# Properties

 Label 240.3.c.e.209.1 Level $240$ Weight $3$ Character 240.209 Analytic conductor $6.540$ Analytic rank $0$ Dimension $12$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$240 = 2^{4} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 240.c (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.53952634465$$ Analytic rank: $$0$$ Dimension: $$12$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ Defining polynomial: $$x^{12} + 34 x^{10} + 305 x^{8} + 616 x^{6} + 305 x^{4} + 34 x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{15}\cdot 3^{2}$$ Twist minimal: no (minimal twist has level 120) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 209.1 Root $$-0.220185i$$ of defining polynomial Character $$\chi$$ $$=$$ 240.209 Dual form 240.3.c.e.209.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-2.72256 - 1.26002i) q^{3} +(-0.689011 + 4.95230i) q^{5} -0.735748i q^{7} +(5.82469 + 6.86097i) q^{9} +O(q^{10})$$ $$q+(-2.72256 - 1.26002i) q^{3} +(-0.689011 + 4.95230i) q^{5} -0.735748i q^{7} +(5.82469 + 6.86097i) q^{9} -10.9451i q^{11} -21.1901i q^{13} +(8.11588 - 12.6148i) q^{15} -7.03488 q^{17} -23.1529 q^{19} +(-0.927058 + 2.00312i) q^{21} -24.7483 q^{23} +(-24.0505 - 6.82438i) q^{25} +(-7.21312 - 26.0187i) q^{27} -32.3284i q^{29} +34.9482 q^{31} +(-13.7911 + 29.7987i) q^{33} +(3.64364 + 0.506939i) q^{35} -37.7818i q^{37} +(-26.6999 + 57.6912i) q^{39} -39.0848i q^{41} +22.6804i q^{43} +(-37.9909 + 24.1183i) q^{45} +39.1076 q^{47} +48.4587 q^{49} +(19.1529 + 8.86409i) q^{51} -60.9179 q^{53} +(54.2034 + 7.54130i) q^{55} +(63.0352 + 29.1731i) q^{57} -7.79696i q^{59} -11.1529 q^{61} +(5.04795 - 4.28551i) q^{63} +(104.939 + 14.6002i) q^{65} +33.3485i q^{67} +(67.3787 + 31.1833i) q^{69} -96.9650i q^{71} +134.535i q^{73} +(56.8802 + 48.8840i) q^{75} -8.05284 q^{77} -121.049 q^{79} +(-13.1459 + 79.9261i) q^{81} -90.2345 q^{83} +(4.84711 - 34.8388i) q^{85} +(-40.7344 + 88.0160i) q^{87} -53.1846i q^{89} -15.5905 q^{91} +(-95.1486 - 44.0354i) q^{93} +(15.9526 - 114.660i) q^{95} +115.001i q^{97} +(75.0940 - 63.7519i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q + 8 q^{9} + O(q^{10})$$ $$12 q + 8 q^{9} - 16 q^{15} + 4 q^{21} + 36 q^{25} + 48 q^{31} + 128 q^{39} - 68 q^{45} - 252 q^{49} - 48 q^{51} + 48 q^{55} + 144 q^{61} + 268 q^{69} - 304 q^{75} - 432 q^{79} - 188 q^{81} + 336 q^{85} + 560 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$$.

 $$n$$ $$31$$ $$97$$ $$161$$ $$181$$ $$\chi(n)$$ $$1$$ $$-1$$ $$-1$$ $$1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −2.72256 1.26002i −0.907521 0.420007i
$$4$$ 0 0
$$5$$ −0.689011 + 4.95230i −0.137802 + 0.990460i
$$6$$ 0 0
$$7$$ 0.735748i 0.105107i −0.998618 0.0525534i $$-0.983264\pi$$
0.998618 0.0525534i $$-0.0167360\pi$$
$$8$$ 0 0
$$9$$ 5.82469 + 6.86097i 0.647188 + 0.762330i
$$10$$ 0 0
$$11$$ 10.9451i 0.995009i −0.867461 0.497505i $$-0.834250\pi$$
0.867461 0.497505i $$-0.165750\pi$$
$$12$$ 0 0
$$13$$ 21.1901i 1.63000i −0.579458 0.815002i $$-0.696736\pi$$
0.579458 0.815002i $$-0.303264\pi$$
$$14$$ 0 0
$$15$$ 8.11588 12.6148i 0.541058 0.840985i
$$16$$ 0 0
$$17$$ −7.03488 −0.413816 −0.206908 0.978360i $$-0.566340\pi$$
−0.206908 + 0.978360i $$0.566340\pi$$
$$18$$ 0 0
$$19$$ −23.1529 −1.21857 −0.609287 0.792950i $$-0.708544\pi$$
−0.609287 + 0.792950i $$0.708544\pi$$
$$20$$ 0 0
$$21$$ −0.927058 + 2.00312i −0.0441456 + 0.0953867i
$$22$$ 0 0
$$23$$ −24.7483 −1.07601 −0.538006 0.842941i $$-0.680822\pi$$
−0.538006 + 0.842941i $$0.680822\pi$$
$$24$$ 0 0
$$25$$ −24.0505 6.82438i −0.962021 0.272975i
$$26$$ 0 0
$$27$$ −7.21312 26.0187i −0.267153 0.963654i
$$28$$ 0 0
$$29$$ 32.3284i 1.11477i −0.830254 0.557386i $$-0.811804\pi$$
0.830254 0.557386i $$-0.188196\pi$$
$$30$$ 0 0
$$31$$ 34.9482 1.12736 0.563680 0.825993i $$-0.309385\pi$$
0.563680 + 0.825993i $$0.309385\pi$$
$$32$$ 0 0
$$33$$ −13.7911 + 29.7987i −0.417911 + 0.902992i
$$34$$ 0 0
$$35$$ 3.64364 + 0.506939i 0.104104 + 0.0144840i
$$36$$ 0 0
$$37$$ 37.7818i 1.02113i −0.859839 0.510565i $$-0.829436\pi$$
0.859839 0.510565i $$-0.170564\pi$$
$$38$$ 0 0
$$39$$ −26.6999 + 57.6912i −0.684613 + 1.47926i
$$40$$ 0 0
$$41$$ 39.0848i 0.953288i −0.879096 0.476644i $$-0.841853\pi$$
0.879096 0.476644i $$-0.158147\pi$$
$$42$$ 0 0
$$43$$ 22.6804i 0.527451i 0.964598 + 0.263725i $$0.0849513\pi$$
−0.964598 + 0.263725i $$0.915049\pi$$
$$44$$ 0 0
$$45$$ −37.9909 + 24.1183i −0.844241 + 0.535963i
$$46$$ 0 0
$$47$$ 39.1076 0.832076 0.416038 0.909347i $$-0.363418\pi$$
0.416038 + 0.909347i $$0.363418\pi$$
$$48$$ 0 0
$$49$$ 48.4587 0.988953
$$50$$ 0 0
$$51$$ 19.1529 + 8.86409i 0.375547 + 0.173806i
$$52$$ 0 0
$$53$$ −60.9179 −1.14939 −0.574697 0.818366i $$-0.694880\pi$$
−0.574697 + 0.818366i $$0.694880\pi$$
$$54$$ 0 0
$$55$$ 54.2034 + 7.54130i 0.985517 + 0.137115i
$$56$$ 0 0
$$57$$ 63.0352 + 29.1731i 1.10588 + 0.511809i
$$58$$ 0 0
$$59$$ 7.79696i 0.132152i −0.997815 0.0660759i $$-0.978952\pi$$
0.997815 0.0660759i $$-0.0210480\pi$$
$$60$$ 0 0
$$61$$ −11.1529 −0.182834 −0.0914171 0.995813i $$-0.529140\pi$$
−0.0914171 + 0.995813i $$0.529140\pi$$
$$62$$ 0 0
$$63$$ 5.04795 4.28551i 0.0801262 0.0680239i
$$64$$ 0 0
$$65$$ 104.939 + 14.6002i 1.61445 + 0.224618i
$$66$$ 0 0
$$67$$ 33.3485i 0.497739i 0.968537 + 0.248869i $$0.0800590\pi$$
−0.968537 + 0.248869i $$0.919941\pi$$
$$68$$ 0 0
$$69$$ 67.3787 + 31.1833i 0.976503 + 0.451933i
$$70$$ 0 0
$$71$$ 96.9650i 1.36570i −0.730557 0.682852i $$-0.760739\pi$$
0.730557 0.682852i $$-0.239261\pi$$
$$72$$ 0 0
$$73$$ 134.535i 1.84295i 0.388436 + 0.921476i $$0.373016\pi$$
−0.388436 + 0.921476i $$0.626984\pi$$
$$74$$ 0 0
$$75$$ 56.8802 + 48.8840i 0.758403 + 0.651786i
$$76$$ 0 0
$$77$$ −8.05284 −0.104582
$$78$$ 0 0
$$79$$ −121.049 −1.53227 −0.766134 0.642681i $$-0.777822\pi$$
−0.766134 + 0.642681i $$0.777822\pi$$
$$80$$ 0 0
$$81$$ −13.1459 + 79.9261i −0.162295 + 0.986742i
$$82$$ 0 0
$$83$$ −90.2345 −1.08716 −0.543582 0.839356i $$-0.682932\pi$$
−0.543582 + 0.839356i $$0.682932\pi$$
$$84$$ 0 0
$$85$$ 4.84711 34.8388i 0.0570248 0.409868i
$$86$$ 0 0
$$87$$ −40.7344 + 88.0160i −0.468212 + 1.01168i
$$88$$ 0 0
$$89$$ 53.1846i 0.597579i −0.954319 0.298790i $$-0.903417\pi$$
0.954319 0.298790i $$-0.0965829\pi$$
$$90$$ 0 0
$$91$$ −15.5905 −0.171325
$$92$$ 0 0
$$93$$ −95.1486 44.0354i −1.02310 0.473499i
$$94$$ 0 0
$$95$$ 15.9526 114.660i 0.167922 1.20695i
$$96$$ 0 0
$$97$$ 115.001i 1.18557i 0.805359 + 0.592787i $$0.201972\pi$$
−0.805359 + 0.592787i $$0.798028\pi$$
$$98$$ 0 0
$$99$$ 75.0940 63.7519i 0.758526 0.643958i
$$100$$ 0 0
$$101$$ 29.1802i 0.288913i 0.989511 + 0.144457i $$0.0461434\pi$$
−0.989511 + 0.144457i $$0.953857\pi$$
$$102$$ 0 0
$$103$$ 89.9481i 0.873283i 0.899636 + 0.436641i $$0.143832\pi$$
−0.899636 + 0.436641i $$0.856168\pi$$
$$104$$ 0 0
$$105$$ −9.28130 5.97124i −0.0883933 0.0568690i
$$106$$ 0 0
$$107$$ 153.586 1.43538 0.717689 0.696363i $$-0.245200\pi$$
0.717689 + 0.696363i $$0.245200\pi$$
$$108$$ 0 0
$$109$$ −59.5623 −0.546444 −0.273222 0.961951i $$-0.588089\pi$$
−0.273222 + 0.961951i $$0.588089\pi$$
$$110$$ 0 0
$$111$$ −47.6059 + 102.863i −0.428882 + 0.926697i
$$112$$ 0 0
$$113$$ 1.01796 0.00900851 0.00450426 0.999990i $$-0.498566\pi$$
0.00450426 + 0.999990i $$0.498566\pi$$
$$114$$ 0 0
$$115$$ 17.0518 122.561i 0.148277 1.06575i
$$116$$ 0 0
$$117$$ 145.384 123.426i 1.24260 1.05492i
$$118$$ 0 0
$$119$$ 5.17590i 0.0434949i
$$120$$ 0 0
$$121$$ 1.20473 0.00995643
$$122$$ 0 0
$$123$$ −49.2477 + 106.411i −0.400388 + 0.865129i
$$124$$ 0 0
$$125$$ 50.3674 114.403i 0.402940 0.915227i
$$126$$ 0 0
$$127$$ 209.731i 1.65142i −0.564091 0.825712i $$-0.690773\pi$$
0.564091 0.825712i $$-0.309227\pi$$
$$128$$ 0 0
$$129$$ 28.5778 61.7488i 0.221533 0.478672i
$$130$$ 0 0
$$131$$ 210.051i 1.60344i 0.597698 + 0.801721i $$0.296082\pi$$
−0.597698 + 0.801721i $$0.703918\pi$$
$$132$$ 0 0
$$133$$ 17.0347i 0.128080i
$$134$$ 0 0
$$135$$ 133.822 17.7944i 0.991275 0.131810i
$$136$$ 0 0
$$137$$ −168.688 −1.23130 −0.615648 0.788021i $$-0.711106\pi$$
−0.615648 + 0.788021i $$0.711106\pi$$
$$138$$ 0 0
$$139$$ 129.251 0.929866 0.464933 0.885346i $$-0.346078\pi$$
0.464933 + 0.885346i $$0.346078\pi$$
$$140$$ 0 0
$$141$$ −106.473 49.2763i −0.755126 0.349478i
$$142$$ 0 0
$$143$$ −231.927 −1.62187
$$144$$ 0 0
$$145$$ 160.100 + 22.2746i 1.10414 + 0.153618i
$$146$$ 0 0
$$147$$ −131.932 61.0590i −0.897495 0.415367i
$$148$$ 0 0
$$149$$ 83.9655i 0.563527i 0.959484 + 0.281763i $$0.0909193\pi$$
−0.959484 + 0.281763i $$0.909081\pi$$
$$150$$ 0 0
$$151$$ −9.04922 −0.0599286 −0.0299643 0.999551i $$-0.509539\pi$$
−0.0299643 + 0.999551i $$0.509539\pi$$
$$152$$ 0 0
$$153$$ −40.9760 48.2661i −0.267817 0.315465i
$$154$$ 0 0
$$155$$ −24.0797 + 173.074i −0.155353 + 1.11660i
$$156$$ 0 0
$$157$$ 162.054i 1.03219i −0.856530 0.516097i $$-0.827384\pi$$
0.856530 0.516097i $$-0.172616\pi$$
$$158$$ 0 0
$$159$$ 165.853 + 76.7578i 1.04310 + 0.482754i
$$160$$ 0 0
$$161$$ 18.2085i 0.113096i
$$162$$ 0 0
$$163$$ 136.172i 0.835411i −0.908583 0.417705i $$-0.862834\pi$$
0.908583 0.417705i $$-0.137166\pi$$
$$164$$ 0 0
$$165$$ −138.070 88.8291i −0.836788 0.538358i
$$166$$ 0 0
$$167$$ 140.931 0.843898 0.421949 0.906620i $$-0.361346\pi$$
0.421949 + 0.906620i $$0.361346\pi$$
$$168$$ 0 0
$$169$$ −280.018 −1.65691
$$170$$ 0 0
$$171$$ −134.859 158.851i −0.788646 0.928955i
$$172$$ 0 0
$$173$$ −132.351 −0.765032 −0.382516 0.923949i $$-0.624942\pi$$
−0.382516 + 0.923949i $$0.624942\pi$$
$$174$$ 0 0
$$175$$ −5.02102 + 17.6951i −0.0286916 + 0.101115i
$$176$$ 0 0
$$177$$ −9.82433 + 21.2277i −0.0555047 + 0.119931i
$$178$$ 0 0
$$179$$ 92.2499i 0.515363i −0.966230 0.257681i $$-0.917042\pi$$
0.966230 0.257681i $$-0.0829585\pi$$
$$180$$ 0 0
$$181$$ 115.896 0.640311 0.320156 0.947365i $$-0.396265\pi$$
0.320156 + 0.947365i $$0.396265\pi$$
$$182$$ 0 0
$$183$$ 30.3644 + 14.0529i 0.165926 + 0.0767917i
$$184$$ 0 0
$$185$$ 187.107 + 26.0321i 1.01139 + 0.140714i
$$186$$ 0 0
$$187$$ 76.9974i 0.411751i
$$188$$ 0 0
$$189$$ −19.1432 + 5.30704i −0.101287 + 0.0280796i
$$190$$ 0 0
$$191$$ 53.1183i 0.278106i −0.990285 0.139053i $$-0.955594\pi$$
0.990285 0.139053i $$-0.0444059\pi$$
$$192$$ 0 0
$$193$$ 271.315i 1.40578i −0.711299 0.702890i $$-0.751893\pi$$
0.711299 0.702890i $$-0.248107\pi$$
$$194$$ 0 0
$$195$$ −267.308 171.976i −1.37081 0.881928i
$$196$$ 0 0
$$197$$ 64.3941 0.326873 0.163437 0.986554i $$-0.447742\pi$$
0.163437 + 0.986554i $$0.447742\pi$$
$$198$$ 0 0
$$199$$ −72.0308 −0.361964 −0.180982 0.983486i $$-0.557928\pi$$
−0.180982 + 0.983486i $$0.557928\pi$$
$$200$$ 0 0
$$201$$ 42.0198 90.7933i 0.209054 0.451708i
$$202$$ 0 0
$$203$$ −23.7855 −0.117170
$$204$$ 0 0
$$205$$ 193.560 + 26.9299i 0.944194 + 0.131365i
$$206$$ 0 0
$$207$$ −144.151 169.797i −0.696382 0.820276i
$$208$$ 0 0
$$209$$ 253.411i 1.21249i
$$210$$ 0 0
$$211$$ −108.583 −0.514613 −0.257307 0.966330i $$-0.582835\pi$$
−0.257307 + 0.966330i $$0.582835\pi$$
$$212$$ 0 0
$$213$$ −122.178 + 263.993i −0.573605 + 1.23940i
$$214$$ 0 0
$$215$$ −112.320 15.6270i −0.522419 0.0726839i
$$216$$ 0 0
$$217$$ 25.7130i 0.118493i
$$218$$ 0 0
$$219$$ 169.518 366.281i 0.774053 1.67252i
$$220$$ 0 0
$$221$$ 149.069i 0.674522i
$$222$$ 0 0
$$223$$ 83.6192i 0.374974i −0.982267 0.187487i $$-0.939966\pi$$
0.982267 0.187487i $$-0.0600342\pi$$
$$224$$ 0 0
$$225$$ −93.2651 204.760i −0.414511 0.910044i
$$226$$ 0 0
$$227$$ 51.6591 0.227573 0.113787 0.993505i $$-0.463702\pi$$
0.113787 + 0.993505i $$0.463702\pi$$
$$228$$ 0 0
$$229$$ −280.974 −1.22696 −0.613480 0.789710i $$-0.710231\pi$$
−0.613480 + 0.789710i $$0.710231\pi$$
$$230$$ 0 0
$$231$$ 21.9244 + 10.1467i 0.0949106 + 0.0439253i
$$232$$ 0 0
$$233$$ 169.192 0.726148 0.363074 0.931760i $$-0.381727\pi$$
0.363074 + 0.931760i $$0.381727\pi$$
$$234$$ 0 0
$$235$$ −26.9455 + 193.672i −0.114662 + 0.824137i
$$236$$ 0 0
$$237$$ 329.564 + 152.525i 1.39057 + 0.643564i
$$238$$ 0 0
$$239$$ 1.12039i 0.00468782i −0.999997 0.00234391i $$-0.999254\pi$$
0.999997 0.00234391i $$-0.000746090\pi$$
$$240$$ 0 0
$$241$$ 153.254 0.635908 0.317954 0.948106i $$-0.397004\pi$$
0.317954 + 0.948106i $$0.397004\pi$$
$$242$$ 0 0
$$243$$ 136.499 201.040i 0.561725 0.827324i
$$244$$ 0 0
$$245$$ −33.3886 + 239.982i −0.136280 + 0.979518i
$$246$$ 0 0
$$247$$ 490.611i 1.98628i
$$248$$ 0 0
$$249$$ 245.669 + 113.697i 0.986623 + 0.456616i
$$250$$ 0 0
$$251$$ 126.692i 0.504751i 0.967629 + 0.252375i $$0.0812118\pi$$
−0.967629 + 0.252375i $$0.918788\pi$$
$$252$$ 0 0
$$253$$ 270.872i 1.07064i
$$254$$ 0 0
$$255$$ −57.0942 + 88.7434i −0.223899 + 0.348013i
$$256$$ 0 0
$$257$$ −396.692 −1.54355 −0.771774 0.635897i $$-0.780630\pi$$
−0.771774 + 0.635897i $$0.780630\pi$$
$$258$$ 0 0
$$259$$ −27.7979 −0.107328
$$260$$ 0 0
$$261$$ 221.804 188.303i 0.849824 0.721467i
$$262$$ 0 0
$$263$$ 394.431 1.49974 0.749868 0.661587i $$-0.230117\pi$$
0.749868 + 0.661587i $$0.230117\pi$$
$$264$$ 0 0
$$265$$ 41.9731 301.684i 0.158389 1.13843i
$$266$$ 0 0
$$267$$ −67.0137 + 144.798i −0.250987 + 0.542316i
$$268$$ 0 0
$$269$$ 104.802i 0.389597i −0.980843 0.194798i $$-0.937595\pi$$
0.980843 0.194798i $$-0.0624053\pi$$
$$270$$ 0 0
$$271$$ 335.355 1.23747 0.618736 0.785599i $$-0.287645\pi$$
0.618736 + 0.785599i $$0.287645\pi$$
$$272$$ 0 0
$$273$$ 42.4462 + 19.6444i 0.155481 + 0.0719576i
$$274$$ 0 0
$$275$$ −74.6935 + 263.235i −0.271613 + 0.957220i
$$276$$ 0 0
$$277$$ 167.790i 0.605739i 0.953032 + 0.302870i $$0.0979447\pi$$
−0.953032 + 0.302870i $$0.902055\pi$$
$$278$$ 0 0
$$279$$ 203.562 + 239.778i 0.729614 + 0.859421i
$$280$$ 0 0
$$281$$ 99.4601i 0.353950i −0.984215 0.176975i $$-0.943369\pi$$
0.984215 0.176975i $$-0.0566312\pi$$
$$282$$ 0 0
$$283$$ 487.022i 1.72093i 0.509512 + 0.860464i $$0.329826\pi$$
−0.509512 + 0.860464i $$0.670174\pi$$
$$284$$ 0 0
$$285$$ −187.906 + 292.069i −0.659319 + 1.02480i
$$286$$ 0 0
$$287$$ −28.7566 −0.100197
$$288$$ 0 0
$$289$$ −239.511 −0.828756
$$290$$ 0 0
$$291$$ 144.903 313.097i 0.497950 1.07593i
$$292$$ 0 0
$$293$$ 343.107 1.17101 0.585507 0.810667i $$-0.300895\pi$$
0.585507 + 0.810667i $$0.300895\pi$$
$$294$$ 0 0
$$295$$ 38.6129 + 5.37219i 0.130891 + 0.0182108i
$$296$$ 0 0
$$297$$ −284.777 + 78.9484i −0.958845 + 0.265819i
$$298$$ 0 0
$$299$$ 524.417i 1.75390i
$$300$$ 0 0
$$301$$ 16.6870 0.0554387
$$302$$ 0 0
$$303$$ 36.7677 79.4450i 0.121346 0.262195i
$$304$$ 0 0
$$305$$ 7.68447 55.2325i 0.0251950 0.181090i
$$306$$ 0 0
$$307$$ 364.627i 1.18771i −0.804573 0.593854i $$-0.797606\pi$$
0.804573 0.593854i $$-0.202394\pi$$
$$308$$ 0 0
$$309$$ 113.337 244.889i 0.366785 0.792522i
$$310$$ 0 0
$$311$$ 121.963i 0.392164i −0.980587 0.196082i $$-0.937178\pi$$
0.980587 0.196082i $$-0.0628219\pi$$
$$312$$ 0 0
$$313$$ 94.8060i 0.302895i −0.988465 0.151447i $$-0.951607\pi$$
0.988465 0.151447i $$-0.0483934\pi$$
$$314$$ 0 0
$$315$$ 17.7450 + 27.9517i 0.0563334 + 0.0887356i
$$316$$ 0 0
$$317$$ 511.282 1.61288 0.806438 0.591318i $$-0.201392\pi$$
0.806438 + 0.591318i $$0.201392\pi$$
$$318$$ 0 0
$$319$$ −353.837 −1.10921
$$320$$ 0 0
$$321$$ −418.146 193.521i −1.30264 0.602869i
$$322$$ 0 0
$$323$$ 162.878 0.504265
$$324$$ 0 0
$$325$$ −144.609 + 509.632i −0.444951 + 1.56810i
$$326$$ 0 0
$$327$$ 162.162 + 75.0498i 0.495909 + 0.229510i
$$328$$ 0 0
$$329$$ 28.7733i 0.0874569i
$$330$$ 0 0
$$331$$ 182.682 0.551909 0.275954 0.961171i $$-0.411006\pi$$
0.275954 + 0.961171i $$0.411006\pi$$
$$332$$ 0 0
$$333$$ 259.220 220.067i 0.778438 0.660863i
$$334$$ 0 0
$$335$$ −165.152 22.9775i −0.492990 0.0685895i
$$336$$ 0 0
$$337$$ 89.0617i 0.264278i −0.991231 0.132139i $$-0.957815\pi$$
0.991231 0.132139i $$-0.0421845\pi$$
$$338$$ 0 0
$$339$$ −2.77147 1.28265i −0.00817541 0.00378364i
$$340$$ 0 0
$$341$$ 382.511i 1.12173i
$$342$$ 0 0
$$343$$ 71.7050i 0.209053i
$$344$$ 0 0
$$345$$ −200.854 + 312.194i −0.582185 + 0.904910i
$$346$$ 0 0
$$347$$ 17.7180 0.0510605 0.0255303 0.999674i $$-0.491873\pi$$
0.0255303 + 0.999674i $$0.491873\pi$$
$$348$$ 0 0
$$349$$ 229.114 0.656488 0.328244 0.944593i $$-0.393543\pi$$
0.328244 + 0.944593i $$0.393543\pi$$
$$350$$ 0 0
$$351$$ −551.337 + 152.846i −1.57076 + 0.435460i
$$352$$ 0 0
$$353$$ 183.760 0.520566 0.260283 0.965532i $$-0.416184\pi$$
0.260283 + 0.965532i $$0.416184\pi$$
$$354$$ 0 0
$$355$$ 480.199 + 66.8099i 1.35267 + 0.188197i
$$356$$ 0 0
$$357$$ 6.52174 14.0917i 0.0182682 0.0394726i
$$358$$ 0 0
$$359$$ 537.837i 1.49815i −0.662484 0.749076i $$-0.730498\pi$$
0.662484 0.749076i $$-0.269502\pi$$
$$360$$ 0 0
$$361$$ 175.056 0.484921
$$362$$ 0 0
$$363$$ −3.27995 1.51798i −0.00903567 0.00418177i
$$364$$ 0 0
$$365$$ −666.260 92.6964i −1.82537 0.253963i
$$366$$ 0 0
$$367$$ 153.740i 0.418909i −0.977818 0.209455i $$-0.932831\pi$$
0.977818 0.209455i $$-0.0671689\pi$$
$$368$$ 0 0
$$369$$ 268.160 227.657i 0.726721 0.616957i
$$370$$ 0 0
$$371$$ 44.8202i 0.120809i
$$372$$ 0 0
$$373$$ 211.056i 0.565833i −0.959145 0.282917i $$-0.908698\pi$$
0.959145 0.282917i $$-0.0913020\pi$$
$$374$$ 0 0
$$375$$ −281.279 + 248.006i −0.750078 + 0.661350i
$$376$$ 0 0
$$377$$ −685.040 −1.81708
$$378$$ 0 0
$$379$$ −699.345 −1.84524 −0.922618 0.385715i $$-0.873955\pi$$
−0.922618 + 0.385715i $$0.873955\pi$$
$$380$$ 0 0
$$381$$ −264.265 + 571.006i −0.693610 + 1.49870i
$$382$$ 0 0
$$383$$ −186.008 −0.485662 −0.242831 0.970069i $$-0.578076\pi$$
−0.242831 + 0.970069i $$0.578076\pi$$
$$384$$ 0 0
$$385$$ 5.54850 39.8801i 0.0144117 0.103585i
$$386$$ 0 0
$$387$$ −155.609 + 132.106i −0.402092 + 0.341360i
$$388$$ 0 0
$$389$$ 288.194i 0.740858i 0.928861 + 0.370429i $$0.120789\pi$$
−0.928861 + 0.370429i $$0.879211\pi$$
$$390$$ 0 0
$$391$$ 174.101 0.445271
$$392$$ 0 0
$$393$$ 264.669 571.877i 0.673457 1.45516i
$$394$$ 0 0
$$395$$ 83.4043 599.472i 0.211150 1.51765i
$$396$$ 0 0
$$397$$ 64.3054i 0.161978i 0.996715 + 0.0809892i $$0.0258079\pi$$
−0.996715 + 0.0809892i $$0.974192\pi$$
$$398$$ 0 0
$$399$$ 21.4641 46.3780i 0.0537947 0.116236i
$$400$$ 0 0
$$401$$ 659.774i 1.64532i 0.568533 + 0.822661i $$0.307511\pi$$
−0.568533 + 0.822661i $$0.692489\pi$$
$$402$$ 0 0
$$403$$ 740.553i 1.83760i
$$404$$ 0 0
$$405$$ −386.760 120.172i −0.954964 0.296722i
$$406$$ 0 0
$$407$$ −413.526 −1.01603
$$408$$ 0 0
$$409$$ 217.863 0.532672 0.266336 0.963880i $$-0.414187\pi$$
0.266336 + 0.963880i $$0.414187\pi$$
$$410$$ 0 0
$$411$$ 459.263 + 212.550i 1.11743 + 0.517153i
$$412$$ 0 0
$$413$$ −5.73660 −0.0138901
$$414$$ 0 0
$$415$$ 62.1726 446.868i 0.149814 1.07679i
$$416$$ 0 0
$$417$$ −351.895 162.859i −0.843872 0.390550i
$$418$$ 0 0
$$419$$ 407.129i 0.971668i 0.874051 + 0.485834i $$0.161484\pi$$
−0.874051 + 0.485834i $$0.838516\pi$$
$$420$$ 0 0
$$421$$ −69.1949 −0.164359 −0.0821793 0.996618i $$-0.526188\pi$$
−0.0821793 + 0.996618i $$0.526188\pi$$
$$422$$ 0 0
$$423$$ 227.790 + 268.316i 0.538510 + 0.634316i
$$424$$ 0 0
$$425$$ 169.192 + 48.0087i 0.398100 + 0.112962i
$$426$$ 0 0
$$427$$ 8.20572i 0.0192171i
$$428$$ 0 0
$$429$$ 631.437 + 292.233i 1.47188 + 0.681197i
$$430$$ 0 0
$$431$$ 452.663i 1.05026i −0.851021 0.525132i $$-0.824016\pi$$
0.851021 0.525132i $$-0.175984\pi$$
$$432$$ 0 0
$$433$$ 226.323i 0.522686i −0.965246 0.261343i $$-0.915835\pi$$
0.965246 0.261343i $$-0.0841654\pi$$
$$434$$ 0 0
$$435$$ −407.815 262.373i −0.937506 0.603156i
$$436$$ 0 0
$$437$$ 572.994 1.31120
$$438$$ 0 0
$$439$$ −188.642 −0.429709 −0.214855 0.976646i $$-0.568928\pi$$
−0.214855 + 0.976646i $$0.568928\pi$$
$$440$$ 0 0
$$441$$ 282.257 + 332.474i 0.640038 + 0.753908i
$$442$$ 0 0
$$443$$ 499.705 1.12800 0.564001 0.825774i $$-0.309261\pi$$
0.564001 + 0.825774i $$0.309261\pi$$
$$444$$ 0 0
$$445$$ 263.386 + 36.6448i 0.591878 + 0.0823478i
$$446$$ 0 0
$$447$$ 105.798 228.601i 0.236685 0.511412i
$$448$$ 0 0
$$449$$ 818.928i 1.82389i −0.410310 0.911946i $$-0.634579\pi$$
0.410310 0.911946i $$-0.365421\pi$$
$$450$$ 0 0
$$451$$ −427.787 −0.948531
$$452$$ 0 0
$$453$$ 24.6371 + 11.4022i 0.0543864 + 0.0251704i
$$454$$ 0 0
$$455$$ 10.7421 77.2090i 0.0236089 0.169690i
$$456$$ 0 0
$$457$$ 311.602i 0.681842i 0.940092 + 0.340921i $$0.110739\pi$$
−0.940092 + 0.340921i $$0.889261\pi$$
$$458$$ 0 0
$$459$$ 50.7434 + 183.038i 0.110552 + 0.398776i
$$460$$ 0 0
$$461$$ 7.18351i 0.0155825i 0.999970 + 0.00779123i $$0.00248005\pi$$
−0.999970 + 0.00779123i $$0.997520\pi$$
$$462$$ 0 0
$$463$$ 557.563i 1.20424i −0.798406 0.602120i $$-0.794323\pi$$
0.798406 0.602120i $$-0.205677\pi$$
$$464$$ 0 0
$$465$$ 283.635 440.863i 0.609968 0.948093i
$$466$$ 0 0
$$467$$ −659.257 −1.41168 −0.705842 0.708369i $$-0.749431\pi$$
−0.705842 + 0.708369i $$0.749431\pi$$
$$468$$ 0 0
$$469$$ 24.5361 0.0523157
$$470$$ 0 0
$$471$$ −204.192 + 441.203i −0.433529 + 0.936738i
$$472$$ 0 0
$$473$$ 248.239 0.524818
$$474$$ 0 0
$$475$$ 556.839 + 158.004i 1.17229 + 0.332640i
$$476$$ 0 0
$$477$$ −354.828 417.956i −0.743875 0.876218i
$$478$$ 0 0
$$479$$ 30.3870i 0.0634384i 0.999497 + 0.0317192i $$0.0100982\pi$$
−0.999497 + 0.0317192i $$0.989902\pi$$
$$480$$ 0 0
$$481$$ −800.598 −1.66445
$$482$$ 0 0
$$483$$ 22.9431 49.5738i 0.0475012 0.102637i
$$484$$ 0 0
$$485$$ −569.518 79.2368i −1.17426 0.163375i
$$486$$ 0 0
$$487$$ 26.5618i 0.0545416i −0.999628 0.0272708i $$-0.991318\pi$$
0.999628 0.0272708i $$-0.00868164\pi$$
$$488$$ 0 0
$$489$$ −171.580 + 370.737i −0.350878 + 0.758153i
$$490$$ 0 0
$$491$$ 19.3354i 0.0393796i 0.999806 + 0.0196898i $$0.00626786\pi$$
−0.999806 + 0.0196898i $$0.993732\pi$$
$$492$$ 0 0
$$493$$ 227.426i 0.461311i
$$494$$ 0 0
$$495$$ 263.978 + 415.814i 0.533288 + 0.840028i
$$496$$ 0 0
$$497$$ −71.3418 −0.143545
$$498$$ 0 0
$$499$$ −313.190 −0.627635 −0.313817 0.949483i $$-0.601608\pi$$
−0.313817 + 0.949483i $$0.601608\pi$$
$$500$$ 0 0
$$501$$ −383.693 177.576i −0.765855 0.354443i
$$502$$ 0 0
$$503$$ 551.684 1.09679 0.548394 0.836220i $$-0.315240\pi$$
0.548394 + 0.836220i $$0.315240\pi$$
$$504$$ 0 0
$$505$$ −144.509 20.1055i −0.286157 0.0398129i
$$506$$ 0 0
$$507$$ 762.368 + 352.829i 1.50368 + 0.695915i
$$508$$ 0 0
$$509$$ 567.057i 1.11406i −0.830492 0.557031i $$-0.811941\pi$$
0.830492 0.557031i $$-0.188059\pi$$
$$510$$ 0 0
$$511$$ 98.9842 0.193707
$$512$$ 0 0
$$513$$ 167.005 + 602.407i 0.325545 + 1.17428i
$$514$$ 0 0
$$515$$ −445.450 61.9753i −0.864951 0.120340i
$$516$$ 0 0
$$517$$ 428.036i 0.827923i
$$518$$ 0 0
$$519$$ 360.333 + 166.764i 0.694283 + 0.321319i
$$520$$ 0 0
$$521$$ 740.223i 1.42077i −0.703811 0.710387i $$-0.748520\pi$$
0.703811 0.710387i $$-0.251480\pi$$
$$522$$ 0 0
$$523$$ 2.11805i 0.00404981i 0.999998 + 0.00202491i $$0.000644548\pi$$
−0.999998 + 0.00202491i $$0.999355\pi$$
$$524$$ 0 0
$$525$$ 35.9663 41.8495i 0.0685072 0.0797133i
$$526$$ 0 0
$$527$$ −245.856 −0.466520
$$528$$ 0 0
$$529$$ 83.4771 0.157802
$$530$$ 0 0
$$531$$ 53.4947 45.4149i 0.100743 0.0855271i
$$532$$ 0 0
$$533$$ −828.210 −1.55386
$$534$$ 0 0
$$535$$ −105.822 + 760.602i −0.197798 + 1.42169i
$$536$$ 0 0
$$537$$ −116.237 + 251.156i −0.216456 + 0.467702i
$$538$$ 0 0
$$539$$ 530.385i 0.984017i
$$540$$ 0 0
$$541$$ 6.61681 0.0122307 0.00611535 0.999981i $$-0.498053\pi$$
0.00611535 + 0.999981i $$0.498053\pi$$
$$542$$ 0 0
$$543$$ −315.535 146.032i −0.581096 0.268935i
$$544$$ 0 0
$$545$$ 41.0391 294.971i 0.0753011 0.541230i
$$546$$ 0 0
$$547$$ 230.092i 0.420644i 0.977632 + 0.210322i $$0.0674512\pi$$
−0.977632 + 0.210322i $$0.932549\pi$$
$$548$$ 0 0
$$549$$ −64.9622 76.5197i −0.118328 0.139380i
$$550$$ 0 0
$$551$$ 748.495i 1.35843i
$$552$$ 0 0
$$553$$ 89.0617i 0.161052i
$$554$$ 0 0
$$555$$ −476.609 306.632i −0.858755 0.552491i
$$556$$ 0 0
$$557$$ 529.620 0.950844 0.475422 0.879758i $$-0.342295\pi$$
0.475422 + 0.879758i $$0.342295\pi$$
$$558$$ 0 0
$$559$$ 480.598 0.859747
$$560$$ 0 0
$$561$$ 97.0184 209.630i 0.172938 0.373673i
$$562$$ 0 0
$$563$$ 131.530 0.233623 0.116812 0.993154i $$-0.462733\pi$$
0.116812 + 0.993154i $$0.462733\pi$$
$$564$$ 0 0
$$565$$ −0.701387 + 5.04125i −0.00124139 + 0.00892257i
$$566$$ 0 0
$$567$$ 58.8055 + 9.67206i 0.103713 + 0.0170583i
$$568$$ 0 0
$$569$$ 172.534i 0.303224i 0.988440 + 0.151612i $$0.0484464\pi$$
−0.988440 + 0.151612i $$0.951554\pi$$
$$570$$ 0 0
$$571$$ −197.935 −0.346646 −0.173323 0.984865i $$-0.555450\pi$$
−0.173323 + 0.984865i $$0.555450\pi$$
$$572$$ 0 0
$$573$$ −66.9302 + 144.618i −0.116807 + 0.252387i
$$574$$ 0 0
$$575$$ 595.209 + 168.892i 1.03515 + 0.293724i
$$576$$ 0 0
$$577$$ 865.374i 1.49978i 0.661562 + 0.749891i $$0.269894\pi$$
−0.661562 + 0.749891i $$0.730106\pi$$
$$578$$ 0 0
$$579$$ −341.863 + 738.673i −0.590437 + 1.27577i
$$580$$ 0 0
$$581$$ 66.3899i 0.114268i
$$582$$ 0 0
$$583$$ 666.753i 1.14366i
$$584$$ 0 0
$$585$$ 511.069 + 805.028i 0.873622 + 1.37612i
$$586$$ 0 0
$$587$$ −30.8886 −0.0526211 −0.0263105 0.999654i $$-0.508376\pi$$
−0.0263105 + 0.999654i $$0.508376\pi$$
$$588$$ 0 0
$$589$$ −809.151 −1.37377
$$590$$ 0 0
$$591$$ −175.317 81.1379i −0.296644 0.137289i
$$592$$ 0 0
$$593$$ 511.286 0.862202 0.431101 0.902304i $$-0.358125\pi$$
0.431101 + 0.902304i $$0.358125\pi$$
$$594$$ 0 0
$$595$$ −25.6326 3.56625i −0.0430800 0.00599370i
$$596$$ 0 0
$$597$$ 196.108 + 90.7603i 0.328490 + 0.152027i
$$598$$ 0 0
$$599$$ 514.866i 0.859543i −0.902938 0.429772i $$-0.858594\pi$$
0.902938 0.429772i $$-0.141406\pi$$
$$600$$ 0 0
$$601$$ 853.532 1.42019 0.710093 0.704107i $$-0.248653\pi$$
0.710093 + 0.704107i $$0.248653\pi$$
$$602$$ 0 0
$$603$$ −228.803 + 194.245i −0.379441 + 0.322131i
$$604$$ 0 0
$$605$$ −0.830071 + 5.96618i −0.00137202 + 0.00986145i
$$606$$ 0 0
$$607$$ 88.0713i 0.145093i 0.997365 + 0.0725464i $$0.0231125\pi$$
−0.997365 + 0.0725464i $$0.976887\pi$$
$$608$$ 0 0
$$609$$ 64.7576 + 29.9703i 0.106334 + 0.0492123i
$$610$$ 0 0
$$611$$ 828.691i 1.35629i
$$612$$ 0 0
$$613$$ 403.346i 0.657987i −0.944332 0.328994i $$-0.893291\pi$$
0.944332 0.328994i $$-0.106709\pi$$
$$614$$ 0 0
$$615$$ −493.046 317.208i −0.801701 0.515785i
$$616$$ 0 0
$$617$$ 365.738 0.592769 0.296384 0.955069i $$-0.404219\pi$$
0.296384 + 0.955069i $$0.404219\pi$$
$$618$$ 0 0
$$619$$ 399.495 0.645389 0.322694 0.946503i $$-0.395411\pi$$
0.322694 + 0.946503i $$0.395411\pi$$
$$620$$ 0 0
$$621$$ 178.512 + 643.917i 0.287460 + 1.03690i
$$622$$ 0 0
$$623$$ −39.1304 −0.0628097
$$624$$ 0 0
$$625$$ 531.856 + 328.260i 0.850969 + 0.525216i
$$626$$ 0 0
$$627$$ 319.303 689.927i 0.509255 1.10036i
$$628$$ 0 0
$$629$$ 265.790i 0.422560i
$$630$$ 0 0
$$631$$ 715.762 1.13433 0.567165 0.823604i $$-0.308040\pi$$
0.567165 + 0.823604i $$0.308040\pi$$
$$632$$ 0 0
$$633$$ 295.625 + 136.817i 0.467022 + 0.216141i
$$634$$ 0 0
$$635$$ 1038.65 + 144.507i 1.63567 + 0.227570i
$$636$$ 0 0
$$637$$ 1026.84i 1.61200i
$$638$$ 0 0
$$639$$ 665.274 564.791i 1.04112 0.883867i
$$640$$ 0 0
$$641$$ 627.158i 0.978406i 0.872170 + 0.489203i $$0.162712\pi$$
−0.872170 + 0.489203i $$0.837288\pi$$
$$642$$ 0 0
$$643$$ 802.039i 1.24734i 0.781688 + 0.623669i $$0.214359\pi$$
−0.781688 + 0.623669i $$0.785641\pi$$
$$644$$ 0 0
$$645$$ 286.108 + 184.071i 0.443578 + 0.285382i
$$646$$ 0 0
$$647$$ 19.9275 0.0307998 0.0153999 0.999881i $$-0.495098\pi$$
0.0153999 + 0.999881i $$0.495098\pi$$
$$648$$ 0 0
$$649$$ −85.3385 −0.131492
$$650$$ 0 0
$$651$$ −32.3990 + 70.0054i −0.0497680 + 0.107535i
$$652$$ 0 0
$$653$$ −78.4638 −0.120159 −0.0600795 0.998194i $$-0.519135\pi$$
−0.0600795 + 0.998194i $$0.519135\pi$$
$$654$$ 0 0
$$655$$ −1040.23 144.727i −1.58815 0.220958i
$$656$$ 0 0
$$657$$ −923.044 + 783.628i −1.40494 + 1.19274i
$$658$$ 0 0
$$659$$ 371.793i 0.564178i −0.959388 0.282089i $$-0.908973\pi$$
0.959388 0.282089i $$-0.0910274\pi$$
$$660$$ 0 0
$$661$$ 782.868 1.18437 0.592185 0.805802i $$-0.298266\pi$$
0.592185 + 0.805802i $$0.298266\pi$$
$$662$$ 0 0
$$663$$ 187.831 405.851i 0.283304 0.612143i
$$664$$ 0 0
$$665$$ −84.3609 11.7371i −0.126859 0.0176498i
$$666$$ 0 0
$$667$$ 800.071i 1.19951i
$$668$$ 0 0
$$669$$ −105.362 + 227.658i −0.157492 + 0.340297i
$$670$$ 0 0
$$671$$ 122.070i 0.181922i
$$672$$ 0 0
$$673$$ 221.323i 0.328860i 0.986389 + 0.164430i $$0.0525785\pi$$
−0.986389 + 0.164430i $$0.947421\pi$$
$$674$$ 0 0
$$675$$ −4.08178 + 674.988i −0.00604707 + 0.999982i
$$676$$ 0 0
$$677$$ 576.855 0.852076 0.426038 0.904705i $$-0.359909\pi$$
0.426038 + 0.904705i $$0.359909\pi$$
$$678$$ 0 0
$$679$$ 84.6116 0.124612
$$680$$ 0 0
$$681$$ −140.645 65.0916i −0.206527 0.0955824i
$$682$$ 0 0
$$683$$ −1272.02 −1.86239 −0.931197 0.364516i $$-0.881234\pi$$
−0.931197 + 0.364516i $$0.881234\pi$$
$$684$$ 0 0
$$685$$ 116.228 835.392i 0.169675 1.21955i
$$686$$ 0 0
$$687$$ 764.969 + 354.033i 1.11349 + 0.515332i
$$688$$ 0 0
$$689$$ 1290.85i 1.87352i
$$690$$ 0 0
$$691$$ −1.61487 −0.00233701 −0.00116851 0.999999i $$-0.500372\pi$$
−0.00116851 + 0.999999i $$0.500372\pi$$
$$692$$ 0 0
$$693$$ −46.9053 55.2503i −0.0676844 0.0797263i
$$694$$ 0 0
$$695$$ −89.0556 + 640.091i −0.128138 + 0.920995i
$$696$$ 0 0
$$697$$ 274.957i 0.394486i
$$698$$ 0 0
$$699$$ −460.637 213.186i −0.658994 0.304987i
$$700$$ 0 0
$$701$$ 550.235i 0.784929i −0.919767 0.392465i $$-0.871623\pi$$
0.919767 0.392465i $$-0.128377\pi$$
$$702$$ 0 0
$$703$$ 874.758i 1.24432i
$$704$$ 0 0
$$705$$ 317.392 493.333i 0.450202 0.699763i
$$706$$ 0 0
$$707$$ 21.4693 0.0303668
$$708$$ 0 0
$$709$$ −430.539 −0.607249 −0.303624 0.952792i $$-0.598197\pi$$
−0.303624 + 0.952792i $$0.598197\pi$$
$$710$$ 0 0
$$711$$ −705.075 830.515i −0.991666 1.16809i
$$712$$ 0 0
$$713$$ −864.907 −1.21305
$$714$$ 0 0
$$715$$ 159.801 1148.57i 0.223497 1.60640i
$$716$$ 0 0
$$717$$ −1.41171 + 3.05033i −0.00196892 + 0.00425429i
$$718$$ 0 0
$$719$$ 460.561i 0.640558i 0.947323 + 0.320279i $$0.103777\pi$$
−0.947323 + 0.320279i $$0.896223\pi$$
$$720$$ 0 0
$$721$$ 66.1792 0.0917880
$$722$$ 0 0
$$723$$ −417.243 193.103i −0.577100 0.267086i
$$724$$ 0 0
$$725$$ −220.621 + 777.514i −0.304305 + 1.07243i
$$726$$ 0 0
$$727$$ 413.275i 0.568467i −0.958755 0.284233i $$-0.908261\pi$$
0.958755 0.284233i $$-0.0917390\pi$$
$$728$$ 0 0
$$729$$ −624.942 + 375.352i −0.857259 + 0.514886i
$$730$$ 0 0
$$731$$ 159.554i 0.218268i
$$732$$ 0 0
$$733$$ 307.003i 0.418831i 0.977827 + 0.209416i $$0.0671562\pi$$
−0.977827 + 0.209416i $$0.932844\pi$$
$$734$$ 0 0
$$735$$ 393.285 611.295i 0.535081 0.831694i
$$736$$ 0 0
$$737$$ 365.003 0.495255
$$738$$ 0 0
$$739$$ 988.511 1.33763 0.668817 0.743427i $$-0.266801\pi$$
0.668817 + 0.743427i $$0.266801\pi$$
$$740$$ 0 0
$$741$$ 618.180 1335.72i 0.834251 1.80259i
$$742$$ 0 0
$$743$$ −652.187 −0.877775 −0.438887 0.898542i $$-0.644627\pi$$
−0.438887 + 0.898542i $$0.644627\pi$$
$$744$$ 0 0
$$745$$ −415.822 57.8532i −0.558151 0.0776552i
$$746$$ 0 0
$$747$$ −525.589 619.097i −0.703599 0.828777i
$$748$$ 0 0
$$749$$ 113.000i 0.150868i
$$750$$ 0 0
$$751$$ −554.876 −0.738850 −0.369425 0.929261i $$-0.620445\pi$$
−0.369425 + 0.929261i $$0.620445\pi$$
$$752$$ 0 0
$$753$$ 159.635 344.928i 0.211999 0.458072i
$$754$$ 0 0
$$755$$ 6.23501 44.8144i 0.00825829 0.0593569i
$$756$$ 0 0
$$757$$ 547.156i 0.722795i −0.932412 0.361397i $$-0.882300\pi$$
0.932412 0.361397i $$-0.117700\pi$$
$$758$$ 0 0
$$759$$ 341.305 737.467i 0.449677 0.971630i
$$760$$ 0 0
$$761$$ 1361.34i 1.78888i −0.447184 0.894442i $$-0.647573\pi$$
0.447184 0.894442i $$-0.352427\pi$$
$$762$$ 0 0
$$763$$ 43.8229i 0.0574350i
$$764$$ 0 0
$$765$$ 267.261 169.670i 0.349361 0.221790i
$$766$$ 0 0
$$767$$ −165.218 −0.215408
$$768$$ 0 0
$$769$$ −396.180 −0.515188 −0.257594 0.966253i $$-0.582930\pi$$
−0.257594 + 0.966253i $$0.582930\pi$$
$$770$$ 0 0
$$771$$ 1080.02 + 499.840i 1.40080 + 0.648301i
$$772$$ 0 0
$$773$$ −664.286 −0.859361 −0.429681 0.902981i $$-0.641374\pi$$
−0.429681 + 0.902981i $$0.641374\pi$$
$$774$$ 0 0
$$775$$ −840.522 238.499i −1.08454 0.307741i
$$776$$ 0 0
$$777$$ 75.6815 + 35.0259i 0.0974022 + 0.0450784i
$$778$$ 0 0
$$779$$ 904.927i 1.16165i
$$780$$ 0 0
$$781$$ −1061.29 −1.35889
$$782$$ 0 0
$$783$$ −841.141 + 233.189i −1.07425 + 0.297814i
$$784$$ 0 0
$$785$$ 802.542 + 111.657i 1.02235 + 0.142239i
$$786$$ 0 0
$$787$$ 957.551i 1.21671i −0.793665 0.608355i $$-0.791830\pi$$
0.793665 0.608355i $$-0.208170\pi$$
$$788$$ 0 0
$$789$$ −1073.86 496.991i −1.36104 0.629900i
$$790$$ 0 0
$$791$$ 0.748964i 0.000946857i
$$792$$ 0 0
$$793$$ 236.330i 0.298021i
$$794$$ 0 0
$$795$$ −494.402 + 768.466i −0.621890 + 0.966623i
$$796$$ 0 0
$$797$$ −643.860 −0.807854 −0.403927 0.914791i $$-0.632355\pi$$
−0.403927 + 0.914791i $$0.632355\pi$$
$$798$$ 0 0
$$799$$ −275.117