# Properties

 Label 1050.3.f.e.601.14 Level $1050$ Weight $3$ Character 1050.601 Analytic conductor $28.610$ Analytic rank $0$ Dimension $16$ CM no Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1050.f (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$28.6104277578$$ Analytic rank: $$0$$ Dimension: $$16$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ Defining polynomial: $$x^{16} - 8 x^{15} + 88 x^{14} - 476 x^{13} + 2744 x^{12} - 10640 x^{11} + 39126 x^{10} - 108488 x^{9} + 259514 x^{8} - 486436 x^{7} + 690168 x^{6} - 725188 x^{5} + \cdots + 33124$$ x^16 - 8*x^15 + 88*x^14 - 476*x^13 + 2744*x^12 - 10640*x^11 + 39126*x^10 - 108488*x^9 + 259514*x^8 - 486436*x^7 + 690168*x^6 - 725188*x^5 + 619745*x^4 - 430504*x^3 + 108130*x^2 + 42224*x + 33124 Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2^{20}$$ Twist minimal: no (minimal twist has level 210) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 601.14 Root $$1.20711 + 3.39361i$$ of defining polynomial Character $$\chi$$ $$=$$ 1050.601 Dual form 1050.3.f.e.601.10

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(-1.57881 + 6.81963i) q^{7} +2.82843 q^{8} -3.00000 q^{9} +O(q^{10})$$ $$q+1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} +2.44949i q^{6} +(-1.57881 + 6.81963i) q^{7} +2.82843 q^{8} -3.00000 q^{9} -8.15965 q^{11} +3.46410i q^{12} -14.6064i q^{13} +(-2.23278 + 9.64441i) q^{14} +4.00000 q^{16} +5.81421i q^{17} -4.24264 q^{18} +33.7736i q^{19} +(-11.8119 - 2.73459i) q^{21} -11.5395 q^{22} -37.2576 q^{23} +4.89898i q^{24} -20.6566i q^{26} -5.19615i q^{27} +(-3.15763 + 13.6393i) q^{28} +9.25305 q^{29} +19.2558i q^{31} +5.65685 q^{32} -14.1329i q^{33} +8.22253i q^{34} -6.00000 q^{36} -63.4350 q^{37} +47.7631i q^{38} +25.2990 q^{39} -8.25880i q^{41} +(-16.7046 - 3.86729i) q^{42} +42.0893 q^{43} -16.3193 q^{44} -52.6901 q^{46} +23.3380i q^{47} +6.92820i q^{48} +(-44.0147 - 21.5339i) q^{49} -10.0705 q^{51} -29.2128i q^{52} -71.3497 q^{53} -7.34847i q^{54} +(-4.46556 + 19.2888i) q^{56} -58.4976 q^{57} +13.0858 q^{58} -42.9350i q^{59} +34.2864i q^{61} +27.2318i q^{62} +(4.73644 - 20.4589i) q^{63} +8.00000 q^{64} -19.9870i q^{66} -4.99889 q^{67} +11.6284i q^{68} -64.5320i q^{69} -38.8120 q^{71} -8.48528 q^{72} -124.629i q^{73} -89.7107 q^{74} +67.5472i q^{76} +(12.8826 - 55.6458i) q^{77} +35.7782 q^{78} +56.1842 q^{79} +9.00000 q^{81} -11.6797i q^{82} +90.3980i q^{83} +(-23.6239 - 5.46917i) q^{84} +59.5233 q^{86} +16.0267i q^{87} -23.0790 q^{88} +16.2289i q^{89} +(99.6102 + 23.0608i) q^{91} -74.5151 q^{92} -33.3520 q^{93} +33.0048i q^{94} +9.79796i q^{96} +82.7605i q^{97} +(-62.2462 - 30.4535i) q^{98} +24.4789 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16 q + 32 q^{4} - 48 q^{9}+O(q^{10})$$ 16 * q + 32 * q^4 - 48 * q^9 $$16 q + 32 q^{4} - 48 q^{9} + 96 q^{11} - 16 q^{14} + 64 q^{16} + 24 q^{21} - 64 q^{29} - 96 q^{36} + 144 q^{39} + 192 q^{44} - 176 q^{46} - 224 q^{49} - 48 q^{51} - 32 q^{56} + 128 q^{64} - 384 q^{71} - 224 q^{74} + 608 q^{79} + 144 q^{81} + 48 q^{84} + 416 q^{86} + 224 q^{91} - 288 q^{99}+O(q^{100})$$ 16 * q + 32 * q^4 - 48 * q^9 + 96 * q^11 - 16 * q^14 + 64 * q^16 + 24 * q^21 - 64 * q^29 - 96 * q^36 + 144 * q^39 + 192 * q^44 - 176 * q^46 - 224 * q^49 - 48 * q^51 - 32 * q^56 + 128 * q^64 - 384 * q^71 - 224 * q^74 + 608 * q^79 + 144 * q^81 + 48 * q^84 + 416 * q^86 + 224 * q^91 - 288 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$451$$ $$701$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.41421 0.707107
$$3$$ 1.73205i 0.577350i
$$4$$ 2.00000 0.500000
$$5$$ 0 0
$$6$$ 2.44949i 0.408248i
$$7$$ −1.57881 + 6.81963i −0.225545 + 0.974233i
$$8$$ 2.82843 0.353553
$$9$$ −3.00000 −0.333333
$$10$$ 0 0
$$11$$ −8.15965 −0.741786 −0.370893 0.928676i $$-0.620948\pi$$
−0.370893 + 0.928676i $$0.620948\pi$$
$$12$$ 3.46410i 0.288675i
$$13$$ 14.6064i 1.12357i −0.827284 0.561785i $$-0.810115\pi$$
0.827284 0.561785i $$-0.189885\pi$$
$$14$$ −2.23278 + 9.64441i −0.159484 + 0.688887i
$$15$$ 0 0
$$16$$ 4.00000 0.250000
$$17$$ 5.81421i 0.342012i 0.985270 + 0.171006i $$0.0547018\pi$$
−0.985270 + 0.171006i $$0.945298\pi$$
$$18$$ −4.24264 −0.235702
$$19$$ 33.7736i 1.77756i 0.458337 + 0.888778i $$0.348445\pi$$
−0.458337 + 0.888778i $$0.651555\pi$$
$$20$$ 0 0
$$21$$ −11.8119 2.73459i −0.562474 0.130218i
$$22$$ −11.5395 −0.524522
$$23$$ −37.2576 −1.61989 −0.809947 0.586503i $$-0.800504\pi$$
−0.809947 + 0.586503i $$0.800504\pi$$
$$24$$ 4.89898i 0.204124i
$$25$$ 0 0
$$26$$ 20.6566i 0.794483i
$$27$$ 5.19615i 0.192450i
$$28$$ −3.15763 + 13.6393i −0.112772 + 0.487116i
$$29$$ 9.25305 0.319071 0.159535 0.987192i $$-0.449000\pi$$
0.159535 + 0.987192i $$0.449000\pi$$
$$30$$ 0 0
$$31$$ 19.2558i 0.621154i 0.950548 + 0.310577i $$0.100522\pi$$
−0.950548 + 0.310577i $$0.899478\pi$$
$$32$$ 5.65685 0.176777
$$33$$ 14.1329i 0.428270i
$$34$$ 8.22253i 0.241839i
$$35$$ 0 0
$$36$$ −6.00000 −0.166667
$$37$$ −63.4350 −1.71446 −0.857230 0.514933i $$-0.827817\pi$$
−0.857230 + 0.514933i $$0.827817\pi$$
$$38$$ 47.7631i 1.25692i
$$39$$ 25.2990 0.648693
$$40$$ 0 0
$$41$$ 8.25880i 0.201434i −0.994915 0.100717i $$-0.967886\pi$$
0.994915 0.100717i $$-0.0321137\pi$$
$$42$$ −16.7046 3.86729i −0.397729 0.0920783i
$$43$$ 42.0893 0.978822 0.489411 0.872053i $$-0.337212\pi$$
0.489411 + 0.872053i $$0.337212\pi$$
$$44$$ −16.3193 −0.370893
$$45$$ 0 0
$$46$$ −52.6901 −1.14544
$$47$$ 23.3380i 0.496552i 0.968689 + 0.248276i $$0.0798640\pi$$
−0.968689 + 0.248276i $$0.920136\pi$$
$$48$$ 6.92820i 0.144338i
$$49$$ −44.0147 21.5339i −0.898259 0.439466i
$$50$$ 0 0
$$51$$ −10.0705 −0.197461
$$52$$ 29.2128i 0.561785i
$$53$$ −71.3497 −1.34622 −0.673110 0.739542i $$-0.735042\pi$$
−0.673110 + 0.739542i $$0.735042\pi$$
$$54$$ 7.34847i 0.136083i
$$55$$ 0 0
$$56$$ −4.46556 + 19.2888i −0.0797422 + 0.344443i
$$57$$ −58.4976 −1.02627
$$58$$ 13.0858 0.225617
$$59$$ 42.9350i 0.727712i −0.931455 0.363856i $$-0.881460\pi$$
0.931455 0.363856i $$-0.118540\pi$$
$$60$$ 0 0
$$61$$ 34.2864i 0.562072i 0.959697 + 0.281036i $$0.0906781\pi$$
−0.959697 + 0.281036i $$0.909322\pi$$
$$62$$ 27.2318i 0.439222i
$$63$$ 4.73644 20.4589i 0.0751816 0.324744i
$$64$$ 8.00000 0.125000
$$65$$ 0 0
$$66$$ 19.9870i 0.302833i
$$67$$ −4.99889 −0.0746102 −0.0373051 0.999304i $$-0.511877\pi$$
−0.0373051 + 0.999304i $$0.511877\pi$$
$$68$$ 11.6284i 0.171006i
$$69$$ 64.5320i 0.935246i
$$70$$ 0 0
$$71$$ −38.8120 −0.546648 −0.273324 0.961922i $$-0.588123\pi$$
−0.273324 + 0.961922i $$0.588123\pi$$
$$72$$ −8.48528 −0.117851
$$73$$ 124.629i 1.70725i −0.520886 0.853626i $$-0.674398\pi$$
0.520886 0.853626i $$-0.325602\pi$$
$$74$$ −89.7107 −1.21231
$$75$$ 0 0
$$76$$ 67.5472i 0.888778i
$$77$$ 12.8826 55.6458i 0.167306 0.722672i
$$78$$ 35.7782 0.458695
$$79$$ 56.1842 0.711192 0.355596 0.934640i $$-0.384278\pi$$
0.355596 + 0.934640i $$0.384278\pi$$
$$80$$ 0 0
$$81$$ 9.00000 0.111111
$$82$$ 11.6797i 0.142435i
$$83$$ 90.3980i 1.08913i 0.838718 + 0.544566i $$0.183306\pi$$
−0.838718 + 0.544566i $$0.816694\pi$$
$$84$$ −23.6239 5.46917i −0.281237 0.0651092i
$$85$$ 0 0
$$86$$ 59.5233 0.692131
$$87$$ 16.0267i 0.184215i
$$88$$ −23.0790 −0.262261
$$89$$ 16.2289i 0.182347i 0.995835 + 0.0911736i $$0.0290618\pi$$
−0.995835 + 0.0911736i $$0.970938\pi$$
$$90$$ 0 0
$$91$$ 99.6102 + 23.0608i 1.09462 + 0.253415i
$$92$$ −74.5151 −0.809947
$$93$$ −33.3520 −0.358624
$$94$$ 33.0048i 0.351115i
$$95$$ 0 0
$$96$$ 9.79796i 0.102062i
$$97$$ 82.7605i 0.853201i 0.904440 + 0.426601i $$0.140289\pi$$
−0.904440 + 0.426601i $$0.859711\pi$$
$$98$$ −62.2462 30.4535i −0.635165 0.310750i
$$99$$ 24.4789 0.247262
$$100$$ 0 0
$$101$$ 87.2055i 0.863420i 0.902012 + 0.431710i $$0.142090\pi$$
−0.902012 + 0.431710i $$0.857910\pi$$
$$102$$ −14.2418 −0.139626
$$103$$ 187.567i 1.82104i 0.413462 + 0.910521i $$0.364319\pi$$
−0.413462 + 0.910521i $$0.635681\pi$$
$$104$$ 41.3131i 0.397242i
$$105$$ 0 0
$$106$$ −100.904 −0.951922
$$107$$ −157.858 −1.47531 −0.737653 0.675180i $$-0.764066\pi$$
−0.737653 + 0.675180i $$0.764066\pi$$
$$108$$ 10.3923i 0.0962250i
$$109$$ 112.073 1.02819 0.514097 0.857732i $$-0.328127\pi$$
0.514097 + 0.857732i $$0.328127\pi$$
$$110$$ 0 0
$$111$$ 109.873i 0.989844i
$$112$$ −6.31526 + 27.2785i −0.0563862 + 0.243558i
$$113$$ 141.987 1.25653 0.628263 0.778001i $$-0.283766\pi$$
0.628263 + 0.778001i $$0.283766\pi$$
$$114$$ −82.7280 −0.725684
$$115$$ 0 0
$$116$$ 18.5061 0.159535
$$117$$ 43.8192i 0.374523i
$$118$$ 60.7192i 0.514570i
$$119$$ −39.6507 9.17955i −0.333199 0.0771391i
$$120$$ 0 0
$$121$$ −54.4202 −0.449754
$$122$$ 48.4883i 0.397445i
$$123$$ 14.3047 0.116298
$$124$$ 38.5116i 0.310577i
$$125$$ 0 0
$$126$$ 6.69834 28.9332i 0.0531614 0.229629i
$$127$$ −202.414 −1.59381 −0.796905 0.604104i $$-0.793531\pi$$
−0.796905 + 0.604104i $$0.793531\pi$$
$$128$$ 11.3137 0.0883883
$$129$$ 72.9008i 0.565123i
$$130$$ 0 0
$$131$$ 141.260i 1.07832i −0.842203 0.539160i $$-0.818742\pi$$
0.842203 0.539160i $$-0.181258\pi$$
$$132$$ 28.2658i 0.214135i
$$133$$ −230.323 53.3222i −1.73175 0.400919i
$$134$$ −7.06949 −0.0527574
$$135$$ 0 0
$$136$$ 16.4451i 0.120920i
$$137$$ 50.6430 0.369657 0.184829 0.982771i $$-0.440827\pi$$
0.184829 + 0.982771i $$0.440827\pi$$
$$138$$ 91.2620i 0.661319i
$$139$$ 74.0256i 0.532559i 0.963896 + 0.266279i $$0.0857943\pi$$
−0.963896 + 0.266279i $$0.914206\pi$$
$$140$$ 0 0
$$141$$ −40.4225 −0.286685
$$142$$ −54.8885 −0.386538
$$143$$ 119.183i 0.833448i
$$144$$ −12.0000 −0.0833333
$$145$$ 0 0
$$146$$ 176.253i 1.20721i
$$147$$ 37.2977 76.2357i 0.253726 0.518610i
$$148$$ −126.870 −0.857230
$$149$$ 226.979 1.52335 0.761676 0.647958i $$-0.224377\pi$$
0.761676 + 0.647958i $$0.224377\pi$$
$$150$$ 0 0
$$151$$ 294.426 1.94984 0.974920 0.222558i $$-0.0714406\pi$$
0.974920 + 0.222558i $$0.0714406\pi$$
$$152$$ 95.5261i 0.628461i
$$153$$ 17.4426i 0.114004i
$$154$$ 18.2187 78.6950i 0.118303 0.511006i
$$155$$ 0 0
$$156$$ 50.5981 0.324346
$$157$$ 65.8596i 0.419488i −0.977756 0.209744i $$-0.932737\pi$$
0.977756 0.209744i $$-0.0672630\pi$$
$$158$$ 79.4564 0.502889
$$159$$ 123.581i 0.777241i
$$160$$ 0 0
$$161$$ 58.8227 254.083i 0.365359 1.57815i
$$162$$ 12.7279 0.0785674
$$163$$ 28.2075 0.173052 0.0865260 0.996250i $$-0.472423\pi$$
0.0865260 + 0.996250i $$0.472423\pi$$
$$164$$ 16.5176i 0.100717i
$$165$$ 0 0
$$166$$ 127.842i 0.770133i
$$167$$ 128.461i 0.769227i 0.923078 + 0.384614i $$0.125665\pi$$
−0.923078 + 0.384614i $$0.874335\pi$$
$$168$$ −33.4092 7.73458i −0.198864 0.0460392i
$$169$$ −44.3469 −0.262408
$$170$$ 0 0
$$171$$ 101.321i 0.592519i
$$172$$ 84.1786 0.489411
$$173$$ 112.446i 0.649976i −0.945718 0.324988i $$-0.894640\pi$$
0.945718 0.324988i $$-0.105360\pi$$
$$174$$ 22.6652i 0.130260i
$$175$$ 0 0
$$176$$ −32.6386 −0.185446
$$177$$ 74.3656 0.420144
$$178$$ 22.9511i 0.128939i
$$179$$ 68.9019 0.384927 0.192464 0.981304i $$-0.438352\pi$$
0.192464 + 0.981304i $$0.438352\pi$$
$$180$$ 0 0
$$181$$ 166.537i 0.920094i 0.887895 + 0.460047i $$0.152167\pi$$
−0.887895 + 0.460047i $$0.847833\pi$$
$$182$$ 140.870 + 32.6129i 0.774012 + 0.179192i
$$183$$ −59.3858 −0.324513
$$184$$ −105.380 −0.572719
$$185$$ 0 0
$$186$$ −47.1668 −0.253585
$$187$$ 47.4419i 0.253700i
$$188$$ 46.6759i 0.248276i
$$189$$ 35.4358 + 8.20376i 0.187491 + 0.0434061i
$$190$$ 0 0
$$191$$ −148.289 −0.776382 −0.388191 0.921579i $$-0.626900\pi$$
−0.388191 + 0.921579i $$0.626900\pi$$
$$192$$ 13.8564i 0.0721688i
$$193$$ −35.1886 −0.182324 −0.0911622 0.995836i $$-0.529058\pi$$
−0.0911622 + 0.995836i $$0.529058\pi$$
$$194$$ 117.041i 0.603304i
$$195$$ 0 0
$$196$$ −88.0294 43.0677i −0.449130 0.219733i
$$197$$ −193.634 −0.982915 −0.491457 0.870902i $$-0.663536\pi$$
−0.491457 + 0.870902i $$0.663536\pi$$
$$198$$ 34.6184 0.174841
$$199$$ 181.838i 0.913759i 0.889529 + 0.456880i $$0.151033\pi$$
−0.889529 + 0.456880i $$0.848967\pi$$
$$200$$ 0 0
$$201$$ 8.65832i 0.0430762i
$$202$$ 123.327i 0.610530i
$$203$$ −14.6088 + 63.1023i −0.0719647 + 0.310849i
$$204$$ −20.1410 −0.0987304
$$205$$ 0 0
$$206$$ 265.260i 1.28767i
$$207$$ 111.773 0.539965
$$208$$ 58.4256i 0.280892i
$$209$$ 275.580i 1.31857i
$$210$$ 0 0
$$211$$ 175.914 0.833717 0.416859 0.908971i $$-0.363131\pi$$
0.416859 + 0.908971i $$0.363131\pi$$
$$212$$ −142.699 −0.673110
$$213$$ 67.2244i 0.315607i
$$214$$ −223.244 −1.04320
$$215$$ 0 0
$$216$$ 14.6969i 0.0680414i
$$217$$ −131.317 30.4013i −0.605149 0.140098i
$$218$$ 158.495 0.727042
$$219$$ 215.864 0.985683
$$220$$ 0 0
$$221$$ 84.9246 0.384274
$$222$$ 155.384i 0.699926i
$$223$$ 20.5675i 0.0922308i −0.998936 0.0461154i $$-0.985316\pi$$
0.998936 0.0461154i $$-0.0146842\pi$$
$$224$$ −8.93112 + 38.5776i −0.0398711 + 0.172222i
$$225$$ 0 0
$$226$$ 200.801 0.888498
$$227$$ 414.087i 1.82417i −0.410001 0.912085i $$-0.634472\pi$$
0.410001 0.912085i $$-0.365528\pi$$
$$228$$ −116.995 −0.513136
$$229$$ 195.520i 0.853799i 0.904299 + 0.426899i $$0.140394\pi$$
−0.904299 + 0.426899i $$0.859606\pi$$
$$230$$ 0 0
$$231$$ 96.3813 + 22.3133i 0.417235 + 0.0965942i
$$232$$ 26.1716 0.112808
$$233$$ −81.3006 −0.348930 −0.174465 0.984663i $$-0.555820\pi$$
−0.174465 + 0.984663i $$0.555820\pi$$
$$234$$ 61.9697i 0.264828i
$$235$$ 0 0
$$236$$ 85.8700i 0.363856i
$$237$$ 97.3138i 0.410607i
$$238$$ −56.0746 12.9818i −0.235608 0.0545456i
$$239$$ 249.265 1.04295 0.521475 0.853267i $$-0.325382\pi$$
0.521475 + 0.853267i $$0.325382\pi$$
$$240$$ 0 0
$$241$$ 262.343i 1.08856i 0.838904 + 0.544280i $$0.183197\pi$$
−0.838904 + 0.544280i $$0.816803\pi$$
$$242$$ −76.9618 −0.318024
$$243$$ 15.5885i 0.0641500i
$$244$$ 68.5728i 0.281036i
$$245$$ 0 0
$$246$$ 20.2298 0.0822351
$$247$$ 493.310 1.99721
$$248$$ 54.4636i 0.219611i
$$249$$ −156.574 −0.628811
$$250$$ 0 0
$$251$$ 141.917i 0.565406i 0.959208 + 0.282703i $$0.0912310\pi$$
−0.959208 + 0.282703i $$0.908769\pi$$
$$252$$ 9.47288 40.9178i 0.0375908 0.162372i
$$253$$ 304.008 1.20161
$$254$$ −286.257 −1.12699
$$255$$ 0 0
$$256$$ 16.0000 0.0625000
$$257$$ 170.843i 0.664757i 0.943146 + 0.332379i $$0.107851\pi$$
−0.943146 + 0.332379i $$0.892149\pi$$
$$258$$ 103.097i 0.399602i
$$259$$ 100.152 432.604i 0.386688 1.67028i
$$260$$ 0 0
$$261$$ −27.7591 −0.106357
$$262$$ 199.772i 0.762488i
$$263$$ 383.417 1.45786 0.728930 0.684588i $$-0.240018\pi$$
0.728930 + 0.684588i $$0.240018\pi$$
$$264$$ 39.9739i 0.151416i
$$265$$ 0 0
$$266$$ −325.726 75.4090i −1.22454 0.283492i
$$267$$ −28.1093 −0.105278
$$268$$ −9.99777 −0.0373051
$$269$$ 154.512i 0.574393i −0.957872 0.287196i $$-0.907277\pi$$
0.957872 0.287196i $$-0.0927232\pi$$
$$270$$ 0 0
$$271$$ 320.328i 1.18202i 0.806664 + 0.591010i $$0.201271\pi$$
−0.806664 + 0.591010i $$0.798729\pi$$
$$272$$ 23.2568i 0.0855030i
$$273$$ −39.9425 + 172.530i −0.146309 + 0.631978i
$$274$$ 71.6200 0.261387
$$275$$ 0 0
$$276$$ 129.064i 0.467623i
$$277$$ 222.854 0.804526 0.402263 0.915524i $$-0.368224\pi$$
0.402263 + 0.915524i $$0.368224\pi$$
$$278$$ 104.688i 0.376576i
$$279$$ 57.7673i 0.207051i
$$280$$ 0 0
$$281$$ 218.973 0.779263 0.389631 0.920971i $$-0.372602\pi$$
0.389631 + 0.920971i $$0.372602\pi$$
$$282$$ −57.1661 −0.202717
$$283$$ 36.3957i 0.128607i −0.997930 0.0643034i $$-0.979517\pi$$
0.997930 0.0643034i $$-0.0204825\pi$$
$$284$$ −77.6240 −0.273324
$$285$$ 0 0
$$286$$ 168.550i 0.589337i
$$287$$ 56.3219 + 13.0391i 0.196244 + 0.0454324i
$$288$$ −16.9706 −0.0589256
$$289$$ 255.195 0.883028
$$290$$ 0 0
$$291$$ −143.345 −0.492596
$$292$$ 249.259i 0.853626i
$$293$$ 168.440i 0.574882i 0.957798 + 0.287441i $$0.0928045\pi$$
−0.957798 + 0.287441i $$0.907195\pi$$
$$294$$ 52.7470 107.814i 0.179411 0.366713i
$$295$$ 0 0
$$296$$ −179.421 −0.606153
$$297$$ 42.3988i 0.142757i
$$298$$ 320.997 1.07717
$$299$$ 544.199i 1.82006i
$$300$$ 0 0
$$301$$ −66.4512 + 287.034i −0.220768 + 0.953600i
$$302$$ 416.381 1.37874
$$303$$ −151.044 −0.498496
$$304$$ 135.094i 0.444389i
$$305$$ 0 0
$$306$$ 24.6676i 0.0806130i
$$307$$ 223.400i 0.727688i 0.931460 + 0.363844i $$0.118536\pi$$
−0.931460 + 0.363844i $$0.881464\pi$$
$$308$$ 25.7651 111.292i 0.0836530 0.361336i
$$309$$ −324.876 −1.05138
$$310$$ 0 0
$$311$$ 46.0396i 0.148037i −0.997257 0.0740186i $$-0.976418\pi$$
0.997257 0.0740186i $$-0.0235824\pi$$
$$312$$ 71.5565 0.229348
$$313$$ 80.0375i 0.255711i 0.991793 + 0.127855i $$0.0408094\pi$$
−0.991793 + 0.127855i $$0.959191\pi$$
$$314$$ 93.1395i 0.296623i
$$315$$ 0 0
$$316$$ 112.368 0.355596
$$317$$ 185.237 0.584343 0.292171 0.956366i $$-0.405622\pi$$
0.292171 + 0.956366i $$0.405622\pi$$
$$318$$ 174.770i 0.549592i
$$319$$ −75.5016 −0.236682
$$320$$ 0 0
$$321$$ 273.418i 0.851768i
$$322$$ 83.1879 359.327i 0.258348 1.11592i
$$323$$ −196.367 −0.607946
$$324$$ 18.0000 0.0555556
$$325$$ 0 0
$$326$$ 39.8914 0.122366
$$327$$ 194.116i 0.593628i
$$328$$ 23.3594i 0.0712177i
$$329$$ −159.156 36.8463i −0.483757 0.111995i
$$330$$ 0 0
$$331$$ 61.4686 0.185706 0.0928529 0.995680i $$-0.470401\pi$$
0.0928529 + 0.995680i $$0.470401\pi$$
$$332$$ 180.796i 0.544566i
$$333$$ 190.305 0.571487
$$334$$ 181.671i 0.543926i
$$335$$ 0 0
$$336$$ −47.2478 10.9383i −0.140618 0.0325546i
$$337$$ 656.501 1.94807 0.974037 0.226387i $$-0.0726914\pi$$
0.974037 + 0.226387i $$0.0726914\pi$$
$$338$$ −62.7160 −0.185550
$$339$$ 245.929i 0.725456i
$$340$$ 0 0
$$341$$ 157.120i 0.460764i
$$342$$ 143.289i 0.418974i
$$343$$ 216.344 266.166i 0.630740 0.775994i
$$344$$ 119.047 0.346066
$$345$$ 0 0
$$346$$ 159.022i 0.459603i
$$347$$ 321.323 0.926002 0.463001 0.886358i $$-0.346773\pi$$
0.463001 + 0.886358i $$0.346773\pi$$
$$348$$ 32.0535i 0.0921077i
$$349$$ 185.135i 0.530474i −0.964183 0.265237i $$-0.914550\pi$$
0.964183 0.265237i $$-0.0854501\pi$$
$$350$$ 0 0
$$351$$ −75.8971 −0.216231
$$352$$ −46.1579 −0.131130
$$353$$ 597.338i 1.69218i −0.533043 0.846088i $$-0.678952\pi$$
0.533043 0.846088i $$-0.321048\pi$$
$$354$$ 105.169 0.297087
$$355$$ 0 0
$$356$$ 32.4578i 0.0911736i
$$357$$ 15.8995 68.6771i 0.0445363 0.192373i
$$358$$ 97.4421 0.272185
$$359$$ −239.446 −0.666982 −0.333491 0.942753i $$-0.608227\pi$$
−0.333491 + 0.942753i $$0.608227\pi$$
$$360$$ 0 0
$$361$$ −779.655 −2.15971
$$362$$ 235.519i 0.650604i
$$363$$ 94.2585i 0.259665i
$$364$$ 199.220 + 46.1216i 0.547309 + 0.126708i
$$365$$ 0 0
$$366$$ −83.9842 −0.229465
$$367$$ 398.743i 1.08649i 0.839573 + 0.543246i $$0.182805\pi$$
−0.839573 + 0.543246i $$0.817195\pi$$
$$368$$ −149.030 −0.404973
$$369$$ 24.7764i 0.0671447i
$$370$$ 0 0
$$371$$ 112.648 486.578i 0.303633 1.31153i
$$372$$ −66.7040 −0.179312
$$373$$ −34.7064 −0.0930466 −0.0465233 0.998917i $$-0.514814\pi$$
−0.0465233 + 0.998917i $$0.514814\pi$$
$$374$$ 67.0929i 0.179393i
$$375$$ 0 0
$$376$$ 66.0097i 0.175558i
$$377$$ 135.154i 0.358498i
$$378$$ 50.1138 + 11.6019i 0.132576 + 0.0306928i
$$379$$ 109.217 0.288172 0.144086 0.989565i $$-0.453976\pi$$
0.144086 + 0.989565i $$0.453976\pi$$
$$380$$ 0 0
$$381$$ 350.591i 0.920187i
$$382$$ −209.712 −0.548985
$$383$$ 336.420i 0.878381i −0.898394 0.439191i $$-0.855265\pi$$
0.898394 0.439191i $$-0.144735\pi$$
$$384$$ 19.5959i 0.0510310i
$$385$$ 0 0
$$386$$ −49.7642 −0.128923
$$387$$ −126.268 −0.326274
$$388$$ 165.521i 0.426601i
$$389$$ 311.173 0.799930 0.399965 0.916530i $$-0.369022\pi$$
0.399965 + 0.916530i $$0.369022\pi$$
$$390$$ 0 0
$$391$$ 216.623i 0.554023i
$$392$$ −124.492 60.9069i −0.317583 0.155375i
$$393$$ 244.669 0.622568
$$394$$ −273.840 −0.695026
$$395$$ 0 0
$$396$$ 48.9579 0.123631
$$397$$ 41.2679i 0.103949i −0.998648 0.0519747i $$-0.983448\pi$$
0.998648 0.0519747i $$-0.0165515\pi$$
$$398$$ 257.158i 0.646125i
$$399$$ 92.3568 398.932i 0.231471 0.999829i
$$400$$ 0 0
$$401$$ −495.642 −1.23601 −0.618007 0.786173i $$-0.712060\pi$$
−0.618007 + 0.786173i $$0.712060\pi$$
$$402$$ 12.2447i 0.0304595i
$$403$$ 281.258 0.697910
$$404$$ 174.411i 0.431710i
$$405$$ 0 0
$$406$$ −20.6600 + 89.2402i −0.0508867 + 0.219803i
$$407$$ 517.608 1.27176
$$408$$ −28.4837 −0.0698129
$$409$$ 359.920i 0.880001i 0.897998 + 0.440000i $$0.145022\pi$$
−0.897998 + 0.440000i $$0.854978\pi$$
$$410$$ 0 0
$$411$$ 87.7163i 0.213422i
$$412$$ 375.135i 0.910521i
$$413$$ 292.801 + 67.7863i 0.708960 + 0.164132i
$$414$$ 158.070 0.381813
$$415$$ 0 0
$$416$$ 82.6263i 0.198621i
$$417$$ −128.216 −0.307473
$$418$$ 389.730i 0.932367i
$$419$$ 482.910i 1.15253i −0.817263 0.576265i $$-0.804510\pi$$
0.817263 0.576265i $$-0.195490\pi$$
$$420$$ 0 0
$$421$$ −523.520 −1.24351 −0.621757 0.783210i $$-0.713581\pi$$
−0.621757 + 0.783210i $$0.713581\pi$$
$$422$$ 248.780 0.589527
$$423$$ 70.0139i 0.165517i
$$424$$ −201.807 −0.475961
$$425$$ 0 0
$$426$$ 95.0696i 0.223168i
$$427$$ −233.821 54.1319i −0.547589 0.126773i
$$428$$ −315.715 −0.737653
$$429$$ −206.431 −0.481191
$$430$$ 0 0
$$431$$ 517.027 1.19960 0.599799 0.800150i $$-0.295247\pi$$
0.599799 + 0.800150i $$0.295247\pi$$
$$432$$ 20.7846i 0.0481125i
$$433$$ 567.712i 1.31111i 0.755146 + 0.655557i $$0.227566\pi$$
−0.755146 + 0.655557i $$0.772434\pi$$
$$434$$ −185.711 42.9939i −0.427905 0.0990644i
$$435$$ 0 0
$$436$$ 224.146 0.514097
$$437$$ 1258.32i 2.87945i
$$438$$ 305.279 0.696983
$$439$$ 622.875i 1.41885i 0.704781 + 0.709425i $$0.251045\pi$$
−0.704781 + 0.709425i $$0.748955\pi$$
$$440$$ 0 0
$$441$$ 132.044 + 64.6016i 0.299420 + 0.146489i
$$442$$ 120.102 0.271723
$$443$$ −476.699 −1.07607 −0.538035 0.842923i $$-0.680833\pi$$
−0.538035 + 0.842923i $$0.680833\pi$$
$$444$$ 219.745i 0.494922i
$$445$$ 0 0
$$446$$ 29.0868i 0.0652170i
$$447$$ 393.140i 0.879507i
$$448$$ −12.6305 + 54.5570i −0.0281931 + 0.121779i
$$449$$ −861.931 −1.91967 −0.959834 0.280570i $$-0.909477\pi$$
−0.959834 + 0.280570i $$0.909477\pi$$
$$450$$ 0 0
$$451$$ 67.3889i 0.149421i
$$452$$ 283.975 0.628263
$$453$$ 509.960i 1.12574i
$$454$$ 585.607i 1.28988i
$$455$$ 0 0
$$456$$ −165.456 −0.362842
$$457$$ −27.5401 −0.0602629 −0.0301314 0.999546i $$-0.509593\pi$$
−0.0301314 + 0.999546i $$0.509593\pi$$
$$458$$ 276.507i 0.603727i
$$459$$ 30.2115 0.0658203
$$460$$ 0 0
$$461$$ 378.183i 0.820353i −0.912006 0.410176i $$-0.865467\pi$$
0.912006 0.410176i $$-0.134533\pi$$
$$462$$ 136.304 + 31.5557i 0.295030 + 0.0683024i
$$463$$ −724.994 −1.56586 −0.782931 0.622108i $$-0.786276\pi$$
−0.782931 + 0.622108i $$0.786276\pi$$
$$464$$ 37.0122 0.0797676
$$465$$ 0 0
$$466$$ −114.976 −0.246731
$$467$$ 371.451i 0.795398i −0.917516 0.397699i $$-0.869809\pi$$
0.917516 0.397699i $$-0.130191\pi$$
$$468$$ 87.6384i 0.187262i
$$469$$ 7.89231 34.0905i 0.0168280 0.0726877i
$$470$$ 0 0
$$471$$ 114.072 0.242191
$$472$$ 121.438i 0.257285i
$$473$$ −343.434 −0.726076
$$474$$ 137.623i 0.290343i
$$475$$ 0 0
$$476$$ −79.3015 18.3591i −0.166600 0.0385695i
$$477$$ 214.049 0.448740
$$478$$ 352.514 0.737477
$$479$$ 860.650i 1.79677i −0.439214 0.898383i $$-0.644743\pi$$
0.439214 0.898383i $$-0.355257\pi$$
$$480$$ 0 0
$$481$$ 926.558i 1.92632i
$$482$$ 371.009i 0.769728i
$$483$$ 440.084 + 101.884i 0.911147 + 0.210940i
$$484$$ −108.840 −0.224877
$$485$$ 0 0
$$486$$ 22.0454i 0.0453609i
$$487$$ −887.173 −1.82171 −0.910855 0.412726i $$-0.864577\pi$$
−0.910855 + 0.412726i $$0.864577\pi$$
$$488$$ 96.9766i 0.198723i
$$489$$ 48.8568i 0.0999116i
$$490$$ 0 0
$$491$$ −50.1823 −0.102204 −0.0511021 0.998693i $$-0.516273\pi$$
−0.0511021 + 0.998693i $$0.516273\pi$$
$$492$$ 28.6093 0.0581490
$$493$$ 53.7991i 0.109126i
$$494$$ 697.646 1.41224
$$495$$ 0 0
$$496$$ 77.0231i 0.155289i
$$497$$ 61.2769 264.683i 0.123294 0.532562i
$$498$$ −221.429 −0.444636
$$499$$ −160.443 −0.321529 −0.160765 0.986993i $$-0.551396\pi$$
−0.160765 + 0.986993i $$0.551396\pi$$
$$500$$ 0 0
$$501$$ −222.501 −0.444113
$$502$$ 200.701i 0.399802i
$$503$$ 742.042i 1.47523i −0.675220 0.737616i $$-0.735951\pi$$
0.675220 0.737616i $$-0.264049\pi$$
$$504$$ 13.3967 57.8665i 0.0265807 0.114814i
$$505$$ 0 0
$$506$$ 429.933 0.849670
$$507$$ 76.8111i 0.151501i
$$508$$ −404.828 −0.796905
$$509$$ 978.447i 1.92229i 0.276038 + 0.961147i $$0.410979\pi$$
−0.276038 + 0.961147i $$0.589021\pi$$
$$510$$ 0 0
$$511$$ 849.927 + 196.767i 1.66326 + 0.385062i
$$512$$ 22.6274 0.0441942
$$513$$ 175.493 0.342091
$$514$$ 241.608i 0.470054i
$$515$$ 0 0
$$516$$ 145.802i 0.282561i
$$517$$ 190.429i 0.368335i
$$518$$ 141.637 611.794i 0.273430 1.18107i
$$519$$ 194.762 0.375264
$$520$$ 0 0
$$521$$ 575.650i 1.10489i 0.833548 + 0.552447i $$0.186306\pi$$
−0.833548 + 0.552447i $$0.813694\pi$$
$$522$$ −39.2573 −0.0752056
$$523$$ 339.090i 0.648355i 0.945996 + 0.324178i $$0.105088\pi$$
−0.945996 + 0.324178i $$0.894912\pi$$
$$524$$ 282.520i 0.539160i
$$525$$ 0 0
$$526$$ 542.234 1.03086
$$527$$ −111.957 −0.212442
$$528$$ 56.5317i 0.107068i
$$529$$ 859.125 1.62406
$$530$$ 0 0
$$531$$ 128.805i 0.242571i
$$532$$ −460.647 106.644i −0.865877 0.200459i
$$533$$ −120.631 −0.226325
$$534$$ −39.7525 −0.0744429
$$535$$ 0 0
$$536$$ −14.1390 −0.0263787
$$537$$ 119.342i 0.222238i
$$538$$ 218.512i 0.406157i
$$539$$ 359.144 + 175.709i 0.666316 + 0.325990i
$$540$$ 0 0
$$541$$ 35.8638 0.0662916 0.0331458 0.999451i $$-0.489447\pi$$
0.0331458 + 0.999451i $$0.489447\pi$$
$$542$$ 453.012i 0.835815i
$$543$$ −288.450 −0.531216
$$544$$ 32.8901i 0.0604598i
$$545$$ 0 0
$$546$$ −56.4872 + 243.994i −0.103456 + 0.446876i
$$547$$ 700.845 1.28125 0.640626 0.767853i $$-0.278675\pi$$
0.640626 + 0.767853i $$0.278675\pi$$
$$548$$ 101.286 0.184829
$$549$$ 102.859i 0.187357i
$$550$$ 0 0
$$551$$ 312.508i 0.567166i
$$552$$ 182.524i 0.330659i
$$553$$ −88.7044 + 383.155i −0.160406 + 0.692867i
$$554$$ 315.163 0.568886
$$555$$ 0 0
$$556$$ 148.051i 0.266279i
$$557$$ −639.349 −1.14784 −0.573922 0.818910i $$-0.694579\pi$$
−0.573922 + 0.818910i $$0.694579\pi$$
$$558$$ 81.6954i 0.146407i
$$559$$ 614.773i 1.09977i
$$560$$ 0 0
$$561$$ 82.1717 0.146474
$$562$$ 309.674 0.551022
$$563$$ 227.519i 0.404120i 0.979373 + 0.202060i $$0.0647636\pi$$
−0.979373 + 0.202060i $$0.935236\pi$$
$$564$$ −80.8450 −0.143342
$$565$$ 0 0
$$566$$ 51.4713i 0.0909387i
$$567$$ −14.2093 + 61.3767i −0.0250605 + 0.108248i
$$568$$ −109.777 −0.193269
$$569$$ −613.901 −1.07891 −0.539456 0.842014i $$-0.681370\pi$$
−0.539456 + 0.842014i $$0.681370\pi$$
$$570$$ 0 0
$$571$$ 366.674 0.642161 0.321081 0.947052i $$-0.395954\pi$$
0.321081 + 0.947052i $$0.395954\pi$$
$$572$$ 238.366i 0.416724i
$$573$$ 256.844i 0.448244i
$$574$$ 79.6513 + 18.4401i 0.138765 + 0.0321256i
$$575$$ 0 0
$$576$$ −24.0000 −0.0416667
$$577$$ 62.1951i 0.107790i −0.998547 0.0538952i $$-0.982836\pi$$
0.998547 0.0538952i $$-0.0171637\pi$$
$$578$$ 360.900 0.624395
$$579$$ 60.9485i 0.105265i
$$580$$ 0 0
$$581$$ −616.481 142.722i −1.06107 0.245648i
$$582$$ −202.721 −0.348318
$$583$$ 582.188 0.998607
$$584$$ 352.505i 0.603605i
$$585$$ 0 0
$$586$$ 238.211i 0.406503i
$$587$$ 176.872i 0.301315i −0.988586 0.150658i $$-0.951861\pi$$
0.988586 0.150658i $$-0.0481391\pi$$
$$588$$ 74.5955 152.471i 0.126863 0.259305i
$$589$$ −650.337 −1.10414
$$590$$ 0 0
$$591$$ 335.384i 0.567486i
$$592$$ −253.740 −0.428615
$$593$$ 154.878i 0.261176i −0.991437 0.130588i $$-0.958313\pi$$
0.991437 0.130588i $$-0.0416866\pi$$
$$594$$ 59.9609i 0.100944i
$$595$$ 0 0
$$596$$ 453.959 0.761676
$$597$$ −314.953 −0.527559
$$598$$ 769.613i 1.28698i
$$599$$ −900.825 −1.50388 −0.751940 0.659231i $$-0.770882\pi$$
−0.751940 + 0.659231i $$0.770882\pi$$
$$600$$ 0 0
$$601$$ 682.387i 1.13542i −0.823229 0.567710i $$-0.807830\pi$$
0.823229 0.567710i $$-0.192170\pi$$
$$602$$ −93.9762 + 405.927i −0.156107 + 0.674297i
$$603$$ 14.9967 0.0248701
$$604$$ 588.851 0.974920
$$605$$ 0 0
$$606$$ −213.609 −0.352490
$$607$$ 367.814i 0.605954i 0.952998 + 0.302977i $$0.0979806\pi$$
−0.952998 + 0.302977i $$0.902019\pi$$
$$608$$ 191.052i 0.314231i
$$609$$ −109.296 25.3032i −0.179469 0.0415488i
$$610$$ 0 0
$$611$$ 340.883 0.557911
$$612$$ 34.8852i 0.0570020i
$$613$$ 117.271 0.191306 0.0956532 0.995415i $$-0.469506\pi$$
0.0956532 + 0.995415i $$0.469506\pi$$
$$614$$ 315.936i 0.514553i
$$615$$ 0 0
$$616$$ 36.4374 157.390i 0.0591516 0.255503i
$$617$$ −1070.18 −1.73449 −0.867245 0.497881i $$-0.834112\pi$$
−0.867245 + 0.497881i $$0.834112\pi$$
$$618$$ −459.444 −0.743438
$$619$$ 532.192i 0.859761i 0.902886 + 0.429880i $$0.141444\pi$$
−0.902886 + 0.429880i $$0.858556\pi$$
$$620$$ 0 0
$$621$$ 193.596i 0.311749i
$$622$$ 65.1098i 0.104678i
$$623$$ −110.675 25.6224i −0.177649 0.0411275i
$$624$$ 101.196 0.162173
$$625$$ 0 0
$$626$$ 113.190i 0.180815i
$$627$$ 477.319 0.761275
$$628$$ 131.719i 0.209744i
$$629$$ 368.825i 0.586366i
$$630$$ 0 0
$$631$$ 472.933 0.749498 0.374749 0.927126i $$-0.377729\pi$$
0.374749 + 0.927126i $$0.377729\pi$$
$$632$$ 158.913 0.251444
$$633$$ 304.693i 0.481347i
$$634$$ 261.964 0.413193
$$635$$ 0 0
$$636$$ 247.163i 0.388620i
$$637$$ −314.532 + 642.896i −0.493771 + 1.00926i
$$638$$ −106.775 −0.167359
$$639$$ 116.436 0.182216
$$640$$ 0 0
$$641$$ −486.990 −0.759734 −0.379867 0.925041i $$-0.624030\pi$$
−0.379867 + 0.925041i $$0.624030\pi$$
$$642$$ 386.671i 0.602291i
$$643$$ 111.425i 0.173289i 0.996239 + 0.0866447i $$0.0276145\pi$$
−0.996239 + 0.0866447i $$0.972386\pi$$
$$644$$ 117.645 508.165i 0.182679 0.789077i
$$645$$ 0 0
$$646$$ −277.704 −0.429883
$$647$$ 737.696i 1.14018i 0.821583 + 0.570090i $$0.193092\pi$$
−0.821583 + 0.570090i $$0.806908\pi$$
$$648$$ 25.4558 0.0392837
$$649$$ 350.334i 0.539806i
$$650$$ 0 0
$$651$$ 52.6566 227.448i 0.0808857 0.349383i
$$652$$ 56.4149 0.0865260
$$653$$ 193.734 0.296682 0.148341 0.988936i $$-0.452607\pi$$
0.148341 + 0.988936i $$0.452607\pi$$
$$654$$ 274.522i 0.419758i
$$655$$ 0 0
$$656$$ 33.0352i 0.0503585i
$$657$$ 373.888i 0.569084i
$$658$$ −225.081 52.1085i −0.342068 0.0791923i
$$659$$ 823.339 1.24938 0.624688 0.780874i $$-0.285226\pi$$
0.624688 + 0.780874i $$0.285226\pi$$
$$660$$ 0 0
$$661$$ 657.833i 0.995208i −0.867404 0.497604i $$-0.834213\pi$$
0.867404 0.497604i $$-0.165787\pi$$
$$662$$ 86.9298 0.131314
$$663$$ 147.094i 0.221861i
$$664$$ 255.684i 0.385066i
$$665$$ 0 0
$$666$$ 269.132 0.404102
$$667$$ −344.746 −0.516860
$$668$$ 256.922i 0.384614i
$$669$$ 35.6239 0.0532495
$$670$$ 0 0
$$671$$ 279.765i 0.416937i
$$672$$ −66.8184 15.4692i −0.0994322 0.0230196i
$$673$$ −727.300 −1.08068 −0.540342 0.841446i $$-0.681705\pi$$
−0.540342 + 0.841446i $$0.681705\pi$$
$$674$$ 928.433 1.37750
$$675$$ 0 0
$$676$$ −88.6938 −0.131204
$$677$$ 385.964i 0.570110i −0.958511 0.285055i $$-0.907988\pi$$
0.958511 0.285055i $$-0.0920118\pi$$
$$678$$ 347.797i 0.512975i
$$679$$ −564.396 130.663i −0.831217 0.192435i
$$680$$ 0 0
$$681$$ 717.219 1.05319
$$682$$ 222.202i 0.325809i
$$683$$ 236.488 0.346249 0.173124 0.984900i $$-0.444614\pi$$
0.173124 + 0.984900i $$0.444614\pi$$
$$684$$ 202.641i 0.296259i
$$685$$ 0 0
$$686$$ 305.957 376.415i 0.446001 0.548711i
$$687$$ −338.650 −0.492941
$$688$$ 168.357 0.244705
$$689$$ 1042.16i 1.51257i
$$690$$ 0 0
$$691$$ 337.426i 0.488316i −0.969735 0.244158i $$-0.921488\pi$$
0.969735 0.244158i $$-0.0785116\pi$$
$$692$$ 224.892i 0.324988i
$$693$$ −38.6477 + 166.937i −0.0557687 + 0.240891i
$$694$$ 454.419 0.654782
$$695$$ 0 0
$$696$$ 45.3305i 0.0651300i
$$697$$ 48.0184 0.0688929
$$698$$ 261.821i 0.375101i
$$699$$ 140.817i 0.201455i
$$700$$ 0 0
$$701$$ 89.2192 0.127274 0.0636371 0.997973i $$-0.479730\pi$$
0.0636371 + 0.997973i $$0.479730\pi$$
$$702$$ −107.335 −0.152898
$$703$$ 2142.43i 3.04755i
$$704$$ −65.2772 −0.0927232
$$705$$ 0 0
$$706$$ 844.764i 1.19655i
$$707$$ −594.709 137.681i −0.841172 0.194740i
$$708$$ 148.731 0.210072
$$709$$ −569.646 −0.803450 −0.401725 0.915760i $$-0.631589\pi$$
−0.401725 + 0.915760i $$0.631589\pi$$
$$710$$ 0 0
$$711$$ −168.552 −0.237064
$$712$$ 45.9023i 0.0644695i
$$713$$ 717.423i 1.00620i
$$714$$ 22.4852 97.1241i 0.0314919 0.136028i
$$715$$ 0 0
$$716$$ 137.804 0.192464
$$717$$ 431.740i 0.602147i
$$718$$ −338.628 −0.471627
$$719$$ 1261.33i 1.75428i 0.480233 + 0.877141i $$0.340552\pi$$
−0.480233 + 0.877141i $$0.659448\pi$$
$$720$$ 0 0
$$721$$ −1279.14 296.134i −1.77412 0.410727i
$$722$$ −1102.60 −1.52714
$$723$$ −454.391 −0.628481
$$724$$ 333.074i 0.460047i
$$725$$ 0 0
$$726$$ 133.302i 0.183611i
$$727$$ 307.746i 0.423310i −0.977344 0.211655i $$-0.932115\pi$$
0.977344 0.211655i $$-0.0678852\pi$$
$$728$$ 281.740 + 65.2258i 0.387006 + 0.0895958i
$$729$$ −27.0000 −0.0370370
$$730$$ 0 0
$$731$$ 244.716i 0.334769i
$$732$$ −118.772 −0.162256
$$733$$ 633.490i 0.864243i 0.901815 + 0.432121i $$0.142235\pi$$
−0.901815 + 0.432121i $$0.857765\pi$$
$$734$$ 563.908i 0.768266i
$$735$$ 0 0
$$736$$ −210.761 −0.286359
$$737$$ 40.7891 0.0553448
$$738$$ 35.0391i 0.0474785i
$$739$$ −749.557 −1.01428 −0.507142 0.861862i $$-0.669298\pi$$
−0.507142 + 0.861862i $$0.669298\pi$$
$$740$$ 0 0
$$741$$ 854.439i 1.15309i
$$742$$ 159.308 688.126i 0.214701 0.927393i
$$743$$ −145.699 −0.196095 −0.0980476 0.995182i $$-0.531260\pi$$
−0.0980476 + 0.995182i $$0.531260\pi$$
$$744$$ −94.3337 −0.126793
$$745$$ 0 0
$$746$$ −49.0822 −0.0657939
$$747$$ 271.194i 0.363044i
$$748$$ 94.8837i 0.126850i
$$749$$ 249.228 1076.53i 0.332748 1.43729i
$$750$$ 0 0
$$751$$ 156.811 0.208803 0.104402 0.994535i $$-0.466707\pi$$
0.104402 + 0.994535i $$0.466707\pi$$
$$752$$ 93.3518i 0.124138i
$$753$$ −245.807 −0.326437
$$754$$ 191.136i 0.253496i
$$755$$ 0 0
$$756$$ 70.8717 + 16.4075i 0.0937456 + 0.0217031i
$$757$$ −296.377 −0.391515 −0.195758 0.980652i $$-0.562717\pi$$
−0.195758 + 0.980652i $$0.562717\pi$$
$$758$$ 154.457 0.203769
$$759$$ 526.558i 0.693752i
$$760$$ 0 0
$$761$$ 312.747i 0.410968i 0.978660 + 0.205484i $$0.0658769\pi$$
−0.978660 + 0.205484i $$0.934123\pi$$
$$762$$ 495.811i 0.650670i
$$763$$ −176.942 + 764.297i −0.231904 + 1.00170i
$$764$$ −296.578 −0.388191
$$765$$ 0 0
$$766$$ 475.770i 0.621109i
$$767$$ −627.125 −0.817634
$$768$$ 27.7128i 0.0360844i
$$769$$ 91.1460i 0.118525i −0.998242 0.0592627i $$-0.981125\pi$$
0.998242 0.0592627i $$-0.0188750\pi$$
$$770$$ 0 0
$$771$$ −295.908 −0.383798
$$772$$ −70.3772 −0.0911622
$$773$$ 417.539i 0.540154i −0.962839 0.270077i $$-0.912951\pi$$
0.962839 0.270077i $$-0.0870492\pi$$
$$774$$ −178.570 −0.230710
$$775$$ 0 0
$$776$$ 234.082i 0.301652i
$$777$$ 749.291 + 173.469i 0.964339 + 0.223254i
$$778$$ 440.065 0.565636
$$779$$ 278.929 0.358061
$$780$$ 0 0
$$781$$ 316.692 0.405496
$$782$$ 306.351i 0.391754i
$$783$$ 48.0802i 0.0614052i
$$784$$ −176.059 86.1354i −0.224565 0.109867i
$$785$$ 0 0
$$786$$ 346.015 0.440222
$$787$$ 318.111i 0.404207i 0.979364 + 0.202104i $$0.0647778\pi$$
−0.979364 + 0.202104i $$0.935222\pi$$
$$788$$ −387.268 −0.491457
$$789$$ 664.098i 0.841696i
$$790$$ 0 0