0.557553	+	0.767406i
$239$	7.47367e6	−	1.02866e7i	0.547444	−	0.753492i	−0.442218	−	0.896907i	$-0.645808\pi$
$239$	7.47367e6	−	1.02866e7i	0.547444	−	0.753492i	0.989663	+	0.143415i	$0.0458084\pi$
$240$	825.827	+	2541.64i	5.97387e−5	+	0.000183857i
$241$			5.99907e6i			0.428581i	0.976770	+	0.214291i	$0.0687440\pi$
$241$			5.99907e6i			0.428581i	−0.976770	+	0.214291i	$0.931256\pi$
$242$	9.77006e6	−	2.23060e6i	0.689368	−	0.157390i
$243$	−46486.1			−0.00323970
$244$	−1.06188e7	+	3.45026e6i	−0.730981	+	0.237510i
$245$	−1.14151e7	−	8.29355e6i	−0.776213	−	0.563952i
$246$	3841.34	−	2790.89i	0.000258034	−	0.000187473i
$247$	1.29728e6	−	3.99262e6i	0.0860881	−	0.264952i
$248$	−3.92631e6	−	1.27573e6i	−0.257412	−	0.0836383i
$249$	6496.91	+	8942.23i	0.000420832	+	0.000579226i
$250$	6.91607e6	−	9.51915e6i	0.442628	−	0.609226i
$251$	−2.50232e6	−	7.70134e6i	−0.158242	−	0.487018i	0.840233	−	0.542225i	$-0.182418\pi$
$251$	−2.50232e6	−	7.70134e6i	−0.158242	−	0.487018i	−0.998475	+	0.0552071i	$0.982418\pi$
$252$			1.22397e7i			0.764837i
$253$	−325418.	+	7.25111e6i	−0.0200946	+	0.447758i
$254$	−2.31547e6			−0.141299
$255$	−10694.1	+	3474.72i	−0.000644945	+	0.000209555i
$256$	−848316.	−	616338.i	−0.0505636	−	0.0367366i
$257$	1.78738e7	−	1.29860e7i	1.05297	−	0.765028i	0.0801961	−	0.996779i	$-0.474445\pi$
$257$	1.78738e7	−	1.29860e7i	1.05297	−	0.765028i	0.972775	+	0.231751i	$0.0744453\pi$
$258$	−3514.08	+	10815.2i	−0.000204622	+	0.000629762i
$259$	1.66774e7	+	5.41882e6i	0.959908	+	0.311893i
$260$	−5.82210e6	−	8.01343e6i	−0.331253	−	0.455930i
$261$	−1.87480e7	+	2.58044e7i	−1.05447	+	1.45135i
$262$	−331287.	−	1.01960e6i	−0.0184205	−	0.0566923i
$263$		−	3.16944e6i		−	0.174227i	−0.996198	−	0.0871135i	$-0.972236\pi$
$263$		−	3.16944e6i		−	0.174227i	0.996198	−	0.0871135i	$-0.0277643\pi$
$264$	1869.14	+	6771.85i	0.000101585	+	0.000368041i
$265$	2.66338e6			0.143118
$266$	−3.42669e6	+	1.11340e6i	−0.182066	+	0.0591569i
$267$	18900.6	+	13732.1i	0.000992983	+	0.000721444i
$268$	−5.37905e6	+	3.90811e6i	−0.279448	+	0.203031i
$269$	−2.23661e6	+	6.88358e6i	−0.114904	+	0.353637i	−0.991927	−	0.126811i	$-0.959526\pi$
$269$	−2.23661e6	+	6.88358e6i	−0.114904	+	0.353637i	0.877023	+	0.480448i	$0.159526\pi$
$270$	−20471.3	−	6651.53i	−0.00104005	−	0.000337933i
$271$	2.25653e7	+	3.10585e7i	1.13379	+	1.56053i	0.780659	+	0.624957i	$0.214884\pi$
$271$	2.25653e7	+	3.10585e7i	1.13379	+	1.56053i	0.353133	+	0.935573i	$0.385116\pi$
$272$	2.59328e6	−	3.56934e6i	0.128867	−	0.177370i
$273$	16348.4	+	50315.2i	0.000803503	+	0.00247293i
$274$			2.06579e6i			0.100423i
$275$	6.31786e6	−	7.92286e6i	0.303789	−	0.380964i
$276$	−5088.17			−0.000242010
$277$	−2.32958e7	+	7.56925e6i	−1.09607	+	0.356134i	−0.800588	−	0.599215i	$-0.795480\pi$
$277$	−2.32958e7	+	7.56925e6i	−1.09607	+	0.356134i	−0.295480	+	0.955349i	$0.595480\pi$
$278$	2.16110e7	+	1.57013e7i	1.00587	+	0.730806i
$279$	1.34505e7	−	9.77234e6i	0.619334	−	0.449973i
$280$	−2.62700e6	+	8.08507e6i	−0.119670	+	0.368307i
$281$	1.42740e7	+	4.63790e6i	0.643319	+	0.209027i	0.612466	−	0.790497i	$-0.290178\pi$
$281$	1.42740e7	+	4.63790e6i	0.643319	+	0.209027i	0.0308528	+	0.999524i	$0.490178\pi$
$282$	−13126.7	−	18067.3i	−0.000585340	−	0.000805651i
$283$	5.50573e6	−	7.57799e6i	0.242916	−	0.334345i	−0.670099	−	0.742272i	$-0.733748\pi$
$283$	5.50573e6	−	7.57799e6i	0.242916	−	0.334345i	0.913014	+	0.407927i	$0.133748\pi$
$284$	−6.88908e6	−	2.12024e7i	−0.300750	−	0.925615i
$285$		−	3168.16i		−	0.000136859i
$286$	−1.43449e7	−	2.17300e7i	−0.613194	−	0.928886i
$287$	1.51041e7			0.638924
$288$	4.01613e6	−	1.30492e6i	0.168124	−	0.0546269i
$289$	−4.50951e6	−	3.27635e6i	−0.186825	−	0.135737i
$290$	−1.79226e7	+	1.30215e7i	−0.734865	+	0.533911i
$291$	−1288.07	+	3964.28i	−5.22711e−5	+	0.000160874i
$292$	−1.13177e7	−	3.67733e6i	−0.454577	−	0.147701i
$293$	8.53265e6	+	1.17442e7i	0.339220	+	0.466896i	0.944213	−	0.329334i	$-0.106824\pi$
$293$	8.53265e6	+	1.17442e7i	0.339220	+	0.466896i	−0.604993	+	0.796230i	$0.706824\pi$
$294$	15282.8	−	21035.0i	0.000601398	−	0.000827754i
$295$	5.43252e6	+	1.67196e7i	0.211609	+	0.651267i
$296$		−	6.04999e6i		−	0.233281i
$297$	−52975.3	−	19880.0i	−0.00202211	−	0.000758836i
$298$	−1.04456e7			−0.394714
$299$	1.79358e7	−	5.82770e6i	0.670977	−	0.218014i
$300$	5746.92	+	4175.38i	0.000212849	+	0.000154644i
$301$	−2.92656e7	+	2.12627e7i	−1.07314	+	0.779684i
$302$	8.08253e6	−	2.48755e7i	0.293445	−	0.903130i
$303$	7780.60	+	2528.07i	0.000279695	+	9.08785e-5i
$304$	730665.	+	1.00567e6i	0.0260075	+	0.0357962i
$305$	1.83568e7	−	2.52660e7i	0.646990	−	0.890505i
$306$	5.49053e6	+	1.68981e7i	0.191624	+	0.589758i
$307$			9.73363e6i			0.336403i	0.985753	+	0.168201i	$0.0537959\pi$
$307$			9.73363e6i			0.336403i	−0.985753	+	0.168201i	$0.946204\pi$
$308$	−7.85155e6	+	2.09224e7i	−0.268722	+	0.716076i
$309$	−5107.04			−0.000173099
$310$	1.09823e7	−	3.56837e6i	0.368645	−	0.119780i
$311$	−1.19505e7	−	8.68257e6i	−0.397289	−	0.288647i	0.371147	−	0.928574i	$-0.378965\pi$
$311$	−1.19505e7	−	8.68257e6i	−0.397289	−	0.288647i	−0.768436	+	0.639927i	$0.778965\pi$
$312$	14766.7	−	10728.6i	0.000486204	−	0.000353248i
$313$	2.77867e6	−	8.55188e6i	0.0906159	−	0.278887i	−0.895470	−	0.445121i	$-0.853161\pi$
$313$	2.77867e6	−	8.55188e6i	0.0906159	−	0.278887i	0.986086	+	0.166234i	$0.0531607\pi$
$314$	6.67464e6	+	2.16872e6i	0.215595	+	0.0700511i
$315$	−2.01233e7	−	2.76973e7i	−0.643823	−	0.886146i
$316$	9.80684e6	−	1.34980e7i	0.310791	−	0.427767i
$317$	1.73744e6	+	5.34730e6i	0.0545422	+	0.167864i	0.974617	−	0.223879i	$-0.0718722\pi$
$317$	1.73744e6	+	5.34730e6i	0.0545422	+	0.167864i	−0.920075	+	0.391743i	$0.871872\pi$
$318$			4907.91i			0.000152621i
$319$	−4.86008e7	+	3.20833e7i	−1.49717	+	0.988342i
$320$	2.93298e6			0.0895074
$321$	−7837.74	+	2546.63i	−0.000236960	+	7.69931e-5i
$322$	−1.30945e7	−	9.51372e6i	−0.392213	−	0.284959i
$323$	−4.23143e6	+	3.07432e6i	−0.125568	+	0.0912307i
$324$	−5.25516e6	+	1.61737e7i	−0.154508	+	0.475527i
$325$	−2.50402e7	−	8.13606e6i	−0.729437	−	0.237009i
$326$	8648.19	+	11903.2i	0.000249616	+	0.000343567i
$327$	39478.9	−	54338.0i	0.00112907	−	0.00155403i
$328$	−1.61031e6	−	4.95602e6i	−0.0456339	−	0.140447i
$329$		−	7.10407e7i		−	1.99489i
$330$	−15363.3	−	12251.0i	−0.000427506	−	0.000340903i
$331$	2.18545e7			0.602638			0.301319	−	0.953523i	$-0.402573\pi$
$331$	2.18545e7			0.602638			0.301319	+	0.953523i	$0.402573\pi$
$332$	1.15371e7	−	3.74863e6i	0.315270	−	0.102437i
$333$	1.97112e7	+	1.43211e7i	0.533803	+	0.387831i
$334$	2.48056e7	−	1.80224e7i	0.665750	−	0.483696i
$335$	5.74698e6	−	1.76874e7i	0.152864	−	0.470467i
$336$	−14898.7	−	4840.87i	−0.000392762	−	0.000127616i
$337$	−2.83912e7	−	3.90771e7i	−0.741812	−	1.02102i	−0.998512	−	0.0545259i	$-0.982635\pi$
$337$	−2.83912e7	−	3.90771e7i	−0.741812	−	1.02102i	0.256700	−	0.966491i	$-0.417365\pi$
$338$	−2.37155e7	+	3.26415e7i	−0.614160	+	0.845318i
$339$	1675.10	+	5155.41i	4.29972e−5	+	0.000132332i
$340$			1.23407e7i			0.313980i
$341$	2.92609e7	−	8.07649e6i	0.737946	−	0.203685i
$342$	−5.00613e6			−0.125148
$343$	1.99548e7	−	6.48371e6i	0.494498	−	0.160672i
$344$	1.00969e7	+	7.33584e6i	0.248035	+	0.180208i
$345$	11514.0	−	8365.44i	0.000280395	−	0.000203719i
$346$	412425.	−	1.26931e6i	0.00995674	−	0.0306437i
$347$	−5.82195e7	−	1.89167e7i	−1.39341	−	0.452748i	−0.486359	−	0.873759i	$-0.661675\pi$
$347$	−5.82195e7	−	1.89167e7i	−1.39341	−	0.452748i	−0.907055	+	0.421011i	$0.861675\pi$
$348$	−23995.3	−	33026.7i	−0.000569362	−	0.000783660i
$349$	−4.11091e7	+	5.65819e7i	−0.967079	+	1.33107i	−0.0235704	+	0.999722i	$0.507503\pi$
$349$	−4.11091e7	+	5.65819e7i	−0.967079	+	1.33107i	−0.943509	+	0.331348i	$0.892497\pi$
$350$	6.98281e6	+	2.14909e7i	0.162864	+	0.501245i
$351$			147013.i			0.00339966i
$352$	7.70222e6	+	345663.i	0.176599	+	0.00792547i
$353$	−3.15798e7			−0.717935			−0.358967	−	0.933350i	$-0.616871\pi$
$353$	−3.15798e7			−0.717935			−0.358967	+	0.933350i	$0.616871\pi$
$354$	−30809.8	+	10010.7i	−0.000694511	+	0.000225660i
$355$	5.04482e7	+	3.66528e7i	1.12761	+	0.819260i
$356$	2.07433e7	−	1.50709e7i	0.459756	−	0.334032i
$357$	20368.2	−	62687.0i	0.000447661	−	0.00137776i
$358$	2.30839e7	+	7.50043e6i	0.503108	+	0.163470i
$359$	1.43161e6	+	1.97044e6i	0.0309415	+	0.0425873i	0.824207	−	0.566288i	$-0.191621\pi$
$359$	1.43161e6	+	1.97044e6i	0.0309415	+	0.0425873i	−0.793266	+	0.608875i	$0.791621\pi$
$360$	−6.94272e6	+	9.55584e6i	−0.148807	+	0.204815i
$361$	1.40826e7	+	4.33417e7i	0.299337	+	0.921266i
$362$		−	3.68637e7i		−	0.777094i
$363$	−38901.3	−	33982.7i	−0.000813288	−	0.000710458i
$364$	5.80624e7			1.20390
$365$	3.16567e7	−	1.02859e7i	0.651009	−	0.211526i
$366$	46558.6	+	33826.8i	0.000949634	+	0.000689950i
$367$	−3.45083e7	+	2.50718e7i	−0.698113	+	0.507209i	−0.879317	−	0.476236i	$-0.842001\pi$
$367$	−3.45083e7	+	2.50718e7i	−0.698113	+	0.507209i	0.181204	+	0.983446i	$0.442001\pi$
$368$	−1.72562e6	+	5.31092e6i	−0.0346260	+	0.106568i
$369$	1.99588e7	+	6.48502e6i	0.397243	+	0.129072i
$370$	9.94677e6	+	1.36906e7i	0.196371	+	0.270281i
$371$	−9.17669e6	+	1.26306e7i	−0.179707	+	0.247345i
$372$	6575.57	+	20237.5i	0.000127733	+	0.000393123i
$373$			3.82591e6i			0.0737239i	0.999320	+	0.0368620i	$0.0117362\pi$
$373$			3.82591e6i			0.0737239i	−0.999320	+	0.0368620i	$0.988264\pi$
$374$	−1.45440e6	+	3.24075e7i	−0.0278015	+	0.619486i
$375$	−60647.6			−0.00115006
$376$	−2.33101e7	+	7.57392e6i	−0.438512	+	0.142481i
$377$	1.22411e8	+	8.89366e7i	2.28452	+	1.65980i
$378$	102078.	−	74163.8i	0.00188997	−	0.00137315i
$379$	1.39910e7	−	4.30598e7i	0.256998	−	0.790960i	−0.736431	−	0.676513i	$-0.763490\pi$
$379$	1.39910e7	−	4.30598e7i	0.256998	−	0.790960i	0.993429	−	0.114447i	$-0.0365096\pi$
$380$	−3.30686e6	−	1.07446e6i	−0.0602649	−	0.0195813i
$381$	7015.05	+	9655.39i	0.000126840	+	0.000174580i
$382$	−3.13135e7	+	4.30993e7i	−0.561748	+	0.773180i
$383$	−2.26472e7	−	6.97010e7i	−0.403105	−	1.24063i	−0.922467	−	0.386076i	$-0.873830\pi$
$383$	−2.26472e7	−	6.97010e7i	−0.403105	−	1.24063i	0.519361	−	0.854555i	$-0.326170\pi$
$384$			5404.72i			9.54507e-5i
$385$	−1.66311e7	−	6.02542e7i	−0.291434	−	1.05586i
$386$	−6.36774e7			−1.10719
$387$	−4.78013e7	+	1.55316e7i	−0.824720	+	0.267968i
$388$	3.70099e6	+	2.68893e6i	0.0633611	+	0.0460345i
$389$	−2.21280e7	+	1.60769e7i	−0.375918	+	0.273120i	−0.759661	−	0.650320i	$-0.774635\pi$
$389$	−2.21280e7	+	1.60769e7i	−0.375918	+	0.273120i	0.383743	+	0.923440i	$0.374635\pi$
$390$	−15776.7	+	48555.7i	−0.000265964	+	0.000818552i
$391$	−2.23460e7	−	7.26065e6i	−0.373826	−	0.121463i
$392$	−1.67728e7	−	2.30858e7i	−0.278451	−	0.383254i
$393$	−3247.98	+	4470.46i	−5.35101e−5	+	7.36504e-5i
$394$	−2.15520e7	−	6.63302e7i	−0.352370	−	1.08448i
$395$			4.66680e7i			0.757231i
$396$	−1.93583e7	+	2.42761e7i	−0.311732	+	0.390925i
$397$	1.07825e8			1.72324			0.861621	−	0.507551i	$-0.169449\pi$
$397$	1.07825e8			1.72324			0.861621	+	0.507551i	$0.169449\pi$
$398$	3.91743e7	−	1.27285e7i	0.621373	−	0.201896i
$399$	15024.5	+	10915.9i	0.000236527	+	0.000171847i
$400$	6.30721e6	−	4.58246e6i	0.0985502	−	0.0716009i
$401$	−5.07246e6	+	1.56114e7i	−0.0786657	+	0.242108i	−0.982654	−	0.185449i	$-0.940626\pi$
$401$	−5.07246e6	+	1.56114e7i	−0.0786657	+	0.242108i	0.903988	+	0.427558i	$0.140626\pi$
$402$	32593.2	+	10590.2i	0.000501706	+	0.000163014i
$403$	−4.63579e7	−	6.38061e7i	−0.708286	−	0.974871i
$404$	5.27749e6	−	7.26384e6i	0.0800356	−	0.110160i
$405$	−1.46992e7	−	4.52396e7i	−0.221274	−	0.681011i
$406$		−	1.29861e8i		−	1.94044i
$407$	2.45075e7	+	3.71247e7i	0.363509	+	0.550655i
$408$	−22740.7			−0.000334828
$409$	5.34885e7	−	1.73795e7i	0.781791	−	0.254019i	0.109186	−	0.994021i	$-0.465176\pi$
$409$	5.34885e7	−	1.73795e7i	0.781791	−	0.254019i	0.672605	+	0.740002i	$0.265176\pi$
$410$	1.17922e7	+	8.56751e6i	0.171097	+	0.124309i
$411$	8614.22	−	6258.60i	0.000124077	−	9.01470e-5i
$412$	−1.73202e6	+	5.33062e6i	−0.0247663	+	0.0762230i
$413$	−9.80075e7	−	3.18446e7i	−1.39126	−	0.452049i
$414$	−1.32186e7	−	1.81938e7i	−0.186287	−	0.256402i
$415$	−1.99443e7	+	2.74509e7i	−0.279045	+	0.384072i
$416$	−6.19026e6	−	1.90517e7i	−0.0859863	−	0.264639i
$417$		−	137686.i		−	0.00189882i
$418$	−8.55742e6	−	3.21134e6i	−0.117169	−	0.0439702i
$419$	−9.52727e7			−1.29517			−0.647585	−	0.761994i	$-0.724221\pi$
$419$	−9.52727e7			−1.29517			−0.647585	+	0.761994i	$0.724221\pi$
$420$	41673.2	−	13540.4i	0.000562482	−	0.000182762i
$421$	−4.43476e7	−	3.22204e7i	−0.594325	−	0.431802i	0.249535	−	0.968366i	$-0.419722\pi$
$421$	−4.43476e7	−	3.22204e7i	−0.594325	−	0.431802i	−0.843860	+	0.536563i	$0.819722\pi$
$422$	−7.16356e7	+	5.20463e7i	−0.953217	+	0.692552i
$423$	3.05016e7	−	9.38744e7i	0.402997	−	1.24030i
$424$	5.12277e6	+	1.66449e6i	0.0672059	+	0.0218365i
$425$	1.92810e7	+	2.65380e7i	0.251167	+	0.345701i
$426$	−67541.5	+	92962.9i	−0.000873659	+	0.00120249i
$427$	5.65711e7	+	1.74108e8i	0.726626	+	2.23633i
$428$			9.04454e6i			0.115360i
$429$	−47153.3	+	125652.i	−0.000597228	+	0.00159146i
$430$	−3.49092e7			−0.439071
$431$	2.40819e7	−	7.82467e6i	0.300786	−	0.0977314i	−0.154736	−	0.987956i	$-0.549453\pi$
$431$	2.40819e7	−	7.82467e6i	0.300786	−	0.0977314i	0.455522	+	0.890224i	$0.349453\pi$
$432$	−35217.8	−	25587.3i	−0.000436829	−	0.000317375i
$433$	1.18289e8	−	8.59421e7i	1.45707	−	1.05863i	0.472960	−	0.881084i	$-0.343185\pi$
$433$	1.18289e8	−	8.59421e7i	1.45707	−	1.05863i	0.984113	−	0.177542i	$-0.0568146\pi$
$434$	−2.09172e7	+	6.43765e7i	−0.255879	+	0.787514i
$435$	108598.	+	35285.7i	0.00131934	+	0.000428678i
$436$	−4.33278e7	−	5.96356e7i	−0.522766	−	0.719526i
$437$	3.89119e6	−	5.35576e6i	0.0466270	−	0.0641766i
$438$	18954.2	+	58335.0i	0.000225571	+	0.000694236i
$439$		−	8.01585e6i		−	0.0947450i	−0.998877	−	0.0473725i	$-0.984915\pi$
$439$		−	8.01585e6i		−	0.0947450i	0.998877	−	0.0473725i	$-0.0150848\pi$
$440$	−1.79977e7	+	1.18810e7i	−0.211281	+	0.139475i
$441$	1.14918e8			1.33990
$442$	8.01610e7	−	2.60459e7i	0.928317	−	0.301629i
$443$	−1.26415e7	−	9.18456e6i	−0.145407	−	0.105645i	0.512703	−	0.858566i	$-0.328644\pi$
$443$	−1.26415e7	−	9.18456e6i	−0.145407	−	0.105645i	−0.658111	+	0.752921i	$0.728644\pi$
$444$	−25228.1	+	18329.3i	−0.000288228	+	0.000209410i
$445$	−2.21621e7	+	6.82080e7i	−0.251496	+	0.774026i
$446$	8.85569e7	+	2.87739e7i	0.998200	+	0.324335i
$447$	31646.3	+	43557.4i	0.000354324	+	0.000487685i
$448$	−1.01056e7	+	1.39092e7i	−0.112390	+	0.154692i
$449$	3.86840e7	+	1.19057e8i	0.427358	+	1.31527i	0.900718	+	0.434405i	$0.143041\pi$
$449$	3.86840e7	+	1.19057e8i	0.427358	+	1.31527i	−0.473359	+	0.880869i	$0.656959\pi$
$450$			3.13965e7i			0.344544i
$451$	2.99574e7	+	2.38887e7i	0.326569	+	0.260413i
$452$	5.94921e6			0.0644235
$453$	−128217.	+	41660.1i	−0.00137927	+	0.000448152i
$454$	−75775.6	−	55054.2i	−0.000809771	−	0.000588333i
$455$	−1.31390e8	+	9.54603e7i	−1.39485	+	1.01342i
$456$	1979.95	−	6093.67i	2.08814e−5	−	6.42665e-5i
$457$	−1.26550e8	−	4.11184e7i	−1.32590	−	0.430812i	−0.441385	−	0.897318i	$-0.645513\pi$
$457$	−1.26550e8	−	4.11184e7i	−1.32590	−	0.430812i	−0.884518	+	0.466505i	$0.845513\pi$
$458$	6.69806e7	+	9.21909e7i	0.697193	+	0.959604i
$459$	107660.	−	148181.i	0.00111331	−	0.00153234i
$460$	−4.82675e6	−	1.48552e7i	−0.0495885	−	0.152618i
$461$		−	5.68475e6i		−	0.0580241i	−0.999579	−	0.0290120i	$-0.990764\pi$
$461$		−	5.68475e6i		−	0.0580241i	0.999579	−	0.0290120i	$-0.00923611\pi$
$462$	111033.	−	30646.9i	0.00112596	−	0.000310785i
$463$	7.63218e6			0.0768964			0.0384482	−	0.999261i	$-0.487759\pi$
$463$	7.63218e6			0.0768964			0.0384482	+	0.999261i	$0.487759\pi$
$464$	−4.26105e7	+	1.38450e7i	−0.426542	+	0.138592i
$465$	−48152.4	−	34984.7i	−0.000478915	−	0.000347952i
$466$	6.21298e7	−	4.51399e7i	0.613963	−	0.446070i
$467$	5.18659e7	−	1.59627e8i	0.509250	−	1.56731i	−0.284257	−	0.958748i	$-0.591747\pi$
$467$	5.18659e7	−	1.59627e8i	0.509250	−	1.56731i	0.793506	−	0.608562i	$-0.208253\pi$
$468$	7.67247e7	+	2.49294e7i	0.748510	+	0.243206i
$469$	6.40782e7	+	8.81961e7i	0.621143	+	0.854930i
$470$	4.02964e7	−	5.54633e7i	0.388126	−	0.534210i
$471$	−11178.3	−	34403.3i	−0.000106983	−	0.000329259i
$472$			3.55537e7i			0.338111i
$473$	−9.16743e7	−	4.11419e6i	−0.866292	−	0.0388777i
$474$	−85997.0			−0.000807511
$475$	−8.78994e6	+	2.85603e6i	−0.0820172	+	0.0266490i
$476$	−5.85236e7	−	4.25199e7i	−0.542638	−	0.394250i
$477$	−1.75493e7	+	1.27503e7i	−0.161698	+	0.117480i
$478$	−2.22266e7	+	6.84063e7i	−0.203511	+	0.626344i
$479$	8.42499e7	+	2.73744e7i	0.766589	+	0.249080i	0.666104	−	0.745859i	$-0.267961\pi$
$479$	8.42499e7	+	2.73744e7i	0.766589	+	0.249080i	0.100485	+	0.994939i	$0.467961\pi$
$480$	−8885.88	−	12230.4i	−8.03483e−5	−	0.000110590i
$481$	6.79360e7	−	9.35059e7i	0.610470	−	0.840241i
$482$	−1.04868e7	−	3.22750e7i	−0.0936484	−	0.288220i
$483$			83426.6i			0.000740395i
$484$	−4.86636e7	+	2.90793e7i	−0.429208	+	0.256477i
$485$	−1.27959e7			−0.112162
$486$	250095.	−	81260.8i	0.00217869	−	0.000707900i
$487$	−6.86063e7	−	4.98454e7i	−0.593987	−	0.431557i	0.249752	−	0.968310i	$-0.419651\pi$
$487$	−6.86063e7	−	4.98454e7i	−0.593987	−	0.431557i	−0.843740	+	0.536753i	$0.819651\pi$
$488$	5.10977e7	−	3.71247e7i	0.439686	−	0.319450i
$489$	23.4348	−	72.1250i	2.00417e−7	−	6.16821e-7i
$490$	7.59107e7	+	2.46649e7i	0.645230	+	0.209648i
$491$	1.44850e7	+	1.99369e7i	0.122370	+	0.168428i	0.865807	−	0.500378i	$-0.166806\pi$
$491$	1.44850e7	+	1.99369e7i	0.122370	+	0.168428i	−0.743437	+	0.668806i	$0.766806\pi$
$492$	−15787.7	+	21729.9i	−0.000132563	+	0.000182458i
$493$	−5.82535e7	−	1.79286e8i	−0.486163	−	1.49625i
$494$			2.37480e7i			0.196991i
$495$	3.89371e6	−	8.67615e7i	0.0321032	−	0.715339i
$496$	2.33536e7			0.191385
$497$	−3.47639e8	+	1.12955e8i	−2.83178	+	0.920101i
$498$	−50584.9	−	36752.1i	−0.000409575	−	0.000297573i
$499$	1.53663e7	−	1.11643e7i	0.123671	−	0.0898523i	−0.524230	−	0.851577i	$-0.675647\pi$
$499$	1.53663e7	−	1.11643e7i	0.123671	−	0.0898523i	0.647901	+	0.761724i	$0.275647\pi$
$500$	−2.05683e7	+	6.33027e7i	−0.164546	+	0.506421i
$501$	−150305.	−	48836.9i	−0.00119525	−	0.000388360i
$502$	2.69249e7	+	3.70589e7i	0.212835	+	0.292942i
$503$	1.15693e8	−	1.59237e8i	0.909080	−	1.25124i	−0.0583994	−	0.998293i	$-0.518600\pi$
$503$	1.15693e8	−	1.59237e8i	0.909080	−	1.25124i	0.967480	−	0.252949i	$-0.0814003\pi$
$504$	−2.13958e7	−	6.58494e7i	−0.167123	−	0.514352i
$505$			2.51141e7i			0.195004i
$506$	−1.09247e7	−	3.95797e7i	−0.0843250	−	0.305507i
$507$	207963.			0.00159574
$508$	1.24572e7	−	4.04759e6i	0.0950231	−	0.0308749i
$509$	8.14204e7	+	5.91554e7i	0.617419	+	0.448581i	0.852019	−	0.523511i	$-0.175378\pi$
$509$	8.14204e7	+	5.91554e7i	0.617419	+	0.448581i	−0.234600	+	0.972092i	$0.575378\pi$
$510$	51460.0	−	37387.9i	0.000387935	−	0.000281851i
$511$	−6.02942e7	+	1.85567e8i	−0.451869	+	1.39071i
$512$	5.64133e6	+	1.83298e6i	0.0420312	+	0.0136568i
$513$	30333.6	+	41750.6i	0.000224684	+	0.000309251i
$514$	−7.34602e7	+	1.01109e8i	−0.540957	+	0.744563i
$515$	−4.84465e6	−	1.49103e7i	−0.0354683	−	0.109160i
$516$		−	64328.6i		−	0.000468226i
$517$	1.12358e8	−	1.40902e8i	0.813078	−	1.01963i
$518$	−9.91968e7			−0.713688
$519$	−6542.48	+	2125.78i	−4.67994e−5	+	1.52060e-5i
$520$	4.53308e7	+	3.29348e7i	0.322391	+	0.234231i
$521$	−3.99840e7	+	2.90501e7i	−0.282731	+	0.205416i	−0.720108	−	0.693862i	$-0.755908\pi$
$521$	−3.99840e7	+	2.90501e7i	−0.282731	+	0.205416i	0.437377	+	0.899278i	$0.355908\pi$
$522$	5.57563e7	−	1.71600e8i	0.391997	−	1.20644i
$523$	−5.51701e7	−	1.79259e7i	−0.385655	−	0.125307i	0.109771	−	0.993957i	$-0.464988\pi$
$523$	−5.51701e7	−	1.79259e7i	−0.385655	−	0.125307i	−0.495426	+	0.868650i	$0.664988\pi$
$524$	3.56464e6	+	4.90631e6i	0.0247755	+	0.0341005i
$525$	68460.4	−	94227.7i	0.000473110	−	0.000651180i
$526$	5.54039e6	+	1.70516e7i	0.0380700	+	0.117167i
$527$			9.82614e7i			0.671353i
$528$	−21893.6	−	33165.1i	−0.000148736	−	0.000225310i
$529$	−1.18297e8			−0.799109
$530$	−1.43290e7	+	4.65576e6i	−0.0962469	+	0.0312725i
$531$	−1.15836e8	−	8.41599e7i	−0.773679	−	0.562111i
$532$	1.64892e7	−	1.19801e7i	0.109513	−	0.0795659i
$533$	3.07635e7	−	9.46804e7i	0.203168	−	0.625286i
$534$	−125690.	−	40839.0i	−0.000825421	−	0.000268195i
$535$	−1.48701e7	−	2.04670e7i	−0.0971075	−	0.133657i
$536$	2.21076e7	−	3.04285e7i	0.143565	−	0.197600i
$537$	−38659.7	−	118982.i	−0.000249653	−	0.000768352i
$538$		−	4.09433e7i		−	0.262928i
$539$	1.96440e8	+	7.37182e7i	1.25448	+	0.470770i
$540$	121763.			0.000773273
$541$	2.36502e7	−	7.68442e6i	0.149363	−	0.0485310i	−0.233381	−	0.972385i	$-0.574979\pi$
$541$	2.36502e7	−	7.68442e6i	0.149363	−	0.0485310i	0.382744	+	0.923854i	$0.374979\pi$
$542$	−1.75693e8	−	1.27649e8i	−1.10346	−	0.801712i
$543$	−153720.	+	111684.i	−0.000960131	+	0.000697576i
$544$	−7.71236e6	+	2.37362e7i	−0.0479061	+	0.147440i
$545$	1.96094e8	+	6.37147e7i	1.21136	+	0.393596i
$546$	−175908.	−	242117.i	−0.00108071	−	0.00148747i
$547$	7.41200e7	−	1.02017e8i	0.452870	−	0.623322i	−0.520141	−	0.854080i	$-0.674121\pi$
$547$	7.41200e7	−	1.02017e8i	0.452870	−	0.623322i	0.973011	+	0.230758i	$0.0741207\pi$
$548$	−3.61113e6	−	1.11139e7i	−0.0219433	−	0.0675344i
$549$			2.54358e8i			1.53720i
$550$	−2.01403e7	+	5.36689e7i	−0.121054	+	0.322578i
$551$	5.31141e7			0.317508
$552$	27374.3	−	8894.44i	0.000162752	−	5.28812e-5i
$553$	−2.21315e8	−	1.60795e8i	−1.30869	−	0.950817i
$554$	1.12099e8	−	8.14450e7i	0.659286	−	0.478999i
$555$	26953.7	−	82955.0i	0.000157667	−	0.000485248i
$556$	−1.43714e8	−	4.66955e7i	−0.836132	−	0.271676i
$557$	7.44189e7	+	1.02429e8i	0.430643	+	0.592730i	0.968101	−	0.250561i	$-0.0806151\pi$
$557$	7.44189e7	+	1.02429e8i	0.430643	+	0.592730i	−0.537457	+	0.843291i	$0.680615\pi$
$558$	−5.52807e7	+	7.60874e7i	−0.318179	+	0.437935i
$559$	7.36785e7	+	2.26759e8i	0.421799	+	1.29816i
$560$		−	4.80897e7i		−	0.273835i
$561$	139544.	−	92118.6i	0.000790356	−	0.000521745i
$562$	−8.49012e7			−0.478305
$563$	1.84718e8	−	6.00184e7i	1.03510	−	0.336325i	0.258296	−	0.966066i	$-0.416839\pi$
$563$	1.84718e8	−	6.00184e7i	1.03510	−	0.336325i	0.776805	+	0.629741i	$0.216839\pi$
$564$	102204.	+	74255.8i	0.000569681	+	0.000413898i
$565$	−1.34625e7	+	9.78109e6i	−0.0746416	+	0.0542303i
$566$	−1.63740e7	+	5.03938e7i	−0.0903034	+	0.277925i
$567$	2.65188e8	+	8.61647e7i	1.45480	+	0.472694i
$568$	7.41263e7	+	1.02026e8i	0.404508	+	0.556758i
$569$	−1.60724e7	+	2.21218e7i	−0.0872457	+	0.120083i	−0.850409	−	0.526123i	$-0.823645\pi$
$569$	−1.60724e7	+	2.21218e7i	−0.0872457	+	0.120083i	0.763163	+	0.646206i	$0.223645\pi$
$570$	5538.14	+	17044.7i	2.99047e−5	+	9.20372e-5i
$571$			1.50373e8i			0.807719i	0.914821	+	0.403860i	$0.132332\pi$
$571$			1.50373e8i			0.807719i	−0.914821	+	0.403860i	$0.867668\pi$
$572$	1.15161e8	+	9.18316e7i	0.615341	+	0.490686i
$573$	274591.			0.00145956
$574$	−8.12599e7	+	2.64030e7i	−0.429676	+	0.139610i
$575$	−3.35893e7	−	2.44040e7i	−0.176684	−	0.128368i
$576$	−1.93257e7	+	1.40409e7i	−0.101127	+	0.0734731i
$577$	−4.26839e7	+	1.31367e8i	−0.222196	+	0.683849i	0.776368	+	0.630280i	$0.217060\pi$
$577$	−4.26839e7	+	1.31367e8i	−0.222196	+	0.683849i	−0.998564	+	0.0535693i	$0.982940\pi$
$578$	2.99884e7	+	9.74381e6i	0.155299	+	0.0504598i
$579$	192920.	+	265531.i	0.000993896	+	0.00136798i
$580$	7.36610e7	−	1.01386e8i	0.377532	−	0.519628i
$581$	−6.14634e7	−	1.89165e8i	−0.313392	−	0.964521i
$582$		−	23579.4i		−	0.000119609i
$583$	−3.81776e7	+	1.05376e7i	−0.192665	+	0.0531787i
$584$	6.73170e7			0.337976
$585$	−2.14607e8	+	6.97301e7i	−1.07196	+	0.348299i
$586$	−6.64352e7	−	4.82680e7i	−0.330145	−	0.239865i
$587$	1.04477e8	−	7.59073e7i	0.516545	−	0.375292i	−0.298756	−	0.954330i	$-0.596572\pi$
$587$	1.04477e8	−	7.59073e7i	0.516545	−	0.375292i	0.815301	+	0.579038i	$0.196572\pi$
$588$	−45450.9	+	139884.i	−0.000223569	+	0.000688074i
$589$	−2.63305e7	−	8.55530e6i	−0.128859	−	0.0418687i
$590$	−5.84538e7	−	8.04547e7i	−0.284614	−	0.391738i
$591$	−211299.	+	290828.i	−0.00102361	+	0.00140888i
$592$	1.05758e7	+	3.25488e7i	0.0509737	+	0.156881i
$593$			1.34409e7i			0.0644559i	0.999481	+	0.0322280i	$0.0102603\pi$
$593$			1.34409e7i			0.0644559i	−0.999481	+	0.0322280i	$0.989740\pi$
$594$	319758.	+	14350.2i	0.00152567	+	6.84697e-5i
$595$	2.02340e8			0.960576
$596$	5.61970e7	−	1.82595e7i	0.265445	−	0.0862482i
$597$	−171761.	−	124792.i	−0.000807240	−	0.000586494i
$598$	−8.63074e7	+	6.27060e7i	−0.403594	+	0.293228i
$599$	−3.47691e7	+	1.07008e8i	−0.161776	+	0.497894i	−0.998784	−	0.0492956i	$-0.984302\pi$
$599$	−3.47691e7	+	1.07008e8i	−0.161776	+	0.497894i	0.837009	+	0.547190i	$0.184302\pi$
$600$	−38217.2	−	12417.5i	−0.000176932	−	5.74885e-5i
$601$	5.53421e7	+	7.61719e7i	0.254937	+	0.350890i	0.917233	−	0.398352i	$-0.130418\pi$
$601$	5.53421e7	+	7.61719e7i	0.254937	+	0.350890i	−0.662296	+	0.749242i	$0.730418\pi$
$602$	1.20280e8	−	1.65551e8i	0.551320	−	0.758827i
$603$	4.68067e7	+	1.44056e8i	0.213479	+	0.657022i
$604$			1.47959e8i			0.671474i
$605$	6.23119e7	−	1.45812e8i	0.281388	−	0.658454i
$606$	−46278.8			−0.000207952
$607$	3.56546e8	−	1.15849e8i	1.59422	−	0.517995i	0.628554	−	0.777766i	$-0.283647\pi$
$607$	3.56546e8	−	1.15849e8i	1.59422	−	0.517995i	0.965670	+	0.259771i	$0.0836471\pi$
$608$	−5.68895e6	−	4.13327e6i	−0.0253117	−	0.0183900i
$609$	−541513.	+	393432.i	−0.00239749	+	0.00174188i
$610$	−5.45928e7	+	1.68019e8i	−0.240517	+	0.740236i
$611$	−4.45320e8	−	1.44693e8i	−1.95231	−	0.634343i
$612$	−5.90780e7	−	8.13139e7i	−0.257734	−	0.354740i
$613$	−4.61243e7	+	6.34846e7i	−0.200239	+	0.275605i	−0.897314	−	0.441393i	$-0.854484\pi$
$613$	−4.61243e7	+	6.34846e7i	−0.200239	+	0.275605i	0.697075	+	0.716998i	$0.254484\pi$
$614$	−1.70150e7	−	5.23668e7i	−0.0735067	−	0.226230i
$615$		−	75129.2i		−	0.000322986i
$616$	5.66756e6	−	1.26287e8i	0.0242468	−	0.540278i
$617$	−3.13058e8			−1.33281			−0.666407	−	0.745588i	$-0.732169\pi$
$617$	−3.13058e8			−1.33281			−0.666407	+	0.745588i	$0.732169\pi$
$618$	27475.8	−	8927.43i	0.000116409	−	3.78234e-5i
$619$	−2.10493e8	−	1.52932e8i	−0.887496	−	0.644803i	0.0477280	−	0.998860i	$-0.484802\pi$
$619$	−2.10493e8	−	1.52932e8i	−0.887496	−	0.644803i	−0.935224	+	0.354057i	$0.884802\pi$
$620$	−5.28469e7	+	3.83955e7i	−0.221740	+	0.161104i
$621$	−71639.2	+	220483.i	−0.000299141	+	0.000920662i
$622$	7.94714e7	+	2.58218e7i	0.330248	+	0.107304i
$623$	−2.47105e8	−	3.40111e8i	−1.02192	−	1.40656i
$624$	−60690.2	+	83532.9i	−0.000249784	+	0.000343798i
$625$	−2.07711e7	−	6.39269e7i	−0.0850785	−	0.261845i
$626$			5.08663e7i			0.207352i
$627$	12534.8	+	45413.2i	5.08528e−5	+	0.000184238i
$628$	−3.97005e7			−0.160294
$629$	−1.36951e8	+	4.44981e7i	−0.550318	+	0.178809i
$630$	1.56679e8	+	1.13834e8i	0.626600	+	0.455252i
$631$	2.20685e8	−	1.60337e8i	0.878383	−	0.638183i	−0.0544401	−	0.998517i	$-0.517337\pi$
$631$	2.20685e8	−	1.60337e8i	0.878383	−	0.638183i	0.932823	+	0.360334i	$0.117337\pi$
$632$	−2.91654e7	+	8.97618e7i	−0.115536	+	0.355583i
$633$	434061.	+	141035.i	0.00171135	+	0.000556052i
$634$	−1.86948e7	−	2.57312e7i	−0.0733591	−	0.100970i
$635$	−2.15349e7	+	2.96402e7i	−0.0841048	+	0.115760i
$636$	−8579.35	−	26404.5i	−3.33490e−5	−	0.000102638i
$637$		−	5.45148e8i		−	2.10910i
$638$	2.05388e8	−	2.57565e8i	0.790884	−	0.991802i
$639$	−5.07874e8			−1.94650
$640$	−1.57794e7	+	5.12704e6i	−0.0601936	+	0.0195581i
$641$	3.79272e8	+	2.75557e8i	1.44005	+	1.04625i	0.988033	+	0.154243i	$0.0492939\pi$
$641$	3.79272e8	+	2.75557e8i	1.44005	+	1.04625i	0.452013	+	0.892011i	$0.350706\pi$
$642$	37715.2	−	27401.7i	0.000142532	−	0.000103555i
$643$	−7.15992e7	+	2.20360e8i	−0.269324	+	0.828895i	0.721341	+	0.692580i	$0.243526\pi$
$643$	−7.15992e7	+	2.20360e8i	−0.269324	+	0.828895i	−0.990666	+	0.136315i	$0.956474\pi$
$644$	8.70789e7	+	2.82937e7i	0.326028	+	0.105933i
$645$	105763.	+	145570.i	0.000394142	+	0.000542490i
$646$	1.73910e7	−	2.39366e7i	0.0645099	−	0.0887902i
$647$	−8.87649e7	−	2.73190e8i	−0.327739	−	1.00868i	−0.970189	−	0.242349i	$-0.922082\pi$
$647$	−8.87649e7	−	2.73190e8i	−0.327739	−	1.00868i	0.642450	−	0.766328i	$-0.277918\pi$
$648$		−	9.62008e7i		−	0.353552i
$649$	−1.44022e8	−	2.18169e8i	−0.526860	−	0.798103i
$650$	1.48938e8			0.542334
$651$	331818.	−	107814.i	0.00120270	−	0.000390781i
$652$	−67334.8	−	48921.6i	−0.000242939	−	0.000176505i
$653$	2.96799e8	−	2.15637e8i	1.06591	−	0.774433i	0.0907414	−	0.995874i	$-0.471076\pi$
$653$	2.96799e8	−	2.15637e8i	1.06591	−	0.774433i	0.975174	+	0.221442i	$0.0710763\pi$
$654$	−117410.	+	361349.i	−0.000419730	+	0.00129180i
$655$	−1.61329e7	−	5.24190e6i	−0.0574101	−	0.0186537i
$656$	1.73269e7	+	2.38484e7i	0.0613775	+	0.0844788i
$657$	−1.59348e8	+	2.19323e8i	−0.561888	+	0.773372i
$658$	1.24184e8	+	3.82198e8i	0.435900	+	1.34156i
$659$			1.69650e8i			0.592787i	0.955066	+	0.296394i	$0.0957840\pi$
$659$			1.69650e8i			0.592787i	−0.955066	+	0.296394i	$0.904216\pi$
$660$	104070.	+	39054.3i	0.000361987	+	0.000135843i
$661$	3.38802e8			1.17312			0.586559	−	0.809906i	$-0.300482\pi$
$661$	3.38802e8			1.17312			0.586559	+	0.809906i	$0.300482\pi$
$662$	−1.17577e8	+	3.82030e7i	−0.405273	+	0.131681i
$663$	−351469.	−	255357.i	−0.00120600	−	0.000876209i
$664$	−5.55166e7	+	4.03352e7i	−0.189635	+	0.137778i
$665$	−1.76171e7	+	5.42199e7i	−0.0599059	+	0.184371i
$666$	−1.31080e8	−	4.25906e7i	−0.443726	−	0.144175i
$667$	1.40246e8	+	1.93033e8i	0.472622	+	0.650509i
$668$	−1.01950e8	+	1.40322e8i	−0.342024	+	0.470756i
$669$	−148310.	−	456452.i	−0.000495328	−	0.00152446i
$670$			1.05204e8i			0.349790i
$671$	−1.63167e8	+	4.34798e8i	−0.540087	+	1.43919i
$672$	88616.8			0.000292017
$673$	−3.50774e8	+	1.13973e8i	−1.15075	+	0.373903i	−0.821427	−	0.570313i	$-0.806822\pi$
$673$	−3.50774e8	+	1.13973e8i	−1.15075	+	0.373903i	−0.329327	+	0.944216i	$0.606822\pi$
$674$	2.21054e8	+	1.60605e8i	0.721968	+	0.524540i
$675$	261844.	−	190241.i	0.000851395	−	0.000618575i
$676$	7.05294e7	−	2.17067e8i	0.228313	−	0.702674i
$677$	3.83968e8	+	1.24759e8i	1.23745	+	0.402073i	0.853409	−	0.521242i	$-0.174531\pi$
$677$	3.83968e8	+	1.24759e8i	1.23745	+	0.402073i	0.384044	+	0.923315i	$0.374531\pi$
$678$	−18024.0	−	24807.9i	−5.78312e−5	−	7.95978e-5i
$679$	4.40882e7	−	6.06822e7i	0.140836	−	0.193844i
$680$	−2.15723e7	−	6.63927e7i	−0.0686072	−	0.211151i
$681$			482.775i			1.52863e-6i
$682$	−1.43305e8	+	9.46013e7i	−0.451761	+	0.298225i
$683$	9.60532e7			0.301474			0.150737	−	0.988574i	$-0.451835\pi$
$683$	9.60532e7			0.301474			0.150737	+	0.988574i	$0.451835\pi$
$684$	2.69329e7	−	8.75103e6i	0.0841618	−	0.0273458i
$685$	2.64440e7	+	1.92127e7i	0.0822726	+	0.0597746i
$686$	−9.60226e7	+	6.97645e7i	−0.297441	+	0.216104i
$687$	181504.	−	558611.i	0.000559778	−	0.00172282i
$688$	−6.71448e7	−	2.18167e7i	−0.206180	−	0.0669921i
$689$	6.04846e7	+	8.32499e7i	0.184921	+	0.254522i
$690$	−47322.1	+	65133.3i	−0.000144051	+	0.000198269i
$691$	1.02148e8	+	3.14378e8i	0.309595	+	0.952837i	0.977922	+	0.208969i	$0.0670107\pi$
$691$	1.02148e8	+	3.14378e8i	0.309595	+	0.952837i	−0.668327	+	0.743868i	$0.732989\pi$
$692$			7.54985e6i			0.0227835i
$693$	3.98036e8	+	3.17403e8i	1.19598	+	0.953698i
$694$	3.46288e8			1.03600
$695$	4.01984e8	−	1.30612e8i	1.19744	−	0.389072i
$696$	186827.	+	135738.i	0.000554131	+	0.000402600i
$697$	−1.00344e8	+	7.29039e7i	−0.296341	+	0.215304i
$698$	1.22258e8	−	3.76271e8i	0.359510	−	1.10646i
$699$	−376462.	−	122320.i	−0.00110227	−	0.000358151i
$700$	−7.51349e7	−	1.03414e8i	−0.219052	−	0.301500i
$701$	−4.42805e7	+	6.09468e7i	−0.128546	+	0.176928i	−0.868439	−	0.495797i	$-0.834876\pi$
$701$	−4.42805e7	+	6.09468e7i	−0.128546	+	0.176928i	0.739893	+	0.672725i	$0.234876\pi$
$702$	−256989.	−	790931.i	−0.000742853	−	0.00228627i
$703$		−	4.05723e7i		−	0.116779i
$704$	−4.20421e7	+	1.16043e7i	−0.120494	+	0.0332584i
$705$	−353363.			−0.00100845
$706$	1.69899e8	−	5.52035e7i	0.482810	−	0.156875i
$707$	−1.19099e8	−	8.65308e7i	−0.337017	−	0.244857i
$708$	148257.	−	107715.i	0.000417749	−	0.000303512i
$709$	7.73325e7	−	2.38005e8i	0.216982	−	0.667801i	−0.782025	−	0.623247i	$-0.785813\pi$
$709$	7.73325e7	−	2.38005e8i	0.216982	−	0.667801i	0.999007	−	0.0445545i	$-0.0141868\pi$
$710$	−3.35482e8	−	1.09005e8i	−0.937334	−	0.304558i
$711$	−2.23412e8	−	3.07500e8i	−0.621581	−	0.855532i
$712$	−8.52538e7	+	1.17342e8i	−0.236197	+	0.325097i
$713$	−3.84325e7	−	1.18283e8i	−0.106030	−	0.326328i
$714$			372860.i			0.00102436i
$715$	−4.11578e8	−	1.84709e7i	−1.12599	−	0.0505325i
$716$	−1.37303e8			−0.374058
$717$	352589.	−	114563.i	0.000956559	−	0.000310805i
$718$	−1.11465e7	−	8.09841e6i	−0.0301138	−	0.0218789i
$719$	−2.00703e8	+	1.45819e8i	−0.539966	+	0.392308i	−0.824072	−	0.566485i	$-0.808303\pi$
$719$	−2.00703e8	+	1.45819e8i	−0.539966	+	0.392308i	0.284106	+	0.958793i	$0.408303\pi$
$720$	2.06475e7	−	6.35466e7i	0.0553186	−	0.170253i
$721$	8.74019e7	+	2.83986e7i	0.233193	+	0.0757689i
$722$	−1.51528e8	−	2.08561e8i	−0.402608	−	0.554142i
$723$	−102814.	+	141511.i	−0.000272042	+	0.000374434i
$724$	6.44402e7	+	1.98326e8i	0.169801	+	0.522595i
$725$		−	3.33112e8i		−	0.874129i
$726$	268693.	+	114825.i	0.000702176	+	0.000300072i
$727$	−2.57862e8			−0.671096			−0.335548	−	0.942023i	$-0.608921\pi$
$727$	−2.57862e8			−0.671096			−0.335548	+	0.942023i	$0.608921\pi$
$728$	−3.12375e8	+	1.01497e8i	−0.809622	+	0.263062i
$729$	3.13428e8	+	2.27718e8i	0.809011	+	0.587781i
$730$	−1.52332e8	+	1.10676e8i	−0.391582	+	0.284501i
$731$	9.17949e7	−	2.82516e8i	0.234999	−	0.723254i
$732$	−309616.	−	100600.i	−0.000789387	−	0.000256487i
$733$	8.60783e7	+	1.18477e8i	0.218566	+	0.300830i	0.904194	−	0.427122i	$-0.140472\pi$
$733$	8.60783e7	+	1.18477e8i	0.218566	+	0.300830i	−0.685628	+	0.727952i	$0.740472\pi$
$734$	1.41827e8	−	1.95209e8i	0.358651	−	0.493641i
$735$	−127131.	−	391270.i	−0.000320177	−	0.000985403i
$736$		−	3.15892e7i		−	0.0792328i
$737$	−1.23987e7	+	2.76274e8i	−0.0309723	+	0.690140i
$738$	−1.18715e8			−0.295348
$739$	6.42366e8	−	2.08718e8i	1.59166	−	0.517161i	0.626631	−	0.779316i	$-0.284433\pi$
$739$	6.42366e8	−	2.08718e8i	1.59166	−	0.517161i	0.965026	+	0.262155i	$0.0844332\pi$
$740$	−7.74455e7	−	5.62674e7i	−0.191118	−	0.138855i
$741$	99027.8	−	71947.9i	0.000243390	−	0.000176833i
$742$	2.72913e7	−	8.39941e7i	0.0668056	−	0.205607i
$743$	1.33963e8	+	4.35274e7i	0.326603	+	0.106120i	0.467729	−	0.883872i	$-0.345072\pi$
$743$	1.33963e8	+	4.35274e7i	0.326603	+	0.106120i	−0.141126	+	0.989992i	$0.545072\pi$
$744$	−70752.9	−	97383.1i	−0.000171801	−	0.000236464i
$745$	−9.71481e7	+	1.33713e8i	−0.234945	+	0.323373i
$746$	−6.68794e6	−	2.05834e7i	−0.0161093	−	0.0495792i
$747$		−	2.76355e8i		−	0.662988i
$748$	−4.88258e7	−	1.76895e8i	−0.116666	−	0.422678i
$749$	1.48296e8			0.352927
$750$	326283.	−	106016.i	0.000773412	−	0.000251297i
$751$	7.54435e7	+	5.48129e7i	0.178116	+	0.129409i	0.673271	−	0.739396i	$-0.264889\pi$
$751$	7.54435e7	+	5.48129e7i	0.178116	+	0.129409i	−0.495155	+	0.868805i	$0.664889\pi$
$752$	1.12169e8	−	8.14952e7i	0.263765	−	0.191637i
$753$	72960.9	−	224551.i	0.000170886	−	0.000525932i
$754$	−8.14035e8	−	2.64496e8i	−1.89902	−	0.617028i
$755$	−2.43258e8	−	3.34816e8i	−0.565232	−	0.777975i
$756$	−419534.	+	577439.i	−0.000970961	+	0.00133641i
$757$	−1.92448e8	−	5.92293e8i	−0.443634	−	1.36536i	−0.883975	−	0.467534i	$-0.845143\pi$
$757$	−1.92448e8	−	5.92293e8i	−0.443634	−	1.36536i	0.440341	−	0.897831i	$-0.354857\pi$
$758$			2.56118e8i			0.588075i
$759$	−131948.	+	165468.i	−0.000301770	+	0.000378432i
$760$	1.96691e7			0.0448067
$761$	1.35752e8	−	4.41084e7i	0.308029	−	0.100085i	−0.150924	−	0.988545i	$-0.548225\pi$
$761$	1.35752e8	−	4.41084e7i	0.308029	−	0.100085i	0.458953	+	0.888461i	$0.348225\pi$
$762$	−54619.1	−	39683.1i	−0.000123447	−	8.96893e-5i
$763$	−9.77798e8	+	7.10412e8i	−2.20128	+	1.59932i
$764$	9.31259e7	−	2.86612e8i	0.208829	−	0.642709i
$765$	2.67376e8	+	8.68757e7i	0.597225	+	0.194050i
$766$	2.43684e8	+	3.35402e8i	0.542176	+	0.746241i
$767$	−3.99237e8	+	5.49502e8i	−0.884798	+	1.21782i
$768$	−9447.79	−	29077.3i	−2.08567e−5	−	6.41905e-5i
$769$		−	4.81323e8i		−	1.05842i	−0.848491	−	0.529209i	$-0.822489\pi$
$769$		−	4.81323e8i		−	1.05842i	0.848491	−	0.529209i	$-0.177511\pi$
$770$	1.94803e8	+	2.95094e8i	0.426702	+	0.646381i
$771$	644178.			0.00140554
$772$	3.42584e8	−	1.11312e8i	0.744585	−	0.241930i
$773$	4.46524e8	+	3.24419e8i	0.966733	+	0.702373i	0.954705	−	0.297555i	$-0.0961712\pi$
$773$	4.46524e8	+	3.24419e8i	0.966733	+	0.702373i	0.0120283	+	0.999928i	$0.496171\pi$
$774$	2.30020e8	−	1.67119e8i	0.496070	−	0.360416i
$775$	−5.36556e7	+	1.65135e8i	−0.115268	+	0.354759i
$776$	−2.46117e7	−	7.99682e6i	−0.0526692	−	0.0171132i
$777$	300531.	+	413645.i	0.000640658	+	0.000881790i
$778$	9.09448e7	−	1.25175e8i	0.193125	−	0.265814i
$779$	−1.07990e7	−	3.32359e7i	−0.0228440	−	0.0703065i
$780$		−	288808.i		−	0.000608590i
$781$	−8.68154e8	−	3.25792e8i	−1.82240	−	0.683893i
$782$	1.32913e8			0.277938
$783$	−1.76897e6	+	574774.i	−0.00368499	+	0.00119733i
$784$	1.30593e8	+	9.48815e7i	0.271002	+	0.196894i
$785$	8.98386e7	−	6.52716e7i	0.185718	−	0.134932i
$786$	9659.45	−	29728.7i	1.98923e−5	−	6.12222e-5i
$787$	3.74259e8	+	1.21604e8i	0.767800	+	0.249473i	0.666623	−	0.745395i	$-0.267739\pi$
$787$	3.74259e8	+	1.21604e8i	0.767800	+	0.249473i	0.101177	+	0.994868i	$0.467739\pi$
$788$	2.31899e8	+	3.19182e8i	0.473937	+	0.652318i
$789$	54318.7	−	74763.3i	0.000110591	−	0.000152215i
$790$	−8.15787e7	−	2.51074e8i	−0.165461	−	0.509237i
$791$		−	9.75445e7i		−	0.197094i
$792$	6.17112e7	−	1.64445e8i	0.124219	−	0.331013i
$793$	1.20662e9			2.41964
$794$	−5.80095e8	+	1.88484e8i	−1.15888	+	0.376542i
$795$	62825.9	+	45645.7i	0.000125037	+	9.08444e-5i
$796$	−1.88507e8	+	1.36958e8i	−0.373756	+	0.271550i
$797$	−1.24868e8	+	3.84303e8i	−0.246646	+	0.759100i	0.748715	+	0.662892i	$0.230671\pi$
$797$	−1.24868e8	+	3.84303e8i	−0.246646	+	0.759100i	−0.995361	+	0.0962075i	$0.969329\pi$
$798$	−99913.1	−	32463.7i	−0.000196614	−	6.38837e-5i
$799$	3.42896e8	+	4.71956e8i	0.672236	+	0.925254i
$800$	−2.59223e7	+	3.56790e7i	−0.0506295	+	0.0696855i
$801$	−1.80501e8	−	5.55525e8i	−0.351222	−	1.08095i
$802$		−	9.28563e7i		−	0.180007i
$803$	−4.13079e8	+	2.72690e8i	−0.797787	+	0.526651i
$804$	−193864.			−0.000373016
$805$	−2.43569e8	+	7.91404e7i	−0.466911	+	0.151709i
$806$	3.60942e8	+	2.62240e8i	0.689338	+	0.500834i
$807$	−170732.	+	124044.i	−0.000324858	+	0.000236023i
$808$	−1.56952e7	+	4.83048e7i	−0.0297531	+	0.0915706i
$809$	−4.32894e8	−	1.40656e8i	−0.817591	−	0.265651i	−0.129782	−	0.991543i	$-0.541428\pi$
$809$	−4.32894e8	−	1.40656e8i	−0.817591	−	0.265651i	−0.687810	+	0.725891i	$0.741428\pi$
$810$	1.58164e8	+	2.17693e8i	0.297613	+	0.409629i
$811$	1.92671e8	−	2.65188e8i	0.361204	−	0.497155i	−0.589280	−	0.807929i	$-0.700588\pi$
$811$	1.92671e8	−	2.65188e8i	0.361204	−	0.497155i	0.950484	+	0.310774i	$0.100588\pi$
$812$	2.27005e8	+	6.98650e8i	0.424002	+	1.30494i
$813$			1.11936e6i			0.00208305i
$814$	−1.96746e8	−	1.56890e8i	−0.364782	−	0.290885i
$815$	232804.			0.000430049
$816$	122344.	−	39752.1i	0.000225172	−	7.31627e-5i
$817$	6.77117e7	+	4.91954e7i	0.124165	+	0.0902108i
$818$	−2.57387e8	+	1.87003e8i	−0.470248	+	0.341655i
$819$	4.08747e8	−	1.25799e9i	0.744051	−	2.28995i
$820$	−7.84183e7	−	2.54796e7i	−0.142225	−	0.0462117i
$821$	1.65502e8	+	2.27794e8i	0.299070	+	0.411635i	0.931934	−	0.362628i	$-0.118121\pi$
$821$	1.65502e8	+	2.27794e8i	0.299070	+	0.411635i	−0.632864	+	0.774263i	$0.718121\pi$
$822$	−35404.0	+	48729.4i	−6.37436e−5	+	8.77355e-5i
$823$	3.26778e7	+	1.00572e8i	0.0586211	+	0.180417i	0.976079	−	0.217415i	$-0.0697626\pi$
$823$	3.26778e7	+	1.00572e8i	0.0586211	+	0.180417i	−0.917458	+	0.397832i	$0.869763\pi$
$824$		−	3.17063e7i		−	0.0566715i
$825$	284815.	−	78613.5i	0.000507225	−	0.000140002i
$826$	5.82946e8			1.03440
$827$	−4.20910e8	+	1.36762e8i	−0.744171	+	0.241796i	−0.656471	−	0.754351i	$-0.727952\pi$
$827$	−4.20910e8	+	1.36762e8i	−0.744171	+	0.241796i	−0.0877000	+	0.996147i	$0.527952\pi$
$828$	1.02920e8	+	7.47754e7i	0.181304	+	0.131725i
$829$	5.00771e8	−	3.63832e8i	0.878974	−	0.638612i	−0.0540062	−	0.998541i	$-0.517199\pi$
$829$	5.00771e8	−	3.63832e8i	0.878974	−	0.638612i	0.932980	+	0.359929i	$0.117199\pi$
$830$	5.93140e7	−	1.82550e8i	0.103734	−	0.319262i
$831$	−679242.	−	220699.i	−0.00118365	−	0.000384590i
$832$	6.66071e7	+	9.16768e7i	0.115651	+	0.159180i
$833$	−3.99219e8	+	5.49478e8i	−0.690679	+	0.950638i
$834$	240685.	+	740751.i	0.000414906	+	0.00127695i
$835$		−	4.85151e8i		−	0.833331i
$836$	5.16525e7	+	2.31808e6i	0.0884041	+	0.00396743i
$837$	969523.			0.00165341
$838$	5.12566e8	−	1.66543e8i	0.870999	−	0.283005i
$839$	−5.44249e8	−	3.95420e8i	−0.921535	−	0.669535i	0.0223702	−	0.999750i	$-0.492879\pi$
$839$	−5.44249e8	−	3.95420e8i	−0.921535	−	0.669535i	−0.943906	+	0.330215i	$0.892879\pi$
$840$	−200532.	+	145695.i	−0.000338334	+	0.000245814i
$841$	−4.07754e8	+	1.25494e9i	−0.685504	+	2.10977i
$842$	2.94913e8	+	9.58231e7i	0.494035	+	0.160522i
$843$	257220.	+	354034.i	0.000429361	+	0.000590965i
$844$	2.94418e8	−	4.05232e8i	0.489709	−	0.674026i
$845$	1.97278e8	+	6.07160e8i	0.326971	+	1.00631i
$846$			5.58362e8i			0.922156i
$847$	4.76790e8	+	7.97898e8i	0.784652	+	1.31310i
$848$	−3.04701e7			−0.0499674
$849$	259747.	−	84396.9i	0.000424451	−	0.000137912i
$850$	−1.50121e8	−	1.09070e8i	−0.244448	−	0.177602i
$851$	1.47452e8	−	1.07130e8i	0.239255	−	0.173829i
$852$	200867.	−	618206.i	0.000324781	−	0.000999573i
$853$	−8.06170e8	−	2.61940e8i	−1.29891	−	0.422042i	−0.423709	−	0.905799i	$-0.639272\pi$
$853$	−8.06170e8	−	2.61940e8i	−1.29891	−	0.422042i	−0.875202	+	0.483757i	$0.839272\pi$
$854$	−6.08704e8	−	8.37809e8i	−0.977310	−	1.34515i
$855$	−4.65591e7	+	6.40831e7i	−0.0744914	+	0.102529i
$856$	−1.58104e7	−	4.86595e7i	−0.0252071	−	0.0775794i
$857$		−	7.76269e7i		−	0.123330i	−0.998097	−	0.0616652i	$-0.980359\pi$
$857$		−	7.76269e7i		−	0.123330i	0.998097	−	0.0616652i	$-0.0196411\pi$
$858$	34037.1	−	758431.i	5.38878e−5	−	0.00120075i
$859$	−7.60625e8			−1.20003			−0.600014	−	0.799990i	$-0.704838\pi$
$859$	−7.60625e8			−1.20003			−0.600014	+	0.799990i	$0.704838\pi$
$860$	1.87811e8	−	6.10236e7i	0.295275	−	0.0959406i
$861$	356288.	+	258858.i	0.000558202	+	0.000405557i
$862$	−1.15882e8	+	8.41932e7i	−0.180923	+	0.131448i
$863$	2.63833e8	−	8.11994e8i	0.410484	−	1.26334i	−0.505744	−	0.862684i	$-0.668782\pi$
$863$	2.63833e8	−	8.11994e8i	0.410484	−	1.26334i	0.916228	−	0.400657i	$-0.131218\pi$
$864$	234200.	+	76096.1i	0.000363116	+	0.000117983i
$865$	−1.24127e7	−	1.70846e7i	−0.0191786	−	0.0263971i
$866$	−4.86162e8	+	6.69145e8i	−0.748561	+	1.03031i
$867$	−50222.9	−	154570.i	−7.70628e−5	−	0.000237175i
$868$		−	3.82910e8i		−	0.585514i
$869$	−1.84642e8	−	6.68952e8i	−0.281365	−	1.01938i
$870$	−645939.			−0.000980921
$871$	6.83371e8	−	2.22041e8i	1.03419	−	0.336030i
$872$	3.37350e8	+	2.45099e8i	0.508782	+	0.369651i
$873$	8.43131e7	−	6.12570e7i	0.126722	−	0.0920690i
$874$	−1.15723e7	+	3.56160e7i	−0.0173335	+	0.0533470i
$875$	1.03792e9	+	3.37242e8i	1.54932	+	0.503405i
$876$	−203947.	−	280708.i	−0.000303392	−	0.000417583i
$877$	1.88629e8	−	2.59626e8i	0.279647	−	0.384901i	−0.645970	−	0.763363i	$-0.723547\pi$
$877$	1.88629e8	−	2.59626e8i	0.279647	−	0.384901i	0.925617	+	0.378462i	$0.123547\pi$
$878$	1.40122e7	+	4.31252e7i	0.0207025	+	0.0637158i
$879$			423266.i			0.000623228i
$880$	7.60588e7	−	9.53809e7i	0.111610	−	0.139963i
$881$	−1.24162e9			−1.81577			−0.907885	−	0.419220i	$-0.862304\pi$
$881$	−1.24162e9			−1.81577			−0.907885	+	0.419220i	$0.862304\pi$
$882$	−6.18260e8	+	2.00885e8i	−0.901084	+	0.292780i
$883$	1.17715e8	+	8.55249e7i	0.170982	+	0.124225i	0.669985	−	0.742375i	$-0.266300\pi$
$883$	1.17715e8	+	8.55249e7i	0.170982	+	0.124225i	−0.499003	+	0.866600i	$0.666300\pi$
$884$	−3.85735e8	+	2.80253e8i	−0.558384	+	0.405689i
$885$	−158398.	+	487498.i	−0.000228517	+	0.000703304i
$886$	8.40661e7	+	2.73147e7i	0.120870	+	0.0392731i
$887$	−3.90030e8	−	5.36830e8i	−0.558891	−	0.769247i	0.432294	−	0.901733i	$-0.357704\pi$
$887$	−3.90030e8	−	5.36830e8i	−0.558891	−	0.769247i	−0.991185	+	0.132486i	$0.957704\pi$
$888$	103686.	−	142712.i	0.000148075	−	0.000203808i
$889$	−6.63651e7	−	2.04251e8i	−0.0944571	−	0.290709i
$890$		−	4.05699e8i		−	0.575485i
$891$	3.89693e8	+	5.90319e8i	0.550921	+	0.834553i
$892$	−5.26733e8			−0.742158
$893$	−1.56322e8	+	5.07921e7i	−0.219516	+	0.0713250i
$894$	−246398.	−	179019.i	−0.000344845	−	0.000250545i
$895$	3.10703e8	−	2.25739e8i	0.433387	−	0.314874i
$896$	3.00539e7	−	9.24964e7i	0.0417808	−	0.128588i
$897$	522961.	+	169920.i	0.000724590	+	0.000235433i
$898$	−4.16239e8	−	5.72904e8i	−0.574796	−	0.791139i
$899$	5.86518e8	−	8.07273e8i	0.807240	−	1.11107i
$900$	−5.48832e7	−	1.68913e8i	−0.0752856	−	0.231705i
$901$		−	1.28205e8i		−	0.175279i
$902$	−2.02929e8	−	7.61533e7i	−0.276519	−	0.103769i
$903$	−1.05475e6			−0.00143247
$904$	−3.20067e7	+	1.03996e7i	−0.0433247	+	0.0140770i
$905$	−4.71890e8	−	3.42848e8i	−0.636642	−	0.462548i
$906$	616979.	−	448262.i	0.000829633	−	0.000602763i
$907$	−2.77147e8	+	8.52971e8i	−0.371440	+	1.14317i	0.574409	+	0.818568i	$0.305232\pi$
$907$	−2.77147e8	+	8.52971e8i	−0.371440	+	1.14317i	−0.945849	+	0.324606i	$0.894768\pi$
$908$	503910.	+	163730.i	0.000673125	+	0.000218712i
$909$	−1.20228e8	−	1.65479e8i	−0.160071	−	0.220319i
$910$	5.40005e8	−	7.43253e8i	0.716595	−	0.986308i
$911$	8.52301e7	+	2.62311e8i	0.112730	+	0.346946i	0.991467	−	0.130360i	$-0.0416133\pi$
$911$	8.52301e7	+	2.62311e8i	0.112730	+	0.346946i	−0.878737	+	0.477306i	$0.841613\pi$
$912$			36245.0i			4.77819e-5i
$913$	1.77277e8	−	4.72399e8i	0.232938	−	0.620721i
$914$	7.52713e8			0.985804
$915$	866029.	−	281390.i	0.00113050	−	0.000367320i
$916$	−5.21511e8	−	3.78900e8i	−0.678542	−	0.492990i
$917$	8.04448e7	−	5.84466e7i	0.104325	−	0.0757968i
$918$	−320179.	+	985409.i	−0.000413871	+	0.00127376i
$919$	−4.10782e8	−	1.33471e8i	−0.529255	−	0.171965i	0.0321862	−	0.999482i	$-0.489753\pi$
$919$	−4.10782e8	−	1.33471e8i	−0.529255	−	0.171965i	−0.561442	+	0.827516i	$0.689753\pi$
$920$	5.19357e7	+	7.14834e7i	0.0666964	+	0.0917998i
$921$	−166817.	+	229604.i	−0.000213532	+	0.000293901i
$922$	9.93730e6	+	3.05839e7i	0.0126787	+	0.0390211i
$923$			2.40924e9i			3.06391i
$924$	−543782.	+	358972.i	−0.000689301	+	0.000455035i
$925$	−2.54454e8			−0.321502
$926$	−4.10611e7	+	1.33415e7i	−0.0517127	+	0.0168025i
$927$	1.03301e8	+	7.50528e7i	0.129678	+	0.0942167i
$928$	2.05042e8	−	1.48972e8i	0.256566	−	0.186406i
$929$	2.36472e8	−	7.27787e8i	0.294940	−	0.907731i	−0.688302	−	0.725424i	$-0.741644\pi$
$929$	2.36472e8	−	7.27787e8i	0.294940	−	0.907731i	0.983242	−	0.182307i	$-0.0583564\pi$
$930$	320215.	+	104044.i	0.000398100	+	0.000129351i
$931$	−1.12482e8	−	1.54818e8i	−0.139390	−	0.191854i
$932$	−2.55350e8	+	3.51459e8i	−0.315419	+	0.434137i
$933$	−133094.	−	409622.i	−0.000163876	−	0.000504358i
$934$			9.49455e8i			1.16529i
$935$	4.01320e8	+	3.20022e8i	0.490972	+	0.391511i
$936$	−4.56356e8			−0.556514
$937$	3.05792e8	−	9.93578e7i	0.371713	−	0.120777i	−0.117203	−	0.993108i	$-0.537393\pi$
$937$	3.05792e8	−	9.93578e7i	0.371713	−	0.120777i	0.488915	+	0.872331i	$0.337393\pi$
$938$	−4.98912e8	−	3.62481e8i	−0.604527	−	0.439215i
$939$	212110.	−	154107.i	0.000256191	−	0.000186134i
$940$	−1.19841e8	+	3.68832e8i	−0.144285	+	0.444064i
$941$	5.10569e8	+	1.65894e8i	0.612753	+	0.199095i	0.598920	−	0.800809i	$-0.295597\pi$
$941$	5.10569e8	+	1.65894e8i	0.612753	+	0.199095i	0.0138329	+	0.999904i	$0.495597\pi$
$942$	120279.	+	165549.i	0.000143892	+	0.000198050i
$943$	9.22750e7	−	1.27006e8i	0.110040	−	0.151456i
$944$	−6.21501e7	−	1.91278e8i	−0.0738799	−	0.227379i
$945$		−	1.99645e6i		−	0.00236571i
$946$	5.00398e8	−	1.38118e8i	0.591075	−	0.163146i
$947$	1.10590e9			1.30216			0.651081	−	0.759008i	$-0.274316\pi$
$947$	1.10590e9			1.30216			0.651081	+	0.759008i	$0.274316\pi$
$948$	462663.	−	150328.i	0.000543050	−	0.000176448i
$949$	1.04042e9	+	7.55911e8i	1.21734	+	0.884447i
$950$	4.22973e7	−	3.07308e7i	0.0493335	−	0.0358429i
$951$	−50659.2	+	155913.i	−5.89002e−5	+	0.000181276i
$952$	3.89184e8	+	1.26453e8i	0.451070	+	0.146561i
$953$	8.46765e8	+	1.16547e9i	0.978328	+	1.34655i	0.937725	+	0.347377i	$0.112928\pi$
$953$	8.46765e8	+	1.16547e9i	0.978328	+	1.34655i	0.0406023	+	0.999175i	$0.487072\pi$
$954$	7.21265e7	−	9.92736e7i	0.0830710	−	0.114337i
$955$	2.60483e8	+	8.01684e8i	0.299068	+	0.920435i
$956$		−	4.06879e8i		−	0.465684i
$957$	−1.69629e6	−	76126.5i	−0.00193537	−	8.68560e-5i
$958$	−5.01116e8			−0.569956
$959$	−1.82226e8	+	5.92088e7i	−0.206611	+	0.0671321i
$960$	69185.4	+	50266.1i	7.81989e−5	+	5.68149e-5i
$961$	2.97217e8	−	2.15941e8i	0.334891	−	0.243313i
$962$	−2.02041e8	+	6.21817e8i	−0.226941	+	0.698453i
$963$	1.95961e8	+	6.36716e7i	0.219427	+	0.0712963i
$964$	1.12837e8	+	1.55307e8i	0.125957	+	0.173365i
$965$	−5.92227e8	+	8.15130e8i	−0.659031	+	0.907079i
$966$	−145835.	−	448834.i	−0.000161782	−	0.000497914i
$967$		−	5.47877e8i		−	0.605904i	−0.953006	−	0.302952i	$-0.902028\pi$
$967$		−	5.47877e8i		−	0.605904i	0.953006	−	0.302952i	$-0.0979721\pi$
$968$	2.10977e8	−	2.41513e8i	0.232600	−	0.266266i
$969$	−152503.			−0.000167613
$970$	6.88415e7	−	2.23680e7i	0.0754285	−	0.0245082i
$971$	−6.33216e8	−	4.60058e8i	−0.691662	−	0.502522i	0.185544	−	0.982636i	$-0.440595\pi$
$971$	−6.33216e8	−	4.60058e8i	−0.691662	−	0.502522i	−0.877206	+	0.480114i	$0.840595\pi$
$972$	−1.20346e6	+	874364.i	−0.00131049	+	0.000952124i
$973$	−7.65630e8	+	2.35637e9i	−0.831151	+	2.55802i
$974$	4.56234e8	+	1.48239e8i	0.493754	+	0.160430i
$975$	−451230.	−	621065.i	−0.000486838	−	0.000670075i
$976$	−2.10009e8	+	2.89052e8i	−0.225885	+	0.310905i
$977$	−3.66035e8	−	1.12654e9i	−0.392499	−	1.20799i	−0.930892	−	0.365294i	$-0.880968\pi$
$977$	−3.66035e8	−	1.12654e9i	−0.392499	−	1.20799i	0.538393	−	0.842694i	$-0.319032\pi$
$978$			428.997i			4.58604e-7i
$979$	4.78132e7	−	1.06540e9i	0.0509565	−	1.13544i
$980$	−4.51515e8			−0.479726
$981$	−1.59710e9	+	5.18929e8i	−1.69170	+	0.549668i
$982$	−1.12780e8	−	8.19396e7i	−0.119096	−	0.0865286i
$983$	9.17152e8	−	6.66350e8i	0.965564	−	0.701523i	0.0111274	−	0.999938i	$-0.496458\pi$
$983$	9.17152e8	−	6.66350e8i	0.965564	−	0.701523i	0.954436	+	0.298415i	$0.0964580\pi$
$984$	46952.3	−	144504.i	4.92801e−5	−	0.000151669i
$985$	−1.04953e9	−	3.41014e8i	−1.09821	−	0.356831i
$986$	6.26807e8	+	8.62725e8i	0.653887	+	0.899998i
$987$	1.21751e6	−	1.67576e6i	0.00126626	−	0.00174285i
$988$	−4.15130e7	−	1.27764e8i	−0.0430441	−	0.132476i
$989$			3.75984e8i			0.388670i
$990$	1.30717e8	+	4.73583e8i	0.134718	+	0.488079i
$991$	4.30307e8			0.442138			0.221069	−	0.975258i	$-0.429045\pi$
$991$	4.30307e8			0.442138			0.221069	+	0.975258i	$0.429045\pi$
$992$	−1.25642e8	+	4.08235e7i	−0.128706	+	0.0418192i
$993$	515520.	+	374548.i	0.000526500	+	0.000382524i
$994$	1.67284e9	−	1.21539e9i	1.70332	−	1.23753i
$995$	2.01401e8	−	6.19849e8i	0.204452	−	0.629240i
$996$	336391.	+	109300.i	0.000340460	+	0.000110622i
$997$	−6.21122e8	−	8.54901e8i	−0.626746	−	0.862642i	0.371076	−	0.928602i	$-0.378989\pi$
$997$	−6.21122e8	−	8.54901e8i	−0.626746	−	0.862642i	−0.997822	+	0.0659605i	$0.978989\pi$
$998$	−6.31547e7	+	8.69250e7i	−0.0635351	+	0.0874486i
$999$	439053.	+	1.35127e6i	0.000440373	+	0.00135533i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.7.d.a.17.2	yes	24
11.2	odd	10	inner	22.7.d.a.13.2	✓	24
11.3	even	5		242.7.b.e.241.22		24
11.8	odd	10		242.7.b.e.241.21		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.7.d.a.13.2	✓	24	11.2	odd	10	inner
22.7.d.a.17.2	yes	24	1.1	even	1	trivial
242.7.b.e.241.21		24	11.8	odd	10
242.7.b.e.241.22		24	11.3	even	5

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	22.d (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.37999 + 1.74806i) q^{2} +(0.0235888 + 0.0171383i) q^{3} +(25.8885 - 18.8091i) q^{4} +(-27.6593 + 85.1266i) q^{5} +(-0.156866 - 0.0509689i) q^{6} +(-308.398 - 424.474i) q^{7} +(-106.400 + 146.448i) q^{8} +(-225.273 - 693.319i) q^{9} -506.330i q^{10} +(59.6730 - 1329.66i) q^{11} +0.933035 q^{12} +(-3288.96 + 1068.65i) q^{13} +(2401.19 + 1744.56i) q^{14} +(-2.11137 + 1.53400i) q^{15} +(316.433 - 973.882i) q^{16} +(4097.66 + 1331.41i) q^{17} +(2423.93 + 3336.26i) q^{18} +(-713.540 + 982.104i) q^{19} +(885.098 + 2724.05i) q^{20} -15.2982i q^{21} +(2003.29 + 7257.88i) q^{22} -5453.35 q^{23} +(-5.01972 + 1.63100i) q^{24} +(6159.39 + 4475.06i) q^{25} +(15826.5 - 11498.6i) q^{26} +(13.1367 - 40.4307i) q^{27} +(-15968.0 - 5188.31i) q^{28} +(-25717.5 - 35397.1i) q^{29} +(8.67762 - 11.9437i) q^{30} +(7047.50 + 21690.0i) q^{31} +5792.62i q^{32} +(24.1957 - 30.3424i) q^{33} -24372.8 q^{34} +(44664.1 - 14512.3i) q^{35} +(-18872.7 - 13711.8i) q^{36} +(-27038.8 + 19644.8i) q^{37} +(2122.06 - 6531.02i) q^{38} +(-95.8972 - 31.1589i) q^{39} +(-9523.63 - 13108.2i) q^{40} +(-16920.8 + 23289.5i) q^{41} +(26.7423 + 82.3043i) q^{42} -68945.6i q^{43} +(-23464.9 - 35545.4i) q^{44} +65250.8 q^{45} +(29339.0 - 9532.80i) q^{46} +(109540. + 79585.2i) q^{47} +(24.1549 - 17.5496i) q^{48} +(-48713.0 + 149923. i) q^{49} +(-40960.1 - 13308.7i) q^{50} +(73.8408 + 101.633i) q^{51} +(-65046.0 + 89528.1i) q^{52} +(-9195.10 - 28299.6i) q^{53} +240.481i q^{54} +(111539. + 41857.3i) q^{55} +94977.0 q^{56} +(-33.6631 + 10.9378i) q^{57} +(200236. + 145480. i) q^{58} +(158898. - 115446. i) q^{59} +(-25.8071 + 79.4261i) q^{60} +(-331837. - 107821. i) q^{61} +(-75831.0 - 104372. i) q^{62} +(-224822. + 309441. i) q^{63} +(-10125.9 - 31164.2i) q^{64} -309536. i q^{65} +(-77.1321 + 205.537i) q^{66} -207777. q^{67} +(131125. - 42605.2i) q^{68} +(-128.638 - 93.4609i) q^{69} +(-214924. + 156151. i) q^{70} +(215284. - 662575. i) q^{71} +(125504. + 40778.8i) q^{72} +(-218584. - 300855. i) q^{73} +(111128. - 152954. i) q^{74} +(68.5978 + 211.122i) q^{75} +38846.3i q^{76} +(-582810. + 384736. i) q^{77} +570.394 q^{78} +(495869. - 161118. i) q^{79} +(74150.9 + 53873.8i) q^{80} +(-429943. + 312372. i) q^{81} +(50322.1 - 154876. i) q^{82} +(360535. + 117145. i) q^{83} +(-287.746 - 396.049i) q^{84} +(-226677. + 311994. i) q^{85} +(120521. + 370926. i) q^{86} -1275.73i q^{87} +(188377. + 150216. i) q^{88} +801254. q^{89} +(-351049. + 114063. i) q^{90} +(1.46792e6 + 1.06651e6i) q^{91} +(-141179. + 102573. i) q^{92} +(-205.486 + 632.422i) q^{93} +(-728442. - 236685. i) q^{94} +(-63867.2 - 87905.6i) q^{95} +(-99.2754 + 136.641i) q^{96} +(44176.6 + 135962. i) q^{97} -891739. i q^{98} +(-935323. + 258165. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 52 q^{3} + 192 q^{4} - 368 q^{5} + 400 q^{6} + 720 q^{7} - 3814 q^{9} + 4366 q^{11} + 3456 q^{12} + 3600 q^{13} - 4288 q^{14} - 2148 q^{15} - 6144 q^{16} - 5880 q^{17} + 18400 q^{18} - 23850 q^{19}+ \cdots + 4890070 q^{99}+O(q^{100}) \) 24 * q + 52 * q^3 + 192 * q^4 - 368 * q^5 + 400 * q^6 + 720 * q^7 - 3814 * q^9 + 4366 * q^11 + 3456 * q^12 + 3600 * q^13 - 4288 * q^14 - 2148 * q^15 - 6144 * q^16 - 5880 * q^17 + 18400 * q^18 - 23850 * q^19 + 11776 * q^20 - 1056 * q^22 - 40096 * q^23 + 12800 * q^24 + 69978 * q^25 + 52224 * q^26 + 4222 * q^27 - 32640 * q^28 - 204800 * q^29 - 134160 * q^30 + 71568 * q^31 + 11242 * q^33 + 88896 * q^34 + 469520 * q^35 + 25728 * q^36 + 309120 * q^37 - 73392 * q^38 - 328640 * q^39 - 107520 * q^40 - 541660 * q^41 - 177760 * q^42 + 213888 * q^44 + 811664 * q^45 + 213120 * q^46 - 299820 * q^47 + 53248 * q^48 - 374658 * q^49 - 364480 * q^50 - 1347330 * q^51 - 291840 * q^52 + 612820 * q^53 + 440004 * q^55 + 70656 * q^56 + 1416050 * q^57 + 552576 * q^58 + 927550 * q^59 + 206336 * q^60 - 1184160 * q^61 - 226640 * q^62 - 921200 * q^63 + 196608 * q^64 + 128672 * q^66 - 515100 * q^67 - 188160 * q^68 + 957220 * q^69 + 207984 * q^70 + 217572 * q^71 - 896000 * q^72 - 590340 * q^73 - 610400 * q^74 - 2208402 * q^75 - 2221964 * q^77 + 3228512 * q^78 + 93240 * q^79 + 196608 * q^80 + 1034076 * q^81 + 312960 * q^82 + 4588350 * q^83 + 2357760 * q^84 + 4132920 * q^85 + 1057632 * q^86 - 772608 * q^88 - 4638852 * q^89 - 6535040 * q^90 - 3916044 * q^91 - 2350208 * q^92 - 556628 * q^93 - 2410800 * q^94 + 661320 * q^95 - 342342 * q^97 + 4890070 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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